Higher Order Floquet Mode Radiating Elements

Higher Order Floquet Mode Radiating Elements (HOFS) in

Low Cost Phased Arrays

Michael J. Buckley, Ph.D.revised 12/16/2016

Active Element PatternE Plane

C Sandwich RadomeTM (Parallel) Polarization Return Loss

AbstractHOFS Radiating Elements vs. Patch Radiating Elements

• HOFS have lower cost – materials, material processing, balanced pcb, and larger unit cell size

• HOFS have higher performance – frequency, scan, and bandwidth

• HOFS flexibility - can emphasize unit cell size, performance, cost, or some combination

• HOFS can address radome integration, small arrays, and surface wave problems

Patch Radiating Element

HOFS Radiating Elementexample



Radiating Elements in Low Cost Active Electronically Scanned Arrays

•Radiating elements in current AESA systems

•Higher order Floquet Mode Radiating Elements (HOFS) in AESA systems

•Current topics in HOFS – radomes, small arrays, balanced printed circuit boards, and surface wave elimination

Current AESA Systems

• AESA systems are used primarily by the military

• Leading edge systems – state of the art technology

• Example would be the F-16 aircraft gimbal (mechanically steered) flat

plate radar is being replaced by an AESA radar

F-16 mechanically steered array

F-16 AESA

• Ability to rapidly track multiple targets

• Reliability ( mechanical gimbals fail)

• Graceful degradation (up to 5% element failure)

AESA Advantages

F-16

Su-27

Mig-29

AESA Front End Diagram

T/R Module

T/R Module

T/R Module

T/R Module

T/R Module

T/R Module

Radiating Element

AESA front end: radiating elements, manifold, and T/R modules

Radiating elements couple the T/R modules to free space

The T/R modules shape and steer the array beam

ground based AESA

Low Earth orbit satellitePotential ApplicationGround Based AESA Satellite Transmission

Radiating Elements in Airborne Military Array Systems

• Examine radiating elements in existing systems (mechanically steered and AESA)

• These radiating elements lack the required combination of low cost, scan performance and frequency bandwidth for low cost radar or UAV systems

F-16

Mig-29F-22

F-16 Flat Plate Antenna

• Narrow frequency band – slotted waveguide (too narrow for internet access applications)

• Mechanically steered – cost, volume, and reliability issues

Mig-29 AESACircular Waveguide Radiating Element

• Scan volume problems

• Manufacturing costs – circular waveguide elements filled with dielectric material

• Feed from module to circular waveguide will have issues

F-22 AESANotch Radiating Element

• Wide frequency band

• Polarization problems in the inter-cardinal plane

• Manufacturing costs

• Linear polarized only

Patch Radiating Elements in AESA Systems

• Low profile

• Planar

• Manufactured using modern printed circuit technologies (materials used are often problematic)

• Usually narrow frequency band (see comments on wide band patches on next page)

Patch Top Down View

etched metal

dielectric material

• Wide band patch radiating elements -dielectric materials are problematic (mixture of foam and Teflon )- unbalanced pcb

• Patch radiating elements in arrays - poor H plane scan performance - poor polarization performance - feed issues - tight array grid (modules $$)

• A radome is a separate item. Radome integration is expensive.

Patch Radiating Elements in AESA SystemsDisadvantages

Patch Cross Section

etched metal

dielectricmaterials

ground plane

radiating electromagnetic field

OneWeb radome

Low Profile Planar ArrayWish List for Low Cost AESA Systems• 20% or > frequency band, excellent scan

performance including polarization without a tight array grid

• Low cost dielectric (dielectric constant range 3 – 3.6 -> low material costs and low manufacturing costs - Rogers 4003, Rogers 3003, or FR-4 (Nelco materials)

• Balanced printed circuit board (pcb) for manufacturing

• Integrated radome

Patch ArrayTop Down View

etched metal

Patch Array Problems:

Poor scan performance

Dielectric material costs

Unbalanced pcb

Radome designed as a separate item

HOFS radiating elements solve the patch array problems

Higher Order Floquet Mode Scattering Structure (HOFS) vs. Patch

• Replace patch with Higher Order Floquet Mode Scattering Structure, replace patch stack with low cost materials

• HOFS can be aperture coupled or probe fed

• HOFS probe fed radiating elements address the patch probe fed H plane xpol problem

etched metalabove a groundplane

Patch HOFSexample

etched metalabove a groundplane

HOFSexample HOFS

example

Radiating Element Patch vs. HOFS Element

Patch element aperture stackis a combination of:Rogers 5880 Duroid (dk = 2.2)Rohacell HF 71 (dk = 1.09)

Patch frequency: 8-11 GHz

HOFS element aperture stack isRogers 3003 (dk = 3.0)

E field 2 mils above HOFS surface (HFSS)

E field 2 mils above patch Surface (HFSS)

HOFS frequency: 12 - 18 GHz

Radiating Element PerformanceHOFS Element vs. Patch 60 Degree H Plane Scan The patch element unit cell

size is significantly smaller than the HOFS element unit cell size

This HOFS elementis aperture coupled -excellent H plane polarization.

Patch frequency: 8-11 GHz

HOFS frequency: 12 - 18 GHz

Radiating Element Performance60 Degree E Plane ScanHOFS Element vs. Patch

-4 -2 0 2 4-4

-2

0

2

4Grating Lobe Lattice

• Wider frequency band for the HOFS radiating element than patch

• For the HOFS radiating element, gratings lobes are closer to visible space than the patch radiating element

8 – 11 GHz

12 – 18 GHz

Wide Scan Angle Performance HOFS Radiating Element n vs. frequency ( gain = (cos(theta))n ), theta = 60 degrees

E Plane

H Plane

Phi = 30.12 degrees

Phi = 59.88 degrees

Element is well behaved at scan angle closest to grating lobe

• Unit cell size HOFS is 1.76 times > conventional patch

• Assuming modules cost $ 100 each, a 1000 element HOFS element array would cost $76,000 less than a 1760 patch radiating element array.

• The HOFS array has larger scan volume and wider bandwidth than the conventional patch array

F-18 radar (LO)

Unit Cell Size ComparisonHOFS vs. Conventional Patch (EuCap 2007)

Dual Polarized Multi-Layer HOFS Radiating Element

• Examine the impact of the top HOFS layer

• Three cases will be considered: 1) no HOFS top layer 2) low frequency HOFS 3) high frequency HOFS

• Rogers 3003 material

top layer of HOFS

feed layer

HOFS Radiating ElementCross-sectional View

no HOFS top layer

low frequency HOFS

high frequency HOFS

Array Normal Scan Results Multi Layer HOFS Radiating ElementsSquare Grid Array with different HOFS Top layers

High frequency HOFShas the best scan performance

No HOFStop layer

Orthogonal slots share samebelow resonant cavity

HOFS Aperture Coupled Dual Polarized Radiating Element

Four unit cells are shown in theground plane view

• 19-21 GHz frequency band, dual polarized, no H plan scan problems

• Scan: +/- 45 degrees in the vertical plane +/- 10 degrees in the horizontal plane

• Largest possible unit cell sizenot an equilateral triangular grid

• Largest possible unit cell size minimizes cost

• Rogers 3003 material

Higher order Floquet modescattering layer addresses co-pol and x-pol requirements

unit cell size = .33λ2

one unit cell is shownin the HOFS view

HOFS Aperture Coupled Dual Polarized Radiating Element

2405/02/23The contents of this document are proprietary to Rockwell Collins, Inc.

Vertical axis45 degrees E plane scan

Horizontal axis10 degrees E plane scan

Vertical axis45 degrees H plane scan

19 GHz

21 GHzarray normal scancross talk is quite low~ -30 dB

unit cell size = .33λ2

HOFS Dual Polarized Radiating Element Measurement

• In order to test the radiating element, a fractional array was built

• E and H plane patterns were measuredPicture of fractionalarray in the range

PCB drawings courtesy of Mr. Dennis Manson

Measurements courtesy of Mr. Michael Davidson

Ohmegaplyresist load

Wilkinson power dividerto generate CP

Gore 100 interconnect

Four unit cells are shown



Axial Ratio MeasurementHorizontal Axis

E Plane Measurementscan in horizontal axissurface wave

Measurements courtesy of Mr. Michael Davidson

horizontal

verticalThe element is asymmetricin the horizontal, hence the pattern is asymmetric

HOFS Unit cell size and higher order Floquet mode scattering

27

E plane scan (horizontal)theta = 27.5 degrees

Smith chart plot of the return loss for the .33 λ2 unit cell radiating element for E and H plane scan along the horizontal axis for theta = 27.5 degrees. Scan blindness occurs in the E plane.

H plane scan (horizontal)theta = 27.5 degrees

unit cell area = .33λ2

HOFS Unit cell size, Floquet mode scattering, scan performance

• Reduce unit cell size from .33λ2 to .18λ2

• Redesign radiating element

• Scan blindness eliminated, scan to 50 degrees (< -10 dB return loss)

E plane scantheta = 27.5 degrees

H plane scantheta = 27.5 degrees

.33λ2 element .18λ2 element

E plane scanhorizontal axis50 degrees

H plane scanhorizontal axis50 degrees

array normal scan

HOFS Unit cell size, Floquet mode scattering, scan performance• In the .18λ2 radiating element reduce the etched

metal and hence the reduce the higher order Floquet mode scattering

• Scan performance degrades• Scan performance is recovered if the unit cell

area is contracted to .117λ2

.18λ2 element

metal eliminated degraded scan performance

Array normaland 50 degree scan

Array normaland 50 degree scan

reduced metal

horizontal axis scan50 degrees

.18λ2 element

reduced metal radiating element unit cell areacontracted - scanperformance improved

.117λ2 element

Performancewith metal

Printed Circuit Board ProducibilityHOFS Radiating Elements

• HOFS radiating elements are manufactured with standard design rules used by Teflon and FR-4 board shops

• Minimum printed circuit board etched metal width for all designs is 10 mils

• Minimum etched metal to etched metal separation distance for all designs is 10 mils

10 mils

10 mils

PCB metal

HOFS Radiating Element Performance Summary

• Higher order Floquet mode structures maximize radiating element performance with respect to unit cell size

• HOFS radiating elements use higher dielectric constant materials (lower material and processing costs)

• HOFS have relatively wide frequency band structures up at ~ 35 % Many innovative structures are possible (more than covered here)

• Next section will discuss why HOFS radiating elements out perform conventional patch radiating elements

HOFS Radiating Element Analysis• Quarter wave transmission line – example of a

transmission line matching structure

• Analysis of HOFS and patch in a periodic structure – electromagnetic field matching structure

• Floquet modes – eigenmodes of a unit cell in an infinite periodic array

• Floquet mode decomposition algorithm – illustrate scattering differences between HOFS and patch

HOFS Array

Patch Array

Quarter Wave Transformer

• Quarter transformer can be viewed as multiple reflections from z1 z2 boundary and z2 zload boundary resulting in low overall return loss

• If the impedance and length of z2 are chosen correctly, a relatively wide band match results

• A patch or HOFS in an array operates in a similar manner, however; a patch or HOFS is a multimode vector field matching problem not a single mode transmission line problem

zloadz1

λ/4 standing wave region

HOFS and Patch as a Matching structure

PatchHOFS

top down view

cross sectionalview

Wave hits the top HOFS metal layer- multiple reflections from the top HOFS metal, the other metal layers, and ground plane occur (similar to a ¼ wave transformer)

ground plane

dielectric layer, standingwave

etched metal

incident wave

Array HOFS or Patch Multimode Vector Field Matching

•The scan direction, vector, and multimode characteristics of the E field significantly affect the match

•The interior elements of a large array are analyzed using a periodic boundary approach – Floquet mode analysis.

•Edge elements are problematical.

dielectric layerstanding wave

HFSS modelcross sectionalview, wave incident on HOFS

HFSS modeltop downunit cell view

Large Finite Array Analysis

• The large finite array is approximated as an infinite array. This is a reasonable approximation for elements in the interior of the array.

• Floquet mode analysis is used to analyze a unit cell of the infinite array. Floquet modes are the eigenmodes of a unit cell with uniform dielectric or vacuum cross section in an infinite array

unit cell, buildingblock of finite array

Part of a large finite array

Vector and Multimode Electromagnetic FieldsFloquet Modes

•A Floquet mode meets the unit cell periodic boundary conditions and solves the wave equation

• There are both propagating and evanescent Floquet modes.

•For both patches and HOFS, evanescent Floquet modes are required to meet the boundary condition of scattering from etched metal (~ pec) on a planar surface

triangular grid unit cell

square grid unit cell

wave equation

• Incident wave on an etched metal

• Reflected wave combines with incident wave to meet Etan = 0 boundary condition on pec surface

• If only the propagating Floquet modes are involved in the scattering, then magnitude of the reflected power is equal to the magnitude of the incident power since Etan = 0 on the etched metal Note further, it follows that that Etan = 0 on the entire surface

pec surfaceEtan = 0

Incident waveE field

Scattering from an HOFS or patch radiating element etched metal top layer evanescent modes must be included

Propagating Floquet Modes Rectangular Unit CellPlane Waves – Two Orthogonal Polarizations

a

b

E field vector

E field vector

Propagating Floquet Modes Triangular Unit CellPlane Waves – Two Orthogonal Polarizations

a

b

E field vector

E field vector

Evanescent TM Floquet Modes: Rectangular Array

x axis

y axis

a

b

0 0

0 0

0

0

0 0 0

0

2 2 2

sin( )cos( )sin( )sin( )

2

2

x

y

xmn x

ymn y

r

zmn xmn ymn

k kk k

mk kank kb

k w

k k

k k k k

( )

2 2

ˆ ˆˆ

( )xmn ymn zmnj k x k yxmn ymn jk zTM

mn

zmn

xk yke e e

ab k k

2 2 2

2 2 2

for m 0 or n 0,

0

mode is evanescent

zmn xmn ymn

xmn ymn

k k k k

k k k

Evanescent TM Floquet Modes: E field in x direction (array normal scan, theta = 0) Rectangular Array

x axis

y axis

a

b

0

0

0 0 0

0

2 2

00

2

0

(2 / )

x

y

xmn

ymn

r

zmn

kk

mka

k

k w

k k

k k m a

((2 / ) )ˆˆ zmnjk zTM j m a xmn

xe e eab

2 2

2 2

(2 / )for m 0,

(2 / ) 0mode is evanescent

zmnk k m a

k m a

vertical axis symmetry

Symmetry Considerations : Incident E field in x direction (array normal, theta = 0)Scattering must be symmetric w.r.t. patch in the horizontal axis

2 2(2 / )0 0

ˆ2ˆ ˆ cos(2 / ) jz k m aTM TMm m

xe e m x a eab

2 2(2 / )

0

ˆcos(2 / ) z m a k

scattered mm

xE A m x a eab

m = 0 term is the reflected plane wave, propagating wavem ≠ 0 terms are reflected modes, evanescent waves,Note that the scattered fields (see slide 53 in particular) do have y dependence. There are some low order TE fields scattered by the patch pec surface. These fields are also evanescent.

x axis

y axis

TM1,0 + TM-1,0 Floquet modes. These are evanescent modes.

E field maxima

Evanescent Floquet Modes Rectangular Unit Cell E Plane Scan Theta = 0 degrees

On the patch surface, tangential E field = 0, lower order Floquet (1,0 and 2,0) modes are required to meet the boundary condition over the continuous metal surface

~ pec boundary, tan E = 0

HFSS fields

cos(2 / )x aa/2

TM2,0 + TM-2,0 Floquet modes. These are evanescent modes. .

E field maxima

Evanescent Floquet Modes Square Unit Cell E Plane Scan Theta = 0 degrees ~ pec boundary, tan E = 0

On the patch surface, tangential E field = 0, lower order Floquet (1,0 and 2,0) modes are required to meet the boundary condition over the continuous metal surface

HFSS fields

cos(4 / )x aa/2

Evanescent TM Floquet Modes: Triangular Array

0 0

0 0

0

0

0 0 0

0

2 2 2


2

2 2tan

x

y

xmn x

ymn y

r

zmn xmn ymn

k kk k

mk kam nk k

a b

k w

k k

k k k k

( )

2 2

ˆ ˆˆ


mn

zmn

xk yke e e

ab k k

b

a/2

tan 2 /b a

2 2 2

2 2 2

for m 0 or n 0,

0

mode is evanescent

zmn xmn ymn

xmn ymn

k k k k

k k k

Evanescent TM Floquet Modes: Incident E field in x direction (array normal, theta = 0)

0

0

0 0 0

0

2 2

00

2

0

(2 / )

x

y

xmn

ymn

r

zmn

kk

mka

k

k w

k k

k k m a

(2 / ), /2

ˆˆ zmnjk zTM j m a xm m

xe e eab

b

a/2

tan 2 /b a

1) Incident field is linearly polarized in the x direction

2) Because of the symmetry of the etched metal, scattered fields are linearly polarized in the x direction

3) k =0, hence m = 2nymn

Symmetry Considerations: Scattering must be symmetric w.r.t. patch in the horizontal axis

2 2(2 / ), /2 , /2

ˆ2ˆ ˆ cos(2 / ) jz k m aTM TMm m m m

xe e m x a eab

2 2(2 / )

0,2,4

ˆcos(2 / ) z m a k

scattered mm

xE A m x a eab

m = 0 term is the reflected plane wave, propagating wavem ≠ 0 terms are reflected modes, evanescent wavesonly modes with indices (m,m/2) are reflectedAs with the patch, there is y dependence in the scattered fields indicating TE mode content. As shown in slide 53, the evanescent modal content for the HOFS radiating element is higher order.

TM10,5 + TM-10,-5 Floquet modes. These are evanescent modes.

E field maxima

Evanescent Floquet Modes Triangular Unit Cell E Plane Scan Theta = 0 degrees

On the HOFS surface, tangential E field = 0, higher order Floquet (10,5) modes are required to meet the boundary condition over the non-continuous metal surface

~ pec boundary, tan E = 0

HFSS fields

cos(20 / )x a

a/2

Evanescent Floquet Mode Scattering

• The scattered evanescent modes determine the performance of the HOFS and patch radiating elements

• The next section will discuss how to determine the modes scattered from the HOFS and patch radiating elements

Floquet Mode Decomposition Algorithm• Export E fields from plane 2 mils above top

HOF layer or patch layer into MATLAB (higher order Floquet modes are evanescent)

• The Floquet modes, form a complete orthonormal set, the Floquet modes are TE and TM ( + TEM for array normal scan)

HFSS E field exported two milsabove the top HOF layer

HFSS E field exported two milsabove the top patch layer These equations were solved

numerically in MATLAB (FortranMathematica, Python would also work)

electric field vectorfrom HFSS

voltageorthonormal Floquet modes

HFSSTMmnm

TMmnTEmnm

TEmn EeVeV

TEmnHFSSTEmn eV E

TMmnHFSSTMmn eV E

Array Normal TM Floquet Mode Expansions: Patch and HOFS

TM Floquet Mode Voltage Distribution TM Floquet Mode Voltage Distribution

m mode numbern mode number n mode number

m mode numbern mode number

voltage amplitudevoltage amplitude

Patch voltage amplitudes cluster about thedominant plane wave

HOFS voltage amplitudes are higher order spread awayfrom the dominant plane wave

dominantTM0,0 mode

dominantTM0,0 mode

Floquet Mode ExpansionArray Normal ScanTE and TM modes

HFSS Floquet Modes (modal indices (m, n))

The Floquet mode expansion for the patch convergesfaster than the Floquet mode expansion for the HOFS

|(m, n)|≤ 5 |(m, n)|≤ 10 |(m, n)|≤ 20 |(m, n)|≤ 45

Increasing number of modes

E Plane 60 Degree Scan TM Floquet Mode Expansions: Patch and HOFS

dominantTM0,0 mode

dominantTM0,0 mode

Patch voltage amplitudes cluster about thedominant plane wave

HOFS voltage amplitudes are higher order spread awayfrom the dominant plane wave

TM Floquet Mode Voltage Distribution

TM Floquet Mode Voltage Distribution

m mode numbern mode numberm mode numbern mode number

Floquet Mode ExpansionE Plane Scan theta = 60 degreesTE and TM modes



|(m, n)|≤ 5 |(m, n)|≤ 10 |(m, n)|≤ 20 |(m, n)|≤ 45


HFSS result

Voltage Amplitude Distribution and Radiating Element PerformanceE Plane 60 Degree Scan

TM10,5 + TM-10,-5 Floquet modes

TM1,0 + TM-1,0 Floquet modes

Admittance (frequency)HOFS radiating element higher order mode scattering reduced admittance variation over frequency vs. patch element

HOFS magnitude of scattering is lower hence the reactive fields are reduced relative to a patch element

Patch is in a tighter unit cell and has lower dielectric constant material. Variation (and hence performance) would be much worse in a larger unit cell and higher dielectric constant material

Evanescent TM Floquet Modes: Triangular Array H Plane Scan Phi = 90 Degrees

0 0

0 0

0

0

0 0 0

0

2 2 2


2

2 2tan

x

y

xmn x

ymn y

r

zmn xmn ymn

k kk k

mk kam nk k

a b

k w

k k

k k k k

( )

2 2

ˆ ˆˆ

( )xmn ymn zmnj k x k yxmn ymn jk zTE

mn

zmn

xk yke e e

ab k k

b

a/2

tan 2 /b a

2 2 2

2 2 2

for m 0 or n 0,

0

mode is evanescent

zmn xmn ymn

xmn ymn

k k k k

k k k

Evanescent TM Floquet Modes: Triangular Array H Plane Scan Phi = 90 Degrees

0

0 0

0

0 0 0

0

2 2 20

0sin( )

2

(2 / ) ( sin( ))

x

y

xmn

ymn y

r

zmn

kk k

mka

k k

k w

k k

k k m a k

0

02 2

((2 / ) sin( ) )

ˆ ˆ(2 / ) sin( )ˆ( )

zmn

TMmn

zmn

j m a x k y jk z

x m a ykeab k k

e e

b

a/2

tan 2 /b a

H Plane 60 Degree Scan TM Floquet Mode Expansions: Patch and HOFS


m mode numbern mode numbern mode number m mode numbern mode number


Patch voltage amplitudes cluster about theorigin

HOFS voltage amplitudes are higher order spread awayfrom the origin

H Plane 60 Degree Scan TE Floquet Mode Expansions: Patch and HOFS

TE Floquet Mode Voltage Distribution TE Floquet Mode Voltage Distribution

m mode numbern mode numbern mode number m mode numbern mode number

Patch voltage amplitudes cluster about theorigin

HOFS voltage amplitudes are higher order spread awayfrom the origin

dominantTE0,0 mode

dominantTE0,0 mode

voltage amplitude

Floquet Mode ExpansionH Plane Scan theta = 60 degreesTE and TM modes



|(m, n)|≤ 5 |(m, n)|≤ 10 |(m, n)|≤ 20 |(m, n)|≤ 45


HFSS result

Multi Layer HOFS Radiating ElementsArray Normal Scan Results with two different HOFS layers

low frequencyHOFS

high frequencyHOFS

Array Normal TM Floquet Mode Expansions: Patch and High Frequency


m mode numbern mode number n mode number

m mode numbern mode number

voltage amplitude

Low frequency HOFS voltages have higher amplitude

High frequency HOF voltages have lower amplitude


m mode numbern mode number m mode numbern mode number

dominantTM0,0 modedominant

TM0,0 mode

Floquet Mode ExpansionArray Normal ScanTE and TM modes


The Floquet mode expansion for the low frequency HOFS converges slightly slower than the high frequency HOFS

|(m, n)|≤ 5 |(m, n)|≤ 15 |(m, n)|≤ 25 |(m, n)|≤ 50


Evanescent TM Floquet Modes: Triangular ArrayDual Polarized Array

0 0

0 0

0

0

0 0 0

0

2 2 2

sin( ) cos( )sin( )sin( )

2

2 2tan

x

y

xmn x

ymn y

r

zmn xmn ymn

k kk k

mk kam nk k

a b

k w

k k

k k k k

( )

2 2

ˆ ˆˆ


mn

zmn

xk yke e e

ab k k

b

a/2

tan 2 /b a

2 2 2

2 2 2

for m 0 or n 0,

0

mode is evanescent

zmn xmn ymn

xmn ymn

k k k k

k k k

Evanescent TM Floquet Modes: Triangular GridArray Normal ScanVertical Polarization, phi = 0

0

0

0 0 0

0

2 2

00

2

0

(2 / )

x

y

xmn

ymn

r

zmn

kk

mka

k

k w

k k

k k m a

((2 / ) )ˆˆzmnjk zj m a x

TMmn

xe eeab

b

a/2

tan 2 /2

b am n

2 2

2 2 2

(2 / )for m 0 or n 0,

0

mode is evanescent

zmn

xmn ymn

k k m a

k k k

Evanescent TM Floquet Modes: Triangular GridArray Normal ScanHorizontal Polarization, phi = 90 degrees

0

0

0 0 0

0

2 2

00

02

(2 / )

x

y

xmn

ymn

r

zmn

kk

knkb

k w

k k

k k n b

b

a/2

tan 2 /0

b am

2 2

2 2 2

(2 / )for m 0 or n 0,

0

mode is evanescent

zmn

xmn ymn

k k n b

k k k

((2 / ) )ˆˆzmnjk zj n b x

TMmn

ye eeab

Top HOFS LayerDual Polarized Radiating ElementVertical and Horizontal Polarization

Vertical PolarizationE field 2 mils above top HOF Layer

Horizontal PolarizationE field 2 mils above top HOF Layer

Voltage Amplitude DistributionArray Normal Scan TM Modes

Voltage modal amplitude distribution for the TM Floquet modes for the horizontal excitation(left) and the vertical excitation(right)

dominantTEM mode

dominantTEM mode

m mode numbern mode number m mode numbern mode number

HOFS Radiating Element Analysis Summary

• Because of the fragmented nature of the HOFS etched metal surface, higher order Floquet modes are scattered from the HOFS surface while lower order Floquet modes are scattered from the continuous conventional patch etched metal surface

• Higher order Floquet modes are less variable over frequency and scan than lower order Floquet modes. A matched HOFS radiating element will have wider frequency band and larger scan volume than a patch radiating element

• HOFS performance can be traded off for higher dielectric constant material, large unit cell size, or balanced pcb stack

manifold layerfeed layer

aperture layer

AESA Cross-Sectional ViewAperture Coupled

manifold layer

aperture layer

AESA Cross-Sectional ViewProbe Coupled

probe feedto module

T/R Module Coupling to Radiating Elements

Probe fed patch radiating elements have H plane scan problemsHigher Order Floquet Mode probe fed radiating elements scan well in the H planeA probe fed radiating element eliminates the feed layer , significantly reducing cost

manifold layerfeed layer

aperture layer

AESA Cross-Sectional ViewAperture Coupled

manifold layer

aperture layer

AESA Cross-Sectional ViewProbe Coupled

probe feedto module

T/R Module Coupling to Radiating Elements

Coupling mechanism, aperture or probe coupled, must be included in the design from the initial stage.

HOFS Radiating Element in a Non-uniformly Spaced AESAAnalysis and Measurement

• Application is a non-uniformly spaced 1D ESA

• Radiating element must be stripline fed

• Stripline feed layer must allow integration of manifold layer

• Will trade frequency bandwidth for ease of integration

interior radiating element unit cell edge radiating

element unit cell

E Plane

-4 -2 0 2 4-4

-2

0

2


grating loberectangular grid

grating lobetriangular grid

Radiating Element Requirements• Frequency 9.4 – 9.5 GHz

• Linearly polarized

• Scan Volume: E Plane +/- 30 degrees, array normal H plane

Grating lobe lattice for an equilateral triangular grid radiating element and a square grid radiating element

The unit cell areas of the triangular and square grid array are equal.

The grating lobes for the square grid lattice are closer to visible space

visible space

Grating Lobe Lattice

Voltage Amplitude DistributionE Plane Scan, theta = 30 degrees TM Modes

HFSSTMmnm

TMmnTEmnm

TEmn EeVeV

narrow and wide element modal amplitudes are spread away the dominant plane wave

TM0,0 mode

Array Normal Scan Narrow and Wide Unit Cell Radiating Elements 9 – 10 GHz

• Narrow unit cell radiating element has much less impedance variation than the wide unit cell radiating element at array normal scan

9 - 10 GHz

-4 -2 0 2 4-4

-2

0

2


visible space

E Plane 30 Degree Scan Narrow and Wide Unit Cell Radiating Elements 9 – 10 GHz

9 - 10 GHz

-4 -2 0 2 4-4

-2

0

2


visible space

• Narrow unit cell radiating element has much less impedance variation than the wide unit cell radiating element at 30 degree E plane scan

Radiating Element TestingUniformly Spaced Fractional Array

Fractional array – Gore 100interconnect is circled.

Enlarged view of fractional array,the majority of the radiating elements are terminated in ohmegaply resist loads

Drawing courtesy ofMr. Dennis Manson

• Initial testing step – build a uniformly spaced fractional array

• Done to verify basic design, HFSS modeling• Nonuniformly spaced array analyzed in CST

and measured in a fractional array

stripline

ohmegaplyresistormaterial

Ohmegaply load return loss (frequency)

Radiating Element TestingUniformly Spaced Fractional Array • Most of the fractional array radiating

elements are terminated in ohmegaply resist material loads

• Gore 100 interconnects ~ $25.00. Gore 100 loads ~ $15.00 400*($40) = $16,000

Measurements courtesy ofMr. Michael Davidson

Gore 100

-80 -60 -40 -20 0 20 40 60 80-60

-50

-40

-30

-20

-10

0

10

degrees

gain

[dB

]

Active Element Pattern

-80 -60 -40 -20 0 20 40 60 80-60

-50

-40

-30

-20

-10

0

10

degreesga

in [d

B]


XPol

CoPol

Gore 100test position

Some distortion in E plane pattern dueto close proximity to edge of array

Position 1: E Plane Pattern

Fractional array measured data E and H CoPol and XPol element position 1freq range : 9 to 10 GHz

E Plane

Position 1: H Plane Pattern


-80 -60 -40 -20 0 20 40 60 80-60

-50

-40

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-20

-10

0

10

degreesga

in [d

B]


-80 -60 -40 -20 0 20 40 60 80-60

-50

-40

-30

-20

-10

0

10

degrees

gain

[dB

]


XPol

CoPol




E plane pattern improved because ofincreased distance from edge of array

E Plane

Measured data summary chart

• For all cases, gain is consistent• Pattern cleans up with more elements

around radiating element lower XPol, symmetrical CoPol, better performance at wide scan angles

-80 -60 -40 -20 0 20 40 60 80-60

-50

-40

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10

degrees

gain

[dB

]


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10

degrees

gain

[dB

]


Position 3 Position 4

E Plane Pattern

Gore 100test position 4

Gore 100test position 3

Array Measurements

• 1D AESA array tested on a ‘stick by stick’ basis

• E and H plane patterns from each stick were measured

• Note that the E plane measurement is a manifold port 28 element stick two element array pattern.

one ‘stick’ of the array

H Plane E Plane

-90 -60 -30 0 30 60 90-40

-30

-20

-10

0

10

20

angle [degrees]

mag

nitu

de [d

B]


H Plane Plots28 Element Horizontal SticksMeasured at 9.44 GHz

Patterns look good overallHigh sidelobe (~2 dB) due tonon-uniform element pattern

H planePeak side lobes ~ -23 dBworst case

Xpol

PCB drawings courtesy of Mr. Dennis Manson

28 element stick

E Plane Plots28 Element Horizontal SticksMeasured at 9.44 GHz

28 element stick

-90 -60 -30 0 30 60 90-40

-30

-20

-10

0

10

20

angle [degrees]

mag

nitu

de [d

B]


E plane

Patterns look good overallSome variation due to locationof horizontal (H plane) sticksw.r.t. to the edgeXpol

AESA’s in the Real WorldAESA radiating elements are designed and tested without a radomeA radome protects the AESA from the environmentRadomes have significant impact on AESA performance, particularly at wide scan anglesEven without a radome, AESA performance is impaired at wide scan angles(return loss, polarization, and projected aperture)

Open Literature Example of an Antenna Radome System

http://mms.businesswire.com/media/20150316005260/en/457593/5/2182838_Rockwell_Collins_ESA_Antenna_Label%5B1%5D.jpg

Impact of radome on AESA

Quartz skins 30 mils minimum

Foam cores 180 mils

Cross Sectional View Ku band C Sandwich Radome• C sandwich for bandwidth

• 30 mil quartz skins to meet structural requirements

• 30 mil quartz at Ku band is a real hit on performance

Side View Ku band C Sandwich Radome and AESA Transmit Mode TM Polarization

Radome

AESA

Direction of PropagationE field vector

Side View Ku band C Sandwich Radome and AESA Transmit Mode TE Polarization

Radome

AESA

Direction of PropagationH field vector

E field vector

Independent of radiating element, the radome isa significant source of return loss for TM polarization radiating element loss < -10 dB

Radome

AESA

Radome

AESA

Independent of radiating element, the radome isa significant source of return loss for TE polarizationradiating element return loss should be < - 10 dB

H field vector

Gogo 2Ku Flight Demo

Low Cost AESA’s and Radome Integration• A radome is a significant source of loss for an AESA

system (return loss and also insertion phase delay for CP systems)

• Increasing the array power results in weight, heat, and input power increases (cost increases)

• This is an issue for ground based and airborne systems

• It is possible to integrate a Higher Order Floquet radiating element with a radome and avoid the performance hit of a separate radome

Low Cost AESA Printed Circuit Board Stack RequirementsLow cost FR-4

Odd number of layers

Balanced PCBsymmetric structure layer 1 = layer 5 layer 2 = layer 4

If the board vendor getsall the items on their wish list,they will add additional items

Layer 1

Layer 5

Layer 4

Layer 2

Layer 3

metal layers

Balanced Printed Circuit Board• If a printed circuit board is not balanced, the board

may be warped during manufacturing

• Board shops can learn to manufacture an unbalanced board- it is expensive and time consuming

• Captive board shop problem

• It is possible to design an HOFS radiating element with a balanced PCB

Examples of printed circuit board warp

Small AESA Systems100 Active Elements

For a small AESA system, the edge elements havepoor active element patterns and reduced gain

36/100 elements are edge elements (100 element array)

76/400 elements are edge elements (400 element array)

Small AESA Systems100 Active Elements96 Edge Elements

The edge element patterns can be improvedby using dummy elements or by surroundingthe array with mag ram. There is a cost/volumeproblem

Edge element treatments and cost issues• Using mag ram or extra elements requires surface array that

may not be available (UAV systems!!!)• They are expensive • It is possible to design a Higher Order Floquet mode radiating

element that has good edge behavior w/o mag ram or dummy edge elements

Array Calibration, Mutual Coupling, and Surface Waves

• Measuring mutual coupling is one possible method of calibrating an AESA

• When an element is excited, surface waves radiate along the surface

• The reflection of the surface from the board edges can drastically affect the mutually coupling measurement and must be accounted for in the calibration procedure.

PCB AESA aperturetop down view(triangular gridcase)

Summary

• HOFS radiating elements are a critical component of low cost AESA systems

• Discussed HOFS radiating element performance

• Floquet mode decomposition showed why HOFS elements provide superior performance

• Current areas of HOFS research include: radome integration, printed circuit board stack, and array edge radiating element behavior

References

[1] J. Herd, “Scanning Impedance of Proximity Coupled Microstrip Antenna Arrays”, Ph.D. thesis, University of Massachusetts at Amherst, thesis advisor Prof. D. Pozar, 1989

[2] A series of papers on higher order Floquet mode scattering was presented at the Allerton Antenna Conference in Allerton, Illinois by M.J. Buckley, et al. from 2008 – 2013. Additional work was published at the 2011 APS/URSI Antenna Conference in Boulder, CO and the 2011 IEEE APS Conference in Spokane, Washington

[3] www.ansys.com

[4] www.cst.com

[5] www.mathworks.com

[6] www.wolfram.com

http://www.ansys.com/

http://www.cst.com/

http://www.mathworks.com/

References continued[7] Robert J. Mailloux, “Phased Array Antenna Handbook,” Chapter 6, Artech House, 1994

[8] R. Erickson, R. Gunnarsson, T. Martin, L. –G. Huss, L. Pettersson, P. Andersson, A. Ouacha, “Wideband and Wide Scan Phased Array Microstrip Patch Antennas for Small Platforms,” Antennas and Propagation, 2007 EuCAP 2007 The Second European Conference on, 11-16 Nov. 2007 Page(s):1-6

[9] S. D. Targonski, R. B. Waterhouse, D. M. Pozar, “Design of Wide-Band Aperture-Stacked Patch Microstrip antennas,” IEEE Transaction on Antennas and Propagation, vol. 46, no. 9, Sept 1998, Pages 1245 - 1251 [10] Arun K. Bhattacharyya, “Phased Array Antennas: Floquet Analysis, Synthesis, BFNs, and Active Array Systems, Chapters 2-3 Wiley, 2006

[11] D. Pozar and D. Schaubert, “Scan Blindness in Infinite Arrays of Printed Dipoles,” IEEE Trans. Antennas and Prop. , Vol. AP-32, pp. 602-610, June 1984

Michael J. Buckley, LLC focuses on the design and testing of antennas, manifolds, and radomes and on planar array synthesis, including shaped beam synthesis for non-separable planar arrays. Mike Buckley developed higher order Floquet mode scattering radiating elements to address the packaging, cost, and performance requirements of low cost AESA systems, antenna radome integration, and small array systems. He also developed local search algorithm techniques for large variable non-convex shaped beam synthesis problems. He previously worked at Rockwell Collins, Northrop-Grumman, Lockheed-Martin, and Texas Instruments. He has numerous patents and publications. He has a Ph.D. in electrical engineering and is a member of Phi Beta Kappa.

HFSS Floquet Modes increasing number of modes

Higher Order Floquet Mode Radiating Elements

Engineering

Transcript of Higher Order Floquet Mode Radiating Elements