Ansys - High frequenty magnetic

High-Frequency Electromagnetic AnalysisGuide

Release 12.1ANSYS, Inc.November 2009Southpointe

275 Technology Drive ANSYS, Inc. iscertified to ISO9001:2008.

Canonsburg, PA [email protected]://www.ansys.com(T) 724-746-3304(F) 724-514-9494

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Table of Contents

1. Overview of High-Frequency Electromagnetic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12. Finite Element Analysis of High-Frequency Electromagnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33. Elements and Commands Available in High-Frequency Electromagnetic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1. Available Elements .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2. High-Frequency Commands .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4. Performing a High-Frequency Harmonic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.1. Creating the Physics Environment .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.1.1. Specifying Element Types .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.1.2. Specifying the System of Units ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.1.3. Specifying Material Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.2. Building the Model, Assigning Region Attributes, and Meshing .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.2.1. Defining Model Region Attributes .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.2.2. Meshing the Model ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.3. Applying Boundary Conditions and Excitations (Loads) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.3.1. Applying Boundary Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.3.1.1. Perfect Electric Conductor (PEC) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.3.1.2. Perfect Magnetic Conductor (PMC) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.3.1.3. Surface Impedance and Impedance Loads .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.3.1.4. Perfectly Matched Layers (PML) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3.1.5. Periodic Boundary Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.3.2. Applying Excitation Sources .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.3.2.1. Excitation Ports ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.3.2.2. Current Source .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.3.2.3. Plane Wave Source .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.3.2.4. Surface Magnetic Field Source .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.3.2.5. Electric Field Source .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.3.2.6. Equivalent Source Surface .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.4. Solving Harmonic High-Frequency Analyses .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.4.1. Defining the Analysis Type .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.4.2. Defining Analysis Options and Estimating Computer Resources .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.4.3. Setting the Analysis Frequencies .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.4.4. Defining a Scattering Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.4.5. Defining a Radiation Analysis for a Phased Array Antenna .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.4.6. Defining a Modal Port Solution .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.4.7. Characteristic Impedance .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.4.8. Starting the Solution .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.4.9. Finishing the Solution .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.5. Postprocessing Harmonic High-Frequency Analyses .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.5.1. Reviewing Results ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.5.2. Commands to Help You in Postprocessing .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.5.3. Calculating Near Fields, Far Fields, and Far Field Parameters ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.5.3.1. Near Fields .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.5.3.2. Far Fields and Far Field Parameters ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.5.3.3. Symmetry .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.5.3.4. Radiation Solid Angle .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.5.4. Calculating Circuit Parameters for High-Frequency Devices .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.5.4.1. Scattering Parameters (S-Parameters) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.5.4.2. Power and Frequency Selective Surface Parameters ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.5.4.3. Voltage, Current, and Impedance .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.5.4.4. Displaying Network Parameters and Losses .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

iiiRelease 12.1 - 2009 SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information

of ANSYS, Inc. and its subsidiaries and affiliates.

4.5.4.5. SPICE Macromodels ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.5.4.6. TDR/TDT Display .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5. Performing a Modal High-Frequency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.1. Entering the SOLUTION Processor and Specifying the Modal Analysis Type .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.2. Setting Options for Modal Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.3. Specifying Modes to Expand .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.4. Applying Boundary Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.5. Solving a Modal High-Frequency Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605.6. Calculating Propagating Constants, Characteristic Impedances, and Effective Dielectric Constants .... 605.7. Reviewing Modal High-Frequency Results ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6. Adaptive Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63I. Basic Wave Radiation Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Harmonic Analysis for a Point Current Radiation Source (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67II. Basic Wave Propagation Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Harmonic Analysis of a Coaxial Waveguide (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Harmonic Analysis of a Coaxial Waveguide (GUI Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

III. Basic Wave Resonance Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Modal Analysis of a Cavity (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Modal Analysis of a Cavity (GUI Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Modal Analysis for a Circular Waveguide (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

IV. Basic Wave Scattering Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Harmonic Analysis for Plane Wave Scattering from a Metallic Plate (Command Method) .... . . . . . . . . . . . . . . . . . . . . . 95

V. Advanced Wave Radiation Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Harmonic Analysis for a JRM Array Antenna (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Harmonic Analysis for a Lee-Jones Array Antenna (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Harmonic Analysis for Line-fed Microstrip Patch Antenna (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Harmonic Analysis for Radiation of a Waveguide Antenna with No Flare (Command Method) .... . . . . . . . . . . . 117Harmonic Analysis for a Half Wavelength Dipole Antenna (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

VI. Advanced Wave Propagation Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Harmonic Analysis for a Microstrip Low-Pass Filter (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Harmonic Analysis for a Three-Stub Rectangular Waveguide Filter (Command Method) .... . . . . . . . . . . . . . . . . . . . . 133Harmonic Analysis for Multi-layer Microstrip Interconnect (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139Harmonic Analysis for Microstrip Meander Line (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145Harmonic Analysis for a Rectangular Waveguide with a Ridge Discontinuity (Command Method) .... . . . . . 149Harmonic Analysis of a Rectangular Waveguide with a Dielectric Post Using Adaptive Meshing (CommandMethod) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153Harmonic Analysis of a Rectangular Waveguide with a Dielectric Post Using S-Parameter AdaptiveMeshing (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157Harmonic Analysis of a Parallel-Plate Waveguide with a Lumped Circuit Load (Command Method) .... . . . 161Postprocessing Scattering, Admittance, and Impedance Parameters ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165SPICE Synthesized Equivalent Circuit for a Line-fed Microstrip Patch Antenna (Command Method) .... . . . 169SPICE Synthesized Equivalent Circuit for a T-type Transmission Line Network (Command Method) .... . . . . 175Harmonic Analysis for Rectangular Waveguide Filled with Two Dielectric Materials (Command Method).... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185Harmonic Analysis of Y-Junction Waveguide Circulator (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189TDR/TDT Display of Shorted Single-Ended Uniform Transmission Line (Command Method) .... . . . . . . . . . . . . . . 195Harmonic Analysis of a Frequency-Dependent Dielectric Loaded Waveguide (Command Method) .... . . . 205

VII. Advanced Wave Resonance Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207Modal Analysis for Resonant Frequencies of a Dielectric Resonator on Microstrip Substrate (CommandMethod) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209Modal Analysis for Dispersion of a Microstrip Line (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

Release 12.1 - 2009 SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.iv

High-Frequency Electromagnetic Analysis Guide

Modal Analysis for Propagating Constants and Characteristic Impedance of Three Coupled MicrostripLines (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

VIII. Advanced Wave Scattering Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225Harmonic Analysis for Scattering of a Metallic Sphere Coated by Lossy Dielectric Layer (CommandMethod) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227Harmonic Analysis for Scattering of a Dielectric Sphere (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231Harmonic Analysis for Scattering of a Metallic Cube (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235Harmonic Analysis for Scattering of a Metallic Sphere Coated by a Dielectric Layer (Command Meth-od) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239Harmonic Analysis of a Thick Bandpass Frequency Selective Surface (Command Method) ... . . . . . . . . . . . . . . . . . 243Harmonic Analysis for Scattering of a Dielectric Grating (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247Harmonic Analysis for a Lossy Free-Standing Ohmic Plate Array (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . 251

Index .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

List of Figures

2.1. Computational Domain for a FEM Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2. Open Microstrip Structure .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3. Equivalent Circuit ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.4. Open Microstrip Structure Model ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.1. Mixed Elements .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2. Object with a Large Aspect Ratio .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.1. Flow Chart for a Harmonic Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.2. Electric Field Distributions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.3. Solid and Finite Element Models ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.4. PEC Boundary Condition .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.5. PMC Boundary Condition .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.6. Impedance Sheet .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.7. Shunt RCL Lumped Circuit on a Surface .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.8. Microstrip Structure with PML Regions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.9. PML Region Attached to Interior Region .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.10. Attenuation Distribution .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.11. Buffer Elements in Interior Domain .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.12. Distance between Source/Objects and PML Region .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.13. Arbitrary Infinite Periodic Structure .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.14. Unit Cell .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.15. Periodic Array Models ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.16. Exterior and Interior Ports ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.17. Interior Ports ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.18. Model for Scattering Analysis of Periodic Structure .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.19. Spherical Coordinates .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.20. Exterior Hard Surface Magnetic Field Excitation .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.21. Soft Interior Surface Magnetic Field Excitation .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.22. Equivalent Source Surface .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.23. Spherical Coordinates .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.24. Solid Angle - Dipole Antenna .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.25. Solid Angle - Monopole Antenna above Ground Plane .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.26. Multi-port Network .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.27. Voltage Paths for Transmission Lines .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.28. Current Paths for Transmission Lines .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.29. Ten-Degree Symmetry Model of a Coaxial Waveguide .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

vRelease 12.1 - 2009 SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information



4.30. Signal Integrity Design Flow .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545.1. Flow Chart for a Modal Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581. Symmetry Model of a Coax Waveguide .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711. Magnetic Field in Coax .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 782. Electric Field in Coax .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 791.Teflon Filled Cavity .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831. Magnetic Field Vector Display of TE101 Mode .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 882. Electric Field Vector Display of TE101 Mode .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 891. 34 JRM Array and FEA Model of Unit Cell .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1012. S-Parameter of JRM Array with E-Plane Scan at 9.25 GHz .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1043. Directive Gain of Unit Cell with E-Plane Scan at 9.25 GHz .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044. Directive Gain of a 2525 JRM Array with E-Plane Scan at 9.25 GHz .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1051. 55 Lee-Jones Array and FEA Model of Unit Cell .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1072. Periodic Boundary Condition for Lee-Jones Array .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1083. S-Parameter of Lee-Jones Array with E-Plane Scan at 9.5 GHz .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1101. Line-fed Microstrip Patch Antenna Geometry and FEA Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1122. S-Parameter of Line-Fed Microstrip Patch Antenna .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1153. Contour of Electric Field Magnitude at 7.5 GHz .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1151. Waveguide Radiator with No Flare .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1172. Radiation Pattern of Waveguide Radiator Without Flare on E-Plane .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1203. Electric Field Contour of Waveguide Radiator Without Flare .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1201. Contour of the Radiated Electric Field of a Half Wavelength Dipole .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1232. Far Electric Field of a Half Wavelength Dipole on E-Plane at r = 10 m .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1243. Radiation Pattern of a Half Wavelength Dipole on E-Plane .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1244. Directive Gain of a Half Wavelength Dipole on E-Plane .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1251. Top and Side views of Low-Pass Filter ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1292. S11 of microstrip low-pass filter ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1323. S21 of microstrip low-pass filter ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1321. Side View and FEA Model of Filter (Dimensions are in mm) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1332. |S11| of Three-Stub Waveguide Filter ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1363. Electric Field Contour of Three-Stub Waveguide Filter at 15 GHz .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1371. Three-layer Interconnect .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1402. S11 of the Multi-Layer Microstrip Interconnect .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1433. S21 of the Multi-Layer Microstrip Interconnect .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1434. Electric Field Contour of Multi-Layer Microstrip Interconnect at 6.5 GHz .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1431. Microstrip Meander Line (Top View) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1452. S11 of the Microstrip Meander Line .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1483. The Contour of Electric Field Magnitude .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1481. Waveguide with Ridge Discontinuity (Dimensions are in mm) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1492. |S21| of the Rectangular Waveguide with a Ridge Discontinuity .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1523. Electric Field Contour of the Waveguide with a Ridge at 15 GHz .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1521. Waveguide with Dielectric Post (Dimensions are in mm) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1532. Initial Mesh Density ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1553. Mesh Density after Second Mesh Refinement Iteration .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1554. |S11| of Rectangular Waveguide with a Dielectric Post from 8 GHz to 12 GHz .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1561. Waveguide with Dielectric Post (Dimensions are in mm) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1572. |S11| of Rectangular Waveguide with a Dielectric Post from 8 GHz to 12 GHz .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1591. 3-D Parallel-plate Waveguide Model ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1612. 1-D Transmission Line Impedance Load .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1613. Lumped Circuit Loads .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1624. Shunt RCL Circuit ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1621. T-type Transmission Line Network .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

Release 12.1 - 2009 SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.vi


2. S11 on Smith Chart ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1663. Y11 on Smith Chart ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1664. S11 and S21 Magnitude vs. Frequency .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1675. Z11 and Z21 Magnitude vs. Frequency .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1671. S-parameters of Line-Fed Microstrip Patch Antenna .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1702. |Y11| Generated by SPICE3 Using Synthesized Equivalent Circuit ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1733. |Y11| Generated by ANSYS Full-Wave Solution .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1731. T-type Transmission Line Network .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1752. SPICE Transmission Line Circuit Model ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1763. SPICE Subcircuit Macromodel ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1764. |Y11| from SPICE TL Model and Equivalent Circuit Macromodel ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1825.Transient Analysis of SPICE Transmission Line Model ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1836.Transient Analysis of SPICE Subcircuit Macromodel ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1831. Two Segment Rectangular Waveguide .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1852. Electric Field Contour of Waveguide .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1871. Y-junction Waveguide Circulator with Central Ferrite Cylindrical Post ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1892. S11 Parameter of Y-junction Waveguide Circulator ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1923. Insertion Loss of Y-junction Waveguide Circulator ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1924. Isolation Loss of Y-junction Waveguide Circulator ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1935. Electric Field Contour at 10GHz .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1931. TDR and TDT Waveforms .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2022. Total Waveform ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2031. Frequency-Dependent Dielectric Loaded Waveguide .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2051. Geometry and FEA Model of Dielectric Resonator .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2092.The Electric Field of TM01 Mode in a DR with a Metallic Enclosure .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2113. The Electric Field of HEM Mode in a DR with a Metallic Enclosure .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2124.The Electric Field of TE01 Mode in a DR with a Metallic Enclosure .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2131. Geometry and FEA Model of the Microstrip Line .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2152. Propagating Constant of Microstrip Line .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2173. Characteristic Impedance of Microstrip Line .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2174. Effective Dielectric Constant of Microstrip Line .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2185. Electric field of the Fundamental Mode in the Microstrip Line at 20 GHz .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2181. Microstrip Structure .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2192. Electric Field of Mode 1 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2223. Electric Field of Mode 2 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2224. Electric Field of Mode 3 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2231. FEA Model for Scattering Analysis of a Lossy Dielectric-Coated Metallic Sphere .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2282. Scattering Electric Field Contour of the Lossy Dielectric-Coated Metallic Sphere .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2303. Normalized RCS of the Lossy Dielectric-Coated Metallic Sphere on E-plane and H-plane .... . . . . . . . . . . . . . . . . . . . . . . 2301. FEA Model for Scattering Analysis of a Dielectric Sphere .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2322. RCS of the Dielectric Sphere .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2343. Contour of the Scattering Electric Field from a Dielectric Sphere .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2341. Scattering Electric Field Contour from the Metallic Cube .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2382. Normalized RCS of the Metallic Cube on E-Plane and H-Plane .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2381. FEA Model for Scattering Analysis of a Dielectric-Coated Metallic Sphere .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2402. Scattering Electric Field Contour of The Dielectric-Coated Metallic Sphere .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2423. Normalized RCS of the Dielectric-Coated Metallic Sphere on E-Plane .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2421. Unit Cell .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2431. Dielectric Grating .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2472. Reflection Coefficient of Dielectric Grating .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2491. Unit Cell .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2512. Power Reflection Coefficient .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254

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List of Tables

2.1. Physical and Model Features .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.1. High-Frequency Elements .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.1. Element DOFs .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2. Material Guidelines .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.3. High-Frequency Boundary Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.4. Surface Impedance Boundary Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.5. High-Frequency Excitation Sources .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.6. Port Types .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.7. Postprocessing Commands .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.8. Plotting Commands ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

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Chapter 1: Overview of High-Frequency Electromagnetic Analysis

The ANSYS program supports high-frequency electromagnetic analysis. This type of analysis calculates thepropagation properties of electromagnetic fields and waves in a given structure. The ANSYS program supportsboth time-harmonic and modal high-frequency analysis.

Except in a few cases, most-high-frequency devices use electromagnetic waves to carry information. For thisreason, frequency plays a vital role in the design of such devices. High-frequency electromagnetic fieldanalysis simulates the electromagnetic phenomena in a structure when the wavelength of the signal is ofthe same order of magnitude or smaller than the dimensions of the model. The high-frequency band rangesfrom hundreds of MHz to hundreds of GHz.

In general, you use high-frequency electromagnetic field analysis to solve interior problems or exteriorproblems. For interior problems, an electromagnetic field propagates or oscillates in a closed structure suchas an accelerator chamber, a microwave filter, or a high-speed electronic package. The oscillating frequenciesand scattering matrix parameter (S-parameter) are usually investigated. For exterior problems, an electromag-netic wave radiates into open space or it is scattered by an object in the open domain. Examples are phasedantenna arrays and radar reflection from a metallic object. The radiation pattern, directive gain, or radarcross section (RCS) is usually investigated.

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Chapter 2: Finite Element Analysis of High-FrequencyElectromagnetic Fields

In practice, finite element analysis (FEA) is one of the most successful frequency domain computationalmethods for electromagnetic field simulation. It provides the capabilities you need to model any geometryand any materials of composition. This material capability is particularly important in electromagnetic fieldengineering since most applications dealing with antennas, microwave circuits, scattering devices, motors,generators, etc. require simulation of nonmetal composite materials. Throughout the frequency spectrum,FEA enjoys wide popularity. It plays a major role in electromagnetic engineering applications such as:

Microwave circuits and devices

High-speed digital electronic circuits

Antennas

Electromagnetic Interference (EMI) / Electromagnetic Compatibility (EMC)

Biomedical applications

The ANSYS high-frequency electromagnetic simulator (ANSYS Emag - High Frequency) uses tangential vectorfinite element technology. It provides 3-D elements to perform harmonic analyses (see Chapter 4, Performinga High-Frequency Harmonic Analysis (p. 13)) and 2-D and 3-D elements to perform modal analyses (seeChapter 5, Performing a Modal High-Frequency Analysis (p. 57)) analyses, with an exp (jt) dependence assumed.

ANSYS Emag - High Frequency has a preprocessor, a solver, and a postprocessor. The preprocessor providesfacilities for describing the high-frequency structure to be simulated, the excitation to be applied, and theboundary conditions or other constraints to be imposed. It includes the following:

Geometry Tool

Solid Model using Built in Modeler and APDL

CAD File Input via Connection Capability

Meshing Tool

Automatic Meshing

Manual Meshing

Adaptive Meshing

Tangential Vector Based Element Library

1st & 2nd Order Tetrahedral, Quadrilateral, and Wedge Elements

1st Order Pyramid Elements

1st & 2nd Order Quad and Triangle Elements

Material Model

Lossy/Lossless Isotropic Material



Lossy/Lossless Anisotropic Material

Boundary Conditions

Perfect Electric Conductor (PEC)

Standard Impedance Boundary Conditions (SIBC)

Matched Waveguide Port

Perfectly Matched Layers (PML)

Periodic Boundary Conditions

Excitation Sources

Waveguide Modal Source

Volume, Surface, Line, and Point Current Density Source

Plane Wave Source

Surface and Line Electric Field Source

Surface Magnetic Field Source

The solver generates the element descriptions, assembles the element matrices into global finite elementmatrices, imposes the appropriate boundary conditions, constraints, and excitation sources, and then solvesthe equations. It consists of the following:

Modal Analysis

Lanczos Eigenvalue Solver

Harmonic Analysis

Sparse Direct Solver

Incomplete Cholesky Conjugate Gradient (ICCG) Solver

Fast Frequency Sweep Solver

The postprocessor provides facilities to calculate parameters and visualize results. This includes the following:

Electromagnetic Field Vectors and Contour Patterns

Cut-off Frequency, Propagating Constant, and Resonant Frequency

Quality Factor (Q-Factor)

S-parameters and Touchstone File

Voltage, Current, and Characteristic Impedance

Conducting Current Density Distribution

Near and Far Electromagnetic Field Extension

Radar Cross Section (RCS)

Antenna Parameters (Radiation Pattern, Directive Gain, Directivity, Radiation Power, Radiation Gain, Ra-diation Efficiency)

Time-Averaged Power

Joule Heat


Chapter 2: Finite Element Analysis of High-Frequency Electromagnetic Fields

ANSYS Emag - High Frequency is a frequency domain simulator that can analyze a large class of high-frequencydevices and systems. This includes uniform wave-guiding structures, cavity resonators, antennas, and antennaarrays. A high-frequency electromagnetic analysis can be coupled with another field analysis to simulatecomplicated physical phenomena, such as RF heating.

To solve the full set of Maxwell's differential equations that govern high-frequency electromagnetic fields,the finite element method discretizes the infinite continuous wave propagating space into a finite elementmodel. Boundary conditions and excitations are applied to the solid model or finite element entities.

A typical electromagnetic configuration simulated by FEA is shown in Figure 2.1: Computational Domain fora FEM Analysis (p. 5).

Figure 2.1: Computational Domain for a FEM Analysis

Plane wave E

inc

Surface enclosing

FEA

Perfect electric

conductor or perfect

magnetic conductor

Dielectric volume

(enclosed by )

Resistive or impedance

surface,

Current volume,

Feed aperture,

Finite element mesh

0

d

f

s

r

The high-frequency FEA procedure uses a weak integral form of the electric field vector Helmholtz equationas the basis. For improved accuracy for scattering applications, the scattered field is investigated instead ofthe total electric field. Refer to High-Frequency Electromagnetic Field Simulation in the Theory Reference forthe Mechanical APDL and Mechanical Applications for more information on the pure scattering field formulation.

The ANSYS high-frequency elements use the tangential vector finite element method. The vector electricfield consists of the linear combination of the vector basis functions. The associated coefficients are the degreeof freedom (DOF) of the final matrix equation. The DOFs of the tangential vector method are the projectionsof the vector electric field on the edges and faces of the element. For example, for the first order tetrahedralelement, its DOFs are the projection of the electric field along the edge of the element at the middle of theedge:

DOF = t E at middle of edgewhere t is the unit tangential vector of the edge.

Refer to the Theory Reference for the Mechanical APDL and Mechanical Applications for details on this method.




As in any other type of ANSYS analysis, you must build a finite element model that correctly represents thesystem. The following table shows how physical features of an electromagnetic system correspond withmodel features.

Table 2.1 Physical and Model Features

Model FeaturesPhysical Features

Finite Element MeshElectromagnetic Structures and Space

Perfect Electric Conductor (PEC) Boundary Condi-tion

Lossless Metallic Surface

Standard Impedance Boundary Condition (SIBC)Non-perfect Electric Conductor, Air-Dielectric Interface,Dielectric Coating on PEC

Perfect Magnetic Conductor (PMC) BoundaryCondition or PEC

EM Field Symmetry

Absorbing Boundary ConditionEM Field at Infinity, Matching Load

Impressed Current DensityCurrent Source, Metallic Wire with Conducting Cur-rent, Excitation Gap

Modal FieldMatched Voltage Source

For an enclosed structure, you must mesh the entire structure. For propagation, radiation, and scatteringproblems, the electromagnetic field extends to infinity. You must trunicate the infinite space using absorbingboundary conditions. Usually, the inside of an electric conductor is not meshed because a high-frequencyelectromagnetic wave can only penetrate the surface a short distance.

If the ohmic loss does not play a significant role or is not a major concern in the design, a perfect electricconductor (PEC) is a very good approximation for metallic objects. The tangential electric field vanishes onthe surface of a PEC. It leads to a constraint condition DOF = 0 on the surface.

Often, meshing the skin of a non-perfect electric conductor or a dielectric coating on a PEC leads to extremelysmall elements inside of those layers. Instead of meshing those very small layers, apply a standard impedanceboundary condition on those surfaces to obtain a good approximation.

You can reduce the size of your model by taking symmetry of the electromagnetic field into account. If thetangential electric field is zero (that is, only the normal electric field exists on the symmetry plane), apply aPEC boundary condition to the symmetry plane. If the tangential magnetic field is zero (that is, only thenormal magnetic field exists on the symmetry plane), apply a PMC boundary condition to the symmetryplane. In a ANSYS high-frequency analysis, a PMC boundary condition is a natural boundary condition. Youdo not need to apply a constraint condition to a PMC symmetry plane.

If an electromagnetic wave radiates into infinity, you must use an absorbing boundary condition to truncatethe finite computational domain. If an electromagnetic wave in a propagating system is absorbed by amatching load, you must replace that matching load with an absorbing boundary condition.

The following example of an open microstrip structure with a capacitance gap shows you how to create amodel.



Figure 2.2: Open Microstrip Structure

The equivalent circuit including a matched source, s-parameter extractor, and matching load is shown inFigure 2.3: Equivalent Circuit (p. 7).

Figure 2.3: Equivalent Circuit

ZL ls Z0

s-parameter extraction

Z0 ZL

To create the model, you need to make use of the characteristics of electromagnetic fields and simplify themodel as follows:

The thickness of the microstrip is assumed to be small compared to the other dimensions and is ignored.The ohmic loss of the microstrip is also assumed to be small and is ignored. These assumptions lead toa PEC microstrip with zero thickness.

For the fundamental mode, the electric field is assumed to be symmetric about a vertical center lineon the cross section. Accordingly, the analysis can be done on a half model. A PMC boundary is appliedto the symmetry plane.

Since the electromagnetic field decays rapidly in the transverse direction with the distance from a mi-crostrip, PEC boundaries are added to enclose the open space at a proper separation distance. Thedistance from the microstrip to the top PEC boundary should be at least equal to two times the heightof the substrate. The distance from the microstrip to the side PEC boundary should be at least two timesthe width of the microstrip.

The wave source is assumed to be a matched electric current source and the output of the two-portnetwork is terminated by a matching load (see Figure 2.3: Equivalent Circuit (p. 7)). Absorbing boundaryconditions are added to represent the matching loads.

The real current source will be equivalent to the impressed current density. Considering the electricfield distribution on the transverse cross section, the line current density pointing from the microstripto the ground will excite the fundamental mode in the microstrip. Since the line current density sourcelaunches a bidirectional electromagnetic wave, an absorber must be located behind the line currentdensity source to prevent a reflected wave.

These electromagnetic field characteristics and assumptions yield the following unmeshed model for theopen microstrip structure.




Figure 2.4: Open Microstrip Structure Model

PEC

PEC microstrip

Line current

S-parameter extraction plane

Absorber

PEC

Substrate

Symmetric plane

Absorber



Chapter 3: Elements and Commands Available in High-FrequencyElectromagnetic Analysis

3.1. Available Elements

Three elements are available for high-frequency analysis: HF118, HF119, and HF120. HF118 is a 2-D elementthat applies only to modal analyses. You can use it to compute dispersion characteristics of high-frequencytransmission lines, including the cutoff frequencies and the propagating constants for multiple modes. HF119and HF120 are 3-D elements. You can perform harmonic analyses or modal analyses with them.

Table 3.1 High-Frequency Elements

DOFsNumber of Nodes and

Shape2-D or

3-DElement

Projection of the electric field E (ANSYS de-gree of freedom "AX")

8-Node Quadrilateral withtriangular degeneracy

2-DHF118


10-Node Tetrahedral3-DHF119


20-Node Hexahedral withpyramid and prism degener-acy

3-DHF120

You can use one element shape (hexahedral, wedge, pyramid, or tetrahedral) or any combination of shapesin your 3-D model. Figure 3.1: Mixed Elements (p. 9) (a) shows a mix of hexahedral and wedge elements and(b) shows a mix of hexahedral, pyramid, and tetrahedral elements. The pyramid elements are transitionalelements between the hexahedral and tetrahedral elements.

Figure 3.1: Mixed Elements

As an example, the following command input listing creates mixed hexahedral and wedge elements:

/prep7et,1,120 ! define hexahedral elementet,11,200,5 ! define 2-D 6-node triangle mesh elementet,12,200,7 ! define 2-D 8-node quadrilateral mesh elementrect,0,1,0,1 ! create area 1rect,1,2,0,1 ! create area 2aglue,all ! glue areas togetheresize,0.25 ! define the element sizeasel,s,loc,x,0,1 ! select area 1



type,11 ! select triangle element typemshape,1 ! define the triangle element shapeamesh,all ! mesh area 1 with triangle mesh elementasel,s,loc,x,1,2 ! select area 2type,12 ! select quadrilateral mesh element typemshape,0 ! define the element quadrilateral shapeamesh,all ! mesh area 2 with quadrilateral mesh elementallsesize,,4 ! define element operation type,1 ! select hexahedral elementasel,s,loc,z,0 ! select 2-D elementvext,all,,,0,0,1 ! create 3-D elements by extruding 2-D elementsfini

As an example, the following command input listing creates mixed hexahedral, pyramid, and tetrahedralelements:

/prep7ch=10.16e-3cw=22.86e-3cl=2.e-2h=2.e-3et,1,hf120,1 ! define hexahedral elementet,2,hf119,1 ! define tet elementblock,-cw/2,0,-ch/2,ch/2,0,cl/2 ! create volume 1block,-cw/2,0,-ch/2,ch/2,cl/2,cl ! create volume 2vglue,all ! glue volumes togetheresize,h ! define element sizetype,1 ! select hexahedral element typemshape,0,3d ! define hexahedral meshmshkey,1 ! use mapped meshvmesh,1 ! mesh first volumemshape,1,3d ! define tetrahedral elementmshkey,0 ! use free meshingvmesh,3 ! mesh second meshtchg,120,119,2 ! covert degen. hexahedral element into tetrahedral elementfini

Although a geometrically complex structure can be meshed with tetrahedral elements, it may require manyelements and that may lead to simulation failure because of computer resources. Even a regular shapedvolume may require many tetrahedral elements if it has a very large aspect ratio. Here, hexahedral or wedgeelements would be a better choice. Figure 3.2: Object with a Large Aspect Ratio (p. 10) illustrates this difference.It shows that the number of tetrahedral elements (a) is much larger than the number of hexahedral elements(b), if a similar mesh density is maintained on the transverse cross section.

Figure 3.2: Object with a Large Aspect Ratio

You can automatically refine a model meshed with HF119 elements. To decrease discretization error, theHFEREFINE macro refines elements that exceed a specified error limit. Moreover, based on the error indicatedby HFEREFINE, you can manually refine a model meshed with HF120 elements. For more information onthis capability, see Chapter 6, Adaptive Meshing (p. 63) in this guide and HFEREFINE in the Command Reference.

See HF118, HF119, and HF120 in the Element Reference for more details on these elements. Refer to High-Frequency Electromagnetic Field Simulation in the Theory Reference for the Mechanical APDL and Mechanical


Chapter 3: Elements and Commands Available in High-Frequency Electromagnetic Analysis

Applications for additional information on the tangential vector finite element method and vector basisfunctions.

You cannot use other ANSYS Emag electromagnetic elements in a high-frequency analysis. They are notbased on a full-wave formulation. They do not account for displacement current.

3.2. High-Frequency Commands

The following commands are helpful in conducting your high-frequency analysis:

High-Frequency Commands

Defines the frequency range in the harmonic response analysis.HARFRQ

Turns a high-frequency adaptive error calculation on or off.HFADP

Defines or displays spatial angles of a spherical radiation surface for antennaparameter calculations.

HFANG

Defines phased array antenna characteristics.HFARRAY

Calibrates S-parameter phase shift.HFDEEM

Specifies high frequency electromagnetic modal analysis options.HFEIGOPT

Automatically refines high-frequency tetrahedral elements (HF119) or listshigh-frequency brick elements (HF120) with the largest error.

HFEREFINE

Calculates electromagnetic field distribution for a modal port.HFMODPRT

Specifies a radiation scan angle for a phased array antenna analysis.HFPA

Calculates propagating constants and characteristic impedance of a transmis-sion line or waveguide over a frequency range.

HFPCSWP

Specifies input data for waveguide, modal, lumped gap, or plane wave ports.HFPORT

Calculates power terms of a multi-port network.HFPOWER

Specifies a high-frequency scattering analysis.HFSCAT

Indicates the presence of symmetry planes for the computation of high-fre-quency electromagnetic fields in the near and far field domains (beyond thefinite element region).

HFSYM

Defines impedance and calibration lines for excitation eigenfield.LPRT

Plots electric far fields and far field parameters.PLFAR

Plots reflection and transmission parameters of a frequency selective surfacesolution.

PLFSS

Plots the electric field in the near zone exterior to the equivalent source surface.PLNEAR

Converts and plots scattering, admittance, or impedance parameters on aSmith chart.

PLSCH

Converts and plots network parameters versus frequency or plots losses versusfrequency.

PLSYZ

Displays TDR/TDT waveforms, an impedance profile, or a total waveform.PLTD

Plots port transmission line data generated by the HFPCSWP or SPSWP macros.PLTLINE

Specifies a free-space time-harmonic incident plane electromagnetic wave.PLWAVE

Defines perfectly matched layers (PMLs) for a high-frequency analysis.PMLOPT

Determines number of PML layers.PMLSIZE



3.2. High-Frequency Commands

High-Frequency Commands

Prints electric far fields and far field parameters.PRFAR

Prints the electric field in the near zone exterior to the equivalent source sur-face.

PRNEAR

Prints the solution results for elements.PRNSOL

Converts and lists scattering, admittance, or impedance parameters.PRSYZ

Calculates the quality factor for high-frequency electromagnetic resonators.QFACT

Automatically refines a HF119 tetrahedral element mesh based on S-parameterconvergence.

SPADP

Performs frequency sweep or angle sweep calculations to determine reflectionand transmission parameters of a frequency selective surface.

SPFSS

Calculates scattering (S) parameters between ports of a network system.SPARM

Computes S-parameters over a frequency range and writes them to a file.SPSWP

Generates a SPICE subcircuit model using S-parameters from a Touchstonefile.

SPICE


Chapter 3: Elements and Commands Available in High-Frequency Electromagnetic Analysis

Chapter 4: Performing a High-Frequency Harmonic Analysis

As in any other type of ANSYS analysis, a harmonic high-frequency electromagnetic analysis consists of thesesteps:

Create a physics environment.

Build a model.

Assign regional attributes to the model and mesh it.

Apply boundary conditions and excitations (loads).

Obtain a solution.

Review the results.

The following flowchart illustrates these steps.

Figure 4.1: Flow Chart for a Harmonic Analysis



The following harmonic analysis topics are available:4.1. Creating the Physics Environment4.2. Building the Model, Assigning Region Attributes, and Meshing4.3. Applying Boundary Conditions and Excitations (Loads)4.4. Solving Harmonic High-Frequency Analyses4.5. Postprocessing Harmonic High-Frequency Analyses

4.1. Creating the Physics Environment

To begin, specify a jobname and a title for your analysis. If you are using the ANSYS Graphical User Interface(GUI) and you wish to perform high-frequency electromagnetic analysis, one of the first things you shoulddo upon entering the GUI is choose the following path: Main Menu> Preferences and select High Frequencyunder Electromagnetic. Doing this ensures that all of the GUI options you need for this type of analysis willbe available to you.

4.1.1. Specifying Element Types

Use either of the following to specify element type numbers and key options for HF119 and HF120:

Command(s): ET,ITYPE,Ename,KEYOPT(1),KEYOPT(2),KEYOPT(3),KEYOPT(4),KEYOPT(5)GUI: Main Menu> Preprocessor> Element Type> Add/Edit/Delete

KEYOPT(1) defines the polynomial order of the elements. KEYOPT(1) = 0 or 1 defines a first order elementwith a 0.5 order polynomial vector basis function. KEYOPT(1) = 2 defines a second order element with a 1.5order polynomial vector basis function. Greater accuracy is obtained using higher order elements (KEYOPT(1)= 2) at the expense of additional degrees of freedom internally generated by the element. The second orderelements are not available for pure scattering or periodic boundary condition problems. The following tableshows the number of DOFs per element.

Table 4.1 Element DOFs

Number of DOFs Per ElementElement Shape

2nd Order1st Order

124Quadrilateral

83Triangle

206Tetrahedral

5412Hexahedral

369Wedge

Not available8Pyramid

You cannot mix first and second order elements in a model. Both first and second order elements havemidside nodes to follow the curvature of a model. If you use MESH200 elements to generate 3-D high-fre-quency electromagnetic elements (HF119 or HF120) choose one of the MESH200 options for midside nodes,KEYOPT(1) = 5 for 3-D triangle elements or KEYOPT(1) = 7 for quadrilateral elements.

KEYOPT(4) allows you to specify element types for special high-frequency electromagnetic applications.KEYOPT(4) = 0 defines the normal element (default). KEYOPT(4) = 1 defines an electromagnetic wave absorbingelement referred to as a perfectly matched layer (PML) element. KEYOPT(4) = 2 defines a special scatteringelement. You need to specify KEYOPT(4) = 2 for the region of the domain receiving the reflected wave whenyou are using a soft magnetic field excitation source that propagates in one direction (BF,,H option). Forexample, the following command input listing defines first order normal and PML elements:


Chapter 4: Performing a High-Frequency Harmonic Analysis

et,1,119,1,,,0 ! define normal tetrahedral elementet,1,119,1,,,1 ! define PML tetrahedral element

See Perfectly Matched Layers (PML) (p. 24) for information on the PML element. See Surface Magnetic FieldSource (p. 36) for information on the scattering element and soft source magnetic field excitation.

The HF118 element applies only to modal analyses. Chapter 5, Performing a Modal High-Frequency Analys-is (p. 57) describes this type of analysis in detail.

4.1.2. Specifying the System of Units

ANSYS Emag - High Frequency always uses the MKS system. In the MKS system of units, free-space per

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