MURI Progress Review: Electromagnetic Simulation of Antennas and Arrays with Accurate Modeling of Antenna Feeds and Feed Networks PI: J.-M. Jin Co-PIs: A. Cangellaris, W. C. Chew, E. Michielssen Center for Computational Electromagnetics Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, Illinois Program Manager: Dr. Arje Nachman (AFOSR) May 17, 2005

Problem characteristics Problem Description Distributed feed network Antenna array elements Antenna/platform interactions Problem configuration  Complex structures  Complex materials  Multi-layers  Passive/active circuit elements  Complex structures  Complex materials  Active/nonlinear devices  Antenna feeds  Very large structures  Space/surface waves  Conformal mounting

Simulation techniques Solution Strategy Distributed feed network Antenna array elements Antenna/platform interactions Problem configuration Time/frequency- domain FEM Time/frequency- domain FEM & IE MLFMA/PWTD coupled with ray tracing Broadband macromodel FE-BI coupling

Accurate Antenna Feed Modeling Using the Time-Domain Finite Element Method Z. Lou and J.-M. Jin Center for Computational Electromagnetics Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, Illinois

Typical Feed Structures  Antenna element (opened for visualization of interior structures)  Details showing coaxial cable, microstrip line and radial stub.

Feed Modeling 1. Probe model (Simple & approximate) 2. Coaxial model (Accurate) At the port: Mixed boundary condition:

Waveguide Port Boundary Condition By mode decomposition: Feed Modeling

Frequency-domain operators: Time-domain operators: Inverse Laplacian Transform Conversion to Time Domain

Time-Domain WPBC Time-Domain Formulation: Assume dominant mode incidence:

Monopole Antennas Measured data: J. Maloney, G. Smith, and W. Scott, “Accurate computation of the radiation from simple antennas using the finite difference time-domain method,” IEEE Trans. A.P., vol. 38, July 1990.

Five-Monopole Array (Geometry) unit: inch Finite Ground Plane: 12’’ X 12’’ Thickness: 0.125’’ SMA Connector: Inner radius: 0.025’’ Outer Radius: 0.081’’ Permittivity: 2.0

Monopole Array (Impedance Matrix)

Feeding mode: Port V excited, Ports I-IV terminated. Freq: 4.7GHz Monopole Array (Gain Pattern)  = 135 o  = 45 o  = 0 o (x-z plane)  = 90 o (y-z plane)

2 X 2 Microstrip Patch Array unit: inch Substrate: 12’’ X 12’’ Thickness: 0.06’’ Permittivity: 3.38 SMA Connector: Inner radius: 0.025’’ Outer Radius: 0.081’’ Permittivity: 2.0

Patch Array (Impedance Matrix)

Impedance Matrix (FETD vs FE-BI)

Patch Array (Gain Pattern at 3.0GHz) y-z plane x-z plane _ _ + + Phasing Pattern: Feeding mode:

Antipodal Vivaldi Antenna Reflection at the TEM port “The 2000 CAD benchmark unveiled,” Microwave Engineering Online, July 2001

Radiation patterns at 10 GHz Antipodal Vivaldi Antenna H-plane E-plane

Layer-by-Layer Finite Element Modeling of Multi-Layered Planar Circuits H. Wu and A. C. Cangellaris Center for Computational Electromagnetics Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, Illinois

Layer-by-Layer Decomposition  3D global meshing replaced by much simpler layer-by-layer meshing  2D-meshing used as footprint for 3D mesh in each layer  3D mesh developed from its 2D footprint through vertical extrusion  If ground planes are present, they serve as physical boundaries between the layers  Otherwise mathematical planar surfaces are used to define boundaries between adjacent layers

Example of Layer-by-Layer Mesh Generation

Layer-by-Layer FEM Solution  FEM models developed for each layer  Overall solution obtained is developed through enforcement of tangential electromagnetic field continuity at layer boundaries  Assuming solid ground plane boundaries, layers interact through via holes and any other apertures present in the model  Direct Domain Decomposition-Assisted Model Order Reduction (D 3 AMORe)  Reduced-order multi-port” macromodels developed for each layer with tangential electric and magnetic fields at the via holes and apertures in the ground planes as “port parameters”  On-the-fly Krylov subspace-based broadband multi-port reduced-order macromodel generation  Overall multi-port macromodel constructed through the interconnection of the individual multi-ports

50-Ohm microstrip 50-Ohm stripline gap Absorbing boundary box Surface-mount cap Via hole Tunable bandpass filter with surface-mounted caps: Demonstration

The filter is decomposed into a microstrip layer and stripline layer. Ground planes are solid; hence, coupling between layers occurs through the via holes. microstrip layer (top)stripline layer (bottom) Connecting ports Input/output ports Connecting ports Pins used to strap together top and bottom ground planes Two Signal Layers

Reference Solution: Transmission line model with ideal 10 fF caps for modeling the gaps. Impact of vias is neglected. D 3 AMORe FEM Solution (w/o surface-mounted cap) Tunable band-pass filter (cont.)

Use of surface-mounted caps help alter the pass-band characteristics of the filter

Hybrid Antenna/Platform Modeling Using Fast TDIE Techniques E. Michielssen, J.-M. Jin, A. Cangellaris, H. Bagci, A. Yilmaz Center for Computational Electromagnetics Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, Illinois

 Higher-order TDIE solvers  TDIE solvers for material scatterers  TDIE solvers for surface-impedance scatterers  TDIE solvers for periodic applications  TDIE solvers for low-frequency applications  Parallel TDIE solvers  PWTD based accelerators  TD-AIM based accelerators  More accurate (nonlinear) antenna feed models  More complex nonlinear feeds  More accurate S- / Z- parameter extraction schemes  Symmetric coupling schemes between different solvers (including cable – EM interactions) Progress in TDIE Schemes Resulting from this MURI Effort Previous code Added

1) A higher-order MOT algorithm for solving a hybrid surface/volume time domain integral equation pertinent to the analysis of conducting/inhomogeneous dielectric bodies has been developed 2) This solver is stable when applied to the study of mixed- scale geometries/low frequency phenomena 3) This algorithm was accelerated using PWTD and TDAIM technology that rigorously reduces the computational complexity of the MOT solver from to 4) H1: Linear/Nonlinear circuits/feeds in the system are modeled by coupling modified nodal analysis equations of circuits to MOT equations 5) H2: A ROM capability was added to model small feed details 6) H3: Cable feeds are modeled in a fully consistent fashion by wires (outside) and 1-D IE or FDTD solvers (inside) Code Characteristics

Nonlinear Feed: Active Patch Antennas *B. Toland, J. Lin, B. Houshmand, and T. Itoh, “Electromagnetic simulation of mode control of a two element active antenna,” IEEE MTT-S Symp. Dig. pp , 1994.

Nonlinear Feed: Reflection-Grid Amplifier Amplifier built at University of Hawaii, supported through ARO Quasi-Optic MURI program. Pictures from A. Guyette, et. al. “A 16-element reflection grid amplifier with improved heat sinking,” IEEE MTT-S Int. Microwave Symp., pp , May 2001.

Each chip is a 6-terminal differential-amplifier that is 0.4 mm on a side RF input Bias RF Output & Bias RF input Bias Bias & RF Output *A. Guyette, et. al. “A 16-element reflection grid amplifier with improved heat sinking,” IEEE MTT-S Int. Microwave Symp., pp , May Nonlinear Feed: Reflection-Grid Amplifier

12 cm 8.0 cm 4 mm Interfacing with ROMs: Mixed Signal PCB with Antenna

-Full-wave solution only at the top layer -Dimension of the 11-port macro-model: 623 -Bandwidth of macro-model validity: 8 GHz -Plane wave incidence & digital switching currents Interfacing with ROMs: Mixed Signal PCB with Antenna

3 m 1.3 m 1.5 m 12 cm 8 cm Interfacing with ROMs: Mixed Signal PCB with Antenna

Received at port 8 Interfacing with ROMs: Mixed Signal PCB with Antenna

13.3 m 3.4 m 16.6 m King Air 200 Cable Feeds: TD LPMA Analysis

Antenna feed-point Antenna feed-network Cable Feeds: TD LPMA Analysis

* Dielectrics not shown 25 MHz 52 MHz 61 MHz 88 MHz Cable Feeds: TD LPMA Analysis

Using Loop Basis to Solve VIE, Wide- Band FMA for Modeling Fine Details, and a Novel Higher-Order Nystrom Method W. C. Chew Center for Computational Electromagnetics Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, Illinois

Volume Loop Basis  Advantages:  Divergence free  Less number of unknowns (A reduction of 30-40%)  Reduction in computation time  Easier to construct and use than other solenoidal basis, e.g. surface loop basis; no special search algorithm is needed.  Stable in convergence of iterative solvers even with the existence of a null space RWG BasisLoop Basis

Volume Loop Basis Example:

Volume Loop Basis Incident Wave: 1 GHz, –z to +z Relative permittivity: 4.0 No of tetrahedrons: 3331 No of RWG basis: 7356 (11.5) No of loop basis: 4965 (10.05) Basis reduction: 32.5% No of iterations: RWG: 159; Loop: 390 Bistatic RCS:

Full-Band MLFMA Incident Wave: 1 MHz θ = 45deg, Φ = 45deg No of triangles: 487,354 No of unknowns: 731,031 7 x 7 fork structure

X Y Z O t d a a=0.1 m d=3 m t=0.173 m f=1.0 GHz Novel Nystrom Method Scattering by a pencil target:

X Y Z O d a a=1 inch d=5 inchs f=1.18 GHz Scattering by an ogive: Novel Nystrom Method

Scattering by a very thin diamond: X YZO h a a Novel Nystrom Method

Higher-order convergence for ogive scattering: Novel Nystrom Method

Higher-order convergence for pencil scattering: Novel Nystrom Method

Conclusion FEM & ROM modeling of multilayer, distributed feed network (Cangellaris) Accurate, broadband antenna/array modeling with frequency- and time-domain FEM (Jin) Linear/nonlinear feeds, cable feeds, antenna/platform interaction, & TDIE/ROM integration (Michielssen) Full-band MLFMA, loop-basis for VIE, and higher-order Nystrom method (Chew) Past progresses: Future work: Hybridization of FEM and ROM to interface antenna feeds and feed network Hybridization of FEM and TDIE (TD-AIM & PWTD) or MLFMA to model antenna/platform interaction Parallelization to increase modeling capability