Solution of optical and microwave problems using HFSS UDC621.3.049.77.029: 681.3.06

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UDC621.3.049.77.029: 681.3.06

This book is a collection of problems,in which the analysis of a number of microwave structures of great practical importance. For the first time describes the HFSS Ansoft version 13 software. HFSS software version 13 is designed for three-dimensional design of microwave devicesand uses several methods of calculation. At the decision of practical problems, more attention is paid to the peculiarities of calculation methods and installation of HFSS software options in the course of constructing three-dimensional models of the waveguide, and microstrip antenna structures. A number of original heterogeneous structures, filters and contemporary antennas having a linear and circular polarization analyzed using HFSS. The solution of physical problems associated with optics, radar, radio physics. For technical workers, studentsand postgraduate students in the design of microwave devices and methods for calculating electromagnetic fields in inhomogeneous structures. atthe need for more detailed information on the proposed CAD, you can take part in seminars held by the authors at the Training and Counseling Center LLC "Orkada". A preliminary application for training as well as for the purchase of the program you can send by email. address:[email protected], telephone +7 (495) 943-5032 and by fax: +7 (495) 943-6032. The authors express their gratitude to "Orkada" LLC for financial support in the publication of manuals.

UDC621.3.049.77.029: 681.3.06 Banks SE, GutzeitEM. Kurushin AA Ltd"Orkada" - mock edition

Content introduction ............................ .............................................. ......................3 1. Modeling nanostructure in an optical frequency range ...... ..7 2. Waveguide array ..................... .. ...................... 18 3. The antenna array of antennas Vivaldi .................................... ... 33 4. The antenna array on the dipole antenna ............................ ... 43 5. Modeling of the frequency-selective surface ................... ... 60 6. Falling plane wave the object and the calculation of RCS ........................ ... 74 7. Calculation EPR object the size of a large electric .......... ...... ... 90 8. Bandpass waveguide filter ........................................... ... .100 9. accounting facilities heating temperature in the HFSS-13 ........................... 116 10.Realizatsiya adjustment mode in HFSS-13 ............................... ... 126 11. ModelingConnector ................................................. ... 132 12. Antenna, mounted on the mast ........................................ ... 141 13. Calculationtemporal process in a microwave integrated circuit .. ............ ... 148 14. Analysis horn antenna in the time domain ........................ .171 15. Design of nanoscale LED modules using electrodynamic simulation programs ........................... ... 191 16. installationcalculating a distributed configuration on multiple computers ........................................................................... ..220 Conclusion ........................................................................... .239 References ............................................................... ............ .240

About the authors: Banks Sergey E.- Doctor of Science, Ch. Scien. et al. IRE. RTF graduated from the Moscow Energy Institute in 1981, graduate in 1986. A specialist in the field of microwave equipment and antennas, an expert in the field of microwave CAD. The author of several monographs, textbooks, 150 scientific articles and 20 patents. Guttsayt Eduard Mihaylovich- Professor of Department. "Light" MEI, RTF graduated from the Moscow Energy Institute. Author of books and monographs in the field of microwave electronics and lighting. The initiator of the introduction of the achievements of microwave technology in nanotechnology. Kurushin Aleksandr Aleksandrovich- Ph.D., Associate Professor of Department. AUiRRV MEI. RTF graduated from Moscow Power Engineering Institute in 1979, graduate in 1985 Ph.D. (1991), thesis "Design of transistor microwave amplifiers with high dynamic range." Since 1996, he taught in various aspects of microwave MIEM, MIREA and MEI. The author of 12 textbooks and 70 scientific articles.

introduction HFSS v. 13 - this is the electromagnetic field calculation program for the design of microwave structures having multiple calculation algorithms [1]. The latest version of HFSS software performs calculations using finite element method in the frequency domain, transient, uses the method of integral equations, as well as a hybrid approach: the finite element method + method of integral equations. Each method in HFSS is implemented as a program in which you want to create a structure under study, set the parameters of materials and calculated characteristics. After that HFSS generates a mesh for solving the problem of the finite element method. In HFSS program grid is generated adaptively in dependence on the characteristics of the structure and characteristics of the field therein. In HFSS v13 made a big step forward compared to previous versions of the program, developed by the firm Ansoft. It modifications made mesh generation algorithms and calculation algorithms. A new fast and stable algorithm generates a TAU better tetrahedral grids. Forming a system of equations, providing a mixed order of its units, as well as decomposition of an arbitrary region solutions, allow implement in HFSS capabilities high-performance calculation (HighPerformance Computing HPC). The program drawing three-dimensional model has been improved operations such as insertion and transfer of two-dimensional and three-dimensional models (imprinting), and the interface has been modified to better use and automation. HFSS calculates a wide range of external devices and the parameters of the microwave antennas, which include electrical and magnetic field, currents, Sparameters, near- and far-field and can also calculate the transient and time change of electromagnetic fields [2-4] Developers can be assured accuracy HFSS when designing devices that include passive and active being introduced "chips" and simulate thus active antennas, multilayer microwave integrated circuits, RF / microwave components and biomedical devices (Fig. B.1, V. 2).

The new properties are HFSS 13.0:

 New, sustainable method of partitioning into tetrahedra;  implementationcurved elements;  Calculationderivatives characteristics change upon variation of the variables;  Reading Files ACIS R19. 2 (19 version);  Improved communicationwith the program ANSYS DesignXplorer;  Calculationtransitional regime;  implementationhybrid finite element method and the integral equation method;  Integration with a common platform ANSYS;  Multiprocessor seal partitioning grid;  Improvedpostprocessing data processing;  Conclusion of broadband characteristics of the studied structures.

Fig. IN 1.Model of five-waveguide filter with the calculated complex ANSYS in temperature distribution

It is also importantthat by HFSS -13 program included a number of examples that can be used as templates, and which show the new features of the program. HFSS uses as the main tool for solving electrodynamic problems finite element method. In this method, the entire volume is divided into tetrahedrons, inside which the field is represented as a volumetric basis functions with unknown coefficients which are found by solving the system of linear equations. In HFSS v13 software module added HFSS-IE, which implements the method of integral equations, which uses a two-dimensional basis functions describing the currents on the surfaces, including objects with a finite conductivity, which allows to describe

dielectric and metal objects with losses. This method is often referred to as the method of moments (MOM). HFSS-IE module is designed for the simulation of large radiating structures. This method can be done in HFSS: • calculationScattering of the radar cross section (Radar Cross Section RCS); • calculationantenna located on a large object such as a vehicle; • calculationcoupling factor between the remote antennas; • calculationelectromagnetic compatibility; • calculation of multi-port microwavestructures and antennas. Methodintegral equations in the field because of the nature calculates formulations boundary problem in infinite space [5,6]. Therefore, it does not need surfaces, simulating the absorption of radiation fields: radiation boundary, perfectly matched layer, etc. This eliminates the need for the user program to surround emitting object closed air volume (box) with radiation conditions on surfaces. Also, it becomes possible to calculate antennas located on the ground surface with finite conductivity. This method works in

standard HFSS interface. Will list its features:

• emitting (open) objects are described without the air box; • there is able to analyze objects, comprising an endless flat structure, including endless screens, etc .; • the program allows the use of discrete sources and excitation source in the form of incident plane waves; • It supports the calculation in the frequency range, defined as discrete points and interpolation mode; • the program calculates the near and far fields; • for structures with large dimensions electrical HFSS-IE uses compression techniques discharged matrix accelerating computational process; • perhaps separation model on composite using different calculation methods.

parts

analyzed

In HFSS 13 is easy to implement insertion of projects of different types to each other. To insert a project or HFSS HFSS-IE, just click Insert

HFSS Design or Insert HFSS-IE Design and the new project appears in the project tree under the name HFSSDesignn or HFSS-IEDesignn, where n - number of added project in the order of its appearance in the overall project. The project can include more than one installation at a decision. And you can specify methods for solving HFSS and HFSS-IE, adding designs, analyzed by different methods. Each installation solutions include the following information:  the general data concerning the decision;

 grid partitioning seal parameters, if needed, to partition the mesh was sealed in regions with high speed field changes;  analyzing frequency range.

In solving HFSS-IE by tasks you can import calculation performed by finite element method in the problem that will be solved by the method of integral equations. To do this, you can import calculated in HFSS far field Far Field Wave or near-field Near Field Wave. The project can include more than one installation at a decision. And you can specify methods for solving HFSS and HFSS-IE, adding structure to be solved in different ways.

Fig. AT 2.The spatial radiation pattern of the antenna array elements in which the HFSS-13 may be slotted, vibrator, spiral, Pace-antennas, Vivaldi and others. Radiating elements

The HFSS-13 introduces a new view of the port - port Floquet. It is used for modeling of periodic structures. The use of this port discuss in the next chapter, which will be simulated infinite boundary between two dielectric media. Thank you for fruitful discussions, screening and discussion of the manuscripts Ph.D., Leading Researcher Mishustina BA and Ph.D. Podkovyrin SI

1. modeling of nanostructuresin the optical frequency range When designing the optical devices is often the problem arises of optimizing the characteristics of reflecting surfaces [7,8]. As a promising reflective surface in research and applied research using a periodic structure consisting of metal cones (see. Fig. 1.1). This structure is considered promising for the development of optical amplifiers, frequency converters and other devices.

a)

b)

at) Fig.1.1. Scheme a) topology and b) an optical amplifier, c) a fragment of the nanostructure pattern used to create optical amplifiers presentedFig. 1.1 Implementation of the reflecting surface is not the only possible. Used as structures with hemispherical ends and elliptical, disk, etc. In all cases before the electrodynamic simulation system is the problem of calculating the frequency characteristic of the reflection coefficient of the periodic structure. Formulation boundary problem as follows: in an infinite periodic structure XOY plane falls from the upper half plane wave. Required to find the scattered field structure. naturalanalysis method of infinite periodic structures is to use periodicity conditions that reduce the problem of the endless structure to the analysis of one period.

It should be noted that the analysis of incidence of a plane wave at an infinite periodic structure is a relatively new object in the application such as the software HFSS. So, before you go directly to the calculation of the structure shown in Fig. 1.1, it is advisable to numerically using the device of periodic boundary conditions to solve test problems and compared with the numerical solution of the analytic. In the interface between two media was chosen as the test structure. For it is known rigorous analytical solution in the form of coefficients of reflection and transmission plane waves [6, 7], which shall be compared with the numerical results. Falling plane wave at the interface between two media .When a plane wave at the interface of two media, its polarization is not changed. If the vector E lies in the plane of incidence, such a polarization is called parallel, if the vector E is perpendicular to the plane of incidence - the perpendicular polarization. Forsimulation of infinite periodic structures in HFSS program uses periodic boundary conditions, which are set on opposite sides of the box, covering the period analyzed structure. Example of the boundary conditions of the type shown in Fig. 1.2. Upper vacuum parallelepiped is filled with a dielectric constant equal to one, the bottom - with a relative dielectric constant of 2.25. boxing center distance 0X 0Y and is in this example 320 nm. Endlessthe boundary between two media, strictly speaking, is not periodic structure. Therefore, application of the apparatus of periodic boundary conditions for analysis needs to be clarified. Consider the known [6] representation of the field within the rectangular channel Floquet. Under the channel portion understood Floquet space bounded by vertical walls (see. Fig. 1.2) on which periodic boundary conditions are set. For a rectangular channel Floquet componentsfieldsE, Hat z0 are as follows

E (X y, Z)

 n .m e

mz

.

a n

W her e

 i  n x i myn,

m

Lx.y- repetition periods structure axes 0X and 0Y (Fig.1.2)

n 0 2n/ Lx. n,

m

m02m/ Ly.

k2 2.

2

(1)

amplituden n, m the wave number of free space.

a n, m -

mharmonics,k-

standing plane wave:

0. 0

are set incident field, which has the form

0ksincos.  0ksinsin.

- meridional angle of incidence of a plane wave, and- the azimuth angle. Row(1) it is in the theory of periodic structures field decomposition on the Floquet harmonics, each of which is a member of (1). Can see what the Floquet harmonicszero indices nm0 that often callthe fundamental harmonic has the field structure, which coincides with the field of the incident wave. Since we are at the halffield of the reflected wave. You can record a similar decomposition(1) when z halfspace0. The main

harmonic in this expansion will correspond transmitted (refracted) wave.

higher harmonicsorders necessary for describing the near field, is excited, if the period has a complicated structure, such as shown in Fig. 1.1 b, c. In the case of a flat surface type electrodynamic problem known solutions [2,6,7]. Field describes the reflected and refracted waves. Floquet harmonics are not excited. Thus, the use of periodic boundary conditions for the analysis of the interfacetwo media is justified by the fact that the reflected and refracted waves are described Floquet fundamental harmonics and higher order harmonics are not excited.

Fig. 1.2. A fragment of the dielectric substrate on which a plane wave.

It is interesting to note that the fieldthe fundamental wave does not depend on periods Lx, y. Therefore, when solving test problem the size of individual cells can be selected arbitrarily, as depending on the size of the periods Floquet harmonics of higher orders, as noted above, are not excited. Decisionthe problem of a plane wave using HFSS. Consider further the decision of test tasks of a plane wave incident on the boundary between two media with the help of HFSS. Drawing structure. Setting the periodic boundary conditions. installationFloquet ports. team Modeler-> Units derive the dialog shown in Fig. 1.3, wherein the length measuring unit ask - nanometer (nm).

Fig. 1.3. Sizing unit structure

Draw a boxsize of 320 nm x 320 nm and 200 nm command Draw-> Box height (Fig. 1.4). Dimensions box in the plane XOY insignificant. We chose them equal to the period of the structure shown in Fig. 1.1. Created box located in the lower half and filled with a material with a dielectric constant different from the unit.

Fig. 1.4. Boxing drawing - a fragment of the dielectric plane

Define its parameters by pressingon the Add Material button (Fig. 1.5).

el ev en

Fig. 1.5.Adding a dielectric constant of 2.25 at the project

Similarly, we define the topthis box, box size of 320 nm x 320 nm and 800 nm in height. This box has a dielectric filling. Click Next F key to move the objecta selection mode and set at the sides of the vertical sides of the upper and lower boxes periodic boundary conditions Master and Slave (Figure 1.6).

Fig. 1.6. Formulation periodic boundary conditions on the side of the boxes

In this way,in the structure will be present 4 pairs Master-Slave type surfaces. Forsolutions of the boundary problem in HFSS system on horizontal surfaces, limiting the Floquet channel vertically, you must install the ports, which are called Floquet ports. To install the Floquet port select the bottom surface of the lower box and define the command Assign Exitation -> Floquet Port, on which opens a dialog Fig. 1.7.

el ev en

Fig. 1.7. Installation Floquet ports on the lower and upper side

Optionsports are set in the dialog shown in Fig. 1.8. This dialog allows you to work with multimode Floquet ports. Therefore, it is possible to specify the number of harmonics, which is used to determine the parameters of the port. We are working with a two-mode Floquet ports. This mode corresponds to a channel with two propagating Floquet harmonics. Both of them have an index n = 0, m = 0, which we will set in this dialog. The difference between the two propagating Floquet harmonics is their different polarization. In our case, we have a wave with parallel and perpendicular polarizations. The terminology used in the HFSS these two waves are designated as TM and TE waves. Therefore, the line number of waves (number of modes) set figure 2 (two waves) and as a select wave modes TM (H) and TE (E).

Fig. 1.8. Installing Floquet port options for solving the problem

In HFSS Floquet ports can be put only on the isotropic medium with a dielectric constant equal to unity. Therefore, set the port, we can not directly on the bottom surface of the dielectric.

12

Us you need to create a certain air gap between the medium and the port. IfFloquet port between the lower and the dielectric medium is a gap (Fig. 1.12), the calculation error is introduced due to the reflection of the waves from the new interface. The need to create such a gap can be considered HFSS software flaw. Forto a secondary reflection excluded, put in place from the bottom port of the absorbing boundary Radiate, in contact with the underside of the dielectric board. In this case we lose the ability to calculate the coefficient of transmission through the structure, because the port at the bottom of said channel Floquet replaced boundary. Nevertheless, the ability to calculate the reflection coefficient is stored. Incident plane wave is specified by the commandAssign Exitation -> Incident Wave -> Plane Wave. dialog appears for this team Fig. 1.9 General Data tab which establish the coordinates of the point at which the incident wave has zero phase.

Fig.1.9. The General tab of the incident wave dialogue

The angle of incidence associated with the angle of directionEoThat is givenin the form of coordinates of the vectorsk (-sin (Teta), 0, sin (Teta)), Eo (- c o s ( Te t a ) , 0 , s i n ( Te t a ) ) , are setIncident Wave Source in the dialog (Fig. 1.10). Teta - the variable that defines an angle of incidence of the wave.

13

Fig. 1.10.Parameterization of the angle of incidence of a plane wave: propagation vector k and the electric field vector E.

To calculate the reflection characteristicsand refraction of the incident wave at different angles of incidence, will change the angle of incidence of a plane wave This is doneusing parametric analysis. Command Optimetric-> Add-> Parametric derive dialog (Fig. 1.11) setting parameters of the parametric assay (Teta parameter busting).

Fig. 1.11.Target parametric analysis when changing the angle of incidence

As a result of this analysis, we obtain the field characteristics, pattern field angles of reflection and refraction of electromagnetic waves of various incidence angles. Known analytical dependence for the reflection coefficientand passing (transmitting) at a wave incident on the boundary between two media, i.e., provided that the thickness of the board tends to infinity. The reflection coefficient of the field for a wave with polarization parallel (Fig. 1.12) is equal to [7]

cos sin2  R  cos sin2 . 

(2)

14

- falls angle of incidence. field transmission coefficient for a wave with polarization parallel to equal

T 

2 cos cos sin2

(3).

By virtue of these features of HFSS, do not allow to install (with [14,15] avg.) Floquet port to the surface with a dielectric constant different from unity, we have to limit the dielectric layer thickness d and set Floquet port in the surface layer separated from the bottom surface of the small gap. In this case, the formula (2) and (3) direct comparison can not be used with the calculated data. They must be modified with the second boundary of the dielectric layer. Such a modification is not difficult to perform, using the relations (2) and (3). As a result, we obtain the following expressions for the coefficients reflectionand passing through the layer plane wave Rs, Ts: 2

R s



R



2ikd

T R 2 2i kd

e

.

(4)

1R e

T2

T  e s 2 2ikd 1R e

ikd .

 sin2.

W k2/ - wave numberfree space. In the formulas (4) her e und R, er T

understood as the reflection coefficientsand the border

section two media for waves of both polarizations. For example, for a wave R ,T parallel polarizationas R, musttake parameters (2), (3).

T

Calculations performedon HFSS and characteristics calculated by the formulas (4) are compared in Fig. 1.12. The curves in Fig. 1.12 plotted for different 15

values of the layer thickness d = 100, 200 and 300 nm. The dots show the data obtained using HFSS, and solid curves of formulas (4). It can be seen that computational and theoretical results are in good agreement.

16

Fig. 1.12.Calculated on HFSS reflectance in the range of incidence angles for different substrate thicknesses

Therefore, we can conclude that for modelingincidence optical range electromagnetic waves on metal surfaces with a complex structure can be used the finite element method, implemented in HFSS.

Fig. 1.13.The reflection coefficient of the incident plane wave with vertical polarization

Making sure that the same numerical calculationswith the theoretical results, it is possible to perform surface modeling, consisting of the conical metal nanostructures are used to enhance luminescence in an optical amplifier (Fig. 1.13).

17

silver surfacelocated on them system nanoscale sharp points, is used to amplify the luminescence mediums adsorbed with the ions of rare earth elements caused by plasmons. With HFSS-13 can obtain parameters of such systems are widely used at present in optical fiber amplifiers to a wavelength of 1.54 microns [4].

18

2. The waveguide array Simulated waveguide array [1,13].Its radiating aperture is made up of the open ends of the square waveguides (Fig. 2.1). We believe that the axis 0z axes directed along the waveguides. The plane z = 0 coincides with the aperture grille. The sequence of operation is as follows:  creature separate emitter at form of segment square waveguide;  the creation of boxing, located on top of the radiator;  assignment of boundary conditions PerfectEon the walls of the waveguide;  the task Floquet ports on the face of boxing;  job waveguide port;  install analysis;  launch in the calculation;  output characteristics.

Fig. 2.1. The geometry of the antenna array

The geometry of the antenna array shownFig. 2.1. We consider a model in the form of an infinite grating. Waveguide ports are in the z0 and have the form of square waveguide ports (Fig. 2.2) with main wave linear polarization. Direction field vectorthis wave is shown in Fig. 2.1 in the form of arrows.

electric

19

Fig. 2.2. Model HFSS single element antenna array coordinate vectors

infinite array analysis can be reducedAnalysis for one period through the Floquet theorem mentioned in Chapter 1. Note that the concept of an infinite lattice directional diagram (DS) can not be correctly identified, since it is introduced only to the radiation source with finite dimensions. Strictly speaking, the NAM infinite array describes the delta - function and physical does not make sense. Nevertheless, there are approximate techniques to use the results of analysis patterns for endless evaluation finite lattice misfit dislocations. On them will be discussed later. Just infinite array analysis gives an indication of its task of coordination with a free space. Fig.2.2 shows the geometry of one cell of an infinite array. The model consists of two areas. The lower part is a waveguide, and on top of it is an air box. periodic boundary conditions are set on the vertical faces of the box. On the upper surface of the box is given by the Floquet port. Creating a model of a separate emitter .To create a separatecell array, perform the following steps:

1. Open the projectand give it a name AGW. 2. team Draw> Box create arbitrary boxing, and then edit its settingsunder Edit> Properties (Figure 2.3) 3. Selectcreated edit box and its transparency (imaging parameter generated by the object) Transparency = 0.8.

20

Fig. waveguide 2.3.Parametry

Fig. 2.4.Parametry air box

4. surgery Draw> Box create the second box, and edit the dimensions and properties Edit> Properties (Fig. 2.4).

The taskMaster and Slave boundaries. 1. presson the F key, translating HFSS in surface selection mode, select the side of the upper box and type the command HFSS> Boundaries> Assign> Master. A dialog Master border. 2. leave the default name like Master1. 3.

Click in the pop up menu U vector, and click New Vector. appears Measure dialog appears and Create Line.

4. Ask vectorU coordinate system in the location shown on the surface in Fig. 2.2. Click the lower right corner (start point), and drag the cursor to the left corner (endpoint) and refine. 5. Click OK, to close the dialog. 6. Select the opposite chamferand call the slave boundary condition HFSS> Boundaries> Assign Slave ... Appears Slave dialogue with the selected tab General (Fig. 2.5). 7. SelectMaster1 as the leading boundary Master. 8. drawU Vector vector as shown in Fig. 2.5. 9. SelectReverse direction mode of the vector V. 10. leave unchangedother settings and click OK.

21

Fig.2.5. Dialog reference phase difference between boundaries of Master and Slave

11. Repeat this procedure forMaster2 Slave 2 and boundaries, as shown in Fig. 2.6. For the vector V on the border Master2 need to install the opposite direction (Reverse direction).

Fig.2.6. Master and Slave Boundaries mounted on opposite faces of the air box antenna model

In the dialog shown in Fig. 2.5 there are two installation phase delay between the Master options boundaries - Slave: corners by scanning Scan Angle and Input Phase Delay phase delay. Setting the waveguide port. waveguide segment contains 4 sides on which to set the boundary conditions PerfectE. This would correspond to that of the metal. Hold down the Ctrl key and select 4 of the lower box and define them as a perfect electric wall command Assign Boundarys -> Perfect E.

21

Fig. 2.7. Setting boundaries ideal conductivity on the waveguide walls

that set the waveguide port: 1. Selectthe lower bound of the lower box (Fig. 2.8). 2. press Right-click and from the pop menu Assign> Excitations> WavePort. It appears WavePort assistant. 3. Installtherein the number of modes equal to 2.

Fig. 2.8. Setting the integral of the square lines of the waveguide port

22

5. In the Integration Line, select New line and draw two perpendicular lines integrated for each mode, as shown in Fig. 2.5. 6.leave other settings using the Next command to transition and click OK to the next page. A given waveguide port appears Excitation in the list. Note that the choiceport in two modes due to the fact that the square waveguide is a bimodal waveguide, in which there are two propagating waves of differing polarization field. integrated lines task shows that we as the waves in the wave port using two orthogonal linear polarizations.

installationFloquet ports. The top of the set top boxFloquet port. Unlike radiation boundary conditions and PML This port allows you to calculate and display the value of S21 transmission coefficient of the waveguide port in Floquet port. perform the following steps to install the Floquet port: 1. Select the top facetop box. 2. Right-clickand select Assign> Excitation> Floquet Port from the pop-up menu. Assistant appears Floquet port (Fig. 2.9).

Fig. 2.9. The choice of destinations verktorov matching Floquet ports

3. Under Lattice Coordinate System determined directions A and B Floquet port. 4. ClickNextTaking Phase Delay default, and then Next to go to page setup Floquet Modes Setup port modes (Fig. 2.10). Default settings dialog Floquet modes includetwo modes port Floquet.Floquet modes are determined by two indices n.m and polarization

23

Polarisation State.

indices

n.m can understandof formula (1) in Chapter 1.

The fundamental mode has zero Floquet indices. This mode (wave) propagatesin all, no matter how small, lattice periods. If the grating period is large enough, then there are propagating waveswith non-zero indices. Each pair of two waves indices n.m comply differing polarization.

Fig. 2.10. selection Channel characteristics Floquet

The last columnfashion table marked "Attenuation (Attenuation)." This damping fashion along a direction normal to the lattice planes in dB per unit length. The values for the mirror mode is 0 dB, as they propagate in free space and is therefore not attenuated. This option is not specified, and is calculated by the program. fashion toptypes can be either propagating or evanescent. their propagation mode independent of scan angle. There are situations in which for small angles of scanning the higher order mode attenuated, while increasing the angle it becomes pervasive. If the grating period less than half the wavelength in free space, then only the two main modes propagate at all angles of scan. In this case, the periods of more than half a wavelength. Therefore, at high angles of scanning in addition to basic modes must appear propagating modes with nonzero index.

24

Fig. 2.11.Target scan angles, which range from the number defined in Floquet modes depends ports

presson Modes Calculator button (Figure 2.12). This dialogue is necessary for the calculation of the parameters and the correct number of Floquet modes of selection events, necessary for the correct description of the port. In the dialog box you need to put the corners, which will be carried out by the beam scanning antenna array. It was noted above that our grill for large scan angles can operate in multimode. We calculate the parameters of ten modes (Fig. 2.12), setting 10 in Number of Modes.

Fig. 2.12. theFashion Floquet ports 25

5. The Post Processing tab, specify the position of the reference plane. Setting the reference plane is used,when the user is interested in the phase of the scattering parameter. The default reference plane is in the plane of the wave port. De-embeding operation allows you to change the position of the reference plane. This change affects only the phase of the scattering parameters, and does not affect their modules. 6. In 3D mode, you can Refinement tab Floquet, who are involved in the adaptive mesh refinement 3D. Grid partition that is created HFSSon the next steps of adaptation it is actually a compromise for the simultaneous analysis of all events at the same time. 7. takeother default settings and click the OK, to close the wizard Floquet ports. Floquet port appears in the project tree in the Excitation section. We define as the scan anglesproject variables, as follows: 1. In the menu, set the command Project> Project Variables. This will bring up a window Properties for this project (Fig. 2.13). 2. Click the buttonAdd. This will cause the Add Property dialog.

Fig. 2.13.Dialogue project variables

3. Install variable name $ Phi_scan, and its value 0 deg. This variable will be used as the azimuth angle. 4. Click OK. Nowvariable $ phi_scan will be a d d e d Properties in the project window. 5. Click the buttonAddthatshow again Add Property dialog.

26

6. Install the name of the variable describing the elevation name = $ theta_scan and a value of 0 deg. 7. Click OK. Dialog Add Property closes and added var iab le Project $ theta_scan. 8. ClickOK,to close the project windowProperties. It should be noted,that when using the scan angles of the unit cell patterns, periodicity plane (here the plane of the array) must be parallel to the plane XOY in the global coordinate system. Installation on a decision . to do installation on the analysis, follow these steps:

1. Right-clickAnalysis on in the project tree and select Add Solution Setup. A dialog opens Solution Setup (Figure 2.14). 2. In the tab General, set the frequency solutions Solution frequency = 299.79 Mhz, Maximum Number of Passes = 5 and Maximum Delta S = 0.02.

Fig. 2.14.Dialogue installation solution

3. In the tab Options, select the Do Lamda Refinement mode and set the option Lambda = Use Default. 4. Set Maximum Refinement Per Pass = 30%, Minimum Number of Passes = 5 and Minimum Converged Passes = 2. 5. Selectbasic functions Order Basis function: First Order, and click OK.

27

Starting the calculationand view the results.Start the calculation of the team HFSS> Analyze. Once completed, clickResults on the icon and select Solution Data. Fig.2.15 shows the window with the scattering matrix, which appears after the calculation. We note the following.

• S-matrix has a dimension of 6 × 6 taking into account a 2-Floquet modes ports. • fashion Flockin the S-matrix are listed in the order specified in the Setup panel of the Floquet port. When referring to this panel, we, therefore, have in mind that FloquetPort1: 1 refers for fashion and Floquet TE00 FloquetPort1: 2 refers to fashion Floquet TM00.

Fig. 2.15.Dialog Data Solution Data solutions

• columnsand rows in a matrix in Fig. 2.15 correspond to the standard definition of the scattering matrix. The columns correspond to the wave incident on the various ports, and line - the waves reflected from different ports. For example, the first column of the matrix corresponds to the excitation wave incident wave port 1. The elements of that column are equal to the amplitudes of waves reflected by the different ports in a state where only one wave is excited port 1. Excitation wave corresponds to the port for transmission grating. • Columns corresponding Floquet ports describe lattice parametersin the receiving mode.

28

parametricsweep scan angle. To show the possibilities of the Floquet port, calculate the dependence of the lattice reflection coefficientport in the wave as a function of scan angle. When scanning occurs in a E-lattice plane at an angle of 27.5 ° is observed glare effect. To show this, we need to find the characteristics in E-plane scan angle when changing from scan = 0 o to scan = 90o.

To perform a parametric analysis: 1. pressOptimetrics on in the project tree and select Add Parametric. itdisplays Setup Sweep Analsysis dialogue with laying Sweep Definitions. 2. Click the Add button. itdisplays the Add / Edit Sweep dialog. 3. Variable from the pop menu, select the $ theta_scan. 4. SelectLinear step. 5. Install Start = 0 deg, Stop = 90 deg, and Step = 3 deg (Fig. 2.17).

Fig. 2.17. Setting range change Theta angle in parametric optimization

Fig. 2.18. selection saving options and fields partitions grid when performing parametric optimization

6. Click the buttonAddand OK, to close the Add / Edit Sweep dialog. DialogSetup Sweep AnalysisIt includesvariable $ theta_scan. 7. Open the General tab, and make sure that the Sim Setup installed Setup1 with the Include mode. 8. Open a bookmarkOptionsto make sure thatOptions Save Fields and Mesh marked, and that the option Copy Geometrically Equivalent Meshes (Fig. 2.18) is not checked. In this case, at each step of the parametric analysis are stored far-field characteristics. 9. ClickOK. The section appears Optimetrics installation Parametric. Current couple the fundamental modes sufficient to describe the normal incidence of the wave, must be supplemented by the higher modes of types to describe 29

latticeat high angles of the scan. Preparation of events for the parametric sweep consists of the following steps: 1. re-signin port installations Floquet panel and click the tab, types of waves. To define a list of events, necessary for modeling at all scan angles, use the calculator mode. 2. Call events calculatorby clicking the Modes Calculator. calculator calculation is additional information to create a list of recommended events forFloquet port. His results need to select the number of modes and do not affect the calculation of the lattice model. 3. Select10 for the port modes (with a margin). Probably, we will reduce this number, but that additional research is required. 4. Set the frequency of 299.97 MHz,where simulation is performed. If two or more sweep frequencies, typically the highest frequency is selected task installation comprise, in order to detect the appearance of propagating high-order modes. 5. To establish a set oftypes of waves which will be sufficient for each scan direction in the parametric sweep, the sweep angles of scanning are entered in the format "start-stop-step". entered angles - spherical polar angles in the global coordinate system. Forthis case the angle Phi = 90 °, so that enter this value as the starting value and the final value of Phi in fields. Theta scan sweep angle changes from 0 ° to 90 ° in steps of 0.5 °, so enter these same values in the Theta calculator fields. 6. Click OK,to start the calculation of the calculator and see the recommended list of events (as in Fig. 2.12).

Fig. 2.20. Characteristics scanning the reflection and transmission characteristics of the wave types

31

Note the following: • initial steamfundamental modes TE00 and TM00 modes remain top of the table Floquet (Fig. 2.12). Attenuation of zero, which means that these modes propagate without attenuation, ie they are propagating. • Thenin the table is a second pair of TE01 and TM01 modes. They extend without attenuation, at least in one direction. • Thenfollowed by six modes with minimum attenuation of 60 dB / m. These modes do not apply in any of the selected areas. Now you need to make the finalSelect the number of events considered in the Floquet port. This choice is based on the following considerations. Any Floquet modes propagating in at least one direction should be included in the mode table. Therefore, it is necessary to include the first four modes, which reached the port Floquet unimpaired. Remainingtypes of waves, having a non-zero attenuation, are candidates to be excluded from the table. From the point of view of efficiency modeling and interpretation of the results is better to remove them. In this regard, we note: since the length ofthe unit cell is 1.25 m, any of the last six events, when excited in a rectangular aperture to reach the Floquet port with attenuation equal to 1.25 * 60.00 = 75 dB, that is very much weakened. Therefore, in most cases such Floquet modes in the description of the port can be neglected. 7. Thus, we introduce a number of modesin the Number of Modes = 4. In the list of events are only the modes TE00, TM00, TE01, and TM01. 8.Click OK, to select the set of events and then run parametric analysis (it will take a certain time of the calculation). review the results of the parametric analysis.

Once the simulation is finished, the S-matrix elementsas a function of scan angle can be seen in Matrix Data tab or on the graph. By analyzing the scattering matrix for different scanning angles, it can be seen that the connection between the TE00 wave types and TE01 very small. To display the module dependencies of reflection coefficientsand transmission TM as scan angle functions perform the following steps: 1. Right clickthe Results in the project tree and select Create Modal Solution Data Report> Rectangular Plot. Report dialog box appears. 2. In the Trace tab, section X, select $ theta_scan. 3. ForY select both S Parameter Category, S (Wave Port1: 1) as a characteristic (Quantity) and Mag module as a Function.

31

4. Click OKTo create a new schedule. The new report is displayed on the screen and adds the name of Result in the project tree with the first trace shown below the graph. Add Trace button becomes active in the Reports dialog. 5. Select the name of the characteristics of the project tree. It displays the properties for the Trace. 6. markName the Specify option to open the Name field and change the name to Reflection. This will change the name on the characteristic. 7. Add two additional graphicsand change their names: mag (S (WavePort1: 1, FloquetPort1: 2)) corresponds TM00 Transmission; mag (S (WavePort1: 1, FloquetPort1: 4)) corresponds TM01 Transmission. 8. In the project tree, select the XY Plot 1. It shows the Properties for a schedule. 9. Edit fields Nameon Reflection and Transmission and press Enter. The results of the parametric analysis are presentedFig. 2.20. Note that the reflectance tends to unity at an angle of 27.5 °. This effect is known as glare effect, since in the vicinity of the angle of glare grating efficiency drops sharply, because all the energy received on the wave port is not radiated into space, it is reflected. Also note,that type becomes TM01 wave propagating at an angle of approximately 30 °. This is evidenced by a sharp increase in the gain of the wave in the wave port TM01 Floquet port at angles greater than 30 °. In this example, the matching questions are addressed: the reflection coefficient of the lattice. The next section will be reviewed and radiation characteristics of the antenna array.

32

3. The array antenna of the Vivaldi antennas The calculation of the antenna array composedof radiating elements, each of which is a broadband antenna Vivaldi. Array of antennas Vivaldi created using periodic boundary conditions and Floquet ports. The antenna is powered coaxial linewith a waveguide port. On the upper surface of the array cells is set Floquet port (see. Fig. 3.1). Periodic boundary conditions are introduced on the sides of the cell. In this opposite and parallel side borders are declared Master and Slave. The substrate has a dielectric constant εr = 6, and a thickness 1.27 mm. Strip conductors are 2D objects with boundary conditions PerE. The calculation is performed at a frequency of 4.5 GHz and interpolation mode in the range of 2 ... 5 GHz.

Fig.3.1. HFSS interface c separate antenna Vivaldi

3.1. Drawing Vivaldi antennas Establish length units- millimeters and draw a dielectric board as a parallelepiped measuring 34 x 60 x 1.27 mm (Figure 3.2.) Create command -> Box.

33

Fig. 3.2. Dimensions Vivaldi antenna, which is an element of the antenna array

will make the insulatorsection variables and define the permeability of the box the box of 4. Parameters can be edited in the dialog Fig. 3.3.

Fig. 3.3. The size of the substrate 6 with a permeability of 1.27 mm thick and

34

Vivaldi antenna operatesa high frequency band, and maximum band width achieved with an exponential change in the gap from the beginning of the horn to raster. Draw aVivaldi antenna conductors using functional relationships. Draw a line, which is defined as a function performed by the team Geometry -> Curve -> Analitic Curve. dialog appears Fig. 3.4, into which the functional dependence of coordinates of points on an edge of the strip conductor by the variable t. Coordinate Z depends on the variable t is linear. Therefore, the dependence of the coordinates Y t can be regarded as dependent on the coordinate Z.

Figure 3.4. Setting functions for which the curve is drawn

useto set the shape of the conductor edges exponential function: X (t) = 0, Y (t) = 0.25 * exp (0.123 * t),Z (t) = t. The width of the gapbetween conductors at the narrowest point at t = 0 is equal to 0.5 mm. The variable t varies from 0 to 33.3 (Fig. 3.4). The functional dependence is set in 24 points. Nowsupplement exponential curves with straight lines and a circle, which play the role of balancing the power system devices Vivaldi antenna (Fig. 3.7).

35

Fig. 3.5. Topology and size of the balancing cavity

Further draw the circle, resonator Vivaldi antenna (Fig. 3.5).

playing

role

balun

Fig. 3.6. circular resonator parameters, which is part of the balun

Now draw a rectangle,which form the slot line resonator and connecting a coaxial line (Fig. 3.7).

36

Fig. 3.7. Draw a rectangle to create a slot line

after trainingplotting to form a complex which includes a circle, an exponential line and all surfaces future Vivaldi antenna, we define command Draw> Line capture audio and perform point exponential curve. When we reach the point where you want to make the transition to the circle, move the drawing mode in Center Point Arc (Figure 3.8)

Fig.3.8. Transfer from the drawing line segments (Straight) in the circumferential drawing mode with the center and radius.

Now we need to combine the exponential segmentwith a broken line Unite team. Next, create a form from a closed plane Modeler team -> Surface -> Cover Line. 37

Fig. 3.9. The strip conductor antenna with a balun Vivaldi

Further select an exponential segment, and deploy it to 180 °, just change the sign of the coordinates Y (t)(Fig. 3.10).

Fig. 3.10.Drawing the second strip conductor

Vivaldi antenna can excite different ways. You can, for example, to put a discrete port between the antenna vibrators.And it is possible to include in the real length of the coaxial line structure, the input of which is switched the microwave generator. Draw the inner conductor of the coaxial line as a cylinder 8 mm in length. Draw the coaxial line runs Draw-> Cilinder team, on which dialogue (Fig. 3.11) appears.

38

Fig. 3.11. The parameters of the internal conductor of the coaxial line radius 0.375 mm 8 mm long

Further draw the external shell coaxial line, commandDraw-> Cilinder,and define the settings shown in Fig. 3.12.

also

Fig. 3.12. Draw external outer cylinder, on its upper surface is automatically set condition Perfect E

Further draw a radiation box that surrounds the antenna Vivaldi, Draw command -> Box and set the dimensions shown in Fig. 3.13.

Fig. 3.13. Target box sizes, ambient Vivaldi antenna 34 x 36 x 60 mm 39

on the sidesthis box we define the boundary condition Radiate. Define the port on the end of the coaxial line (Fig. 3.14).

Fig.3.14. Creating a wave port in a section of coaxial line

Fig.3.15. Cell array antenna, covered by periodic boundary conditions

Port Floquet used in the simulation of infinite periodic structures (see chap. 1 and 2). Analysis of the endless structure is to analyze the structure of one period (unit cell). On its opposite sides defined periodicity conditions. On the upper surface must do one of the possible 'Open' boundary conditions simulating the radiation processin free space. As surfaces to "open" boundary condition in HFSS used PML, radiation surface and Floquet port. dignityFloquet port is that it can be used to describe not only the reflection of the wave arriving at the antenna input of Vivaldi, but also the transfer of energy in space. In the infinite periodic structure field in free space has the form Floquet harmonics. Each of these harmonics is a plane wave propagating in the space at a certain angle. As noted in Chapter 1 and 2, most Floquet harmonics is evanescent, and the main harmonic and one or two types of higher harmonics can be propagated. Thus harmonics of higher orders may under some angles of the scan to be propagated, and at the other nonpropagating. UsingFloquet port allows the calculation of the gains of the waveguide port in the Floquet harmonics, and vice versa. As in

41

case waveguide port, this information is given in the form of the S-matrix, linking reflectedand the incident waves (Fig. 3.19-3.24).

Fig. 3.16. Floquet port settings in the table specified number of the mode, statepolarization mode index, damping and sealing mode Affects Refinements

Furtherwe define the center frequency of 4.5 GHz, and performing the calculations of the antenna array in the frequency range of 2 to 5 GHz. The results of calculation of the frequency characteristic | S11 | are shown in Fig. 3.17.

Fig. 3.17. The frequency characteristic of the reflection coefficient of the Vivaldi antenna

41

Fig. 3.18. near Field sectional Vivaldi antenna and current on the surfaces of the strip conductors

Fig. 3.18 shows that the antenna is excited symmetrically, which was not I would be if there was no balun in structure.

Fig.3.19. The first mode channel Floquet

Fig.3.20. The second mode channel Floquet

Note thatin terms of the use of electrodynamics lattice pattern in the form of a channel can not be expected Floquet Nam this type of antenna, since this model may strictly be used solely for analyzing an infinite lattice which has NAM zero width, i.e. in the form of delta functions. However, it is possible to calculate HFSS Nam Floquet channel by replacing one of the ports on the Floquet radiation surface. This possibility should be treated with caution, meaning that the resulting Nam is neither grating Nam or separate component thereof. It gives a qualitative idea of the NAM lattice when it is driven by one of its inputs. The antenna technique such Nam called NAM emitter composed of a lattice. However, we must remember that the calculation method described above allows you to get the mentioned characteristics are only approximately.

42

4. The antenna array on the dipole antenna Considerantenna array of four dipole antennas with a metal reflector (Fig. 4.1). In such a lattice beam position can be controlled by changing the phase of the voltage applied to its individual elements. Reflective grating panel improves characteristics by creating a unidirectional radiation in the horizontal plane. Run analysis of such array can bea unitary construction, i.e. without using periodic boundary conditions.

Fig. 4.1. The array antenna with reflector

lattice elements are arrangedon Teflon backing thickness 1.6 mm. Excitation carried out via the digital ports. radiation boundary is given on the sides of the air box. Variable phase shift for postprocessing has phase_shift name. The center frequency at which the antenna array operates 1.9 GHz.

43

Fig. 4.2. The geometry of one of the four antennas disposed with a step on the axis Z equal to 103 mm

Draw a dielectric substrate 1.6 mm thick (dielectric constant4), Draw-> Box team. The obtained dimensions of the substrate can be adjusted in Fig dialog. 4.3.

Fig. 4.3.Conversation piece dielectric board

Move the coordinate systemon the plane on which will draw vibrator first cursor highlighting one of the planes (pre-pressing F), command Modeler-> Coordinate System -> Create -> Face CS.

44

Next, draw a vibratorpoint by point how polygon, setting the command Draw -> Polyline.

Fig. 4.3. Draw one of the vibrator

Next, createnew coordinate system shifted with respect to the X axis of the system by 18 mm, equal to half the length of the substrate command Modeler-> Coordinat System -> Create -> Relative CS-> Offset. And make a U-turn with a copy of this part of the vibrator 180 ° command Edit-> Duplicate-> Around Axis.

Fig. 4.4. Selection Y axis about which the vibrator copying scrolls

Now between linesvibrator draw a rectangle (Fig. 4.5) discrete port on which the then established > Excitation-> Assign-> Lumped Port.

team

HFSS-

45

Fig. 4.5. Formulation of an integrated line on discrete port

Furtherperform up-shift of the dipole antenna to receive antenna 4 constituting an antenna array (Fig. 4.7). reflector Draw. metallic reflector angular configurationsuch as shown in Fig. 4.6. The mutual arrangement of the reflector and the dielectric board with vibrators is shown in Fig. 4.7. The reflector comprises a hole that can be used to output the exciting lines and connecting them with a power divider outputs, which acts as a lattice supply circuit.

Fig. 4.6. Regulation reflective plane array antenna with reflector

The total height of the dielectric substrate420 mm, and the dielectric constant ε = 4. After drawing the lattice can specify settings for calculation and analysis of the frequency range. When conducting the calculation of the lattice should be noted that the antenna array is the RF multipole having four inputs. HFSS calculates the scattering matrix of the multipole in the prescribed frequency range. However, the values obtained reflection coefficients are not equal, representing the greatest practical interest reflection coefficients of the lattice in the operating mode in which simultaneously excites all four inputs.

46

Fig. 4.7. Structure and the size of the antenna array. The total height of 420 mm reflector

To determine the reflection coefficients of the latticeSi in the working mode, j_corr (i, j = 1, ... 4) necessary to calculate them from the elements of the scattering matrix S (i, j) according to the formulas which are shown in Fig. 4.8.

Fig. 4.8. The variables considered in which S-parameters of the antenna at its inputs simultaneous excitation

Fig.4.8 refers to a complex voltage Vi amplitude excitatory lattice elements. 47

It is known that forreducing sidelobe level of the antenna array elements extreme need to initiate a smaller amplitude than in the center. The amplitudes of the excitation can be set as a variable (see. Fig. 4.8). If we take V_port1 = V_port4 = 0.66 and V_port2 = V_port3 = 1, we get the NAM, as shown in Fig. 4.9. The difference in power phasetwo adjacent antennas is set variable in step phase_shift postprocessing. To create such a regime in the dialogue, is led away by a team HFSS> Fields> Edit Sources, which is a variable offset phase. Set phase_shift factor variable phase shift. askphase_shift variable can by clicking on HFSSDesign2 project name in the project tree. The variables of the project can be seen in the Properties window. In this window, you can change the value phase_shift. We choose phase_shift = 30º, that would be consistent with the pattern in Fig. 4.9.

Fig. 4.9. Nam separate vibrator array antenna

48

Fig. 4.10. Three-dimensional Nam antenna array

With a large number of antenna array elementsit is no longer possible to calculate in a single design. To solve this problem you need to use periodic boundary conditions. Excitation of each antenna array element is performedusing a multichannel power divider (MDM). EXAMPLE MDM together with the vibrator shown in Fig. 4.11. In the case of in-phase excitation ports are excited so that the far field are summarized in the direction 0y axis. This process can be seen from the field distribution shown in Fig. 4.11.

Fig. 4.11. nearfield in the plane of the antenna array xOy 49

It should be noted that the joint calculationemitting lattice together with the power scheme is for HFSS very complex task that requires a lot of computer resources costs. This situation is due to the fact that the branched microstrip circuit realizing MDM requires for its analysis of the use very dense mesh. An example of such a network is shown in Fig. 4.12, which also shows the distribution of currents in metallic conductors.

Fig. 4.12. Vibrator grating reflector and distribution circuit

Given the largethe complexity of solving the discussed problems in HFSS, is of interest to use an integrated approach which combines the use of different software to calculate various pieces of complex structure. When each part is analyzed using methods in the most adequate physics of its functioning. CalculationMDM system in MWO. Power distribution circuit will design in Microwave Office system (MWO) using EMSight routine that calculates the stripe structures of the method of moments. Such an approach for analyzing stripline circuits much more efficient method of finite elements, which is used in HFSS. Wherein the transmitting grating is analyzed using HFSS. Below, we discuss the possibility of correct use of data obtained from a single system for the calculations in the other. In this case, the MWO. The problem of reconciling the calculation data receivedin different projection systems it is solved by the use of discrete ports. For this model is used for modeling vibrators shown in Fig. 4.13. Its feature is the use of two discrete P1,2 ports connected between the conductors of the transmission line which excites the vibrator and the metal reflector. In this representation array element is calculated as a microwave HFSS multipole eight outputs (in shestnadtsatipolyusnik

51

the terminology used in Russian and English-language terminology for vosmipolyusnik - eight port junction).

Fig. 4.13. Modelvibrator with two ports

Using this model allows us to calculate the scattering matrix grilleMDM without 8x8. We next consider the main stages of designMDM system in MWO. MDM is a combination of several elementary power dividers EDM into two channels connected with each other via transmission lines. MDM structural scheme is shown in Fig. 4.14.

51

Fig. 4.14. structure MDM

The composition of MDM shown in Fig. 4.14 D1 EDM includes performing division of power in half, EDM D2, power dividing in a ratio of 3: 7 and exciter vibrators V. The unequal power division in the EDM D2 provides decaying field distribution at the edges of the grating, which reduces the side lobe level in its vertical plane Nam . exciterThe device acts as a power dipole antenna. 1,2 outputs it is connected to a vibrator which has two inputs (see. Fig. 4.13). First stepMDM design includes the design of the EDM and the pathogen. Their topology is shown in Fig. 4.15 ac. Fig. 4.15 a, b shows the topology D1,2 dividers, and Fig. 4.15 in the exciter topology. They are made on a substrate with a permeability of 4.6 and 2 mm thick.

52

a

b

at Fig. 4.15.Topology EDM and exciter 53

Because thedivider D1 has symmetry relative to ports 2 and 3, it reduces to design harmonization of entry 1. All the outputs of the device are formed as microstrip lines with characteristic impedance of 50 ohms. The discrete ports are used as ports. Lateral shoulders divider comprise quarter-wave transformers that provide output matching transmission lines with input line. Fig. 4.16 shows the frequency response of the input reflection coefficient divider 1. It is seen that the best match is achieved in the vicinity of the frequency 1.7 GHz. When removing it from the reflection coefficient increases, but remaining sufficiently low value not higher than - 26 dB in the band 1.6 - 1.8 GHz.

Fig. 4.16. frequency divider D1 Input 1

addiction

module factor

reflection

divider D2It does not have symmetry relative to the inputs 2 and 3, as it provides an asymmetrical division of power. Therefore, it requires not only the design matching at the input 1, but also the realization set values of transmission factors of the input 1 to the inputs 2 and 3. They mustbe equal to the following values: dB. S211.5 dB S315.34 OnFig. 4.17 shows the frequency dependence of the modules reflection Sel and transmission coefficients S a S31 divider D2. It is seen, 21 nd eve n 54

whatit is sufficiently well aligned for entry 1 and provides a predetermined value of transmission coefficients.

Fig.4.17. Frequency characteristics divider D2 excitervibrator must perform the following functions. It performs power division, arriving at input 1 in equal relation between the inputs 2 and 3. In this phase signals at ports 2 and 3 must be shifted to 1800. In this case, the two-wire line which feeds the vibrator is excited its fundamental wave, whose currents on the conductors and phase-shifted by 1800. It is also important to the driver outputs are matched with the input impedance of the vibrator. Its parameters HFSS chosen in such a way that the input impedance at the points of accommodation ports had active portion of 60 ohms, and a zero reactive part. proceedingof these conditions, the pathogen was carried out to optimize the topology. As a result, frequency characteristics are obtained as shown in Fig. 4.18 a, b. Fig. 4.18 and shows the frequency dependence of the reflection coefficient at the input 1, and Fig. 4.18 b frequency depending on phase coefficients transfer S21 S31. It is seen, a what nd exciter well-coordinated and provides the complementary division of power. 55

The MWO system it is possible to visualize the current distribution on the strip conductors. An example of such a distribution on the conductors exciter shown in Fig. 4.19.

a

b Fig. 4.18. frequencypathogen characteristics 56

Fig. 4.19.Current distribution on strip conductors of the pathogen

finalMDM design step is to calculate its output parameters. MDM topology is shown in Fig. 4.20.

Fig. 4.20.MDM topology

As an example, in Fig. 4.21 shows the frequency dependence of the reflection coefficient for the central MDM entry 1 (see. Fig. 4.14). It can be seen that the alignment MDM somewhat worse matching EDM, however, in the frequency band the reflection coefficient is less than - 20 dB. The next step consists lattice designa calculation of its parameters based MDM design results and emitting portion of the lattice in the form of four vibrators formed in HFSS. This part of the work is convenient to perform,exporting data files from the HFSS and MWO and treating them with the help of computer systems like Mathcad or Matlab. files Data include multiport scattering matrix, calculatedin HFSS and MWO. grating scattering matrix Sa is a 8x8 matrix in accordance with the number of its inputs. Similarly matrix scattering MDM Sd It has a dimension of 9x9. 57

Fig. 4.20. frequency dependenceMDM reflection coefficient at the input 1

Matrix

Sd It has the following structure:

Seleven Sd 

S1

S1  .  

S

- input group with the numbers 2 - 9. Thus, 8x8,

size 8x1 and

S1 - matrix - the line size 1x8,



(5)

S - a matrix S1- Matrix - column

Seleven- the reflection coefficient at the input 1.

For calculation of resultant antenna reflection coefficient R necessary to analyze cascadingtwo multiport shown in Fig. 4.21.

58

Fig. 4.21. cascadeMDM compound and the lattice

59

For define relations given in 20]:

factor

reflection

R

We use the

RSele S1(E SSa )1 SS . ven

(6)

1

where E - the identity matrix of size 8x8. Also, analysis of cascade-connected multiport, we can to find the amplitude of the incident wave to the inputs of the lattice

U n. n1 ... 8. Their

60

can be used further for the taskConditions Lattice excitation with the influence MDM. Knowing the amplitude, we can use HFSS to calculate the antenna pattern (Fig. 4.10). Using different software describedabove allows efficient use of them to solve those problems that can be solved with the help of their computer resources with the least cost. In this case HFSS used to analyze the three-dimensional radiating structure and for analyzing MWO planar stripline circuit. As a result, the total time required for obtaining the final result is significantly reduced. In addition, the increased accuracy and reliability of the solution.

5. Modeling the frequency-selective surface

Among the most interesting problems of applied electrodynamics are the problems of wave diffraction by periodic structures. Widespread use are twodimensionally periodic planar lattice, which are called frequency-selective surfaces (CHSP). They are used as spatial filters, polarizing filters, antenna radomes, radioprotection agents, etc. Special mention deserves the use ChSPin quasi-feeders reflector antennas meteorological satellites. Application ChSP to build frequency selective devices can significantly improve their weight and size. By devices of this type of strict requirements. For example, the radiometer ESA MASTER must provide signal separation ranges 294-306, 316-326 and 342349 GHz [13-17]. Thus the insertion loss should not be greater than 0.5 dB, and the isolation between channels is not less than 20 dB for reliable detection of weak radiations molecules in the atmosphere. In order to minimize insertion loss used ChSP aperture, allowing to exclude dielectrics and losses associated with it. Improving polling characteristics can be achieved using multilayer structures containing several parallel layers and multielement periodic structures comprising several reflectors (apertures) in one unit cell of the periodic structure CHSP. Design of such devices is an urgent task, Creating a model ChSP .We analyze CHSP using periodic boundary conditions, allocating unit cell structures as Floquet channel. The unit cell may CHSPIt is created using boundaries associated with periodic boundary conditions and two Floquet ports. Result solutions boundary CHSP analysis task is represented as a matrix of S-linking Floquet modes in the respective ports. As an example, consider that in this chapter is a conductive screen having a hexagonal lattice of circular apertures (holes). The geometry of the lattice shown in Fig. 5.1. Fig. 5.1 shows the angle of the lattice vectors. The angle between the lattice vectors is 60 °.

61

Figure 5.1. The geometry of the frequency-selective surface

Consider a normal incident plane waveon the screen with the polarization vector of the electric field shown in Fig. 5.1 red arrows. We calculate the modulesand phase of the scattering matrix elements as functions of frequency. The frequency band of 8 to 20 GHz. Modelone cell is shown in Fig. 5.2. Side length equal to 1.73 cm circular aperture diameter is 1.2 cm and height equal to 4 cm cell. It can be seen that the cell consists of a planar metal rhombus with a hole and boxing rhombic shape, the surfaces of which are given periodic boundary conditions and Floquet ports. We begin to create elementary HFSS means the cell. In the first stage will create rhombic box.

Creature

rhombic

Boxing. For

solutions

tasks

follow

these steps: 1. Open the a new project and name it RhombicArray. Set the length of the unit centimeters (Cm).

61

Fig. 5.2. Rhomboid hexagonal cell CHSP

2. Click Draw> Line,Click at an arbitrary position to set the starting point, and then click the other three arbitrary points, and then return to the starting point to close the figure. 3. Right-click to bring up popup menuand then click Done. This polygon is created. 4. In the project tree, expand Sheets> Unassigned> CreatePolyline, selecting the first operation CreateLine to see the properties of this line.

5. Set the coordinates of the first point Point1 = (0,0,0). 6. Edit coordinates Point2= (0.865, 1.4982, 0). This will shift the segment of the first broken line, which will give the desired object resolution.

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7. Repeatthis process with the following three operations in the tree CreateLines create and edit them the values Point2, Point3 and Point4 (Figure 5.3.) as follows: Point2 (0.865, 1.4982, 0) Point3 (2.595, 1.4982, 0) Point4 (1.73, 0, 0) Created flat rhombus can be usedto create a diamond-shaped boxing. Before that, make, Copy command, a copy of the rhombus, which will be useful for creating metallic diamond.

Fig. 5.3. Rhombus as a section future cell frequency-selective surface

8. To convert a flat 2D object to 3D cell, press Draw> Sweep> Along Vector. 9.The status bar, enter all zeros in the cell X, Y, Z, to set the starting point. This places the cursora first point defining the vector, and changes the message on status bar "Input the second point of the sweep vector (to enter the second point scan vector)." Tags cell shows the shift amounts dX, dY, and dZ. 10. In the status bar, enter 0, 0 and 4, and press Enter. This draw a line from the start point to the end point, and displays the dialog Sweep Along Vector (Fig. 5.4).

11. In the dialog box Sweep Along Vector, leave 0 deg as a draft angle, and select from the drop down menu, Round as the type Draft type. Then click OK.

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Fig. 5.4. Completion operation sweep along vector

12. This operation converts diamond in the 3D object. 13. Now move the this object down to 2 cm from the operation Edit> Arrange-> Move. 14. opensMeasure data dialog and there is a possibility to enter through the status bar as well as the cursor, the reference point X, Y, and Z, as a first point offset vector. 15. In the status bar, set the Z = 0, and press Enter. 16. In the status bar, set the dZ = -2.0 and press Enter. This will move the objectto the desired length. Creating a flat diamond-shaped with a hole.If you make a copy of a flat rhombus, the further it can be used.Otherwise, repeat steps 1 - 7.

1. Click copy flat diamond. 2. Command Draw> Circle Draw a circle with the cursor in the center of the polygon. 3. Open dialogue properties circle and set the radius of 0.6 cm. 4. Select at the same time a circle and a rectangle and click Modeler> Boolean> Subtract. Subtract dialog opens. Fig. 5.5. The cell-frequency selective surface

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5. Move Rectangle Blank in the list, and the circle in the Tool list. 6. Click OK, to close the dialog and create a circle by subtracting the aperture of the rectangle.

The taskMaster and Slave boundaries. ForIn order to simulate CHSP which consists of periodically arranged elements necessary to set the periodic boundary conditions on the opposite walls. Define Master borderand Slave to the rhombic object as follows. 1. Select the surface shown in Fig. 5.6 and set command HFSS> Boundaries> Assign> Master.Appears Master Boundary dialog. 2. leave the default name like Master1. 3. that set the vector U along the edge click New Vector. appears Conversation Measure dialog and Create Line. 4. draw vectorU vector on the selected surface. Click on the lower left corner as a starting point, and draw a cursor to the right corner and refine Master1.

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Fig.5.6.Zadanie Master boundaries (leading) and the Slave (slave)

5. The Master Boundary dialog for vector V Vector, select Reverse directionand click OK. 6. Select the oppositeand set aside the command HFSS> Boundaries> Assign Slave. Slave appears a dialogue with the selected tab General. 7. For this slave select Master1 surface as the leading boundary. 8. drawU Vector vector as shown in Fig. 5.6 and click OK. 9. Repeatprocedure for Master2 Slave boundaries and 2.

Fig. 5.7. Creating a second pair of periodic boundaries

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Next, askPerfect E boundary condition for a diamond-shaped with a hole. To do this, choose Aperture surface of wood chronology and define the command HFSS> Boundaries> Assign> Perfect E. PerfE1 border appears in the Boundary list.

Setting Floquet ports. ports Floquet must be installed on the upper and lower surfaces of the model. 1. Select the topsurface of the model and click HFSS> Excitations> Assign> Floquet Port. Assistant appears Floquet port, showing General page. 2. For the coordinate system Lattice Coordinate System,from the pop-up menu to the direction A, choose New Vector. 3. Draw the vector, pressinglower angle Z axis start point, and then pressing the adjacent corner along the axis X. When you double-click to complete construction of the vector, dialogs Measure Data and Create line disappears and reappears assistant Floquet Port, showing that a vector is defined. Repeat this procedure for the vector b. 4. In Modes setup tab, enter Number of Modes = 14. Thus, the table is full Mode, which will have fourteen lines (Fig. 5.9).

Fig. 5.8. Floquet port in the space-frequency selective surface of the cell 5. Click the buttonModes Calculatorfor informationInstallation modes. mod calculator appears. Set Frequency = 20 GHz frequency (fig. 5.9).

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Fig. 5.9. Calculator modes and setting its start

6. leave the remaining default values and click OK, to close the calculator. This will fill the table with the calculated data. 7. SelectDeembed option, and set the Distance = 2.0 cm. 8. ClickNextfortransition to 3D Refinement page. 9. For 1st Fashion Mode 1, select seal Affects Refinement (Fig. 5.10) and click Next to go to the Post Processing page.

Fig. 5.10. results operation modes calculator 68

10. ClickOK. The first port Floquet appear in Excitations section in the project tree. 11. Select the bottom surface of the model, and repeat the process to set up a second port Floquet. Information first port Floquet copied.

Fig. 5.11. near Field sectional frequency selective surface of the cell Installation on the test. For Follow these steps:

1. Right-clickAnalysis on in the project tree and select Add Solution Setup. A dialog Solution Setup. 2. In the General tab, set Solution frequency = 20 GHz. Install Maximum Number of Passes = 10 and Maximum Delta S = 0.02. 3. In the tab Options, select the Do Lamda Refinement mode, and set Lambda target = 0.2. 4. Set Maximum Refinement Per Pass= 20%, the Minimum Number of Passes = 6 and Minimum Converged Passes = 2. 5. Select functionFirst Order Basis.and click OK.

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Fig. 5.12. Selecting types of waves, which is controlled by the process of convergence

Calculation characteristics in the frequency range. that perform a calculation in the band: 1. Right clickon Setup1 in the project tree and select Add Frequency Sweep. Appears Edit Sweep dialog. 2. To Sweep Type, selectcalculating data smoothing option Interpolating frequency range. 4. Set Max Solutions = 50, and Error Tolerance = 0.5%. 5. Click the buttonadvanced Optionsthatshow dialogue Interpolating Sweep Advanced Options. 6. Set Minimum Solutions = 5 and Minimum number of Subranges = 1. 7. Forinstallation convergence Interpolation Convergence, select the button Use Selected Entries Radio, and click Select Entries button. Dialog appears Interpolation Basis Convergence (Fig. 5.12). 8. The Interpolation Basis Convergence, leave Entry Selection and Mode Selections as All dialog box. This means that all Floquet modes are listed in the table. Then, use the vertical scroll bar, find the line FloquetPort2 1 and set to ON in FloquetPort1 column: 1. 9. In line FloquetPort1: 1 and in line Floquet Port2: 1 and set the option ON. 10. pressOK,to close this dialog box, the OK to close Interpolating Sweep Advanced Options, and OK, to close the Edit Sweep dialog. On Fig. 5.13 - 5.14, the calculated field distribution different Floquet channel modes.

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Fig. 5.13.Golf 2nd fashion Floquet

Fig. 5.14. Field 4 th mode Floquet

11. click Analyzeto start calculation.

Viewing the results of calculations. Severalfrequency dependencies of the modules and phases of the reflection coefficients and transmission of the main types of waves shown in Fig. 5.15, 5.16.

Fig. 5.15. Phase response transfer factor from port 1 to port Floquet 2 by main wave

Fig.5.15 shows that CHSP has frequency selectivity for the fundamental mode. From 5.16 it shows that at a frequency of 18 GHz CHSP completely transparent to the incident wave, because at this frequency it reflectance goes to zero. It is also interesting to calculate the properties of ChSPfor waves incident at various angles to a frequency-selective surface. In this case it is necessary to specify a plane wave, wherein the incidence angle will vary parametrically.

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Fig. 5.16. The frequency characteristics of the reflection coefficients and moduli CHSP transmission of fundamental wave

Note that you can also calculate the properties ChSPfor waves incident at various angles to a frequency-selective surface. In this case it is necessary to specify a plane wave, wherein the incidence angle will vary parametrically. For frequency selective surfaces include resonant structure, discussed in Chapter 1. Materials so that you can setthey will have the frequency dependence of its parameters. An example of the frequency dependence of the materials shown in Fig. 5.17.

Fig. 5.17. frequency dependencematerial (from Example ViaWizard) Library HFSS material can be replenished models with polygonal linearly frequency dependence of the Debye model of a model, models Dvorzheka, Sakharov, as well as custom models, all parameters which can be entered in tabular form [1]. 71

6. Falling plane wave to the object and calculation of radar scattering cross section The radar cross section for the scattering characterizesthe ability of an object scatters the incident electromagnetic waves at him. In English literature it is equivalent to the term Radar Cross Section (RCS). This parameter is used to assess the ability to detect an object (target) by radar [4,5]. Also this parameter for assessing parameters used radar cross-section (EPR). Consider determining the parameter RCS. There are two different cases.In the first transmitting antenna, irradiating the object under study and the receiving antenna, receives a reflected wave from it in one place. In this case we speak of monostatic location and purpose of the parameters describe using monostatic RCS. Inthe second case, the transmitting and receiving antennas located in different locations (see. Fig. 6.1). In this case we speak of bistatic radar and used, respectively, the bistatic RCS.

Fig. 6.1. Scheme bistatic radar

parameters RCS and ESR are related as follows: RCS = σ / λ2. where λ - wavelength in free space, σ - EPR [m2]. certain ratio (6.1) call

(7)

also

RCS, normalized

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radar factor reflection because the he is andimensionless quantity. EPR is determined by the electric field of the incidentEpad wave on the object to place the object location and the field strength of the wave scattered by the object in the direction of the receiving antenna at a location Eotr receiving antenna: σ = 4πr2 | ENeg|2/ | Epad|2. (8) where r - distance from the object to the receiving antenna. Note that the ratio(6.2) can be used as in the case of bistatic and monostatic radar the corresponding change in the field intensity of the scattered wave. from the relation(6.2) that it characterizes EPR extremely energetic properties of the object, since its definition includes the absolute values of the field. If the interest is the phase of the scattered wave, in which case a complex PCP, defined by the complex ESR:

  4r ENeg/ Epad

(9).

HFSS-13 counts bistatic normalized bistatic, complex bistaticmonostatic and PCP. In this example, we will calculate the normalized PCP for bistatic and monostatic radar positions and goals. IWavePhi changing the angle from 0 to 180 degrees (Fig. 6.2), we would like to make "flying around" goals, irradiating the target with all sides (Fig. 6.3), and taking the return signal.

Fig. 6.2. plane wave parameters with the settings to calculate the monopulse RSC

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Overallprocedure for calculating RCS object by finite element method in the frequency domain, consists of the following steps: 1. CreatureHFSS project. 2. drawing geometrical model, including:  installation drawing area (boxing,wherein the object) will be placed;  object creation;  object reference material(In this case, the object to which a plane wave, perfectly conducting). 3. installationsolving the problem of parameters:  setting the boundary conditions on the box surfaces (we will use the PML conditions);  installing a driving source (a plane wave);  setting criteria for convergence and partitioning options. 4. Calculation of RCS. 5 . Post-processing for rendering RCS. applicablethe algorithm for calculating the scattering from a simple object - a perfectly conducting cube in space.

Creating a model (RCS Model).ChoosingDriven Modal type of task. to install unit of length: 1. ClickModeler> Units. Dialog appears Set Model Units. 2. Select the meter unitSelect units from the menu. Option Rescale to new units not included. If you have installedoption Rescale to new units, the geometric grid automatically scales the distance between the grid lines to the units introduced in such a way that the difference would meet the established units. 3. Click The OK, to install the meters as the unit of length for this model. Build a perfect conductor(PEC) cube surrounded by an air box (Figure 6.3). On Boxing PML surfaces boundary conditions are set. OnThis cube plane wave. Calculations RCS- Radar Cross Section.

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Fig. 6. 3. The conductive cube inside the air box

For creation Cuba, use team conducting cube has an edge length0.75 m (Figure 6.4).

Draw> Box.

Perfectly

Fig. 6.4. The parameters of the conductive cube

that set the properties of a cube: 1. Selectdesigned box and click Properties from the pop-up menu. This displays the Properties dialog box. 2. Give the name of the object. 3. In the material set pec material from the list and click OK. 4. In the Properties dialog, edit the color and select red. 5. Set transparency 0.6. 6. ClickOK, that choose these settings and close the dialog.

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Creating an air box. Draw a box size1.4 m with a center at the origin, with transparency 0.9. Call it air_box. Draw a box on the air command Draw> Box, and edit it in the dialog size, shown in Fig. 6.5.

Fig. 6.5. The dimensions of the air box

Side of the air boxThey will be removed from the test perfectly conducting cube at a distance greater than the wavelength, given the frequency of 300 MHz, which we will use. Setting boundaries PML. To create a PML boundaries: 1. Install option choice surface and enter team Edit> Select> Face.or by pressing F. 2. Select Edit> Select> By Name.or select the menu. This displays a dialogue Select by Face.

3. In the list of object names to select air_box. This l i s t i s c a l l e d air_box faces. 4. Holding Ctrl key, click on each surface of the box. Air_box All surfaces should be highlighted (Fig. 6.6).

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Fig. 6.6. Selection of all sides of the air box

5. In the drawing window, call the right-click pop-up menu and select Assign Boundary> PML Setup Wizard. Setup Assistant appears (Fig. 6.7).

Fig. 6.7. Fitting Assistant PML surface

6. In the Uniform Layer Thickness (Fig. 6.7), set the layer thickness of 0.4 m. Parameters PML layers will be corrected automatically in accordance with the new thickness. 7. Installoption matching angles and edges: Create joining corner and edge objects, and click Next. This will create a PML objects and dialog appears Material Parameters (Fig. 6.8).

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Fig. 6.8. Fitting for calculating parameters PML

8. Install minimum frequency Min Frequency = 0.3 GHz, and minimu m dist anc e radiat i on Min imu m Radiating Distance = 0.3 m. 9 .Click Next to display the final dialogue PML Summary (Fig. 6.9).

Fig. 6.9. The final installation of the assistant PML

10.ClickFinishto closedialogue Fig. 6.9. PML border there appear in the Boundaries section of the project tree, and PML objects listed in the project tree.

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partitioning tetrahedra in the air box. PSettingspartitioning air_box boxing will greatly affect the accuracy of the calculation of the radiation pattern. To set these parameters:

1. Highlight the box surfaceair_box. 2. Right clickon Mesh Operations in the project tree. 3. Click Assign> On Selection> Length Based. This displays a dialogue Element Length Based Refinement (Fig. 6.10).

Fig.6.10. Dialog division setting parameters

4. Installthere parameter Maximum length of Elements = 0.2 m. 5. Click OK to closethis dialogue. In the project tree in the Mesh Operations folder icon appears Length1. Setting the parameters of the incident wave. 1. Ask teamMenu HFSS> Excitations> Assign> Incident Wave> Plane

Wave. A page Incident Wave Source: General Data (Figure 6.11.). 2. typethe source name in the Name box. 3. Selectsee Vector Input Format as the Spherical. 4. Enter 0, 0,0 for X-, Y-, and Z-coordinates of the Excitation Location and / or Zero Phase Position (starting point for an incident wave).

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Fig.6.11. Setting the incident planar wave phase center

5. ClickNext. 6. appearsdialogue Incident Wave Source: Spherical Vector Setup (Figure 6.12.). a. In the IWaveTheta, enter Start =0 deg,Stop= 90 deg, and Step = 3deg. For the monostatic case, the RCS will be calculated only for IWaveTheta angles, imposed here. Therefore way radar reflection coefficient will be calculated for thirty angles. b. Click View Point List (Fig. 6.12) in order to see the set values of the angle θ.

Fig.6.12. Parameters incident plane wave

7. ClickNext. A page Incident Wave Source: Plane Wave Options (Figure 6.13.).

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8. In the Type of Plane Wave Select Regular / Propagating; all other fields will be inactive.

Figure 6.13. incident wave parameters

10. ClickFinish. The incident wave that you have determined is added to the list of Excitations and its fall line can be seen in Fig. 6.14.

Fig. 6.14. The test cube and corners, which will be calculated RCS

Next we describe how to performThe Setup endless areas for monostatic and bistatic experiment. These configurations can be calculated graphs normalized bistatic and monostatic RCS. Create infinite scope to determine the far-field.to calculateradiated far field, it is necessary to establish a sphere that surrounds the light object.

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Forthis example, create a setting for the bistatic and monostatic cases. Whenyou set the spherical surface to analyze the short-range field and far field, you specify the range of variation and pitch angles change φ and θ (azimuth angle and elevation angle). They indicate the direction in which you want to evaluate radiated fields (see. Fig. 6.15). For each value of the angle φ has a corresponding range of values for θ, and vice versa. This creates a spherical grid. The number of grid points determined by the step size for φ and θ.

Fig. 6.15.The spherical coordinate system Setting in monostatic case Monostatic Setup . 1. Click HFSS> Radiation> InsertFar Field Setup> Infinite Sphere.

appearsConversation Far Field Radiation Sphere Setup (Fig. 6.16).

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Fig. 6.16.Target spheres, which are set points which are calculated in the far-field characteristics

2. The Infinite Sphere tab, type a name for the scope in the Name box. For monostatic scope, type the name of the monostatic. 3. Determine the range of variationin the dialogue corners Fig. 6.16. angles do not change for monostatic case, since the position of the receiving antenna is fixed and coincides with the position of the transmitting antenna. Therefore, RCS is calculated only in the direction determined by the incident wave. This direction is determined by the angles and IWavetheta IWavephi, which have already been set in the determination of the excitation source (Figure 6.12). 4. Open a bookmarkCoordinate System(Fig.6.16) and orient the sphere in the global coordinate system (CS). Select the Use global coordinate system. If you want to orient the scope in accordance with the coordinate system selected by the user, you can select Use local coordinate system, and select a coordinate system from the list Choose from existing coordinate systems. 5. Click bookmarkRadiation Surface. Leave the selection of UseBoundary Radiation Surfaces. If you want to specify a different type of surface, it is necessary to use the Use Custom Radiation Surface. 6. Click OK. Monostatic sphere is created. the scope of the task in the bistatic case .

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1. In the project tree, right click on the Radiation and from the pop-up menu, click Insert Far Field Setup> Infinite Sphere. Appears Far Field Radiation Sphere Setup dialog. 2. entername "Bistatic". 3. Set the value of Phi Start, Stop, and Step = 0. 5.

InstallTheta Start = 0, Stop = 180 deg and Step = 1.

6.

ClickOK, to close the dialog.

installation Bistatic Radiate appears in the section of the project tree. askFurther frequency of 0.3 GHz and run the program for the calculation. Creating graphics for bistatic the graph, follow these steps:

RCS. that set the parameters of

1. Right-clickthe Results in the project tree and select Create Far Fields Report> Rectangular Plot. New Report dialog box will appear - New Traces. 2. leaveSolution option in the section select the solutions both Setup1: LastAdaptive. 3. To display the graph of the RCS, you chooseone of the geometries in the list Geometry.To do this, select the schedule Bistatic. 4. Under Category, select Normalized Bistatic RCS. This choice implies Quantity list to show for NormRCS Total, Phi, Theta, X, Y,and Z, with a choice of Total Selected. 5. Forthis function, select dB. After this selection box section Y TraceIt shows db (NormRCSTotal).

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Fig. 6.17. selection characteristics bistatic radar reflectance

6. Open a bookmarkFamiliesand check that the angle IWaveTheta = 0. 7.Click New Report. Displays a graph in Fig. 6.18.

Fig. 6.18. Schedule for bistatic radar RCS case

axially x this schedule - the angle of observation. Creating graphics for monostatic RCS.The sequence of creating a schedule monostatic RCSsimilar to that described above for the bistatic case.

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1. Right-clickResult on the icon in the project tree and select Create Far Field Report> Rectangular Plot. This opens the dialog characteristics (Fig. 6.19). 2. In the Context box, select the Geometry section Monostatic. 3. In the Category, select MonostaticRCS, and the list Quantity select MonostaticRCSTotal. 5. From the Function list, select dB.Then the reflection coefficient will be dB. 6. SelectX in the characteristics IWaveTheta. 7. pressNew Report. This creates the report and adds it to the project tree.

Fig. 6.19.Dialog for setting parameters generated in the case of monostatic

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Fig. 6.20. RCS dependence on the angle of incidence of the incident plane wave (monostatic mode)

On Fig. 6.20 shows a plot of RCS as a function of angle of incidence of a plane wave.

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7. ESR calculation object of a large size electrical To solve the problems,which are modeled by objects having large electrical dimensions, the method of integral equations. For its designation in HFSS system uses the acronym EFIE. The significant difference of an integral equation of the finite element method, which has long been the only method for solving of electrodynamic problems in HFSS, is that in the sampling method of integral equations not exposed space, and the body surface, the scattering of electromagnetic waves. Obviously, with this order of the system of linear equations is considerably less than in the case of finite element method. Reducing the dimension of the system allows for real time analysis of the fields generated by the objects with large electrical dimensions. comparing the twomethod of solving boundary value problems of electrodynamics, it should be noted that the finite element method is a universal method that has no fundamental restrictions on the analyzed structure. The method of integral equations demonstrates greater efficacy only in certain cases. The fact that the recording of integral equations is based on the knowledge of the Green's function. In the simplest form of the Green's function is known only for a limited set of objects, which include: a homogeneous space, layered structure with endless layers, infinite baffle, etc. For them, it is advisable to use the method of integral equations. However, as soon as it comesan analysis object of arbitrary shape, e.g., a complex configuration of the dielectric body, the advantages of the integral equation method becoming less apparent, since formulation of these equations is complicated. Essentially, we have to look for unknown numerically analytically Green's function, which requires a significant investment of computer resources. As a result, efficiency of the two methods becomes comparable. scattering wave metal bodies arranged in the free space is one of the tasks for which the method of integral equations is very effective, as for the formulation of the boundary value problem is sufficient to know only the Green's function of a homogeneous medium, which is written in a very simple manner. In this design (RCS of an Ogive) using the method of integral equations calculated effective scattering surface (EPR) metal airship. The airship is modeled

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form of rotation. axis (see. Fig. 7.1).

object, which the body three-dimensional Surface airship created by rotation 0x curve around the

Fig. 7.1. The model airship

Structure reviewed at a plane wave incidentangles

frequency 1.18 GHz. it is irradiated .. Consider a fall wave

XOY plane.The angle θ = 90o, and the angle φ is changed from 0 to 180o from step 2o. Let us count the EPR for the case of a monostatic radar,when the direction of the point of observation coincides with the direction at which the wave is incident on the object under study. The analysis results in a monostatic EPR can be seen on the graph, which shows the dependence on the angle of the EPR irradiation target IWavePhi, varying from 0 to 180º. most r ef lec t i on c oef f i c i en t p r op or t i on a l t o a n ef f ec t i ve sc a t t er i n g s u rf ac e, i s exp ec t ed t o r ea ch at an angle of 90º. Considercreating a further sequence of the airship and its pattern analysis system HFSS method of integral equations. The model is created as follows. First, in the plane XOY curve is drawn, which is a rotating body the generatrix. Creating a curve occurs using the equation in analytical form. Then, the curve is rotated around the X axis to create a 3-D object. Drawing forming the airship performed by team Draw-> Create Equation Curve. dialog appears for this team Fig. 7.2 in which the coordinates of a curve-dependent variable variable _t.

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Fig. 7.2. Draw the curve in space using Equation parametric curve

The equation generator airship is as follows:

F (x)



F (X) y . 1cos

cos. 

(10)

where x, y, z defined in inches (inches), and α - forming an angle selected  for 22.60 The default unit of measurement of length can now be changed to inches, but they may change later. 1. Click Draw> Equation Based Curve. Dialog appears Equation Based Curve (Fig. 7.3). As a parameter using a variable _t, which coincides with the coordinate x: x = _t. The equation for the y coordinate becomes: 2 ฀t

1 ฀sin 0.3948฀฀ cos 0.3948

y

฀5

฀ 1cos 0.3948

Angles are enteredin radians. It should also specify the length of the unit, which we multiply each an (x and y) by an amount (1in). So, in the Equation Based Curve dialog box, enter the equation as follows (Figure 7.3.): 91

X (_t)= _t * (1in) Y (_t) = (sqrt (1 - (_ t * sin (.3948) / 5) ^ 2) -cos (.3948)) / (1-cos (.3948)) * (1in)) Z (_t) = 0 We define the starting point Start _t = -5, endpoint End _t = 5 and the number of dots in a line Points = 24 (Fig. 7.3).

Fig. 7.3. Drawing forming an airship

press OK, to see a curved line. findHistory in the tree section Lines link Equation Curve1 and double-click CreateEquationCurve. This allows you to see the Properties window. If the line does not match the expected mean (Fig. 7.4), it can be edited. The HFSS-IE curved elements are missing. So, all the curved surface approximated segmented models. With this in mind we recommend entering the required number of segments in the Number of Segments.

Fig. 7.4. Drawing images of objects

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2. Select the curve EquationCurve1 and then click Draw> Sweep > Around Axis. Dialog appears Sweep Around Axis (Fig. 7.5). 3. In Sweep Around Axis dialog box, select the X axis, Angle of sweep = 360 and Numberof segments = 24. Click OK.

Fig. 7.5. rotation curve parameters to create a three-dimensional model

Material The default for this object, select, for example, copper. Typically airships (Fig. 7.6) are made of aluminum.

Fig. 7.6. Type of object to be analyzed with the direction of observation

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4. SelectOgive object and in the Properties window, click in the section Material copper and choose the Edit ... (Fig. 7.7). This will open the Materials dialog.

Fig. 7.7. Modify the properties of the material

5. The material selection window, select «aluminum» and click OK. Creating the model is finished. It has no air box, as in the method of not using integral equations. Installation incident plane wave .Now you need to add the source of the incident plane wave. We will count the monostatic RCS in the xy plane. Those. radar reflection coefficient will be considered, in the airship circling the xoy plane (Fig. 7.6). Since this is the monostatic RCS, you will need to include a range of angles of incidence. To get an accurate picture, you can select the step change angle is equal to 3 °. The incident wave is given by the following steps:

1. Deselect model and right-click AssignExcitation> Incident Wave> Plane Incident Wavefrom the pop-up menu. A dialog opens Incident Wave Source: General Data (Figure 7.8.). 2. In this dialog, select the Spherical option to cover the format of the airship and leave the position of the phase center at the point (0,0,0).

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Fig. 7.8. Target point plane wave radiation

3. Click Next and set the window Spherical Vector Setup (Fig. 7.9) meaningcorners Iwave Phi: Start = 0, Stop = 180, and Step = 3. 4 .For IWave Theta select Start = 90, Stop = 90 Step = 0. 5. Then, set the value Eo Vector Phi = 1 and E Theta = 0.

Fig. 7.9. Setting the parameters of the scope of the far field

6. Click Next and then Finish. Excitation set. The incident wave (Incident Plane) appears in the section of Excitations in the project tree. If you select it, the window appears with the image of the airship "fan" in the form of calculated angles. Excitation set. The incident wave (Incident Plane) appears in the section of Excitations in the project tree. If you select it, then in the window 95

airship pattern appears with the "fan out" in the form of angles, which deviates the incident plane wave. This setting on the decision to address the incident waves at θ = 90 ° and φ = 0 180 ° for 61 points. ... Polarization is determinedan angle φ, what we can calculate monostatic radar directed So, reflectance (monostatic RCS). NowPerform a solution for that: 1. pressRight-click on Analysis in IEDesign section in the Project Manager window and select Add Solution Setup, to open a dialogue Solution Setup (Fig. 7.10). 2. The General tab to change the frequency Frequency = 1.18 GHZ. The other parameters, leave the default.

Fig.7.10. Frequency setting calculation

3. Review the data in tab Options - seal partitioning into cells lambda refinement = 0.25 (= λ0/4).the calculation of the installation completed. To run the simulation: 1. pressRight-click the Setup, and then click Analyze. 2. Save your problem and enter the name of the project. Simulations were performed for two iterations.

Output current on a surface. that see the current to the airship surface (Figure 7.11.): 1. Select the surface of the model and set the output current distribution Fields command> J> Mag_J. This opens the Create Field Plot dialog.

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Fig. 7.11.

The currents on the surface of the airship

2. Click Done. You You should see an induced current that is induced in the metal when subjected to an incident plane wave.

conclusion schedule RCS coefficient. To graphically display the RCS, you must first enter the setting far-field - the same way as is done in HFSS. Create far field installatio = 0 ° and one angle θ = 90 °. weWe will graphically depict the dependence of monostatic RCS when changing the incidence angle phi of the plane wave. Therefore each observation point corresponds to only one corner (Fig. 7.12).

Fig. 7.12.Monostatic radar graph of reflectance when changing the incidence angle of Phi

To display the schedule dependency monostatic RCS depending on the azimuthal angle phi incident plane wave: 97

1. Right-click on Radiation in the project tree and select Insert Far Field Setup> Infinite Sphere ... Appears Far Field Radiation Sphere Setup dialog. 2. enterStart and Stop for Phi equal to 0, and a step 10º (Fig. 7.13). 3. enter Startand Stop for Theta = 90º and Step size = 10º.

3. Click OK. This will close the dialog and create the scope InfiniteSphere1 in the Radiation section of the project tree.

Fig. 7.13.Schedule setting far field calculation data. In fact, one corner and one angle

5. To create a graph, click on Results in the project tree and set the command Create Far Fields Report> Rectangular. So,This section is intended radar reflection coefficient for the object whose size is much larger than the wavelength. The calculations use the method of moments, implemented in the HFSS-IE program.

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8. The bandpass waveguide filter In this section we will look at the analysis using HFSS bandpass filter, which is widely used in practice, the comb structure. Further, the band pass filter model, we will use HFSS to illustrate additional features, such as accounting for the temperature dependencies and Tune tuning mode. microwave synthesisthe filter can be performed using the first stage of designing popular program Microwave Office [6]. Utility Synthesis Filter This program allows you to calculate generalized parameters that make up the filter transmission lines, as well as their sizes are realizing the predetermined frequency characteristics. Note that the calculation of the geometric dimensions is possible only for transmission lines planar type: stripline, microstrip, etc. Similarly, analysis of the frequency response of the filter in MWO system can be carried out only for stripline constructions. At the same time, in practice, often used comb filters based on transmission lines with the cylindrical and rectangular conductors, which have a much higher quality factor than the strip line. The analysis of such structures can HFSS means. We perform an analysis of three-dimensional comb bandpass filter (Fig. 8.1) with 1 GHz bandwidth. The filter consists of eight pins, each of which is a cavity. At the inlet of the first pin connected to a coaxial transmission line with a characteristic impedance of 50 ohms.

Fig. 8.1. Type of filter in HFSS-13 interface

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pectinatebandpass filter has an order related to the number of resonators. It depends on the number of resonators of the filter quality: transmission passband, and the recession is the transmission coefficient bandwidth. The length of the individual resonators is not more than a quarter wavelength, and often much less due to the effect of shortening that occurs due to the capacitance between the terminal pin and the wall of the housing. The distance between the pins determines the coupling coefficient between the resonators (Fig. 8.2).

Fig. 8.2. The dimensions of the comb filter

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atsolving this example uses many HFSS program features, including the calculation of the filter characteristics depending on the ambient temperature. Driven Terminal feature of the method lies in the fact that the ports are set up as the sources relative to the outer casing. Create a new project. To create a new project, click the command File> New New. From the Project menu, click Insert HFSS Design Design. To install the solution method, click HFSS> Solution Type. Dialog appears Solution Type (Fig. 8.3), in which select the Driven Terminal.

Fig. 8.3. The choice of method of calculation of the bandpass filter

MethodDriven TerminalIt calculates S parameters for ports that are formed multiconductor transmission lines (multi-conductor transmission line ports). Elements of S-matrix are then determined by the voltage and currents that distinguishes its standard power determine the scattering matrix through the wave power. Note, however, that for the transmission lines with the TEM - waves (coaxial symmetric stripline, etc.), both determination of the scattering matrix give equivalent results. Creating a three-dimensional model. Set the model unit. To do this, follow these steps:

1. Click Modeler> Units. A dialog opens Set Model Units (Fig. 8.4). 2. Select:in (inches). 3. Click OK.

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Fig. 8.4. Installation length Units - inch (34.5 mm)

In this example, when drawing will apply in the line of the coordinate input state, i.e., in the form of numbers (Fig. 8.5). To draw a three-dimensional substrate: 1. Click Draw> Box. 2. Use input field coordinates, a we coordinate input X: -1.0, Y: -1.7, Z: -0.3125, pressing each time Enter.

Fig. 8.5. Indication status line

Fig. 8.6. The dimensions of the filter housing in inches (in)

3 . Using the coordinate input field, we introduce the opposite corner Boxing dX: 2.0, dY: 3.4, dZ: 0.0, pressing Enter. 4.Using the coordinate input field, we introduce the substrate height dX: 0.0, Y: 0.0, Z: 0.625, pressing Enter. The filter housing will have the form shown in Fig. 8.6. Creation of the outer cylinderan input coaxial line. To create an outer conductor of the coaxial line:

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1. Click Modeler> Grid Plane> YZ, to select the active plane, which will be plotted base of the cylinder. 2. Click Draw> Cylinder. 3. Using the coordinate entry field, enter the central position 1.0, Y: -0.9, Z: 0.0 and press Enter.

X:

Fig. 8.7. coordinate input field at the bottom of the interface HFSS

4 .Using the coordinate entry field, enter the cylinder radius (Figure 8.7.) DX: 0.0, dY: 0.14, dZ: 0.0 and press Enter.

Fig. 8.8.The filter housing and the first cylinder of the coaxial line

5 .Using the coordinate entry field, enter the cylinder height dX: 0.75, dY: 0.0, dZ: 0.0 and press Enter. In the Properties window, select the name filled the vacuum (Fig. 8.9). Click OK.

feed1and leave the cylinder

Fig. 8.9. Selection vacuum to fill the space Creature internal conductor coaxial draw inner conductor of the coaxial line filter at the inlet:

lines.

that

1. Click Draw> Cylinder. 2. Using the coordinate entry field, enter the center position 103

X: 1.0, Y: -0.9, Z: 0.0 and press the Enter key. 3. Using the coordinate entry field, enter the cylinder radius dX: 0.0, dY: 0.06, dZ: 0.0 and press Enter. 4.Using the coordinate entry field, enter the cylinder height dX: 0.75, dY: 0.0, dZ: 0.0 press Enter. Define the name of the cylinder (Fig. 8.10) as the feedpin1 material and fill it as the PEC.

Fig. 8.10. internalconductor of the coaxial input

This inner core has continued into the filter housing. To draw a line inside the coaxial line (pin): 1. Click Draw> Cylinder. 2. Using the coordinate entry field, enter the center position X: 1.0, Y: -0.9, Z: 0.0 and press Enter. 3.Using the coordinate entry field, enter the cylinder radius dX: 0.0, dY: 0.06 dZ: 0.0 and press Enter. 4.Using the coordinate input singing, the value of the height of the cylinder dX: -0.15, dY:0.0 dZ: 0.0 press Enter. Specify a namethis feedprobe1 cylinder.

Fig.

8.11. Pin connection with filter 104

Creating resonators Resonators are plotted as a metal box. Drawing parallelepiped (fig. 8.12) is given point, and then dimensions. To create the cavity with the name l1: 1. Click Draw> Box. 2. Using input field coordinates, enter the position of boxing X:0.85, Y: -0.9625, Z: -0.03, press Enter. 3.Using the coordinate entry field, enter the opposite corner Boxing dX: -1.7, dY: 0.125, dZ: 0.06, press Enter.

Fig. 8.12.Drawing a first line filter

To create a filter with the name of the pin l2 (Figure 8.13.): 1. Click Draw> Box. 2. In the field enter the coordinates, enter the boxing position X: -1.0, Y: -0.75, Z: -0.03, press the Enter key. 3. Next, enter the coordinates of the opposite corner Boxing dX: 1.818, dY: 0.125, dZ: 0.06, press Enter.

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Fig. 8.13.Draw a second line filter

To create a third pin of the filter named l3 (Figure 8.14.): 1. Click Draw> Box. 2. Using the coordinate entry field, type a parallelepiped: X: 1.0, 0.48, Z: -0.03, press Enter. 3. Using input field coordinates, enter the size of the X: dX: 1.818, dY: 0.125, dZ: 0.06, press Enter.

Y: -

Fig. 8.14. Draw a third line filter

To create a fourth resonator l4 (Figure 8.15.): 1. SelectDraw> Box team. 2. Using input field coordinates, enter the boxing position: X: 1.0, Y: -0.2, Z: -0.03 and press Enter. 3. Using input field coordinates, enter the opposite corner Boxing: dX: 1.818, dY: 0.125, dZ: 0.06, press Enter. 106

Specify the name of the l4 element in the Properties window and click OK.

Fig. 8.15.Created fourth resonator filter

Fig. 8.16.A dedicated section of the port

Creating a wave port highlight chamferport (Figure 8.16.), as follows: 1. Click the command Edit> Select> Faces (or press F). 2. Select the external chamfer coaxial line at X = 1.75in. To set the excitation wave in the port: 1. Click HFSS> Excitations> Assign> Wave Port. dialog appears Reference Conductors for Terminals (Fig. 8.17). 2. Ask as the name of the port p1. 3. Select the option to name the terminal Use port object name. 4. leaveoption Use as Reference (Fig. 8.17) unchecked.

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Fig. 8.17. Description port

Fig. 8.18.Load icon in the project tree and dialogue terminal

5.Click OK. In the project tree under Excitations sign appears p1 load. The method

Terminal solution to each port is given the reference impedance. Therefore, at the same time c port appears and the load icon in the project tree (Fig. 8.18). Next, we execute a rotation around the center of the housing with copying for the created of the filter. To select objects to replicate: 1. press"O".At the command Edit> Select> By Name Select Object dialog box appears (Fig. 8.19). 2. Select it with the names of objects: feed1, feedpin1, feedprobe1, l1, l2, l3, l4, hold down Ctrl + Left.

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Fig. 8.19.Dialog selection of objects

Fig. 8.20.Conversation not duplicated and rotation of the

3. ClickOK.To create the rest of the pin filter, follow up with a turn at 180º for that click Edit> Duplicate> Around Axis, and then in Figure dialog. 8.20 choose: Axis:Z Angle: 180 Total Number: 2 and click OK.

Fig. 8.21.Duplicate half elements by rotation about an axis

bandpass filter model takes the form shown in Fig. 8.21.

View boundary conditions.To check how the boundaries are set, click HFSS> Boundary Display (Solver View). After a preliminary decision, a dialog Solver View of Boundaries (Fig. 8.22). In this dialog box Visibility option, you can mark boundaries for which you wish to see. Note the following:

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- Ground plane background (Perfect Conductor) is shown if the name of the noted outer (Fig. 8.22).

Fig. 8.22.Display Options borders

- All Guides, which are assigned to the boundary conditions Perfect Conductors will be shown as a border smetal. Click View> Visibility, visibility to remove any parts of the project. You can also change the type of boundary conditions and ports. Visibility of objects can be set in the dialog box that appears on the command View-> Active View Visibility (Fig. 8.23).

Fig. 8.23. selection the visibility of the objects included in the project

Viewing visibility of boundary conditions and facilities allowing verify the correctness of the design creation. Click also HFSS-> Validate Check, to run the validator checks geometric construction problem. If after checking the Validator no comments, you can make settings for analysis.

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Settings for analysis.

Click HFSS> Analysis Setup> Add Solution Setup. Dialog appears Solution Setups (Fig. 8.24). In the General tab, make the settings shown in Fig. 8.24.

Fig.8.24.Dobavlenie calculation in the frequency range

Fig. 8.25.Target calculation in the frequency range by means of fast scan

To calculate the frequency range refine HFSS> Analysis Setup> Add Sweep. Appears Edit Sweep dialogue in which we define the parameters indicated in Fig. 8.25.

Calculationcharacteristics of the bandpass filter.To start the process of solution, click HFSS> Analyze. To see the process of dialogue and solutions Solution Data: 1. Click HFSS> Results> Solution Data. Solution Data dialog appears. 2. Open the tab Profile, to see the solution file. 3. Open theBookmark Convergence, to see details of the convergence solutions. Convergence can be seen in the tabular form (Table Table), or in a graphical representation (Plot). 4. The Matrix Data tab, you can see the matrix. And to see a change Matrix Data matrix data during calculation in select Setup1 Last Adaptive. 5. ClickBookmark Mesh Statistics, to see the data on the grid subdivision.

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CalculationIt is formed on a center frequency 1.5 GHz and a frequency range of 0.6 to 2.4 GHz. C-scan type Fast calculation is executed in the frequency points where the filter characteristics are changed at a high speed.

Output characteristics of the graph.To derive the frequency dependence of the filter S-parameters of the frequency: 1. Click HFSS> Results> Create Terminal Solution DataReport> Rectangular Plot. A dialog Reports. 2. Ask following options: Solution: Setup1: Sweep1 Domain: Sweep Quantity:St (feed1_T1, feed1T1); St (feed1_T1, feed1T2) Function: dB 3. Click New Report button. 4. Click Close.

Fig. 8.27. frequency characteristicwaveguide comb filter and adding markers on the graph

Thenyou can add another characteristic of St (feed1_T2, feed1_T1) in dB,Add Trace by pressing the button and then the Done button.

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Fig. 8.28.Chastotnye filter characteristic

For the convenience of viewing the schedule can be changed Do the following:

scale. F o r

1. Twiceclick on the Y-axis. Dialog appears Y-axis properties. 2. Click tab Scaling, which sets out options: Autoscale: Remove this option Min: -1.0 max:0.0 3. Click OK. In this case, you can more accurately see the change in the gain of the filter passband.

Viewing field inside the filter.This filter need to install a source that has an internal resistance. Such a source is called Terminate Port. To install the port load: 1.Click HFSS> Fields> Edit Sources. Appears Edit Sources dialog in which concentrated on all the project data sources. In this dialog box, select: Select source: p2: T1Terminated: Checked Resistance: 50 4. Click OK. reactance:0

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Fig. 8.29. Editing sources included in the project

Conclusion calculated field in the section. Select the plane XoY,activating Global XY Plane. 1. Using the Model Tree, expand Planes folder. 2. Select Global plane: XY. 3. Click HFSS> Fields> Fields> E> Mag_E. Create Field Plot opens a dialog in which to choose: Solution:Setup1: LastAdaptive, Quantity: Mag_E, In Volume: All. 4. Click the Done button. IfWe need to change the form of the field graphics, for example to emphasize the weak fields, click HFSS> Fields> Modify Plot Attributes. Opens the Select Plot Folder dialog. Select E Field, and then the following options in the dialog E-Field1 Click the Scale tab. Select Use Limits, and set: Min: 5 Max: 1500 Scale:Log. Click Close.Fieldon the surface becomes more understandable form (Fig. 8.30) which can be estimated and resonance phenomena in the filter.

Fig. 8.30. Type field in the middle of the filter section 114

So, in this section was carried out drawing and calculation of threedimensional filter to the pins. To perform further optimization of the filter, you must specify the variables to select the method and optimization objective function. Objects that are used as components in Ansoft complex designs, which are arranged in the interface circuits (Workbench Project Schematic) may be regarded as system. The complex Ansoft programs that serve to solve the circuit and system tasks, is: Rmxprt 14.0, Designer 6.1, and Simplorer 9.0. Such Ansoft products as HFSS 13.0, Maxwell 14.0 and Q3D Extractor are used to solve the electrodynamic structures. If you call ANSYS DesignXplorer (Fig. 10.31), the variables of any project are also exported to the project and are available from the interface Workbench.

Fig. 8.31. Adding modes and optimization solutions

All products Ansoft united a common interface Workbench team,management, etc. One of the opportunities available in HFSS v.13 - calculation of the temperature. These features will be described in the following chapter.

12. The antenna is mounted on the mast This example is solved by the method of integral equations, which is implemented in HFSS_IE block. This method makes it possible to analyze the structure of large electrical size. Consider as an example of an antenna mounted on the metal mast. It consists of three dipole antennas (ris.12.1). The mast is located on the infinite ground plane.

Fig. 12.1. The antenna on an aluminum leg

The mast hasheight 3.1 m. vibrators are modeled as a 2-D objects with boundary PerfE. Excitation - discrete ports. Mounting structure modeled polystyrene holders. The mast stands on a conductive ground, so the project is set active option infinite ground InfGndPlane1 board under boundary conditions (Fig. 12.1). Create a new project by clicking on the . Choosing a unit of length, see the dialog (Figure 12.2.), Called Modeler team -> Units.

Fig. 12.2.Unit of length for drawing objects

Options method for solving HFSS-IE c a n set in Fig dialogue. 12.3 which is caused HFSS-> Options command.

Fig. 12.3.method of installation options HFSS-IE

Draw a mast with a height of 270 cm, a section of 20 cm x 20 cm (12.4 in Fig.) And the fill material from the library: aluminum.

Fig. 12.4. Dialogue parallelepiped - mast antenna

Next, draw the pin,creating a first octagon, and then converted into the threedimensional volume, holding it on the axis Z (Fig. 12.5) command Draw-> Sweep> Along Vector.

Fig.12.5. Dialog, wherein the edited-size antenna mast

drawing polystyrene Further fulfill dimensions first shown in Fig. 12.6.

holders

(Fig.

12.6).

Fig. 12.6.polystyrene holders

the creation of threepolystyrene holders execute the command Edit -> Copy. Further fulfill drawing vibrators of Draw rectangles team -> Rectangle.

antennas (Fig.

12.7)

at form

Fig.12.7. Dialogue vibrator antenna

Vibrators consist of two arms, between which is installed a discrete port. Platform for the port also draw a rectangle as a team Draw-> Rectangle. Geometric port settings are shown in Fig dialogue. 12.8.

Fig.12.8. site parameters for the discrete port dipole antenna

The antenna on the mast is above the infinite ground. This fact is reflected in the fact that the project is put into an earthen Board of infinite size (Figure 12.9.) Team HFSS IE -> Boundary-> Assign-Infinite Ground Plane.

Fig.12.9. The antenna on the mast

Fig. 12.10. The task endless plane

earthen

Groundcard is always set in XOY plane. In the dialog box Fig. 12.10 inputting coordinates on Z and roughness of the surface from which depend ground board loss. The material can be set by pressing the Select Material button. on the job is created modeling Add Solution command on which the figure is displayed dialogue. 12.11. Carrying out tasks for the calculation of the antenna by HFSS-IE.

Fig. 12.11. Specifying installation calculation and decomposition of the grid in the method HFSS-IE

Calculationantenna characteristics is performed at the same frequency of 0.9 GHz, so establish the adaptation process at this frequency (Fig. 12.11).

Fig. 12.12. Characteristics antenna match

Start the solution by clicking Analyze. After calculation command HFSS-> Fields -> Edit Sources establish excitation on all three ports (Fig 12.12.), And viewing the current flowing through the metal coating of the mast and the directional pattern (Fig 12.13, 12.14 fig..). Radiation Pattern 0 -thirty

1 thirty

12.80

9.60 -60

60 6.40

3.20

-90

90

-120

120

-150

150 -180

Fig. 12.13. The currents on the

Fig. 12.14. NAM-section of the antenna on the mast

In conclusion, the method of integral equations allows to perform modeling of structures both with dimensions much larger than the wavelength, and with dimensions much smaller than the wavelength. As a practical example may be mentioned calculation wire antenna (Fig. 12.15) 100 m in height, operating in the wavelength range 100 kHz.

Fig. 12.15. Wire antenna with stretch marks

The sizethis antenna is much smaller than the wavelength. The input impedance of the antenna at a superlong range is very small. Increase it, you can use the selection of the number of braces, the choice of the angle at which the backstay are relative to the ground. The input impedance also significantly depends on the conductivity of earth surface. The main task of designing such an antenna can be regarded as an increase in efficiency (Fig. 12.16), which depends on the frequency.

Fig. 12.16. The frequency dependence of the efficiency of the umbrella antenna height of 110 m and 110 m in length braces.

In such an antenna structure can occur very high voltages. To calculate the voltage between the antennas can be decomposed extensions distance from individual antennas to ground fragments to form individual elements. The program calculates the field strength and voltage in these fragments, using, for example, Exell program can be integrated to find the total voltage and the voltage between the antenna and the ground. HFSS canand work in tandem with other programs: Mathlab, MathCAD, AutoCAD.

13. Calculation of the temporal process in a microwave integrated circuit It is known that methodscircuit theory and calculation can be performed in the frequency domain and the time domain. The HFSS-13 can perform a calculation in the time domain in order to see a short pulse propagation through the device, in addition to receiving the S -parameters. A program for calculating the transient HFSS Transient - expects to dynamically change the electromagnetic field using a discrete Galerkin (DGTD - Discontinuous Galerkin Time Domain). This method uses a tetrahedral mesh partitioning, and the fundamental finite element method, which made HFSS standard of accuracy in electromagnetic simulation. You can now research by asking a short radio pulse, penetrating the ground, electrostatic discharges and electromagnetic discharges lightning. It is also possible to get a picture of the field, which varies in time (TDR) at an arbitrary given time signal at the input. Consider the topology (Fig. 13.1) Alinks_BGA project, located in the Help folder of the installation folder HFSS (and not in the Example folder). In the simulation process in the project is calculated S-parameters in the frequency range, and there is a short pulse propagation. Geometry has four signal lines that are connected to the ports and the ground bus. We perform modeling of geometry already created (Fig. 13.1). Add excitement and to install solution before analysis and calculation of output data.

Fig. 13.1. structure of distributionlines

Click HFSS> Solution Type and set the calculation method Transient (Fig. 13.2). This method of calculating process in time domain.

Ris.13.2. Methods for solving the problem in HFSS

WorkaroundTransientIt hasNetwork Analysis option. If you choose Network Analysis option when installing on a calculation appears Input tab that allows you to, for example: • Modeling of the excitation pulses in the form of such structures as a broadband antenna, light fibers, electrostatic surge; • field visualizationwhen exposed to a short pulse; • analysis of time-dependent reflektomerov. Verify boundary conditions on the installation of the finished geometry. The analyzed structure is a fragment of the microwave chip. He covered the surface air_box, which assign boundary conditions Radiate (Fig. 13.3). To the left in Fig. 13.3 shows the boundary conditions that can be set in the method of calculation of the transition process.

Fig.13.3.Slozhnaya form surface Radiate

RadiationBoundary- the boundary of the radiation (Figure 13.3.). To accurately model the volume form on the sides of which are set radiation limits must be sufficiently large. Another boundary condition in the Boundaries section, ReferencePlanes set on the excavation fee ( "the base") to the ports. Since the signal and earth lines are connected with these planes, each of the signal current must be a closed path. We distinguish immediatelytwo planes (Fig. 13.4) BONDWIRE_REFPLANE_1 and SOLDERBALL_REFPLANE_1 and they we define conditionsPerfect E named Reference Plane.

Fig. 13.4.Target reference plane (counterpoise)

These planes will be used in describing the excitation sources. Fig.13.3, you can see what the boundary conditions can be applied in HFSS Transient mode. The boundaries are not available for use in this mode 151

This frequency-dependentborder (laminate impedance, the impedance of the display screening impedance), which can not be implemented directly in the time domain.

The task structure of the excitation sources. 1. Select the first of the planes yet undescribed LINK_12_BW in the project tree and set it on a digital port (Figure 13.5.) Command Assign Axitation -> Lumped port.

Fig. 13.5.team task to create a discrete port project

2. dialog appears Fig. 13.6, in which the column "Use as reference", a check mark to select conductor SOLDERBALLREFPLANE_1 as a reference plane for the terminal.

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Fig. 13.6.Definition of port options in Driven Terminal mode

In the same way, we create all4 ports from the reference conductor SOLDERBALLREFEPLANE_1. 3. Open the Properties dialog for the properties of the port and its Transient tab (Fig. 13.7). Not every port must be "Active" (if you specify all ports active, it will take a great time to get all the S-matrix).

Fig. 13.7. selection the port status in the mode of calculation of the transition process

Ifyou want to reduce the calculation time, make only a few ports active. Passive ports will work as terminals. Then you get only a partial S-matrix. 4. Open bookmark Post Processing, and leave the Do Not Renormalize option.

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Fig. 13.8.Bookmark postprocessing data

If you chooseanother option, Renormalize All Terminals' Spectral Domain Date, the data are normalized to the thermal data of spectral analysis. 5. Highlight the port area (in the Lumped Port) and right-click on this icon in the Excitation port section and select "Auto-Assign Terminals". According to the operation sequence of each port is automatically generated terminal (load). Note that there mayand the other excitation method HFSS Transient. However, some problems are not solved yet in this method v13: individual cell of the periodic structure (phased array antennas, periodic chastotnoselektivnye surface) or a magnetic pattern with an offset (ferrite circulator, ferrite phase shifters). These examples are better calculated in the frequency domain using HFSS.

Installations for the calculation of the transition process.

first, we define list of facets, which will remain calculated fields of the transition process, as follows: 1 .Switch to the selection mode of facets F and move the cursor to the upper chamfer for both signal and ground plane (Fig. 13.12), hold down the Ctrl key.

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Fig. 13.12. Selecting several surfaces

2. Create a list of facets Modeler command> List> Create> Face List. In the List list appears FaceList1. Change the name on PlotFields. Then prepare to install solution for that: 1. Right-click Analysis> Add Solution Setup. 2. The tab General (Fig. 13.13), we define the maximum number of grid compaction steps equal to 6.

Fig.13.13. The General tab

Frequency, on which the partition of the grid will be automatically selected on the basis of time-dependent. 3. Select the tab Input Signal (Fig. 13.14).

154

4. Ask Broadband pulse from DC to 10 GHz, and request the calculation S-parameters every10 MHz. Note that the calculation in the time domain can be done by askingminimum and maximum frequencies. If you specify a lower cutoff frequency equal to zero, the waveform will change to include the frequency to DC. Also note,that in addition to the sweep frequency can be determined TDR pulse. This - pulse whose spectrum extends from DC to some highest frequency of which depends on the rise time. Finally, note that you specify here one time dependence for all active excitations. In the project with more than one common transition process ( "non Network Analysis"), you can set different time according to different excitations, and run the simulation at the same time with all the excitations. The method of calculation of the transition process, all active excitation have the same time dependence, you get a simulation result when a single active drive.

Fig. 13.14. Input tab

5. Duration Select the tab (Fig. 13.15).

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Fig. 13. 15. Target damping level transient

Modeling is executed until the transient fields are attenuated to a level Target Residual (Fig. 13.15). Furthermore, the maximum time is determined by simulation 20x (model size) / (Speed of light). In this transmission line 1 nsec duration signal can move several times from the source to the load and back end. Therefore, it is reasonable to limit the time of calculating the value At most = 1.25 ns (Fig. 13.16), which is equal to the aforementioned 1 nsec plus input duration.

Fig. 13.16. Page parameter setting time process

Open bookmark Saved Fields (Fig. 13.17), and set the mode to save the field in the planes, setting option PlotFields. Keep field every 4 ps. During the 4 ps signal deepened by 0.6 mm in the insulator, so that such frequency samples is to provide smooth animation of the model.

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Fig. 13.17. Saving installation on the field during the transition process

In Radiated Fields tab (fig. 13.17) will choose the frequency at which field will be stored. Modeling requires about 400 MB of RAM per excitation. If you set all ports active and have the opportunity to perform a distributed simulation, select this calculation. In a distributed simulation with at least eight processors and the RAM enough, each of the eight excitation give its own process, and they will all be addressed simultaneously. So: 1. Save the project and run the simulation. HFSSwill first perform an adaptive calculation in the time domain. After that,He will perform simulations of eight, one for each excitation. 2. Afterhow the calculation is running, you can right-click the Results> Create Terminal Solution Data Report> Rectangular Plot, to follow in the calculation process for the input and output signals to the various ports as you complete the simulation. Depending derive by selecting the desired characteristics in Fig dialogue. 13.17.

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Fig. 13.17. The output characteristics in the time domain

SelectInput Input (LNK_12_bwire_T1), as well as signals Output (TXCLK_12_bwire_T1, LNK_12_bwire_T1) and Output (TXCLK_12_sball_T1, LNK_12_bwire_T1). Then create a graph in Fig. 13.18.

Fig. 13.18. Schedule time process

Fig. 13.19 on Y axis output parameter Residual (difference) in dB. This - the value of any of the process, which is used as a stopping criterion. It is installed in the Duration tab. By default, when

158

peak field decreases to 0.001 with respect to maximum, Modeling deemed to be fulfilled. ControlResidualschedule duringcalculation provides information which may be required during simulation. Windowthe state provides additional information; thisbased on the maximum simulation time.

Fig. 13.19. Schedule of the transition process

The difference is not reduced to a value of -60 dB, so we stopped modeling before.

postprocessing matrix data In the Report, in the Context section, change the option from Time Solution to the Spectral. This enables a schedule S-parameters in the frequency domain obtained by the simulation of the transient. Even when the simulation is still running, transient solver already give S-parameters in the frequency domain on the basis of information about the transition process, which is adapted to the present time. Schedule will be updated very often. Modeling can be slow because each modification requires a transformation from the time domain to the frequency.

159

Fig. 13.20. Output frequency dependences S parameters obtained by FFT in the spectral region

Details of S-parameters outputted duringsimulation are shown in Fig. 13.21. Sparameters plotted on this graph - a transmission and reflection coefficient for a particular signal line.

Fig. 13.21. The frequency response of the signal line

To display field propagating along the line: 1. In the model tree, select the list PlotFields planes. 2. In the Project Manager, right-click on the Field Overlays> Plot Fields> E_t> Mag E_t. 161

3. Select Done. At this command will be output in a plane tangential nye components of the electric field. The field can be animated in the plane of the resonator in the last moment of time, ie, animate from 0.6 ns to 1.25 ns with a scale for adjusting the pitch. EXAMPLE animation field shown in Fig. 13.23.

Fig. 13.22. Output fields and animation it

Fig. 13.23. Type running current in accordance with a time process

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Canalso see the animation field distribution and resonance phenomena in the last time. Animation from 0.6 ns to 1.25 ns can be seen with adjustments to field scale.

Fig. 13.24. Type traveling field along the structure

Graphics output in the time domain Studyin the time domain is to calculate the response (reflection) in the time domain (Time-Domain Reflectometry TDR) at excitation signal structure as the shock exposure (transfer function). In this calculation you need to choose the method of interpolation. After calculation in the Report dialog, you need to choose Time from the Domain list. You must also specify the input signal, or a step or impulse.

Fig. 13.25. Selection signal type when specifying temporal process

at Time The choice of the area, you can choose from several Categories and related Quantities, to make the schedule, such as | S11 |. When you compose the graph in the time domain, each parameter in the frequency

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the

at first converted in temporary region before than the calculation is performed according to the formula. For example, if you want to display dependency Seleven/ (1 - Seleven)

(eleven)

and output this function in the time domain, transform IFFT:

it uses inverse Fourier

IFFT (S11 * input) / (1 - IFFT (Seleven* input))

(12)

It should be noted, that this expression does not match the words IFFT (S11 * input)/ (1 - Seleven)* input).

(13)

These two expressions are not equivalent. Ifyou choose Time Domain Impedance as a category Category, you can choose the amount of TDRZ. It determines how TDRZ (t)= Zref * (1 + IFFT (S11 * input)) / (1 - IFFT (Seleven* input))

(14)

where "input" represents an input signal (step or impulse), and "IFFT (.)" denotes the inverse Fourier transform. This equation is a ratio of the instantaneous voltage in the time domain v (t) to the instantaneous value of the current i (t). Voltage and current are determined (in frequency domain) in terms of incident and reflected waves a and b, and are

V  Z0(ab)

I

1 Z0

(a b ) 

Z0(1Sii) a

1

(1Sii) a

Z0

(15)

(16)

Suppose that the incident waveis input in the form of steps, and thus, when we take the inverse Fourier transform (IFFT) for V and I, we obtain v (t) and i (t) in the time domain. Let's create this relation as a function of time, and then get TDRZ function (t). Default Zo = 50 ohms. To create a schedule in the time domain: 1. For the project with the existing frequency range, perform the following steps 2 - 4 to save the properties. 163

2. In the dialog Report, in the Domain list, click Time. This allows you to select the TDR Options button, and for the calculated load data include Terminal TDR Impedance in the list of Category. 3. Click the Options button to the TDR. Appears TDR Options dialog. 4. Select signal input, Step (a jump) or Impulse (Dirac pulse). Step size is a jump signal change, whereas there is a short Impulse excitation. Impulse is very narrow rectangular pulse with a rise time of zero time and fall with the magnitude of a time step of 1 and a height equal to 1 / (time step). Selecting Step makes field Rise Time and Impulse inactive. 5. Ifyou have selected Step, enter the pulse rise time in boxing Rise Time. Timerise should correspond to frequencies. With a bandwidth from DC to Fmax, better time resolution that can be achieved is equal to 1 / (2Fmax). Rise time 1 / (2Fmax) is a very short rise time, which can be solved. However, the rise time of 0 s gives the same information, so 0 is the default value of this panel. 6. entertotal time on the chart in the text box Maximum Plot Time. Defaultmaximum time TDR Options dialog box associated with the frequency range Δf: it is equal to the time 1 / 2Δf, during which IFFT outputs information. This length of time is often a very long relative to the time delay, which corresponds to the length of the test on your device, so you may want to reduce this value. Alternatively, you can edit the time-axis characteristics TDR after it was created. 7. Installnumber of time points for outputting a graph for a box Delta Time. By default, it may be equal to the number of points in the frequency range. Time difference based on the frequency bandwidth: a frequency band from DC to Fmax minimum time resolution that can be obtained is equal to 1 / (2Fmax). IFFT algorithm provides frequency interval between the values of 1 / (2Fmax), but you can smoothly interpolate between

164

points, settingthe very best solution is, for example, 1 / (10Fmax), due to the additional computation time. 8. Optional,TDR in box, change the type of box and width. Windowfunction algorithm FFT Fast Fourier transform signal to obtain a nonzero value must be removed from Fmax. Each window function between the ability to resolve signals of comparable frequency and the ability to resolve signals of different strength and frequency. List of window types include: window function Rectangular

use cases Functionlow dynamic range giving good resolution for signals with similar amplitude. Not suitable where the signals are very complex amplitude. w (n) = 1.

Bartlett

Function high dynamic range, low-resolution, suitable for a wide range of applications. Function high dynamic range, low resolution, designed for a wide range of applications. upgraded function dynamic range established for Examples a narrow strip. Function modified dynamic range, c a l c ul a t e d f or e xa m pl e with a narrow passband. The choice of the Kaiser function also allows you to define the area of related parameter of the Kaiser. The larger the parameter of the Kaiser, the wider the window. It controls the tradeoff between the width of the central lobeand the area of petals from the sides. This approach is applied parabolic shape to a window with the data in the frequency domain.

Blackman Hamming Hanning (Default) Kaiser

Welch

9. You canuse the Save as Default to set the current values as a default, and the Use Defaults button to use previously saved options. Note that when you select a feature, first shows the values corresponding selected char ac t eri s ti cs. 10. Click OK. To display characteristic Terminal TDR Impedance (which means either calculate S-parameters for waveport1 port in the frequency range, instead of calculating the delay time with respect to specific impedance), do the following: a. In the Category, click Terminal TDR Impedance. b. The Quantity list, click the value for the application of the schedule.

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The default impedance (Zo) for the magnitude of TDRZ is 50 ohm, unless you specify otherwise, when you set the renormalization for the impedance of the terminals, which are created in the model. If you want to change the impedance value, it can be edited in the Report dialogue (as shown below), or you can create a variable Zo × (1 + Sii) / (1-Sii) selected Zo. Edit value Zo can be Report dialogue, for which: 1. Under Category, select Options Terminal TDR Impedance, Port and Function.

Fig. 13.26. The timing of the x-axis

2. Edit the value to be set in the Value field. In this example, the value for Zo varies from the default value of 75 ohms when administered 'Zo = 75ohm' column in the Y-field.

Fig. 13.27. Selecting functions for Y axis

c. Under Function, select the mag for the module output. 3. Click Done. Characteristic appears in the preview window. IfS11 = 0 at DC, a step time interval goes to zero, and tends to move TDRZ Zref. If S11 is different from zero in the DC, the step response the time interval is set to a nonzero value, and TDRZ set at a value different from Zref. Pulse time interval will always fall to zero, as can be seen from the characteristics of the derivative. Pulse transition process TDRZ will always be normalized to Zref. The chart below shows the difference between the short rise time of nonzero and zero rise time to the transmission line segment 94 ohms. Note that characteristic with zero rise time starts with the correct line impedance, while the impedance at the other time points perenormalizuetsya. In addition, one

166

characteristic- shifted copy of another (Figure 15.25.). The reason for this is that the voltage and current of a load connected to 50 ohm, so that the time interval is stored, v = Zref * i. When the pulse increases, TDRZ characteristic begins to change from a steady state, because there is reflected back to the source, the impedance of which differs from the characteristic impedance of the transmission line.

Fig. 13.28. Transitional process TDRZ impedance changes

note the following points to keep in mind when using TDR:spatial resolution c x 2B

(17)

where c - velocity of light in the medium, and B - the signal bandwidth. Since TDR is usually based on the frequency range, which starts with a constant current, the spatial resolution becomes

x

c 2F max

(18)

where Fmax - the highest frequency in the frequency range. For example, if Fmax = 15 GHz, and the medium has a permittivity εr = 4, then the step will be equal to the spatial (1.5E8 m / s) / (3E10 1 / s) = 5 mm. The spatial resolution equal to c / (2Fmax) corresponds to time resolution:  t 1 / (2Fmax)

(19)

167

Let N - number of points in IFFT. N equals the number of time samples, and it is also equal to twice the number of frequency samples. The density of the time samples in sweep frequency is:

where T - total time. Increased frequency sample density leads to an increase in the total time T. In practice, this often leads to large transient decay time. Therefore, TDR Options dialog can be set at a maximum time value. InterfaceTDR Options also allows selection minimal Δt, than given by equation (3) above. When you select a smaller .DELTA.t, you increase the Fmax "complement zero", that is, adding zero to S11 is the estimated bandwidth. In practice, this leads to a smoother signal TDR. HFSS allowsset the rise time of the input signal. The rise time must be equal to at least 1 / (2Fmax). The input signal with a large rise time is less dense at higher frequencies and will result in less "ringing" in the TDR response. Hamming or Hanning filteralso reduce the high frequency content and results in a more smooth characteristic TDR. With these filters can be chosen width. Width 100% often - a good choice. To calculate the temporal process is necessary to obtain broadband SPICE model. This is the model that reflect the behavior of electrodynamic structures, but represent a model with nodes. It executes the program Full-Wave SPICE, which allows you to perform a simulation of frequency-dependent models of SPICE, which are generated in HSPICE format, PSpice or Spectre RF for accurate simulation in the time domain. It provides broadband SPICE models at the touch of a button. Program Full-Wave SPICE - is an additional module for HFSS and Ansoft Designer. It calculates accurate broadband SPICE model. This capability allows developers of electronic components take into account the effects of microwave. Program Full-Wave SPICE enables the user to implement: 

 

MethodTranslation of wave types to nodes Modes-to-nodes technology; MethodFast sweep ALPS fast-sweep technology; algorithmscreating a SPICE circuit models.

Calculationtemporal process often requires a lot of computer resources - memory and time. Therefore it is recommended to use a distributed simulation in solving these problems. distributed simulationIt requires a license for the calculation tasks that require large computational resources. This license is called the High Perfect Computing 168

(HPC). Distributed Simulation mode set in the Options tab of an Analysis, which is located in the dialog Tools> Options> General Options.

169

Fig. 13.29. Task allocation calculation options

For example, in Figure dialog. 13.29 The user has access to a computer with eight or more processors is caused by command \\ large_many_proc_machine. In the dialog box Fig. 13.29 computer are listed eight times, according to the number of processors. Supposethat the computer has 16 processor. This case corresponds to the plant shown in Fig. 13.30. This number can be defined in tab Solver dialogue HFSS Options.

Fig. 13.30. Options HFSS: number of processors in a distributed mode

170

In this example, for those processes that can not be executed in a distributed fashion, the user requests the use of all 16 processors. But such transient HFSS better finds in multiprocessor mode. For distributed modeling, two processors in the section Number of Processors (Fig. 13.30) can be chosen. Detailed implementation techniques of distributed simulation will be discussed in Section 17.

14. Analysis of the horn antenna in the time domain In this example we will use the method of calculation of the transition process to get the S-parameters of a horn antenna in a wide frequency band. The broadband antenna may be used to transmit short pulses, for example as part of the radar system of the earth subsurface location. weWe will use existing examples in the library model containing the antenna geometry, create the rest of the model and choose the method of calculation of the transition process. This section explains how to prepare the model and the analysis of the transition process in the horn antenna in the time domain.

launch HFSS and discovery model. 1. Run HFSS 13. 2. teamFile> Opendownload filebroadbandhorn.hfssfrom the Help folder in the installation directory HFSS 13. This arrangement differs from the arrangement in the example folder. You'll add borders, excitement and set the surface on which are displayed field.

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Fig. 14.1. Viewhorn antenna

172

Fig. 14.2. dimensions horn antenna and port construction

3. Set menu HFSS> Solution Type, to select the type of solutions Transient Network Analysis(Fig. 14.3).

Fig. 14.3.Dialog select the type of solutions

5. Set the properties of the materialmouthpiece as copper and objects pin. The geometry also includes an air box, the sides of which are covered with layers of PML. 6. Create an air box with initial vertex (X, Y, Z) = (- 100, -250, 180) and the size (dX, dY, dZ) = (550, 500, 360). The properties of this box are shown in the dialog shown in Fig. 14.4.

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Fig. 14.4.Parameters base box horn antenna

chamferthis box are arranged at a distance greater than 100 mm from a speaker. Since we are going to use the PML, and the minimum frequency is 0.7 GHZ, it is even more than you need. Fill the air, boxing, give it a name, color, and permeability. On the sides of the box we define the boundary conditions PML. 7. highlightAll of the air box bevel. 8. Select Boundaries> PML Setup Wizard. Wizard appears perfectly absorbing surfaces (Fig. 14.5). Master itself corrects the material parameters to obtain a good absorption in a layer with a predetermined thickness.

Fig. 14.5.Create perfectly matched layer Thickness = thickness with 100 mm in the assistant PML

9. Click Next. 173

10. Set the minimum frequencyand the minimum distance to the plane Minimum Radiating Distance radiation, as shown in Fig. 16.6: 0.7 GHz and 100 mm. These settings need to HFSS generated the correct parameters PML layer.

Fig. 14.6.Setting the frequency and distance of PML assistant

11. ClickNextand then Finish.

Setting planesto output the dynamically changing fields.You need to decide in advance,where we want to see the field in complete three-dimensional model at each time step change. Create two perpendicular deployed rectangle on which we want to keep the field (Fig. 16.7,16.8). 1. Create rectangle in XY plane with the point (X, Y, Z) = (- 100, -250, 0) the size (Xsize, Ysize) = (550, 500).

174

Fig. 14.7. The horizontal plane intersectinghorn antenna

Fig. 14.8. Plane,which displays the field

2. Create rectangle in XZ plane with the point (X, Y, Z) = (- 100, 0, -180) and the size (Xsize, Zsize) = (550, 360). 3. Derive theserectangles in the form of frames. Now we need to define this list as a "list" in order to later save the field for them. 4. Select both rectangles. 5. Askteam Modeler> List> Create> Object List (or press Face List if you selected them in chamfers selection mode).

Fig. 14.9. selectionnamed "Objectlist1" on "PlotFields" in the properties window Properties

6. Specify the name of the list, for example,"PlotFields", as shown below, through the model tree and the properties window. 7. Save the model Save.

175

sources excitation.

Plane"Source" is the wave port.

1. ClickTools> Options> HFSS Options,to bring HFSS Options dialog. Of General tab, in the Assignment Options section, check the option Auto-assign terminals on ports is not checked and click OK.

Fig. 14.10.The General tab dialog HFSS Options

2. In the project tree, select a plane named "source". 3 View> Fit Selection. Note what this an object is an the coaxial cable, externalwhose outer conductor is part of a circle.

section of

4.AskWave Portforthis plane.

176

Fig. 14.11. Selecting an object for the reference (ground) plane

5. GivePort p1 name and click Next. 6. AskActive port option. Click Next.

Fig. 14.12. wave port assignment active

7. Select "Do Not Renormalize" (Fig. 14.13). The impedance of the port is expected to be exactly 50 ohm, and is considered as a valid impedance which will be correctly matched to the impedance models.

Fig. 14.13. The last step is to install a waveguide port

8. Click Finish. 177

The draft with the method Transient Network Analysis with multiple ports, to complete the S-matrix to provide a signal on one of the ports. This port is called active. Each simulation with one active port provides one column of the S-matrix. When you define a port as a passive, this means that the signal is not supplied to it, and it is loaded by a matched load. The project with the calculation of transient (non-network analysis), all active ports will be simultaneously included (ON), while remaining passive ports will only act as terminators (OFF).

Terminal Specification.since the program HFSS Transient uses Terminal-Driven ports, we need to set the resistance of a port. 1. P1 Click the right mouse button in the project tree and select Auto Assign Terminals.

Fig. 14.14. Selection option automatically detecting terminal

Fig. 14.15. Specification conductors related to the port, which will be a counterweight

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Fig. 14.16. The components of the wave port

2. Select Reference horn as the reference plane, so that the pin will be terminal.

Calculation and output the results.

This section describes the installation of the decision of the interim process and view the results. 1. In the project tree, select Analysis> Add Solution Setup. 2. Gridthe transition simulation is created on the basis of simulation in the frequency domain. In this simulation, the program stops at an appropriate frequency to perform an adaptive calculation. In this case, use mixed orders of the elements and the iterative solver. Accept the defaults in the tab General (Fig. 14.17).

Fig.14.17. The settings in the General tab

3. The Input Signal tab (Fig. 14.18), set the bandwidth from 700 MHz to 1.6 GHz. This band corresponds to the modulated Gaussian pulse in the time domain, which can be seen in the panel.

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Fig. 14.18. Time process to the input port

4. The Duration tab, you must specify a time when the boundaries of the analysis of the transition process. For this example, select Auto Terminate.

Fig. 14.19. Building of the accuracy of calculation of the temporal process

ParameterTarget Residual(Difference until convergence) represents the minimum field in the model at a given time relative to its largest value. As soon fall below 0,001 field from the highest value, the simulation may be stopped. Additionally, you can specify a maximum (At most) and minimum (At least) time intervals in which to simulate the transition process. Embedded minimum and maximum time intervals are suitable in most cases. They take into account the size of the model and the type of signal. 5. The tab Saved Fields (Fig. 14.20), select the option Object List or Face. 181

Set interval that will be stored field value equal to 30 ps. It is - "sufficiently small" part of the broadband pulse duration to obtain further smooth animation field.

Fig. 14.20.Filing Options tab field Save Fields

6. In the Radiated Fields set saving options and fields in the time and frequency domains at a frequency of 1.2 GHz, as shown in Fig. 14.21.

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Fig. 14.21. Select the frequency at which the radiated field is saved

7. Stepinstallation solution Solution Setup is executed. Click OK.

Modeling. 1. Start modeling.

The whole areaProgress solutions (see. Fig. 14.22) corresponds to the maximum simulation time in the Duration dialog tab Solution Setup, or if it is not specified, the value of 20 * (diagonal pattern) / (speed of light). FIELD red arrow indicatessimulation time relative to the maximum time during which the simulation is performed.

182

Fig. 14.22. Observation of the calculation process, showing the simulation relative to the total calculation time

In the simulation, you can see the progress of the calculation in a different way. 2.pressRight-click on Results in the project tree and select Create Terminal Solution Data Report> Rectangular Plot.

Fig. 14.23. Selection of characteristics in the time domain

Output Input and Output on the same graph, and a Residual dB20 on another.

183

rice14.24. Voltage Input and Output (excitation and reflection) as a function of time

InputOutput and show excitement and reflection on the port as a function of time. Characteristics Residual (ris.14.25) indicates a measure for the level max field in the model. Simulation is complete when Residual spada- is below 0.001 with respect to its peak at any time.

Fig. 14.25. ParameterResidual logarithmic scale as a function of time

184

Visualization structure characteristics .

1. To display the characteristics of the S-parameters as a function of frequency, right-click again on the Results of the project tree and select Create Terminal Solution Data Report> Rectangular Plot. 2. changechoice in the Solution window on Spectral as shown in Fig. 14.26.

Fig. 14.26. Preparation concluded parameters S-parameters as a function of frequency, i.e. a spectrum time process

3. Apply module| S11 |. The resulting graph is shown in Fig. 14.27. This graph changes when the calculation is still ongoing. This allows you to see this chart in the early steps of calculation.

Fig.14.27. The frequency characteristic | S11 | broadband horn antenna

Traveling field of the horn antenna.

185

To create a traveling field, select the list called "plotfields" in the model tree, ie, a list containing the two rectangles that you have created to display the field. In the project tree, right click Field Overlays> Plot Fields> E_t> Mag_E_t and select an arbitrary non-zero time on the next panel (Fig. 14.28). You can always adjust the time by changing his choice of Modify.

Fig.14.28. Creating a traveling field at a given time t = 3.044 ps

Now thereopportunity to observe traveling field. Moreover, unlike the method FEM, here we see the field, which varies in time according to the time process the input signal (Fig. 14.29).

Fig. 14.29. Distribution of the field in two perpendicular planes

186

3.changethe scale field to make a visible field in a range of 0 to 10 V / m. 4. Animation graphics wave propagation can be done by right-clicking on the name of the graph and selecting Animate. The Setup Animation window, you can select the number of steps. If necessary, HFSS perform interpolation between the stored field solutions.

Fig. 14.30. animation field setting window

visualization of the field radiation. To calculate the field in the time domain: 1. Right-click on the Radiation and choose Insert Far Field Setup> Infinite Sphere.

Fig. 14.31. Execution of the far-field installations

2. In the project tree, right-click on the Radiation and choose Insert Far-Field Setup> Infinite Sphere. Set the angle range, as shown in Fig. 14.32. This range in the XZ plane, and range from zenith to horizon in the direction of the direct radiation of the antenna.

187

Fig.

14.32. Specifying only one point in the field of far field

3. Now at tree project, click right Results> CreateFar- Fields Report> Rectangular Plot.

button

mouse on

4. Select rEz characteristic as a function of time.

Fig. 14.33. The output characteristics of the field intensity in the far field

5.

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Fig. 14.34. Bookmark families output characteristics

clarification: The component Ez isdominant. Therefore, it is selected in Fig. 14.33. r product of Ez useful because it does not depend on the distance from the source to the observation point in the far field. RE parameter has the dimensions [B], since the field has a dimension E [V / m], and the distance r [m]. OnFig. 14.35 shows the time dependence of the shape of the far field. This graph shows how the distorted signal emitted by the antenna. This information can be used to improve the antenna design, such as placing a reasonably resistive ribbons in some of its points. It - also useful information at the stage of postprocessing data calculation.

Fig. 14.35. Changefar-field radiation, co-polarized, in the center of the main beam.

IfYou need, you can also create a frequency-dependent far field when changing solutions to the Spectral and change the angle Theta as the primary variable, as shown in Fig dialogue. 14.36.

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Fig. 14.36. The output characteristics of the far field in the spectral region

The Families tab (Fig. 14.36), we can see that the previously set frequency 1.2 GHz, in Radiated-Fields bookmarking solution Solution Setup, and thus, you can select Spectral.

15. Design of nanoscale svetodiodiodnyh modules oneof the actual problems arising at the interface between the optical and microwave - ranges, is to provide an effective light-emission of electromagnetic waves in media with complex frequency dependence of their properties. These media, in which the analysis of electromagnetic waves is rather complicated problem can be attributed electrodeless discharge plasma metamaterials with negative permittivity and permeability, as well as semiconductor heterostructure. This section covers the possibility of increasing the efficiency of the LED modules on the basis of resonator quantum systems with sources of electromagnetic radiation [8]. The development of microwave technologywith increasing frequency are always constrained by the technological possibilities. Therefore, for example, in the submillimeter wavelength range could not be used as an effective resonator and slowing down the system as in the centimeter range. butcurrently in connection with the successes in the development of nanotechnology, such opportunities have emerged, and now you can use the rich experience in the development of microwave systems in devices of optical range, including lasers and LEDs. Furthermore, the results of simulation of streams of electrons and photons allow modeling active and passive elements in a single process. Thus as sources of electromagnetic radiation can be set point sources in the form of short current segments. Developers should consider HFSSsuch opportunities. The library materials can include nanoscale isotropic and anisotropic materials. However it required to check the accuracy of work programs of the calculation of structures with extremely 190

small dimensions which exist vozdeyst- electromagnetic light wave and microwave wavelengths. Especially important is the fact that it is necessary to correctly describe the sources of light waves. In the electromagnetic simulation programs as radiation sources can use voltage or current source with governmental Properly speaking dimensions much smaller than the wavelength. Consider light emitting diodes (LEDs)a cavity resonator (ER), which are considered promising [8], as have significant advantages of the compared with conventional LEDs. For example, the intensity of the spontaneous emission of the LED using a high-Q resonator increases the order of magnitude due to the narrowing of the luminescence spectrum. Besides, improving spectral purity and enhanced orientation and thermal stability of the radiation, as stated in [8].

191

and 15.1. Modeling structure sourcesin the optical wavelength range

excitation

The operating principle of LEDs based on the use of semiconductor heterostructures, which are composed of layers of n- and p-conductivity Stu. Due to different concentration of charge carriers in the individual layers and the presence of this complex structure of the areas in which there is a rapid accumulation of charges, there are conditions for the transition of charge carriers from one energy level to another, and there are photon emission, providing illumination in a certain wavelength range. These plots concentration of charge carriers are called quantum wells, threads and dots depending on how they are localized photons [9- 11]. Simple models of these quantum portions in accordance with [10] are shown in Figure 15.1.

a)

b)

at)

Figure 15. 1. The active regions of heterostructures in which the light sources are presented in the form of quantum wells (a) and filaments (b), and points (a)

In [8] are real pictures and LED structure with the PR, which are used in fiber optic communication systems dia- pazona infrared wavelengths. As most short-LED emitting at a wavelength of 650 nm is represented by the structure depicted here ris.15.2 as well.

a) b) Ris.15.2. Structure (a)spectra and (b) the LEDs based on GaInP / AlInGaP with Bragg mirrors and MQW of layers of AlAs / AlGaAs.

192

The resonator formed multilayer Bragg mirrors. The region of the active LED comprises a plurality of quantum wells (MQW). The emission spectra of the LEDs are illustrated in ris.15.2 b, where for comparison the intensity and Shih Rine shows also a conventional CD spectra at different currents. From ris.15.2 should be used, that the introduction ofOR provides an increase in the intensity of luminescence in a given direction. Wherein the lighting govo ryat the possibility of obtaining a highly concentrated light intensity curve, and electrodynamics terminology used in this case the concept of narrow directivity pattern. atdesigning LEDs with ER in [8] is recommended to select the smallest resonators are long excited at a fundamental oscillations (VC) and that have the highest Q-factor of its own, i.e., minimum absorption (loss) in the cavity. However, the actual CD with the PRs, including distributed Bragg mirrors and running on the VC, not quite meet these recommendations. To solve the problems of optical range using electrodynamic simulation program and simulation of discrete point sources of light waves, as well as distributed sources can be done, you can use the current segments along the transmission line. Absorption losses in the metal and can be modeled as it is done in the microwave range, i.e. a skin effect, a metal pattern with negative permittivity, using the surface impedance (resistance to transverse dimension of the square). So, after the formalization of the problem and solving the problem of modeling the structure, it is possible to consider the problem of designing and optimization of passive structures of the LED modules.

15.2. Falling plane wave to a frequency-selective surface An important task in practical light range, calculation can be regarded as a light wave falling on the surface with a complex structure. Surface with an arbitrary structure can be attributed to the special case of tea the frequencyselective surface. Therefore, we pose the problem to calculate the electrodynamic characteristics of the surface to various shapes, materials and the losses inherent in the surface. If we assume that the spectrum of the light wave emitted heterostructure swarm, has the form shown in Fig. 15.2, b, knowing the coefficient of reflexion of the frequency-selective surface reflection spectrum can be obtained

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zhennoywave. In order to solve the problem of electromagnetic wave is incident on a surface, it is necessary to model the structure of infinite size and apply periodic boundary conditions, which are implemented in the HFSS software. Using periodic boundary conditions greatly reduces the amount of tasks and allows on a modern computer with RAM 4 GB to solve the problem with the necessary accuracy. Consider an infinitemulti-pin structure consisting of a cylindrical rod shown in Fig. 15.3 and graphic HFSS tools. For the simulation of infinite structures need to use special boundary conditions, the so-called associated periodic boundary conditions. Calculations showed that the wave incident on the pins (Fig. 15.4), stimulates the in-phase field Me- forward pins. HFSS program allows to solve the problem of incidence of the electromagnetic wave on an endless structure with an arbitrary shape and a loss into account. Above and below the structure covered by periodic boundary conditions, we choose a point at which the calculated near field plane before and behind the plane (i.e., the reflected and transmitted waves). Of interest to determine the frequency characteristics of the selective surface with different structures, different surface roughness as pins, pictures, shapes, sizes structure, its periodic or random repetition character. Frequency characteristic can be determined by performing simulation of incidence of a plane wave on the surface, as well as exciting the structure by means of point light sources. One embodiment of a quarter-wave devices PR and RT in the form of quantum discs (CD) is shown in Fig. 15.3, where a perspective and projection of the whip shows multicavity system (MSHS) with semiconducting heterostructure and phosphor. On ris.15.3 b shows the electric powerMSHS inlet line and CD gallium nitridebased blue luminescence instigating lyu- yellow phosphors were used. The length l of pins corresponds to a quarter of the wavelength of blue color, i.e., about 115 nm. The spatial period (pitch) frequency-selective structure is 3-4 times less than the length l. Point sources in the form of a CD By arranging lozheny staggered through one pin in the common-mode electric fields push-mode oscillations (π-type). This VC, as is known in the art of microwave, is the most stable. CD Dimensions (Fig. 15.3 in) taken[11], where it was noted that the structure of CT GaN AlN in a matrix formed on a sapphire substrate by molecular beam epitaxy.

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a)

b)

at)

Fig.15.3. LED module based on quarter-wave multi-pin RS (a, b) with quantum dots in a quantum CD discs (c).

On ris.15.3 bdiagram also shows the electric field in and near MSHS quantum disks. The electromagnetic field from penetrating into the semi-MSHS Vodnikova structure decreases exponentially and it is important to select the dimensions of the pins with intervals therebetween so as to obtain the maximum electric field in the quantum nai- disks to provide more effective interaction with the pin systems heterostructure. Sequence solve the problem in HFSS system can summarized as follows. teamDraw-> Cilindercreate a metal cylinder with a radius of 50 nm and 200 nm in height. Then we use the command Edit-> Duplicate Copy for copying and reproduction coordinate pins X and Y-coordinate on the pitch distance (Fig. 15.4).

Fig. 15.4. Radiusand the height of the pins - Parameterisable variables variables with initial values of 50 nm and 200 nm

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We define a planewave incident on the structure of the command Source -> Plane Wave.on ris.15.5- 15.7 shows the fields falling fragments, razhonnoy The relative and total waves. askboundary conditions surrounding this piece box. In order to set this piece as an infinitely repeated, must be set on opposite sides of the periodic boundary Master-Slave conditions. On the lower plane Ground ask Perfect E, and on top of the plane - the ideal condition for absorption Radiate. Define the calculation frequency, e.g., 400 THz.

Ris.15.5. Leaning component (Incident)

Ris.15.6. The reflected component (Scattering)

Fig. 15.7.The total field (Total)

Onthis frequency, after the calculation, it is possible to deduce the incident reflected component of the total field and a sectional frequency-selective surface (Fig. 15.5-15.7). Now add command analysis frequency bandAdd Sweep.In the resulting dialog, this command Fig. 15.8 will make optical THz frequency range 100 - 1000 THz to 20 THz step.

Fig. 15.8.Setting the frequency range.

Run the command calculation HFSS -> Analyzes All. As a characteristic of the reflection wave from the frequency-selective surface

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can bringvalue RCS (Radar Cross Section), which depends on both the frequency and the angle of incidence of a plane wave. Another way to determine the frequency of the surface properties is to set the discrete radiation sources in staggered manner, which will simulate quantum dots. On ris.15.9 and 15.10 shows the calculated electric field vectors and sources of electromagnetic radiation.

Fig. 15.9. FieldE sectional pins modeled surface

Fig. 15.10. Detail of the surface with the pins, on which are deposited discrete sources (quantum dots)

ForIn order to control the excitation of the quantum dots, defined as discrete sources of electromagnetic radiation (. Fig 15.10), we define command HFSS -> Fields -> Edit Source Modules and set equal to the excitation source 1, and missing springs - equal 0. Excitation structure using discrete sources enabling a graph parameter | S11 |, which characterizes the frequency range reflection coefficient of the surface (Fig 15.11.).

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Fig. 15.11. The frequency characteristic of the frequency-selective reflection from the rough surface in the optical range

frequencyet al. characteristics depend on the shape of pins. If the pins have square cross section, then it is concentrated on the edges of the electric field, which leads to increased losses and the corresponding change in the resonance characteristics.

15.3. Characteristics light at multiresonator structures

radiation

Also interdigitated (open almost all sides) nanoscale structures of interest resonator systems of different shape, open at one end only, i.e. quarter-OP. Closed OR have a higher Q factor and therefore provides a more effective radiation. On ris.15.12 shows a multicavity system with quarter cylindrical resonators (CHTSR) excited at lower H111 kinds oscillations. Resonators are cylindrical recesses in the copper plate. SystemIt consists of a chain of coupled resonators (CSR). Quantum dots (QDs) are disposed in the cavity through one-phase electromagnetic fields.

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Fig. 15.12.Resonant-cavity surface Related

Distances between CSR should be considerably greater than the distances between the resonators to avoid communication between the rows and to provide excitation VC H111 with orientation along the electric power line CSR. We choose size in nm frequencies in THz. Draw a base portion fragment surface that will create a roughened surface (see Fig. Ris.15.13), Draw-> Box command.

Fig. 15.13. Detail of the surface with a chain of coupled resonators

Furtherdraw a cylinder height h = 100nm and subtract from the parallelepiped constituting the fragment surface. excite this surface (Ris.15.14) or discrete sources.

can

falling

flat

wave

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Fig. 15.14. Field in the cross section of the resonance holes when falling on the flat surface of the wave

To solve the problem, the fragment will cover the surface of the periodic boundary conditions (Fig. 15.15), since, as was done in chapters 2-4.

Fig. 15.15. Detail of the reflective structure with cylindrical cavities open (infinite structure connecting the periodic boundary conditions of a separate fragment consisting of four resonators)

notice, thatthe results obtained in HFSS, confirmed that the system with cylindrical resonators has a higher Q than the interdigital structure. Using a cylindrical coordinate system is

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thoroughly discussed in the following sections. Here when considering fields near rough surfaces back to the multi-pin system. To display the near field along the line, you must first draw the line you want to add Insert Near Field Setup command in the project tree in the Radiation section. This line is shown in ris.15.16 for interdigital structures. Also shown are near-field vectors in the upper sections of the resonant rough surfaces.

Fig. 15.16. Fields sectional resonators near rough surfaces

To perform a parametric analysis of the rough surface with round pins, ask team Optimetric. As parametrically variable height pin select variables from 60 nm to 220 nm. On ris.15.17 shows the resonance characteristics obtained for different heights of cylindrical pins.

Fig. 15.17. The frequency characteristics of the structure (reflection type), for different heights of the cylindrical pins

Based on experimental calculations confirmed that the maximum electric field strength is achieved in the upper section of the pins

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andMS.The diagram of the electric field and the electric vectors are shown in ris.15.18.

a) RS, consisting of round bars.

Fig.

15.18. (a)

b) MS, consisting of rectangular bars.

multi-pin structure and rectangular (b) bars.

from

round

For the structure shown in Fig. 15.18 and round pins, we present results of calculation of the operating bandwidth and quality factors, which are obtained in HFSS for materials with different conductivities, and roughness.

Fig. 15.19. Conversation job boundary condition to the finite conductivity of the material, which can be entered in the form of additional parameters roughness (Surface Roughness) surface material.

Copper

Copper

Molybdenum fr

om

Tungsten

= . ∙

rough surface

= .

100 THz

200

250

220

Q = 10

5

4

4.5

7

S/m

∙

7

S/m

= .

∙

7

S/m

It should be noted that the valuesQ-factors listed in the table are too small. Therefore, instead of the more open structure multi-pin system consider other resonator with a high Q factor. Here we pay attention to the possibility of using inferior and VC ensure dimensioned resonators to VC fundamental resonance spectrum corresponds to the maximum emission of the active medium, in which as in the present case it is assumed the use of quantum wires and dots.

15.4. Modeling stabilizing resonance structures with resonators The technique of stabilizing the microwave resonators are often used, which affect the open cavity so that the self-resonant frequency becomes more stable by increasing the unloaded Q of the resonator entire system [8]. This phenomenon can be used to create a complex surface, operating in the optical wavelength range. As a first example, consider the use of a stabilizing resonator of the resonator system consisting of two quarter-cylindrical cavities associated with prismatic stabilizing a half-wave resonator. This system is a triad of blue, green and red CT shown in ris.15.20. The cylindrical resonators are excited in antiphase oscillations lower N111 types that are supported and stabilized views N103 oscillations in a stabilizing cavity created on the basis of a rectangular waveguide with the wavetype lower H10.

Fig. 15.20. The system in the form of a triad consisting of a quartercylindrical cavities with prismatic stabilizing resonators.

This system uses the coupling slots in the magnetic field, disposed at a distance of half a waveguide wavelength in a prismatic cavity. The active element is supposed to use the quantum dot (QD) as a nanoscale diameter disc t, disposed between the quarter-cylindrical cavities in high electric field (Fig. 15.21). The dimensions of the stabilizing cavity for the blue, green and red wavelengths (λ1 = 460 nm, λ2 = 525 nm and λ3 = 635 nm) are defined by where b View Edit Materialcall the dialog in Fig.9.1, in which: 1. noteThermal Modifier mode, see View / Edit Modifier for.

Fig. 9.1. Turning to the properties of the temperature characteristics of the description materials

In this case, a table of material properties Properties of the Material will be expanded to include a column Thermal Modifier. 2. Select Edit ... from the pop-up menu, or None. dialog appears Edit Thermal Modifier. 3. Select the Expression button to display the text field Parameters Modifier or Quadratic button to show the table for Basic Coefficient Set and Advanced Coefficient Set. In the case of describing the dependence of expression Expression, we can write an equation for the temperature dependence in the field Parameters Modifier. markoption Use temperature dependent data set in the Modifier text field. Now it is possible on the temperature dependence of the characteristics entered in tabular form set Add / Import Dataset data. IfQuadratic option is selected, a Basic Coefficient tab, you can edit a field and to TempRef units and golf C1 and C2 to the following equation: P (Temp)= Pref [1+ C1 (Temp - TempRef) + C2 (Temp - TempRef) ^ 2] where Pref is determined by the relative permittivity (eg). In this formula P-parameter.

• Ifselected Quadratic, the tab Advanced Coefficient Set (Fig. 9.2) can be set lower and upper limit temperature (TL and TU, respectively).

Fig. 9.2. Selection of the upper and lower temperature boundary changes

Default,They are calculated automatically. Removing Auto Calculate TML option, TMU¸ can introduce new bottom value (TML) and the upper temperature boundary changes (TMU). Setting the temperature of objects. To set the temperature of the object:

1. Use the HFSS and HFSS-IE> Set Object Temperature, to display the Temperature of Objects dialog box (Fig. 9.3). This dialog is reduced to objects of the project table. The first column lists the object name, then the material, then switch-on the temperature dependence of the properties option, and then the temperature unit.

Fig. 9.3. Dialog inclusion of temperature dependences of individual objects in the thermal analysis of structure

2. To edit a property, select the option Include Temperature Dependence. This makes it possible to select objects and set them on the temperature. The column headings for the Object Name and Material columns include arrows for sorting direction. You can invert the sort direction by clicking on the header of each column. Ifthe list is large, you can use the field Select by name. Enter the name of the object and press Select. The selected objects are displayed. You can make several choices. 3. To set the temperature to the selected object or objects, enter a variable or a specific amount, or select an existing name in the text field. 4. Select the unit of the column Unit. 5. Click Set, to apply this value to the selected object, or click Set Default to set this value by default. If you press Set Default, the column for the selected objects will show the magnitude of temperature. 6. To edit a material object, when the dialog is closed, you can click on a column material, and see a list of the material in the pop up menu, and click Edit ....

Byteam HFSS-> Set Object Temperature can be set to the temperature of an object. after the calculationtemperature distribution, it can be derived as a field team Fields-> Plot Fields-> Other ... -> Temperature (Figure 9.4.).

Fig. 9.4. The output of the temperature field distribution in a horn antenna body

The dialogue shows the temperatureFig. 9.5. It should be noted however, that a fully-fledged calculation was based on the temperature dependence of linear expansion of materials, etc. performed in ANSYS complex.

Fig. 9.5.Dialog display the temperature distribution maps 121

The ANSYS interface project tree are options and operations that are designed to communicate the temperature characteristics of the object (Fig. 9.6).

Fig.9.6. The project tree in the program ANSYS Mechanical

Opportunity feedback temperature Mechanicaland HFSS.

between ANSYS

Thisoption appears in the Advanced tab of the Solution Setup dialog. Open this tab if you want to use a bidirectional thermal connection between HFSS and Maxwell and ANSYS interface. You must make this choice before starting on the solution (Fig. 9.7). Then you will have the opportunity to bidirectional transmission of the temperature distribution data of the ANSYS Workbench interface to HFSS and Maxwell.

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Fig. 9.7. Optional inclusion of temperature parameters

Beforehow to solve the set on HFSS and Maxwell, for this type of object, you have to put the initial value for the temperature dependence of the object (Fig. 9.8).

Fig. 9.8. Setting the initial temperature for each object, taking into account the temperature dependence

Ifyou mark the option Enable Thermal feedback from ANSYS Mechanical, will create a subdirectory with the extension .THM in the Solution folder included in the project when the import will be carried out through the data interface of HFSS and Maxwell. In this directory, the file is written a new centroid.xml (Fig. 9.9) to be used in the future withdrawal

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the temperature distribution. ANSYS Workbench 12 program consistently exporting temperature information in a file called mechanical.ths in the same Project directory itself.

Fig. 9.9. The location of the files with the temperature data

In the interface of ANSYS Workbench has 12 Export Results command.

Calculation of temperature distributionusing the connection with the program ANSYS Thermal. after the decisionProject on HFSS 13 or Maxwell, with the installation of "Enable Thermal Feedback from ANSYS Mechanical" option in the Advanced tab in the setup analysis, and after the related thermal analysis in ANSYS Workbench 12, you can get the temperature distribution of thermal solutions. ANSYS Workbench 12 writes the feedback files directly in the Project Solution HFSS directory, or Maxwell C: \ Ansoft \ HFSS13.0 \ Help \ hfss. chm :: / savinganewproject. htm> directory. In this case: 1. Open the project in HFSS and Maxwell. 2. Start the analysis of the project, automatically using feedback from ANSYS Workbench 12. NotWe need to make any additional changes to the settings in HFSS solutions or Maxwell. Just run the analysis Analyze command. HFSS or Maxwel know that the decision need to use information about the changes in temperature. HFSS or Maxwell will give altered the results based on the new temperature distribution, which can be imported through ANSYS Workbench 12 created earlier ANSYS Termal Link. To do this, follow these steps: 1. Close the project HFSS and Maxwell.

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2. In ANSYS Workbench interface 12, command clear Cleanpreviously imported data. 3. Import the new results from the HFSS and Maxwell. 4. Run thermal simulations again (Fig. 9.10).

Fig. 9.10. Calculationtemperature characteristics via Re-solving After ANSYS Thermal Link Feedback

The Edit Thermal Modifier tab can be set lower and upper bounds, which will be true quadratic dependence of the temperature change defined above. Afterthe end of the calculation, you need to select the object (Figure 9.11.), in which we want to lead the field and temperature values, and then ask the team HFSS -> Set Object Themperature.

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Fig. 9.11. The output of the temperature field in the plane of the analyzed objects

In the Field there is a temperature profile at the site (Fig. 9.12).

Fig. 9.12. icon in the project tree, which shows the preservation temperature distribution

Thus, Ansoft systemcomprising program electrodynamic analysis and analysis program mechanical structures in the temperature mode, will execute an electroanalysis in the conditions of geometry changes with temperature. To solve these problems need a special license.

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10. Implementation of the adjustment mode in HFSS In earlier versions of HFSS had several options to optimize the structure to be analyzed. Frequently used busting operation when changing one or two parameters, while the others remain unchanged. To solve this problem HFSS program for each of the searched parameter completely solve electrodynamic problem. In the version of HFSS-13 have an opportunity to solve this problem quickly and efficiently Tune operation, so that after the decision can be changed by hand engine to the setting, and immediately see how changing the characteristics of the analyzed device. In order to realize the Tune operation, you first need to have variables in the project. Then Solution Setup dialog tab appears Derivative, in which it should be noted that the program should find derivatives, ie, increment of the function depending on the variation of the argument. After the calculation of such an option, derivatives used by Tune Report team for instant display and study of small design variations, without having to re solutions. "Nominal" solution, plus derivatives contain all the information needed to learn how to change characteristics with small changes of design parameters. Consider the example of F-shaped antenna Pace (Fig. 10.1). It consists of broken out in the form of letter F vibrator which is shorted to ground the board at the right end and has an open line to the other.

Fig. 10.1. Side viewF on the planar shaped antenna to adapt to the position of the port

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Fig. 10.2. View from aboveon the F-planar antenna

Foodfrom a discrete source is supplied to the antenna through the cylindrical wire with 1 mm radius. Suppose a variable displacement feed point F-shaped antenna (equal to 4.8 mm in Fig. 10.2). The position of its feed point determines the input impedance at the central frequency of the working range. To HFSS calculated derivatives to a variable: 1. Open Derivative Solution Setup tab in the dialog (Fig. 10.3). 2. Forvariable feed_pos, which will adapt to, select Use.

Fig. 10.3. Setting options for the calculation of the derivative feed_pos

In this mode derivatives feed_pos parameter will be calculated, and then the calculation can be menu command Tune Report Result visible change S-parameters for varying the position of the feedpoint of the antenna. This feature does not apply to the frequencies and near fields.

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Creating a model F-shaped antenna .The global coordinate system construct the antenna base. Command Create -> Box draw a box, the parameters of which are shown in Fig. 10.4.

Fig.10.4. The base antenna height of 5 mm.

Furtherdraw the top of the planar antenna operation Draw-> Box, to the dimensions shown in Figure dialog. 10.5.

Fig. 10.5. Pace-top antenna thickness 1 mm

line, position which change when Cylinder coaxial it changes variable feed_pos (Ris.10.5) created surgery Draw> Cilinder. and its dimensions can be adjusted in Fig dialogue. 10.6. Positionthe center can be changed by introducing the option feed_pos.

Fig. 10.6. cylinder parameters

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coverage model antenna box, which draw the command Draw Box (Fig. 10.7) and on the surface of which set the boundary condition Radiate.

Fig. 10.7. The size of the radiation box that covers the antenna

The lower part of the coaxial line supply port, releasing the cylinder (Fig. 10.8).

Fig. 10.8. Installing a port in a section of coaxial line

Now we define a reference for calculation in the frequency range of 1.5 GHz - 2 GHz (Figure 10.9.).

Fig. 10.9. Setting the frequency range in interpolation mode 129

Press Start. Afterwe define the calculation output characteristics partial MagS (1,1, feed_pos) on a two-dimensional graph (Fig. 10.10), and then under derivative Derivative (Fig. 10.11) select a variable feed_pos.

Fig. 10.10. Output Options characteristics

Fig. 10.11. characteristic selection TuneS (1,1, feed_pos)

Nowyou need to open a dialogue operation Tune Report Report Tuning (Fig. 10.12).

Fig. 10.12. Observation of the frequency response of the displacement process of the antenna when the position of the feed point

By changing the position of the slider in the window Report Tuning, you can change the position of the feedpoint of the antenna, and thus see how this changes the frequency characteristic.

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Fig.10.13. The output characteristics of axis y

After can perform adjustment for the predetermined supply bias point position calculated far-field characteristics. The spatial radiation pattern F-shaped antenna is shown in Fig. 10.14.

Fig. 10.14. NAM planar antenna

So,In this section, we met with such an operation, as the adjustment. In addition, the HFSS geometry optimization can be performed for a given objective function, which includes the characteristics of the antenna. The HFSS-13, gradient search techniques realized minimum of the objective function Quasi Newton, simleks method, and the random search techniques Pattern Seach and Genetic Algorithm (genetic algorithm).

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11. Connector Modeling In this example, the calculated characteristics associated lines complex shape. Two extreme line connector (Reams. 11.1) are short-circuited with the ground plane. Connector This project is located in the Examples folder and is executed by Driven Terminal. The structure has 4 ports, twisted wires are connected. Ground fee the same for all ports, and are at the bottom, and are at the top of the structure.

Fig. 11.1. The design of linked 4 curved lines

TOonnektor (Fig. 11.1) has discrete ports at each end of the two inner ends of the curved guides (pin). The two outer conductors are earthed on both sides. The last fastening parallelepipeds (substrate) are filled FR4 material. Boundary Radiate radiation is applied to the surrounding boxing. Calculationperformed an adaptation of the mesh partition of the center frequency 5 GHz. We choose calculation method Driven Terminal (Fig. 11.2) and unit of measurement mm.

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Fig. 11.2. selection method of calculation

AllGuides in the connector designed as three-dimensional objects made of copper. The finished project in the Connector Examples folder set the port and boundary conditions. Ports and terminals arranged in FR4 substrates, which are arranged above and below the associated lines (Fig. 11.3).

Fig. 11.3.Setting ports and terminals

Ports are applied to the rectangular plane and the top of the rib set terminals (Fig. 11.4). Driven Terminal feature of the method is that in one section can specify multiple ports with a common earth bus.

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Fig. 11.4. ports1 and 2 and the terminals on the left and the right - short circuit

will establishports 1 and 2 on the middle pad (Fig. 11.4). Ports 3 and 4 are connected to the same lines that begin port 1 and 2, but on the other hand coupled lines (Fig. 11.5).

Fig. 11.5. Setting the port between the conductor and the ground plate

deriveConversation determining ground plate (Fig. 11.6) Assign Automatic command.

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Fig. 11.6. In the dialog box indicates that the conductor gnd becomingthe reference plane for all wireline

It is

Selecting gnd as the "Use as Reference" shows that the board gnd established one for each wire, for all ports. The calculation in the frequency band perform interpolation method so that the calculation is performed from the DC to DC upper frequency of 5 GHz.

Fig. 11.7. Type of connector Connector

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Fig.

11.8. Installation on a decision

To calculate the frequency range ask Add Sweep command Interpolating mode select and define the frequency from 0 GHz to 5 GHz in steps of 0.01 (Fig. 11.9).

Fig. 11.9.Target analysis frequency band

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Afterstart the decision-making process can be seen by pressing the right mouse button on Setup1 and selecting Profile to open a dialogue Solution. Details of the decision can be seen in the section Convergence, Matrix Data, and Mesh Statistics. S matrix can be seen as well as the characteristics of ports (Fig. 11.10).

Fig.

11.10. S-calculated matrix connector

To see a graph of S parameters can be displayed in the Cartesian coordinate system, adding the schedule section Results (Fig. 11.11).

Fig. 11.11. Frequency response parameters S

Of frequency characteristics of Fig. 11.12 you can draw the following conclusion: the line have a good harmonization, but link between separate linesconsiderable. So, between a number of lines reaching | S23 | = 0.8.

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Fig. 11.12. The electric field in the cross section of connector pins

In concluding this section we note that the Driven Terminal method is used when there are several lines, and associated with one bearing an earthen foundation.

Fig. 11.13. Calculated E field in a section of transmission lines in the excitation of the 1st port

In order to observe and study the distribution of the field in the excitation of a port, or a certain type of waves in this port, you need to set the Edit Source command and bring the rice dialogue. 11.14, in which the opt-ins and phase sources operating in the project.

Fig. 11.14.Ustanovka excitation sources on ports

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Discrete portsimplemented in the HFSS-IE.The HFSS-IE implemented discrete ports which HFSS-IE method different from those ports to HFSS. Discrete port in HFSS-IE has a voltage of 1 V between the terminal and the reference terminal to ground plane, while the port logic determines in HFSS electric field at the site. Discrete ports (fig. 11.15) are similar to traditional wave ports, but may be placed inside the structure, and should have a user-specified complex impedance. Discrete port S-parameters calculated in the port section.

This port is an internalto the field of solutions. Rectangle that is placed port regards to the signal line, and on the other hand comes to earth board

This port is an internalto the field of solutions. On one side of a rectangle with regard to the signal line, and on the opposite - from the ground plate

this portinternal to the field of solutions. Port is set in a circle around the ball

Ris.11.15.Implementation of ports in HFSS-IE

Discreteport can be set on a rectangle, going from the edge of the line to the ground plate (Fig. 11.15). On all edges of the discrete ports that are not in contact with metal or other boundaries must be set boundary condition Rerfect H. These settings depend on the selected mode: modal or terminal. It is important to note the following: • complex impedance port must be non-zero, and the resistance must be nonnegative. • allowedonly one mode, or load only one (terminal), if the decision is carried out in the terminal mode. • for signal ports integral line must be determined. • each load It must be connected to the border with perfect or infinite conductivity ground board.

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Consider,that the port is set up correctly only if the maximum distance from the terminal to ground the board less than one-twentieth of the wavelength. If this condition is violated, a warning appears. Modern digital devices operate at microwave frequencies. Characteristics of transmission lines between the processors and digital blocks affect the performance of computers. Not less important is the creation of supercomputers with tens, hundreds of computers connected in a single supercomputer. Therefore, one of the most pressing contemporary challenges consists in modeling and design of communication lines in digital systems and devices.

15.5.2. The resonator system quantum rings You can imagineor more simple devices emitters using "quantum rings." One of these emitters is shown schematically in Fig. 15.27.

Ris.15.27. emitterwith the quantum ring.

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This radiator to some extent, is an analogue of cells shown in Fig. 15.19. It uses several quarter-cylindrical resonators (e.g. four) circumferentially disposed. In this example, these resonators are excited species phase oscillations N111 connected through a communication slot (mc) with a stabilizing cavity based on a half-wave of the circular waveguide with N01r view (the figure shows lines of force oscillation type N012). Instead KH provided in a cell introduced blue quantum ring (CCM) arranged in its matrix (M) along the electric force lines. Thus, the radiating element in the present emitter is like CN, coiled into a ring. On ris.15.28 shownpattern of the electromagnetic field in the resonator system and in the near zone of the emitter in a fixed time, and the frequency characteristic of the resonator system without semiconductor structures, which were obtained in HFSS.

Fig. 15.28. Frequency response and the pattern of the electromagnetic field at the operating frequency of 650 THz

From ris.15.28 seen thatin the frequency range from 500 to 1000 THz several resonance characteristics obtained, one of which corresponds to the resonance N012 VC in CP at a frequency of 650 THz. Proof of this fact is a picture of two variations of the field along the axis of the superlattice. Note that the VC N012 is not a lower, and therefore resonances are observed at lower frequencies. However, separation of the VC is quite sufficient in order to avoid any "parasitic" oscillations, lowering the radiation efficiency at the operating frequency. must be pay attention to the fact that the resonant characteristics of the PC with the CP on the VC N012 is the most narrow, indicating the high quality of the PC at the operating frequency.

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On ris.15.29 shownfield pattern at the time point when cracks due electric field reaches the maximum value, and near the CC and the zero field, as is kk at a distance of a quarter wavelength from mc. On ris.15.29 alsoshows the distribution of the azimuthal component of the electric field in the radial direction, i.e. along the line shown in the figure. The azimuthal component of the electric field on the VC N01r is the only and the curve corresponding to an operating frequency of 650 THz, which indicates where the maximum electric field and where to put the spacecraft.

Ris.15.29.The electric field distribution in the radial direction and an illustration of the radiation at the time point when cracks due maximum electric field.

Note that the crossemitter dimensions considered limited diameters quarterwave resonators, which should not exceed 0,6 λ, so that they allow the occurrence of only the lower VC N111, and the diameter of the CP, which should not be substantially greater than 1,2 λ, so that no set higher VC. This fact is in contrast with the need to ensure adequate technological sizes for effective manufacture of semiconductor structures on the basis of the CT in a matrix InGaN GaN [19]. Therefore, it is desirable to increase the size of the matrix to RT. For this purpose, the emitter is provided an apparatus schematicallyshown in ris.15.30, which uses a coaxial CP excited on oscillations as H011 and disposed within multiresonator system consisting of a cylindrical quarter-wave resonator (CR) with views N111 oscillations. Fig. 15.30 8 shows resonators antiphase oscillations in communication with through one CP CR. Above these resonators is circular matrix

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(MM) CT. Calculated dimensions resonators for blue and red CT according to the markings on ris.15.30 shown in Table. Table. Dimensions (in nm) of the radiator shown in ris.15.30. D CR D cf. Colour Wavel d h1 h2 ength Blue 460 340 680 100 555 370 Red 640 480 960 140 750 755

Dm

1360 1920

Fig. 15.30. Emitter stabilizing coaxial resonator.

Forprovide the most efficient electromagnetic coupling between the CP and the CR their dimensions should be chosen so that the lengths of waveguides of which are obtained resonators have the same critical and, accordingly, the waveguide wavelength, i.e., h = 1 3 / h and 4λv λv = 2/2. Device considered emitter convenient in that the diameter Dm matrix can be increasedby increasing the number of the Czech Republic. With increasing diameter dav is correspondingly necessary to increase the diameter d of the rod to maintain the resonance frequency. Summarizing consideration proposed emitters should be noted that the luminous flux of such nanoscale devices is very small, and these 211

radiators should be collected in an array. Each emitter can be supplemented with the reflector. Such transducers can be grouped, for example in full-color (blue, green and red) triad. The resulting light emitting device can be used as the light source with adjustable chroma chromatic or white radiation and also be used in displays with high resolution. luminous efficiencyradiator with blue KN combined with a yellow phosphor is largely dependent on its own Q-multiresonator system, tuned to the frequency of the blue. When used without the color triads of phosphors luminous efficiency of each color element also greatly depends on the quality factor and adjustment system with stabilizing multiresonator resonator to the wavelength emitted by the quantum asterisk or quantum ring.

15.6. Analysis of the structure composed of eight resonators in the optical wavelength range Consider the analysis stepsresonator structure in the optical range of wavelengths in the example system HFSS emitter shown in ris.15.30. At the first stage, the drawing and creation of the resonator structure. We choose drawing unit "nm" and "THz" frequencies. For blue light? c = 460 nm D = 1.5 microns, Dc = 750 nm, d = 100 nm, Dch = 380 nm, lch = 490 nm and lc = 325 nm; forred λk = 640 nm D = 2.1 microns, Dc= 1050, d = 150 nm Dch = 525 nm Dlinych = 675 nm and lc = 450 nm. The length of the coupling slots 400 nm. resonatorstructure and size with said quantum ringlet executed graphically HFSS, ris.15.31 shown in a perspective and plan.

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Ris.15.31.The structure in which slots are arranged through one external resonator, i.e., linked to the central coaxial resonator 1,3, 5, and 7, the outer cylindrical resonators

Creaturethese figures carried out using the following commands. Draw a baseline resonator structure command Draw-> Box (ris.15.32).

Ris.15.32. dimensions base metal box

Furtherin this boxing need to cut one central cylinder radius of 525 nm and an 8cylinder radius of 262.5 nm. 8 resonators are arranged so that the side is located between the central coupling slot (ris.15.33 and 15.34).

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Fig. 15.33.Tsentralny cylinder

Ris.15.34. small cylinders

Command Edit-> Duplicate-> Around Axis duplicate the cylinders around an axis and is multiplied by 8. Next draw the inner rod located along the axis Z (ris.15.35)

Ris.15.35. dimensions internal metal rod.

Furtherat 400 nm draw the ring, subtracting one from another cylinder (ris.15.36 and 15.37).

Ris.15.36. dimensions the outer cylinder.

Ris.15.37. dimensions the inner cylinder.

As a result of subtraction we obtain planar ring 20 nm wide. We establish the Perfect E boundary conditions on the quantum ring. To insert the ring 8 ports that will excite

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consistent

current at ring, thinned ring 8 planar rectangles,size of the first of which corresponds to Fig. 15.38.

at

Fig. 15.38.rectangle coordinates in the gap of the quantum ring, which set a discrete port.

By creating this rectangle, ask him a discrete port command HFSS-> Exitation> Assign Lumped Port, and setting impedance line down the middle of the rectangle. Further fulfill this rectangle overlaps with the preservation of boundary conditions with respect to the axis Z.

Ris.15.39.Dialogue discrete port supplied in the gap of the quantum ring.

Created a structure shown in Fig. 15. 31, will cover the box, created by a team Draw-> Box, which is in the nanometer size are shown in Fig. 15.40.

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Ris.15.40. Dimensions Radiate boxing.

On This will install a box radiation boundary conditions, and on the side wall periodic boundary Master-Slave conditions on the opposite wall of the radiation box (Figure 15.41.).

Ris.15.41.Formulation periodic boundary conditions Master-Slave on opposite sides of box covering one resonator cell.

Perform a calculation HFSS- team> Analysis setup-> Add Solution Setup. The center frequency of 467 THz respectively. wavelength 640 nm (Fig. 15.42).

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Ris.15.42.Setting the center frequency analysis

Ris.15.43.Target bandwidth (mode interpolation)

Notethat if the quantum dots are arranged uniformly in the quantum ringlet, they will be excited in antiphase in accordance with the fields in cylindrical resonators. radiation pattern in this case is shown in ris.15.44 and 15.45.

Ris.15.44. Radiationelectromagnetic wave optical range of quantum ringlet in a system with an internal coaxial resonator stabilizing

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Ris.15.45.Near field in the cross section of the resonator when installing antiphase excitation of the quantum dots.

On ris.15.46 shows the frequency characteristic, and ris.15.47 - a picture of the electromagnetic field when excited CT located in CC through one resonator. XY Plot 1

ansoft LLC 0.00

HFSSDesign1 Curve Info dB (S (1,1)) Setup1: Sw eep1

-2.50

-5.00

-7.50

dB (S (1,1))

-10.00

-12.50

-15.00

-17.50

-20.00

-22.50 200.00

300.00

400.00

500.00

600.00 Freq [thz]

700.00

800.00

900.00

1000.00

Fig. 15.46. The frequency response of Selevenfor each port, the introduction of QC (8 ports)

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Ris.15.47. Painting electromagnetic field when excited CT located in the cavity through one QC

Analyzing the dynamic movement pattern of the electromagnetic field, Thoroe Ko is calculated by changing the phase of the excitation source, it is possible to see how the interactions of electromagnetic fields radiated from the individual resonators, and the overall picture of the field types of waves that resonate in separate cylindrical cavities resonators.

Conclusions.Options considered SDMbased OR quantum dots, rings or sprockets and in no way limit the variety of these devices. Not difficult to imagine, and other design options based on SDM quarter Multiresonator systems with other types of vibrations, including a variety of high-Q resonators stabilizing. Currently, the representation of the emitters in the form of quantum zvozdocheck and rings may seem unreal fantastic and Modeling such sources still requires a multifaceted experimental confirmation. However, the progress of the theoretical analysis of promising nano-materials and nano success shows that it will be realized in the near future. numerous publications which show the use of HFSS show that it can be successfully used to optimize the structure of the LED module. It is safe to say that the search for optimal solutions when creating the SDM on the basis of electro- dynamic systems with quantum dots will significantly improve the parameters of lighting devices with nanoscale The radiation sources.

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16. The configuration for distributed based on multiple computers

HFSS -13 has the ability to solve problems of enormous size, the number of tetrahedra of the partition can reach many hundreds of thousands. In the last 10 years have seen tremendous progress in enhancing computer-tools to solve large-scale problems - from the creation of large computer servers, to the distributed multiprocessor clusters and desktop workstations. In parallel went the improvement of mathematical algorithms and programs to implement them. Fig. 16.1 It shows the progress of milestones in terms of physical problems in the mechanical analysis, and solution of electrodynamic problems Ansoft field. It is now believed that the use of HFSS in the design process by 15% accelerates the development of new products from idea to implementation in hardware.

Fig. 16.1. growth story system performance characteristics HFSS

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One way to increase productivity is to parallel simulation. Fig. 16.1. It shows that in 1998-1999 it was possible to solve a system of equations 10M cells. In 2004, HFSS Ansoft solved the structure of a cell 100M. Today ANSYS may analyze the structure of 1 billion cells, and the level of simulation accuracy is very high. Currently, the key is a new method for the implementation of which is necessary to have a special license for High Performance Computing (HPC). This method allows for the calculation of 2 sets: 1) Domain Decomposition, 2) Multi-processing. HPC Solution method reduces to the calculation of multiprocessing using distributed calculation options that can combine up to 100 multiprocessor cores. Note that description in this section, the term "Computer" mayrelate to a personal, as well as a super-computer. Yadry and processors can characterize any of these machines. Starting with HFSS v.12, Ansoft company develops HPC method using the method of the task decomposition. Method MP (multi-processing) has been implemented in HFSS-7. Option distributed DSO solutions implemented since HFSS-10. These options are used today to reduce simulation time from days to hours, allowing the engineer to perform multiple simulations within one working day. For this purpose have been developed and proposed special methods multiprocessor and multicomputer calculation HPC and implemented additional improvements in HFSS v.12 (enhanced partitioning into mesh and mixed orders of the elements of the partition) to substantially increase productivity. Let us clarify the terms,that came in designing, together with the strengthening of the power of the numerical simulation. 1. HFSS HPC -A new option,which appeared in HFSS 12 HPC = High Performance Computing 2. Enables Domain Decomposition, decomposition method -a new method for solving in HFSS 12. DDM = Domain Decomposition Method. A new method of DMP in HFSS. DDM - is a method of high-paralleling, where: – this method of combining memory and nuclei number of computers via a network;

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– DDM It realizes a significant increase in memory for large and very large-scale problems; – DDM providesa quick solution, using a large number of processors. 3. Multi-Processing - Multiprocessorparallelization method separation, pull a memory, introduced in HFSS 7. MP = Multi-Processing – "Traditional" multiprocessing SMP. 4. The number of licenses "HPC licenses" depends for modeling the number of cores that are required for the calculation. 5. Work Package mode (Packs) or "floating (pool)" mode. – Packsallowsa predetermined number of nuclei for the program; – "Pool" licenses allow you to use any number of cores managed by multi-servers. • SMP = Shared Memory Parallel. • DMP = Distributed Memory Parallel. • DSO = Distributed Solve Option - mNogo-parametric (geometry, frequency) parallel simulation. • RSM = Remote Simulation Manager -A new control programdistributed analysis, appeared in HFSS v12, designed to work in computer network

Sample calculations which are made using HPC license Example 1. The antenna is located at the military vehicle Humvee.

• • • • •

The problem is solved for electromagnetic compatibility 1.8GHz frequency and - where the wavelength at the operating frequency, m) and uses: basis a second order function (2nd order); 730,000 tetrahedra; 14M unknown in the matrix (it is even a little, to use the method DDM); Perform calculations with the help of three related groups of computers; Shared memory = 115GB.

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Fig. 16.2. Calculation Example antenna structures on a moving object

The calculation resultsthe spatial pattern of the pokaza- in Figs. 16.2.

Example 2. The antenna mounted on the body fighter F35. Analyzed slot antenna (Fig. 16.3) is in the bottom of the wing of the aircraft fuselage • The F-35 Joint Strike Fighter: UHF blade antenna @ 350 MHz • The size of the problem= 1400λ3

Fig. 16.3. Military fighter F-16 with the antenna at the bottom of the fuselage

Ris.16.4. Slot antenna

at solving this problem, a method of DDM. • DDMsubregion split into partitioning net in small sub-regions "sub-domains" so that the field in which is calculated in parallel on multiple computers. For this is done: - Selection of unit "master" of the iterative solver for the general solution 223

- Automatic partition of solutions on a subdomain • User determines set N available computers for use by DDM: – n = 1 is the node "master", a single nucleus; – n = 2 to N is nodes subdomains solutions compared to direct solution.

Fig. 16.5. partition of based on tetrahedra, region and subregion

The calculation results are the same,HFSS directly in solving program, and using the method of DDM. However, the calculation time significantly different.

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Fig. 16.6. The cross-section of the radiation pattern antenna on the aircraft body

Fig. 16.8. frequency characteristic

Fig. 16.7.The spatial radiation pattern

Fig. 16.9. time calculationdepending on the number of areas partitioning

Example 3: Two-mirror parabolic antenna(Fig.

16.10) createdKossegrena scheme. The size of the problem ~ 17,500 λ3. Time solutions on 8-core computer 22049 seconds. The solution is accelerated in 17-24 times using HPC license.

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Fig. 16.10. Two-mirror parabolic antenna

The table in Fig. 16.11. given machine resources expended for modeling twomirror of a parabolic antenna, which depend on the number of nuclei. And accelerate the process of solving the problem with the inclusion of additional cores. We see that acceleration comes to shevti compared with a basic configuration with 8 cores. Note that the acceleration calculation as compared with the work can not be performed on a single processor.

Fig. 16.11. Computer resources required for solving the two-mirror antenna. Accelerating the Speed-up compared to the base computer with 8 cores

For

solutions like modeling RSM

establish managerremote of tasks must (Remote Simulation Manager). This

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program is installed asa separate program and automatically creates a remote or related to the simulation of network communication mode "links". • Method new distributed analysis work on remote computers • activates solver capabilities in DDM mode, DSO and solutions mode on remote computers.

Installation configuration distributed calculation. To create a new configuration based on a distributed multiple computers: 1. Click or HFSS HFSS-IE> Tools> General Options to display the dialog General Options and select the tab Analysis Options.

Fig. 16.12. Dialogue HFSS options

2. Selectbookmark Analysis Options, and in the section Analysis Machine Options, select the Distributed option. These changes will be displayed in the tab Analysis Machine Options and show the panel for viewing and editing computers configuration (Fig. 16.13).

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Fig. 16.13. Options analysis computer in the network

3. Click Edit Distributed Machine Configurations button.

Fig. 16.14. Dialogue distributed calculation configurations

This displays a dialogue Distibuted Machines Configurations (Fig. 16.14). This list shows all the existing configurations of the machine and the selected configuration, as well as information, they are locked or not. Here you can add a new configuration by clicking Add, Edit to edit the configuration command to delete the selected configuration Delete command, or duplicate the existing configuration Clone command, usually editing the name and configuration content. 4. To create a new configuration, click on the figure the dialogue. 16.14 buttonAdd. This opens a dialog Distributed Analysis Machines (Fig. 16.15). Clicking Edit or Delete also opens Distributed Analysis Machines dialogue, but also includes having the selected configuration.

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Fig. 16.15. Dialogue list of machines used in the calculation of the distribution

Here You can edit the configuration name, type, adding, tes- tirovanie and blocking machines in the list. 5. Askconfiguration name. It can not be empty and can not have previously given or reserved word. 6. For each machineTo manually add a list, under Remote Machine details, set the IP address, DNS name or UNC name. You can also use the Import Machines from File ... to use a text file to simplify the process.

Fig. 16.16. Section, which are included in the list of machines

button controls allow the machine to add to the list Add machine to list command (Fig. above) or remove the Remove command (Fig. below) of the machine from the list.

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Each machine in the current list has the Enabled box. You can block or connect any machine in the list according to your desire. On top of the table, the dialogue takes into account the total number of cars, and this number can be enabled or disabled.

Fig. 16.17. Blocking and the inclusion of machines in the calculation of the distribution

In general, the HFSS and HFSS-IE use machines in distributed analysis machines listed in the order in which they appear. If you have selected distribution method of calculation, and you run some calculations from the same interface, the HFSS and HFSS-IE choose machines that perform the least amount of computers in the order in which the computer is on the list. For example, if the list contains 4 cars, and you run a simulation that requires a single machine, the HFSS chooses the first machine in the list. If another simulation run, while the previous is done, and this simulation requires two machines, the HFSS chooses the machines 2 and 3 from the list. If the first modeling then completed, and we run another simulation, requiring three machines, the HFSS chooses the machine in the order 1, 4, and 2. Displayed list always shows the order in which you entered them regardless of the load on the machines. To control the order in the list, select one or more machines, and use the Move up or Move down buttons. Moving up and down are allowed when you select one or more adjacent machines is. Also, when you select one or more host names, you will see a text field below the power supply control, showing the name of the first car, how many times it appears, it allowed and blocked.

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Fig. 16.18. The movement of vehicles on the list to change their switching sequences

7. TestMachines- When several users on the network using a distributed remote solution.you need to check the status of these machines before the simulation can be run to make sure that no other processes are not running Ansoft. To do this, you can select one or more of the machines in the dialog (Fig. 16.18), and click Test Machine button. Opens Test Machines dialog. After the test is given a report on the status of each machine. Testing can be performed on a group of machines that are included in the calculation of the distribution. Enable or disable the machine can be in the list dialogue Fig. 16.18. 8. Click OK, to save your changes and close the dialog Distributed Analysis Machines. Only machines marked as Enabled appear in the list of machines distributed in the Analysis tab. independentlyfrom the machine on which the analysis is actually performed, the number of processors and installation Desired RAM Limit, and the default process priority settings are now read from the machine from which you run the analysis. If configuration is set, you can select it on the instrumental panel, you choosing icons:

Fig. 16.19. HFSS buttons on the panel, allowing switches between the local mode, remote and distributed work

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Note that this option is only active if there are several machines for distributed analysis. distributed analysis mode is recommended in the event that not enough resources of a single computer. HFSS on the same computer works as follows. Grid - essentially a large matrix, which must be inverted and solved. HFSS is trying to do it all in RAM. As soon as the available RAM is exhausted, the HFSS starts to divide the matrix into pieces, in which some elements of the matrix are written to the hard disk, and other parts are stored in RAM. However, there is a minimum size of the matrix that is to be stored in the RAM, and must remain in the memory space to be able to invert the matrix and solve. If the matrix is so large (ie, mesh partitioning very dense), that the minimum size no longer fits in RAM, HFSS stop. the user hastwo several options. It can 1) increase the computer's RAM, or 2) can be usediterative solver, or 3) to use the license, and therefore HPC method to solve the problem. We recommend using the iterative solver. Using Iterative Solver option can dramatically reduce RAM requirements.

Terms of Use iterative solver 1. The iterative solver works more efficiently when the structure does not contain many excitation sources. (For example, number of excitations - less than twice the number of processors). 2. If you want totake advantage of the iterative solver, and your analysis includes calculation of many discrete frequencies, adaptive decision should better go to the highest frequency in the frequency band.

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Fig.16.20. Section Solution Options, comprising selecting the order of the basis function and the parameters of the iterative solver

3. Relative ResidualIt provides a stopping criterion. The difference in estimatesiterative solver for solving a matrix equation. Value acts on the performance of the iterative solver as follows: • Defaultit is equal to 1E-4. This gives accurate S-parameters and fields which are indistinguishable from those obtained in the usual calculation. Ansoft recommends setting this value Residal. • In largervalue Residual, e.g., 1E-1E-3 or 2, the iterative process stops with a smaller number of iterations, and the solution will converge less. S-parameters will not differ much from the results obtained by direct solution, for example, the difference is in the third or the second digit. Fields and antenna pattern - visually the same. • Residual = 0.1 size can be used for fast adaptive grid refinement early in the adaptive process, but the S-parameters will differ significantly. • valueResidual = 1 should never be used. In the box there is no opportunity to enter the value Residual than 0.1.

Selecting the order of the basis functions.The HFSS-13 can select a basic function using HFSS field interpolation values between the tetrahedra nodes. To do this, see Options dialog Solution Setup

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selectedOption Order of Basis. It can be a Zero Order, First Order (the default), Second Order, or Mixed order. Options Order of Basis affect the mesh seal criterion Lambda Refinement and selected as follows. Option zero order (Zero Order) is useful when the model is divided into a grid with more than 100,000 tetrahedra, but the size of the model is small compared with the wavelength. Higher orders increase the number of unknowns for each tetrahedron, and are used when greater accuracy is required for calculating the field. If you choose Zero Order Solution Basis, all tetrahedra in the model must have a length of the ribs is less than 1/20 of the wavelength.

Installation options when running on the same computer

Fig. 16.21. Options computer calculation to work independently

For multiprocessing, select Enable multiprocessing using HPC licenses. This option allows the use of HPC license, including multiprocessing. the RAM requirements increase linearly with an increase in size of the model. When using the iterative solver is also the case for linear increase RAM requirements. If you are using a basic solver, the RAM requirements increase linearly. Settingssolutions with domains always use licensing HPC. Even at Tom, what domains distributed and

can use

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multiprocessingtreatment, they do not use a distributed solution or a multi-license all this is included in the licensing of HPC, including domains. HPC license is based on a calculation of the total number of cores in the simulation. For example, performing a distributed solution using 10 nodes with multiprocessing consisting of 2 cores per node, the total number of nuclei 2x10, or twenty nuclei. License HPC restricts the type and number of licenses to be verified for a given number of nuclei. For HPC, one type of license is checked for each kernel is used. Thus, the modeling of twenty cores would require twenty HPC licenses. For license type HPC Pack, one pack includes working with eight cores, and each additional package includes four times more cores. Thus, modeling with twenty two cores require HPC Pack licenses covering operation with a 8x4, or 32 nuclei. 5. Formultiprocessing, check Enable multiprocessing using HPC licenses option. This option allows the use of HPC license, including multiprocessing, even on tasks that do not include the area of domains. In this case, HPC licenses serve as MP license. 6. Select one of the following priorities from a list of Default Process Priority: • Critical (highest) Priority (Not recommended) • Above Normal Priority (not recommended) • Normal Priority (Normala priority) • Below Normal Priority (below normal) • Idle (lowest) Priority (slow priority) Can set these values using the additional programming in Visual Basic.

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Fig.16.22. Dialogues properties working dialogue Ansoft To transfer dataand management solution to the problem using dialogue Submit HPC Job (Fig. 16.22). To submit a job using the Submit HPC Job dialog box should be set to the main cluster host name. Selecting the command Tools> Windows HPC> Select Head Node ... prompted (Fig. 16.23), the choice of the cluster host name that you want to use.

Fig. 16.23. Selecting a host name

You can enterthe main name of the cluster node in the dialog box, and you can click on the button [...] to browse the network for the cluster that you want to use.

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Fig. 16.24. Defining multiple calculation settings dialog

After setting the node headerhostname, select Tools> Windows HPC> Submit HPC Job ... You canselect the installation section Analyze Setups (Fig. 16.24). Here you can choose from the following options: • All setups in the project; • All setups in a specified design: youYou select a project from the opening Gosia list; • Specify setups: You can addone or more settings By using Add Setups dialog ... Ifyou specify multiple settings, called the task sequentially in the order displayed in the edit box. BlockResource RequirementsIt manages the computing resources used. settingsDistributed Analysismanage the use of resources for part of the analysis, which may be distributed on various 237

cores. Settings Non-Distributed Analysis controlled initial part of the analysis that works before starting any distributed analysis - this initial part can not be allocated to separate components, and should be performed on a single core. There are two settings Distributed Analysis. The number of "machines" - a number of groups of computers that run in parallel; computers can run on individual nodes. The set number of cores on one computer controls the degree of parallel processing within each computer; these parallel execution of data flows must be on the same site. In each case HFSS distributed mechanism represents one large domain model part of the frequency sweep analysis or analysis part Optimetrics installation. There is only one setting for not distributed analysis, because this part of the analysis should take place on a single node. Number of cores controls the degree of parallelism used for this part of the analysis. mark Log Analysis Progress, to record the review process in the file . This file It contains messages about errors,prevention and other. Information. Clicking Next takes the current settings, and improves the dialog box Submit HPC Job: Properties. Clicking Cancel closes the dialog box.

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conclusion HFSS v13 software developed by the American company Ansoft, the development of which is in the learning process of the subject of this book - not the only, which has been widely used in Russia in the scientific and studied vatelskih and educational institutions. The greatest distribution was received by the so-called "troika»: HFSS, CST, FEKO. Oftensoftware selection is dictated by tradition, or speed training on the software product. The HFSS, starting with versions developed Hewlett Packard companies and the Agilent, was the most popular in Russia among software electromagnetic modeling of three-dimensional structures, and contributes to the learning process in many Russian universities. The structure of the radio now firmly divided into tsif- rovuyu part and the radio - radio receivers and transmitters, and often radio-technical part - is the antenna and the very first stages following them. Digital processing occurs and recaptures all of the bol- Shui radio. Moreover, in the management of a large antenna array performs the role of the digital part. Therefore, we can say that for the development of radio engineering HFSS - only part of the way of preparation. Selection software actually boils down to finding a compromise between the speed of calculation, the available computing resources and a volume of (the size in terms of wavelength). It all boils down to the problem of optimizing the design process variables present-microwave devices, the development of the relation between analytical and numerical methods, solving urgent problems facing both the organizers of the scientific work, and in front of the performers from researchers to engineers. The process of development of modern software on the bench of undergraduate, driven to understand the intricacies of the process proektiro- Bani, is a new and salutary step of education and training qualifications radiospe- ists. We hope that the problems of the analysis method usedthe tutorial - step through the construction and analysis of the results - will help developers master the microwave devices HFSS program and widely use it in their work.

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Literature 1. HFSS- High Frequency Structure Simulation. Manuals, Ansoft, 2010. www.ansoft.com - website of Ansoft-ANSYS - HFSS software developer. 2. Computer-aided design of microwave devices. Ed. VV Nikolsky / AM Radio and Communications, 1982. - 272 p. 3. Roger Harrington, Time Harmonic Electromagnetic Fields, McGraw-Hill, New York, NY in 1961. 4. K.A. Balanis. Antenna Theory: Analysis and Design, Wiley & Sons, 2 nd edition, 1997, 942 pp. 5. Baskakov From.AND.Fundamentals of Electrodynamics, Moscow, Moscow, Sov. Radio, 247 p. 6. Andrew Peterson, Scott Ray, Raj Mittra, Computational Methods for Electromagnetics, IEEE Press, New York, NY in 1998. 7. LER Peterson et al. "Analysis of Periodic Structures via a Time-Domain Finite-Element Formulation with a Floquet ABC" IEEE Trans, AP, March 2006, pp 933- 944. 8. Schubert F. Light Emitting Diodes. Second edition. - Cambridge University Press, 2006. Schubert FE LED / Per. from English. ed. AE Yunovich - M .: FIZMATLIT, 2008.- 496 p. 9. Zhores Alferov The history and future of semiconductor heterostructures. FTP, 1998, v. 32, №1, pp 3-18. 10. Zvezdin AK Optical microcavities,waveguides, photonic crystals. Nature. 2004. №10. 11. Alexandrov IA, KS Zhuravlev, VG Mansurov, Nikitin Yu Nonradiative recombination in the quantum dots GaN / AlN // Abstracts 6th VC "Nitrides of gallium, indium and aluminum - structures and devices". June 18-20, 2008. St. Petersburg. Physico-Technical Institute. AF Joffe RAN.- S.210,211. 12. Guttsayt E. M. technology and devices at microwave frequencies. Radio and communication, 1994. 224 p.

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13. Banks SE, Kurushin AA Calculation of antennas and microwave structures with the help of HFSS Ansoft - M, ZAO "NPP" Rodnik ", 2009, 256 p. 14. www.microwavestudio.com - company-developers program Microwave StudioCST.15.www.edem3d.ru (program EDEM). 16. Siteofficial dictribyutera modern software company OAO "Rodnik"www.rodnik.ru. 17. Distance Learning Sitedesign and application of microwave techniqueshttp://ipso.ioso.ru/distance . 18. Shlifer EDElectronic devices microwave M-type, coaxial and reverse coaxial magnetrons // Results of science and technology. Ser. Electronics. T.17.- M .: VINITI, 1985. - s.169-209. 19. VS Sizov, AA Gutkin, AV Sakharov, VV Lundin, Brunkov PN Tsatsulnikov AF phase decompositionand nonradiative recombination of the carriers in the active regions of the light-emitting devices based on InGaN quantum dots in a matrix of GaN or AlGaN // FTPP. 2009 t.43, vyp.6, s.836-840. 20. DM SazonovAntennas and microwave devices. M .: Higher. wk. 1988. 432 c.

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