#### Read Pattern Synthesis, Aperture Design, and Radome Interaction for Complex Antenna Systems text version

Pattern Synthesis, Aperture Design, and Radome Interaction for Complex Antenna Systems

J. DeLap, Ansoft Corporation N. Hirth, Ansoft Corporation D. Thompson, Ansoft Corporation

Introduction

· Most antenna systems are rarely simulated using a 3D electromagnetic tool · System specifications are determined using a combination of Matlab code or spreadsheets · 3D simulations only take place on a component basis · Electrically large simulations not always attempted

Design Flow

· Single element simulation · Infinite array simulation · Finite array

· Radiator design and verification · Element weighting optimization · FSS radome design and optimization

· Finite Array combined with FSS radome

Phased Array Design

Basics

· Small single elements Low gain / difficult steering · Large single antennas High gain / difficult steering · Phased arrays many closely spaced antennas

· Work together High gain & steerable

· Phased array beam can be shaped by weighting element excitations

Phased Array Design

Pattern Creation

· The array's pattern is determined from a superposition of the individual element patterns

M E Array ( , ) = Am Em ( , ) m =1

where: Em(,) is the E-Field pattern of the mth element Am is the complex weighting of the mth element · The E-Field pattern for each element must include the mutual coupling of near by elements and structure. · Must be in the array environment · Em is not necessarily identical for all m elements

Infinite Array Calculations

· Assumptions

· Element pattern of every element is identical · Mutual coupling of every element taken into account · No edge effects included (well it is infinite) r

· Simplifications

· Element pattern can be factored out of summation

M

r`m,n

E Array ( , ) = E ( , ) Am e jk ( r·r `m ) = E ( , ) AP

m =1

· Unit Cell can be simulated instead of entire array reducing required simulation resources and time.

· Consequences

· Finite array effects are not accounted for

Finite Array Calculations

· Reality of Finite Array Analysis

· Element pattern of every element is not identical · Edge affects can be significant to array's performance · Entire array needs to be included in the simulation model · Significant increase in model complexity · Simulations can be very large and require large amounts of memory and time · Complicated interactions between array, radome and circuitry are not accounted for

· Challenges for Finite Array Modeling

Modeling Finite Arrays with HFSS

· New improvements in software make it practical to model finite arrays

· 64 bit solvers dramatically increases solvable model size · Improvements in Mesher produce better quality meshes with fewer adaptive passes · Improvements in Matrix Solver reduce simulation time · Scripting capabilities automate array construction and data exporting · External post-processing eliminates the need to model at multiple scan angles · Radome interaction included in the simulation through HFSS-to-HFSS DataLink

Single Element Design

Array element description

· Circularly polarized waveguide

Dielectric Sheath

· Circular waveguide element Dielectric Plug · Dielectrically loaded with a dielectric plug at the array aperture Dielectric Filled · Dielectric sheath used for wide-scan Waveguide performance · Triangular lattice (1.1008"x0.3178") allows scanning out to 60o · Design from Chao-Chun Chen,"Wideband Wide-Angle Impedance Matching and Polarization Characteristics of circular Waveguide phased Arrays", IEEE Trans. Antennas Propagat., vol. AP-22, pp 414-418, May 1974.

1.1008"

0.3178"

Single Element Simulation

Model Setup · Free-space element performance

· Shows how mutual coupling impacts the element's performance · Actually optimized for array environment

· Model creation

· Element drawn using cylinders and boxes · AirBox created above the element to allow for radiation · PML used on 5 sides of the AirBox to absorb the radiated energy and approximate free space environment · PML surface seeded to /6 for better pattern calculations

Single Element Simulation

Model Setup

· Port Setup

· WavePort placed at end of circular waveguide · 2 modes defined both polarized · Integration lines drawn for both TE11 modes

Single Element Simulation

Performance Results

Infinite Array Simulation

Infinite Array Simulation

· Unit Cell Creation

Model Setup

· Port Setup

· Same element that was used in single element simulation · Hexagonal Unit Cell drawn from polyline Master/Slave · Hexagon vertices derived from array lattice Boundaries · AirBox created by sweeping Unit Cell polyline · PML created on top face of AirBox · Master/Slave boundaries used to create array periodicity and include mutual coupling affects · Exactly the same as the single element simulation · 2 modes with integration lines defined for Waveguide port · Both modes are polarized to enforce field alignment

Integration Lines

PML

Infinite Array Simulation

Model Setup · Master/Slave boundaries steer the array to a desired scan angle · Scan performance determined from a series of simulations at different scan angles · Simulation time greatly reduced with Optimetrics and Distributed Solve Option

· Optimetrics allows you to sweep the parameterized scan angles and access all the results in the post-processor · Distributed Solve Option allows you to solve many scan angle instances simultaneously through a network of computers

Simulation used Distributed Solve Option (DSO)

· · · · 6 Machines + 1 Host DSO Elapsed Time: 43min One Machine Elapsed Time: 217 min Speed Increase Factor: 5.04 Array Active Impedance Over Scan Realized Swept Boresight Gain

Infinite Array Simulation

Finite Array Simulation

Finite Array Simulation

Model Setup · Array Creation

· Same element that was used in single element simulation · Script used to create array from single element design

· Unit Cell from single element copied into array configuration · Array shape chosen to be a hexagon · AirBox and PMLs updated for new antenna size

· Seeded Mesh on PML boundaries for better pattern calculations · Array terminated with rectangular dielectric sheath in a ground plane

· Port Setup

· 2 orthogonal TE11 modes defined on each waveguide port · 2 integration lines are defined and polarized

Finite Array Simulation

Boresight Performance Results

Array Pattern

Active Match

Finite Array Simulation

Statistics

· 37 Element Dual Polarized Array

· 3 Rings in triangular lattice · Tetrahedra: 116745 · Unknowns: 657288 · Memory: 2.25GB · Adaptive solution + 7 discrete frequency points · Solve Time: 5hours:51minutes:53seconds

Finite Array Simulation

Distributed Solve Option

· By utilizing the distributed power of Ansoft, the user can significantly cut down total simulation time.

... ...

· Simulation on one computer: 5 hours · Distributed simulation: 2.5 hours

Finite Array Pattern Synthesis

Deriving Scan Performance From Boresight Performance

· Array E-Field pattern is obtain from superposition of individual element patterns M

E Array ( , ) = Am Em ( , )

m =1

· The array is steered by adding a progressive phase shift to the element excitations (Am) M

E Array ( , ) = Am e jAm Em ( , )

m =1

[

]

· The Array Far-Field Pattern is calculated from this E-Field pattern 2 4U ( , ) 2 E Array ( , ) G Array ( , ) = = Pinc Pinc · The scanned array pattern can be quickly calculated in Matlab once the E-field patterns are exported from HFSS and the incident power (Pinc) is determined.

Finite Array Pattern Synthesis

· Export all antenna element patterns from HFSS ONCE! · Element patterns include ALL mutual coupling

Far-field patterns for arbitrary array weightings are calculated from element patterns in milliseconds!!

HOW?

Finite Array Pattern Synthesis

Element Patterns

· Excite each port independently · Export Re/Im parts of E and E electric farfield to files · A simple .vbs script automates the task

20 15 10

26 29 28 27 30 35 34 13 19 18 11 6 12

25 16 7 1 5 17 32

20 15 Re/Im E

24 14 2 3 4 10 31

23 20 15 9 8 36 33 21 22 37

5 0 -5 -10 -15 -20 -90 -60 -30 0 30 60 Theta [degrees] 90

Re/Im E

10 5 0 -5 -10 -90 -60 -30 0 30 60 Theta [degrees] 90

Finite Array Pattern Synthesis

Post-Process Exported Element Patterns

E(, )FarField =

m m

A (E

e

jE

^ ^ + E e jE

)

Weight for the mth element (declare this in MATLAB)

From exported HFSS element patterns

% Matrix summation method (total pattern for phi = 0 cut [for all theta]) Eth_sum_ph0 = Am * (abs(Eth0) .* exp(j*angle(Eth0))); Eph_sum_ph0 = Am * (abs(Eph0) .* exp(j*angle(Eph0))); = vector [1 x m] = matrix [m x length(theta_export)]

Finite Array Pattern Synthesis

Post-Process Exported Element Patterns to Obtain Far-Fields Resulting from Given Weights Left with

^ ^ E( , )FarField = E + E

Now find Etot

Etot = E + E

% In MATLAB Emag_tot_atPhi0cut = sqrt(abs(Eth_sum_ph0).^2 + abs(Eph_sum_ph0).^2);

Why didn't we just export Etot to begin with? The weights require proper phase information for pattern processing, and the phase from Etot is ambiguous.

Finite Array Pattern Synthesis

A Practical Example

· Syntesize a pattern with < -30dB sidelobes for all Phi

New pattern after optimizationweights Original pattern with uniform using MATLAB

0 Normalized Gain [dB] -10 -20 -30 -40 -50 -90

Phi 0 Phi = = 0 Phi 30 Phi = = 30 Phi 60 Phi = = 60 Phi = = 90 Phi 90

...and verified in HFSS

-60

And the exported element patterns allow far-field These will always be exactly the same! calculations to be completed almost instantly (msec).

-30 0 30 Theta [degrees]

60

90

Finite Array Pattern Synthesis

Boresight Gain

Original Results Scale 20dB to -20dB

Optimized Results

Sidelobes are maintained < -30 dB from peak for all phi!

Finite Array Pattern Synthesis

Determination of Element Weights · Pick Mag based on beam shape · Pick Angle distribution based on steering · Convert the array weights to the real/imaginary format

Am = Mag

Am = Mag cos( ) + jMag sin ( )

Finite Array Pattern Synthesis

Weighting for Beam Shaping/Steering

· Amplitude tapering for sidelobe reduction · Common weighting functions: · Dolph · Taylor · Binomial

+ +2 +3 +4 +5 +6

constant phase lines

Finite Array Pattern Synthesis

Beam Synthesis Example · Goal:

· Beam steer to = 15°, = 0°

· Procedure:

· Set magnitudes and phases in Matlab using specialized array functions · Calculate the far-field in Matlab with the element weights · Iterate as necessary to achieve the goal · Only ~ 0.034 sec per iteration to calculate the farfield!

Finite Array Pattern Synthesis

15° Steer

Uniform Excitation Optimized Excitation

For 15° steer a value of ~45° was needed

For 15° steer a value of ~50° was needed

A MATLAB optimization yielded the phases for the 15° steer.

Finite Array Pattern Synthesis

Returning Weights to HFSS · Am weights are "voltage" excitations multiplied by both E and E components · To get weights back in HFSS use these relationships: · The HFSS phase comes directly from the angle of Am

HFSSmag = 2*(|Am|)2 HFSSphase = angle_deg(Am)

Note: When N feeding polarizations are present, then N element patterns exist for each physical element. That does not change these equations, but then N Am vectors exist. They should be applied respectively to the excitations of each polarization.

FSS Radome Design and Optimization

FSS Radome Design

· Array needs to have an FSS embedded in the radome for:

· Jamming immunity · Minimize array RCS minimize detection

· Specifications

· Fo = 10.8 GHz · Valid out to 30° scan angle

FSS Radome Design

FSS Design

· Starting point

· "Frequency Selected Surfaces: Theory and Design," Ben Munk

· Simple cross slot array chosen · Variables

· Slot length · Slot Width · Unit cell

FSS Radome Design

FSS Design within unit cell · Unit cell parameterized in HFSS, and optimized for desired center frequency · Final design values

· · · · Slot length = 11.2 mm Slot width = 2 mm Unit cell = 14 mm Substrate thickness = 40 mil

FSS Radome Design

Scan Performance Verification

Increasing

Performance degrades with > 30 °

FSS Radome & Finite Array Linked Simulation

FSS & Finite Array simulation

· Let's put some of these pieces together · Utilize HFSS-to-HFSS DataLink so that fields from one project are the source of fields for a different project. · Distance between projects is arbitrary.

HFSS to HFSS DataLink

Overview

· Source project

· Radiation or PMLs set up normally

· Target project

· Radiation / PML BC Incident / Enforced · Incident Wave Far / Near Field

HFSS to HFSS DataLink

Example Source Model Target Model

HFSS to HFSS DataLink

Source Example

· Radiation BC on all faces of air box

HFSS to HFSS DataLink

Boundary Example

· Boundary Setup

· One face set as Radiation BC with Advanced Options · Rest normal Radiation BC

HFSS to HFSS DataLink

Incident Wave Setup Example

· Excitation setup

· Near Field Incident Wave

HFSS to HFSS DataLink

Data Link Options Example

· DataLink Options

Can modify mag/phase of sources in linked source

Can even modify geometry in linked source

HFSS DataLink Example - Results

Source Project

Target Enforced Field Near Field Incident Wave

Target Incident Field Far Field Incident Wave

FSS & Finite Array Simulation

Setup

1 inch separation

FSS & Finite Array Simulation

Results

What happened to our nice high directivity pattern ?

FSS & Finite Array Simulation

Factors determining Results

· FSS area too small · Increase FSS area, and re-simulate

FSS & Finite Array simulation

Double original FSS size

Sidelobes have gone down, but not as clean as original array

FSS & Finite Array simulation

Quadruple Original FSS Size

That's more like it !!

Conclusion

· It is feasible to simulate entire antenna systems with HFSS, users are no longer limited to single antenna simulations. · Utilizing HFSS scripting capability allows rapid synthesis of desired antenna performance. · Utilizing HFSS-to-HFSS DataLink allows the simulation of large antenna systems · Applications are far reaching from large finite arrays to complex antenna and environment interaction

#### Information

##### Pattern Synthesis, Aperture Design, and Radome Interaction for Complex Antenna Systems

55 pages

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