higher order floquet mode radiating elements
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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
HOFS Radiating Elementexample
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
Ohmegaplyresist load
Ohmegaplyresist load
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
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
( )xmn ymn zmnj k x k yxmn ymn jk zTM
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
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
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
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
( )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
TM Floquet Mode Voltage Distribution TM Floquet Mode Voltage Distribution
m mode numbern mode numbern mode number m mode numbern mode number
voltage amplitudevoltage amplitude
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
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
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
TM Floquet Mode Voltage Distribution TM Floquet Mode Voltage Distribution
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
voltage amplitudevoltage 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
HFSS Floquet Modes (modal indices (m, n))
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
Increasing number of modes
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
( )xmn ymn zmnj k x k yxmn ymn jk zTM
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
4Grating Lobe Lattice
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
4Grating Lobe Lattice
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
4Grating Lobe Lattice
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]
Active Element Pattern
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
Gore 100test position
-80 -60 -40 -20 0 20 40 60 80-60
-50
-40
-30
-20
-10
0
10
degreesga
in [d
B]
Active Element Pattern
-80 -60 -40 -20 0 20 40 60 80-60
-50
-40
-30
-20
-10
0
10
degrees
gain
[dB
]
Active Element Pattern
XPol
CoPol
Fractional array measured data E and H CoPol and XPol element position 2freq range : 9 to 10 GHz
Position 2: E Plane Pattern
Position 2: H Plane Pattern
E plane pattern improved because ofincreased distance from edge of array
E Plane
-80 -60 -40 -20 0 20 40 60 80-60
-50
-40
-30
-20
-10
0
10
degreesga
in [d
B]
Active Element Pattern
-80 -60 -40 -20 0 20 40 60 80-60
-50
-40
-30
-20
-10
0
10
degrees
gain
[dB
]
Active Element Pattern
XPol
CoPol
Position 4: E Plane Pattern
Gore 100test position
Fractional array measured data E and H CoPol and XPol element position 4freq range : 9 to 10 GHz
E plane pattern improved because ofincreased distance from edge of array
E Plane
Position 4: H Plane Pattern
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
-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
degrees
gain
[dB
]
Active Element Pattern
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]
Active Element Pattern
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]
Active Element Pattern
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
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
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