Electronic Scanned Array Design
SCF01 John S. Williams
The Aerospace Corporation (retired)
Slide 1 of 255
Course Objectives
• Provide a basic understanding of ESA design principles, history and applications – Presentation will focus on antenna hardware – Radar antennas are the focus of this presentation • Communications and receive antennas differ only in details – ESA functionality enables or enhances radar modes but radar modes will not be addressed in any detail
Slide 2 SCF01 Electronic Scanned Array Design of 255 Abstract
Design Principles and Approaches GfGeneral design principles of aperture antennas are applied to the specific case of ESA design. System applications set the framework for requirements allocation and flowdown. Antenna Architectures and Functional Partitioning The advantages and disadvantages of ESA and reflector antennas as well as ESA feeds for reflectors are compared and contrasted. Common ESA design issues are described, including array partitioning and subarrays, lattice tradeoffs, feed design, causes and mitigation of sidelobes, beam steering approaches and techniques for beam shaping. Numerical examples using Matlab illustrate performance of specific designs. Practical Design Considerations ESA performance is constrained by the selection and limitations of specific components. Objectives of size, weight, power, thermal dissipation, performance and cost drive tradeoffs among radiating elements, T/R modules, monolithic microwave integrated circuits (MMICs), microwave distribution and packaging. Proposed and Operational Examples Recent radar satellite designs will be assessed to illustrate actual performance and design tradeoffs. Current L-band syyppstem proposals contrast different desigppgn approaches.
Slide 3 SCF01 Electronic Scanned Array Design of 255
Antennas
• One of the most important determinants of microwave system (radar, communications, other) performance • Requirements are determined by system performance allocation and flow-down • Attributes include: – Beam width, shape and sidelobes • Uniform illumination sidelobes -13 dB (rectangular aperture) or -17 dB (circular aperture) are too high for most purposes – Instantaneous and tunable bandwidth –Size • SAR (square) vs GMTI (rectangular) Aspect Ratios • Deployment – Thermal Dissipation – Weight –Cost • Thermal dissipation and power consumption will restrict system duty factor
Slide 4 SCF01 Electronic Scanned Array Design of 255 Electronicallyyy() Scanned Array(ESA)
• An ESA combines multiple elements with phase or time delays to form a beam in a specified direction – In contrast to a mechanically steered antenna physically rotates an antenna to point a beam in a specified direction • Phase or time delayyq is required to scan the beam • Gain control is required for beam shaping • ESA’ s commonly include amplifiers – overcome distribution and control loss – Replace transmitter power amplifier (TWTA)
Slide 5 SCF01 Electronic Scanned Array Design of 255
Reflector Antenna Radar Block Diagram
Exciter Transmitter bal
Frequency mm Data request Control & Timing Processor Gi Antenna
Reference Duplexer
Radar data Signal Processor Receiver Receiver Protection
Power Supply ESA incorporates functions shown in dashed box Slide 6 SCF01 Electronic Scanned Array Design of 255 Electronically Scanned Array Radar Block Diagram
TRM s) Exciter on ii
(( TRM
TRM
TRM anifold Distribut Frequency MM TRM Data request Control Processor & Timing B TRM
Reference e TRM orming & Logic ff a TRM m TRM Beam Power TRM Radar data Signal Processor Receiver(s) TRM
Power Supply ESA incorporates functions shown in dashed box Slide 7 SCF01 Electronic Scanned Array Design of 255
ESA Benefits
• Multiple beams • Instantaneous beam steering (agile beam) – Reduces slew and settle time • Mainlobe shaping, sidelobe control and nulling for clutter and interference mitigation • Multiple phase centers for MTI & multi-channel SAR – Enables angle of arrival measurement – Additional degrees of freedom for clutter and interference mitigation • Multiple concurrent radar modes. • Lower loss between amplifiers and free space • Inherent redundancy (multiple elements) – Graceful degradation • Electronic Attack (EA) with very high Effective Radiated Power (ERP) • Stealth – Better match to free space – much less reflection/reradiation • Antenna surface deformation (deliberate or accidental) may be compensated • Space combining (low loss) of solid state power amplifiers
Slide 8 SCF01 Electronic Scanned Array Design of 255 ESA Performance Improvement
26 -3 dB • Multiple Azimuth Beam 24 – Improved SAR resolution 22 • MltilMultiple Eleva tion Beam 20 – Improved stripmap area km)
(( 18 rate ← Boresight 16 – SCORE (SCan On
Range Range Receive) 14
12 Sensor altitude is 10.0 km 10 Range to horizon is 357.3 km Boresight range is 20.0 km 8 Grazing angle = 30.0°
-10 -5 0 5 10 Cross Rangg(e (km )
Slide 9 SCF01 Electronic Scanned Array Design of 255
Technology Environment
• ESAs have recently become very prevalent for the sole reason that they have become much more affordable (they were always known to offer significant benefits but were unaffordable) • T/R modules are a small fraction of radar system cost and a very small fraction of system cost
Slide 10 SCF01 Electronic Scanned Array Design of 255 Aperture Design
Slide 11 SCF01 Electronic Scanned Array Design of 255
Antenna Function
• Antenna objective is to create a current/voltage distribution which creates a specified beam pattern or v/v. – Omni directional radio signals of little use (except for broadcasting) • Difficult to arrange in general – Arrays permit a sampled representation of current/voltage permiiitting a lmost any des ire d arrangement • Two design approaches – analysis and synthesis
Slide 12 SCF01 Electronic Scanned Array Design of 255 Basic Appperture Shapes
b
a
•Sqqpuare aperture • Round aperture – 4 by 8 wavelengths – 3 wavelengths radius – First sidelobe is -13.2 dB – First sidelobe at -17.8 dB – 3 dB beamwidth = ± 0.866 λ/D – 3 dB beamwidth = ± 1.03 λ/D – first null at ± λ/D – first null at ± 1.22 λ/D
From Balanis “Antenna Theory” Chapter 11
Slide 13 SCF01 Electronic Scanned Array Design of 255
Analysis Regions (exact to approximate)
Fresnel or Fraunhofer Near Field Transition or Far Field Region Region Region tenna nn A
Nominal Beamwidth
2 D2 D2 D2 D2 2D λ 0 For = 3cm and 16λ 4λ 2λ λ λ
D = 1 meter 2m 8m 17m 33m 67m
D = 10 meter 208m 1,667m 3,333m 6,667m 833m Illustration from Lynch (© SciTech Publishing,Slide Inc), 14 SCF01 Electronic Scanned Array Design of 255 Regions
EtEvanescent NFildNear Field FFildFar Field Fresnel Fraunhofer Near limit 0 3λ 2D² /λ Far limit 3λ 2D²/λ∞ Power decay R-n 1R-1 E and H No Yes Yes orthogonal Ω Z0 = 377 No Yes Yes
• Laser Pointer • Ȝ = 630 nm, D = 1 mm => farfield at 3 meters
Slide 15 SCF01 Electronic Scanned Array Design of 255
Another Visualization
4λ
Slide 16 SCF01 Electronic Scanned Array Design 3λ 2D²/λ of 255 General Concepts
• Linearit y and superpositi on • Reciprocity (Lorenz) – System behavior is independent of direction of energy transfer, ie antenna pattern ihis the same for transm it an d rece ive • Antenna pattern is the Fourier transform of aperture illumination – Discrete (sampled) vs continuous – The sample interval is the element spacing – λ/2 element spacing assures no grating lobes (Nyquist-Shannon sampling theorem) – Reso lu tion lim it (Ray le ig h cr iter ia ) – Round vs square • Projected aperture (cosine θ dependence) – Wheeler - Pozar • Polarization and principal planes •Radar R an ge E quati on
Slide 17 SCF01 Electronic Scanned Array Design of 255
Resolution
• RtiditlltdtbdidthRange measurement is directly related to bandwidth – Wide bandwidth waveform (eg chirp) required •AnAnglegle measurementmeasurement isis ddirectlyirectly relatedrelated to aantennantenna (ape(aperture)rture) size – Can generate “synthetic” apertures larger than physical antenna size by exploiting own platform motion • Angular resolution (Rayleigh criterion) – Coherent or non-coherent – Deconvolution of PSF allows higher (super) resolution subject to S/N – Consider two point sources (sinx/x) separated by small distance, fit sinx ’/x ’ an d ta ke difference, loo k a t Pd/Pfa – Elements spaced closer than Ȝ/2 potentially provide better resolution
Slide 18 SCF01 Electronic Scanned Array Design of 255 Projjpected Aperture
• Projected aperture is the apparent angular extent of the aperture as viewed from a specified direction • AtAntenna gai n i s propor tiona ltl to pro jec tdted aper ture • Harold A. Wheeler derived this relationship in an early paper
Broadside θ=30 θ=60 θ=90 Slide 19 θ=0 SCF01 Electronic Scanned Array Design of 255
Radar Ranggqe Equation
• Radar range determined by antenna size (area), transmit power, receive noise figure and bandwidth
P G262< SNR = t 3 4 (4:) kTeBF LR
Pt = transmit power G = antenna gain λ = wavelthlength σ = target cross section k = Boltzmann's constant T = system temperature B = system bandwidth F = system noise figure L = system losses R = range to target Slide 20 SCF01 Electronic Scanned Array Design of 255 Friis Transmission Equation
• Ratio of power received to power transmitted – Describes one-way radio links – Assumes antennas are aligned – Factor in parenthesis is free space loss
P 6 2 r = G G P t r 4:R t 3 4
Pr = received power Pt = transmitted power Gt = transmit antenna gain Gr = receive antenna gain
Slide 21 SCF01 Electronic Scanned Array Design of 255
Noise Eqqguivalent Sigma Zero
4:r 3 2Lsin3 k TB NESZ(< )= i B 0 6 P G G c= 2 2 3 4 t r pd prop sys
σ 0 ithbis the bac ksca ttittering cross-section P = (peak) transmitted power
Gt and Gr are the transmit and receive antenna gains c = speed of light
ʏPD = Pulse width λ = Radar wavelength r i= Range kB = Boltzman constant B = Bandwidth θ i = Incidence angle η’s (<1) are the propagation and system losses. Slide 22 SCF01 Electronic Scanned Array Design of 255 SAR Desiggpn Optimization
• For a system limited by thermal noise, we can: • Reduce system losses and noise figure (hard to do) • Ddtth(tkhit)Decrease data swath (take coverage hit) • Increase transmit power • Increase pulse duration (may cause pulse timing issues) • Decrease pulse bandwidth (for resolved targets) • Increase PRF (may cause range ambiguity problems) • View target from more favorable angle • Increase antenna area ((pexpensive , may lessen coverag g)e) • Decrease slant range (may compromise mission performance)
Slide 23 SCF01 Electronic Scanned Array Design of 255
ESA Design Approach
Slide 24 SCF01 Electronic Scanned Array Design of 255 Apppproach
• Arrays represen t sampl es o f id ea l aper ture illum ina tion function – Sampling theorems apply – Undersampling ⇔ grating lobes – Oversampling associated with “super directivity” • Arrays discussion assumes isotropic radiators – Array patterns are two-sided, element pattern is source of single- sided pattern • Elemen t eff ect s generall y d o no t aff ect overall patt ern – Mutual coupling tends to narrow beams – Can create nulls (()pscan blindness) in unexpected directions • Analysis • Synthesis
Slide 25 SCF01 Electronic Scanned Array Design of 255
Discrete Representation
• For a continuous illumination function f(x), the resulting beam pattern as a function of u (= sin θ) is ` +1 F (u)= f(x)expjux dx 2 Z!1 • If we sampl e th e ill um ina tion func tion a t equa l in terva ls Δ Δ x where ` =(M-1)* x and f(m) = am, then M!1 jkum"x F(u)= am exp m=1 X • AMAs M ∞ and Δx 0th0 the sum becomes the in tegra l. • In practice M > 10 is a fairly good approximation
Slide 26 SCF01 Electronic Scanned Array Design of 255 Arrayyp Concepts
• Array factor and Element Pattern • Array partitioning and sub-arrays – Phase shift – Time Delay – Digital domain • Grating and quantization lobes – Sparse array • Amplitude and phase control for beam pointing and shappging, notabl y for sidelobe control
Slide 27 SCF01 Electronic Scanned Array Design of 255
Real and Syygnthetic Beam Forming
• Real beamforming uses samples collected at one point in time – Limited by number of elements/receivers • Synthetic beamforming uses samples collected over a time span – Allows computation of multiple-beams, conceptually equal to number of pixels in scene
Slide 28 SCF01 Electronic Scanned Array Design of 255 Arrayy(y)s in Time (Synthetic)
• Near field Scanner • Displaced Phase Center • SAR ⇔ array • Removes mutual coupling from consideration • Adds requirement for time coherence
Slide 29 SCF01 Electronic Scanned Array Design of 255
Antenna Conventions
• Radiated f{(fields have an exp{j(ω·t-k·r)} dependence which is consistently omitted. It does not contribute to pattern calculations and is a constant factor in all calculations. – ω is angular frequency • Equal to 2πf – k is “”(f)“wavenumber” (spatial frequency) • Equal to 2 π /λ • Gain computed relative to an “isotropic” antenna which radiates equally in all directions (4· π steradians). – This is one of the few antennas which is impossible (unrealizable) due to th e t ransverse nat ure of th e EM wave • Directivity is pattern of lossless antenna Gain is directivity times efficiency (1 – loss)
Slide 30 SCF01 Electronic Scanned Array Design of 255 Lattice Attributes
• Rectangular lattice and square aperture leads to a separable array pattern – Numerically equivalent to produce to two linear arrays at right angles •Triangggypular lattices slightly more complicated
Slide 31 SCF01 Electronic Scanned Array Design of 255
Beam Pattern Analysis
Slide 32 SCF01 Electronic Scanned Array Design of 255 Generalized array (and coordinate system)
• Plus Z direction is normal to the array face • Theta (θ) is measured relative to the +Z axis • Phi (ϕ)i) is measure did in the X-YlY plane re ltitthXlative to the X ax is • Array is represented by the lattice of circles in the X-Y plane Plus Z
30
240 210 270 180 60 300 150
330 120
90 90 Plus X Plus Y Slide 33 SCF01 Electronic30 Scanned 60Array Design of 255
General Case
• CidlltifConsider a collection of
Z radiating elements located at (xi, yi, zi) and an observer P (X, Y, Z) Y located at (x,y,z) • Each radiating element is
R0 represented by a square (X1, Y1, Z1) • The radiated field at the 3 observer’s location is the r1 `1 su m of the fields of each of ? X the radiating elements as
ri seen at the same location • This formulation used to analyze cases at end of presentation After Mailloux Figure 1.5 Slide 34 SCF01 Electronic Scanned Array Design of 255 Element Contribution
• Each element i generates the field
Ei(r, 3, ?) = fi(3, ?) exp(!jkRi)/Ri
• Where k =2:/ 6
• Using the identity Ri = R ! ˆr " ri
• We can rewrite the second term as
exp(!jkRi) exp(!jkR) = exp(+jkri " ˆr) Ri R ! ˆr " ri
Slide 35 SCF01 Electronic Scanned Array Design of 255
Fraunhofer Approximation
• FdiFor distances large compare d to t he array s ize, ie R > ˆr " ri exp(!jkRi) exp(!jkR) = exp(+jkri " ˆr) Ri R
• So that exp(!jkR) E (r, 3, ?)= f (3, ?)exp(+jkr " ˆr) i R i i
• Adding a complex weight ai to each element, the resulting antenna pattern is exp(!jkR) E(r)= a f (3, ?)exp(jkr " ˆr) R i i i i X Slide 36 SCF01 Electronic Scanned Array Design of 255 Identical Elements
• It is customary to assume that each element has the same pattern so the element pattern may be taken out of the sum exp(!jkR) E(r) = f(3, ?) a exp( jkr " ˆr) R i i i X
• This formulation partitions the antenna pattern into – Element factor – Space factor – Array factor
Slide 37 SCF01 Electronic Scanned Array Design of 255
Assumptions
• The f ormul ati on i s quit e general except th e f oll ow ing assumptions (which are more or less true) • Far field assumption R > ˆr " ri
– It is generally considered that R 6 2 l 2 / 6 is sufficient; this is termed•the •Fraunhofer • region Antenna•pattern•is•the•product•of•an•array•factor•and•an• element•factor – The•array• fac tor•i s•en tire ly• de term ine d• by• the•geome tr ic•pos ition•o f• the•radiating•elements – Identical•element•patterns•(which•is•violated•for•elements•near•the• edfthdttllifft)dges•of•the•array•due•to•mutual•coupling•effects) – The•element•factor•variation•mostly•affects•large•steering•angles• and•far•out•sidelobes
Slide 38 SCF01 Electronic Scanned Array Design of 255 Pattern Seppyarability
• AhhdiilAssume that the radiating elements are arrange dild in a rectangular grid in the X-Y plane such that
ri = rmn = m"x xˆ + n"y yˆ m =0, '1 ' 2 ' 3 ... n=0, '1 ' 2 ' 3 ... ˆr = ˆxu + yˆv + ˆz cos 3 u =sin3 cos ? v =sin3 sin ? • Then
ri " ˆr = m"xu+ n"yv
exp(!jkR) E(r)=f(3, ?) a exp ( jk (m"xu+ n"yv)) R mn i X Slide 39 SCF01 Electronic Scanned Array Design of 255
Pattern Decomposition
• If we further assume that the complex element weight ai may be decomposed into x and y components
amn = am an
• AdthttlAnd the total array fact or i s th e prod uct of separat e array factors in x and y
exp(!jkR) E(r)=f(3, ?) a exp ( jk (m"xu)) a exp ( jk (n"yv)) R m n mn X X
Slide 40 SCF01 Electronic Scanned Array Design of 255 Pattern Multiplication
• The overall beam pattern is the product of the element pattern and the array pattern • AFtiDitFiTfArray Factor is Discrete Fourier Transform of fAt Aperture
Weights (ai) – Sampling theorem – Element spacing
Slide 41 SCF01 Electronic Scanned Array Design of 255
16 Element Arrayyy = 4 x 4 Element Array
20 16 element linear array 0.5 λ element spacing ° 10 0 steering angle (dB) 0
nna Gain -10 Ante
-20
-30 -90 -60 -30 0 30 60 90 AlAngle
Slide 42 SCF01 Electronic Scanned Array Design of 255 1-D Beam Formation ((g)boresight)
• Start with N elements equally spaced in a line
–am represents the element factor M!1 jkm"x sin 3 cos ? AF = ame m=0 X
• Assume the am are equal and define A = k"x sin 3 cos ? • Then t he summat ion has a c lose d form as fo llows
M!1 jA M m 1 ! e AF = a e jA = 1 ! e jA m=0 ! " X ! "
Slide 43 SCF01 Electronic Scanned Array Design of 255
Maximum Gain
• The maximum value of AF is M and occurs whenever the denominator is zero. sin[M A/2] sin[MA/2] AF = e jMA/2 AF = sin(A/2) sin(A/2) | | ------sin(A/2) = 0 A/2=n: - -
A =2n:,n=0, '1,...
Slide 44 SCF01 Electronic Scanned Array Design of 255 Selected Boresigg()ht Case (M=10)
10 10 λ = 3 cm λ = 3 cm 8 8
6 6
4 4
2 2
0 0 AF AF -2 -2
-4 -4
-6 -6 Δ x= 1 cm Δ x= 1 cm -8 Δ x= 2 cm -8 Δ x= 2 cm Δ x= 3 cm Δ x= 3 cm -10 -10 -90 -60 -30 0 30 60 90 -1 -0.5 0 0.5 1 θ u (sin θ) 2n: n6 • Maxima occur at 3 =arcsin =arcsin k"x "x 3 4 3 4
Slide 45 SCF01 Electronic Scanned Array Design of 255
1-D Beam Formation (()steered)
• To steer the beam, we apply a linear phase (only) slope in the element weights
!jmk"x sin 3s cos ?s !jmAs am = e = e
As = k"x sin 3s cos ?s
M!1 jkm"x sin 3 cos ? AF = ame m=0 X M!1 AF = e jkm"x(sin 3 cos ?!sin 3s cos ?s) m=0 X Phase only (steering Spoiling, nulls, Sidelobes as-is) Slide 46 SCF01 Electronic Scanned Array Design of 255 Scanned Array Factor
• Which reduces to
M!1 AF = e jm(A!As ) m=0 X
sin [M(A ! As)/2] AF = e jM(A!As)/2 sin [(A ! As)/2]
sin[M (A ! A )/2] AF = s sin[(A ! A )/2] | | - s ------Slide 47 SCF01 Electronic Scanned Array Design of 255
Selected Steered (30°))() Case (M=10)
10 10 λ = 3 cm λ = 3 cm 8 8 6
6 4
2 4 0 AF 2 -2
-4 0 -6
AF Δ x= 1 cm Δ -2 -8 x= 2 cm Δ x= 3 cm -10 -1 -0.5 0 0.5 1 -4 u (sin θ)
-6 Δ x= 1 cm -8 Δ x= 2 cm Δ x= 3 cm -10 -90 -60 -30 0 30 60 90 θ 2n: n6 • Maxima occur at 3 =arcsin =arcsin k"x "x •Grating lobe for ǻx = 3 cm 3 4 3 4
Slide 48 SCF01 Electronic Scanned Array Design of 255 Some Linear Arrays
Eight Element Single Element Three Element Eight Element Phase Shift
Σ
Σ Σ
1 0 1.2 1 0 1 0 3 element linear array 8 element linear array 8 element linear array λ 0.5 λ element spacing 0.5 element spacing 0.5 λ element spacing ° 0° steering angle 0 steering angle 30° steering angle 1 0.8 -1.9 1 element linear array 0.8 -1.9 0.8 -1.9 )
0.8 0.6 -4.4 0.6 -4.4 0.6 -4.4
0.6
0.4 -8.0 0.4 -8.0 0.4 -8.0 Amplitude Amplitude Amplitude Amplitude 0.4 Alitd(dB) Alitd(dB) Alitd(dB)
0.2 -14.0 0.2 -14.0 0.2 -14.0 0.2
0 -99 0 0 -99 -900 -60 -30 0 30 60 90 0 -99 -90 -60 -30 0 30 60 90 -900 -60 -30 0 30 60 90 -900 -60 -30 0 30 60 90 Angle Angle Angle Angle Slide 49 SCF01 Electronic Scanned Array Design of 255
More Elements Provide Better Performance
16 Element 32 Element 64 Element
20 20 20 16 element linear array 32 element linear array 64 element linear array 0.5 λ element spacing 0.5 λ element spacing 0.5 λ element spacing Beamwidth = 1.4° 0° steering angle 0° steering angle Beamwidth = 3.0° 0° steering angle 10 10 10 Beamwidth = 6.3° ) ) ) BB BB BB
0 0 0
-10 -10 -10 tenna Gain (d tenna Gain (d tenna Gain (d nn nn nn A A A -20 -20 -20
-30 -30 -30 -90 -60 -30 0 30 60 90 -90 -60 -30 0 30 60 90 -90 -60 -30 0 30 60 90 Angle Angle Angle
• Gain improves - proportional to number of elements (array length) • Beamwidth improves - inversely proportional to number of elements (lth)(array length) • Sidelobe magnitude is unchanged • At X -band (3 cm) and λ/2 spacing, array lengths are about ¼, ½, and 1 meter respectively Slide 50 SCF01 Electronic Scanned Array Design of 255 Linear Phased Arrayyp Example
• Circles represent radiation from individual elements, which start at different times (or phases)
Broadside Equal Phase Front
30° Scanned Beam
Radiating Elements
Q§ Q§ Q§ $ L $ L $ L
Phase Shifters or 7 Δφ 6 Δφ 5 Δφ 4 Δφ 3 Δφ 2 Δφ 1 Δφ 0 Δφ Δτ = 50 psec Time Delay Units 7 Δτ 6 Δτ 5 Δτ 4 Δτ 3 Δτ 2 Δτ 1 Δτ 0 Δτ
Feed Network
ent Spacing =3.0 cm Wavelength = 3.0 cm Antenna Input Slide 51 SCF01 Electronic Scanned Array Design of 255
Limitations on Beam Formation
• ESAs which use phase shifters for steering have an additional design constraint relating aperture size and instantaneous bandwidth because of beam squint – Time delay units have no inherent frequency limitation • Element spacing of one-half wavelength provides full hemisphere steering without grating lobes – Between one-half and one wavelength spacing provides limited steering volume without grating lobes – One wavelength or greater spacing results in grating lobe(s) at all steering angles (including mechanical boresight)
Slide 52 SCF01 Electronic Scanned Array Design of 255 Beam steering: phase shift versus time delay
• The b eam of an ESA i s st eered pref erabl y by app ly ing a progressive time delay, Δτ, constant over frequency, across the antennas of the array. • Invariance of time delay with frequency is the primary characteristic of a true time delay (TTD) phase shifter or a time d e lay un it (TDU). • Usage of TTD phase shifters avoids beam squinting or frequency steering. • The steering angle, θ, is expressed as a function of the pppghase shift progression, β, which is a function of the frequency and the progressive time delay, Δτ, which is invariant with frequency:
Slide 53 SCF01 Electronic Scanned Array Design of 255
Phase Shifters cause Beam to Steer with Frequency
• Phase shift at each element, n· 2·π·d/λ, is dependent on frequency • As the frequency changes, the beam moves and eventually moves off th e t arget • Bandwidth limitation for phase-only scanning is "f K " 6 = f L " sin(3)
• K is a factor approximately equal to one
•For L = 1 meter, λ = 3 cm and θ = 30° the resulting fractional bandwidth is 6%
Slide 54 SCF01 Electronic Scanned Array Design of 255 Time Delayyg Steering
• Required maximum time delay is equal to antenna length times sine of the scan angle – Minimum time delay set by quantization requirements • NbNumber o ftidlif time delays is equa ltl to num ber o flf elemen ts – Number of elements proportional to antenna length – Element spacing between 0.5 and 1.0 wavelengths • Use cables to provide time delay – Have to make up cable loss with additional gain •Tooatal l en gth of r equedcabessodeoequired cables is order of
(L2 " sin azimuth " H2 " sin elevation)/62 =(Area2 " sin azimuth " sin elevation)/62
• Total cable mass (()yand volume) limits array size
Slide 55 SCF01 Electronic Scanned Array Design of 255
Linear Phase Array with Time Delay – Steered
• Proper time delay (50 picoseconds) between Broadside adjacent elements • Generates beam in 30° Scanned Beam desired• direction• (30°)
Radiating•Elements
Q§ Q§ Q§ $ L $ L $ L
Phase•Shifters 7•Δφ 6•Δφ 5•Δφ 4•Δφ 3•Δφ 2•Δφ 1•Δφ 0•Δφ Δφ•=•180° (modulo•2π)••
Feed• Network
Element•Spacing•=3.0•cm Wavelength•=•3.0•cm Antenna•Input
Slide 56 SCF01 Electronic Scanned Array Design of 255 Linear Phase Array with Phase Shifters – Unsteered
• With no phase shift between elements Broadside No phase shift • BibdidBeam is broadside • Pattern null at 30°
30° Scanned Beam
Radiating Elements
Q§ Q§ Q§ $ L $ L $ L
Phase Shifters or 7 Δφ 6 Δφ 5 Δφ 4 Δφ 3 Δφ 2 Δφ 1 Δφ 0 Δφ Δφ = 0° Time Delay Units 7 Δτ 6 Δτ 5 Δτ 4 Δτ 3 Δτ 2 Δτ 1 Δτ 0 Δτ
Feed Network
Element Spacing =3.0 cm Wavelength = 3.0 cm Antenna Input
Slide 57 SCF01 Electronic Scanned Array Design of 255
Linear Phase Array with Phase Shifters – Steered
• Proper phase shift (180°) between Broadside adjacent elements • Generates beam in 30° Scanned Beam desired direction (30°)
Radiating Elements
Q§ Q§ Q§ $ L $ L $ L
Phase Shifters 7 Δφ 6 Δφ 5 Δφ 4 Δφ 3 Δφ 2 Δφ 1 Δφ 0 Δφ Δφ = 180° (modulo 2π)
Feed Network
Element Spacing =3.0 cm Wavelength = 3.0 cm Antenna Input
Slide 58 SCF01 Electronic Scanned Array Design of 255 Wideband capabilities
• Antenna selection determines waveform selection • Beamforming for wideband – Slope/Step Chirp Waveforms – Amplitude/Frequency/Linear Frequency Modulation (chirp) • Can spin phase shifters on transmit, limits swath width if used on receive • Stretch = dechirp or deramp
Slide 59 SCF01 Electronic Scanned Array Design of 255
Grating Lobes and Thinned Arrays
Slide 60 SCF01 Electronic Scanned Array Design of 255 Grating Lobes and Thinned (sparse) Arrays
• AthiA thinne d array may be de fine d as an array w ith e lemen t spac ing > λ – Resulting in grating lobes at all beam positions – Grati ng l o bes degra de per formance by transm itting power in unwan te d directions/receiving noise and signals from unwanted directions – Restricts addressable field of regard – Reduces cost and complexity – Also reduces electronic field of regard – ESA Fed reflector is a variant of this technique • Must mitigate (suppress) grating lobes to have a useable system – Element pattern is primary technique • Lattice spacing determines presence or absence as well as location oftilbf grating lobes • Radiating element must efficiently illuminate desired beam directions and suppress radiation in undesired beam directions
Slide 61 SCF01 Electronic Scanned Array Design of 255
Grating Lobes
θ θ λ • GtilbGrating lobes occur a tit sin p = sin 0 + p· /d wh ere θ – P = grating lobe direction θ – 0 = beam direction – λ = wavelength – d = element spacing – p = ±(1, 2, 3, … ) • Beam directions θ arcsin(λ/d-1) are free of grating lobes – If λ/d 1 (ie d λ) then all beam steering directions experience grating lobes – Ultimate limit on beam scanning is θp=p = - θ o (equal and opposite) θ λ •sin 0 = p· /(2·d)
Slide 62 SCF01 Electronic Scanned Array Design of 255 Grating Lobes in u-v Space (Rectangular Lattice) 2 λ = 3.0 cm ΔX = 2.3 cm (-2,1) (-1,1) (0,1) (1,1) (2,1) ΔY = 2.0 cm
1 ) φ s oo c
θ⋅ 0 (-2,0) (-1,0) (1,0) (2,0) (sin VV
-1
(-2,-1) (-1,-1) (0,-1) (1,-1) (2,-1)
-2 -3 -2 -1 0 1 2 3 θ⋅ φ U (sin sin ) Slide 63 SCF01 Electronic Scanned Array Design of 255
Grating Lobes in u-v Space (Triangular Lattice) 2 λ = 3.0 cm ΔX = 2.3 cm (-2,1) (0,1) ΔY = 2.0 cm
1 (-1,1) (1,1) ) φ s oo c
θ⋅ 0 (-2,0) (sin VV (-1,0) (1,0) -1
(-2,-1) (0,-1)
-2 -3 -2 -1 0 1 2 3 θ⋅ φ U (sin sin ) Slide 64 SCF01 Electronic Scanned Array Design of 255 Scan Volume Comparison
2 λ = 3.0 cm Rectangular Case ΔX = 2.3 cm Triangular Case ΔY = 2.0 cm Visible Space
1 ) φ s oo c
θ⋅ 0 (sin VV
-1
Rectangular Scan volume = 0.86 Steradians Triangular Scan volume = 1.02 Steradians Triangular lattice has 19.2% greater scan volume -2 -3 -2 -1 0 1 2 3 θ⋅ φ U (sin sin ) Slide 65 SCF01 Electronic Scanned Array Design of 255
Element Spacing > λ/2 Grating Lobes g 90 Grating Lobe Onset (θ ) 1 Grating Lobe Direction = Beam Direction (θ ) 75 2 θ = asin(λ/Δx -1) 1 s) θ =asin(= asin(λ/2Δx) 2 60 (degree nn 45 ← 41.8° Directio
mm 30
Bea 19.5° → 15
0 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 Element Center Spacing (in wavelengths) Slide 66 SCF01 Electronic Scanned Array Design of 255 Element Spacing > λ/2 Grating Lobes
• Dipo le array or ien te d norma l to p lane o f p ic ture • Dipoles have uniform element pattern in plane of picture leading to pairs of mainlobes • For element spacing of λ/2, grating lobes appear only at 90° beam direction 8 elements, 0.5 λ apart 360° delta phase 0° beam direction
Slide 67 SCF01 Electronic Scanned Array Design of 255
Element Spacing > λ/2 Grating Lobes
• Dipo le array or ien te d norma l to p lane o f p ic ture • Dipoles have uniform element pattern in plane of picture leading to pairs of mainlobes • For element spacing of 0.75· λ, grating lobes appear only at > 19.5° beam direction 8 elements, 0.75 λ apart 360° delta phase 0° beam direction
Slide 68 SCF01 Electronic Scanned Array Design of 255 Techniques for Grating Lobe Suppression
• Restricted radiating element pattern will avoid feeding the grating lobes – This is almost always the case because elements larger than a wavelength become directional • Overlapped subarra ys • Introduce uncorrelated errors – Redistributes•gggrating•lobe•radiation•so•that•the•peaks•are• reduced•although•the•total•power•is•unaffected
Slide 69 SCF01 Electronic Scanned Array Design of 255
Second Part
Slide 70 SCF01 Electronic Scanned Array Design of 255 Beam Pattern Synthesis
Slide 71 SCF01 Electronic Scanned Array Design of 255
Optimization
• Sidelobe Disadvantages – Reduce gain in beam direction – Introduce target-like artifacts – Introduce additional background (noise) • Main beam shaping
Slide 72 SCF01 Electronic Scanned Array Design of 255 Amplitude Weighting (Taper) for Side Lobe Control
• Adjust gain at each element to optimize performance • Sidelobes may be reduced by reducing the power near the ed ge o f the array – Reduces effective size of aperture and broadens beam • Non-uniform weighting in transmit is problematic – Element amplifiers operate near saturation – Reduces total radiated power – Reduces aperture efficiency (area utilization) • Appyerture efficiency 2 ( m am ) ATE = | | 2 M am P m | | P Slide 73 SCF01 Electronic Scanned Array Design of 255
Schelkunoff Representation
• Schelkunoff assessed the excitation polynomial
M!1 jm(A!As) AF = ame m=0 X
A = k"x sin 3, As = k"x sin 3s
z = e j(A!As)
M!1 M!1 m AF = amz = aM (z ! zm) m=0 m=0 X Y Slide 74 SCF01 Electronic Scanned Array Design of 255 Single Beam
• Cons ider the un iform illum ina tion case AF = zM + zM!1 + zM!2 + ... + z2 + z +1 M M!1 m AF = z = (z ! zm) m=0 m=0 whose rootsX are: Y (2m!M):/M M zm = e Meven,m =1:M,m = 6 2 (2m!M!1):/M M +1 zm = e Modd,m= 1 : M,m= 6 2 • One missing root with value of one. • ItiitInsert missing root – Mainbeam disappears – only sidelobes left AF = (z ! 1) zM + zM!1 + zM!2 + ... + z2 + z + 1 AF = zM+1 ! 1 Slide 75 ! of 255"
Addition of Missing Root
Uniform Method Uniform Method 12 Imaginary λ = 3 cm λ = 3 cm Unit Circle M = 11 M = 11 Roots 10 Δx = 1.5 cm Δx = 1.5 cm Beam Space
8 Half Power Beamwidth = 9.2° lts) oo 6 Real AF (v 4
2
0 Aperture Taper Efficiency = 100.0% -1 -0.5 0 0.5 1 Aperture Taper Efficiency = 0.00 dB u (sin θ) Uniform Method Uniform Method 12 Imaginary λ = 3 cm λ = 3 cm Unit Circle M = 12 M = 12 Roots 10 Δx = 1.5 cm Δx = 1.5 cm Beam Space
8 ))
6 Real AF (volts 4
2
0 Aperture Taper Efficiency = 16.7% Slide 76 -1 -0.5 0 0.5 1 SCF01 Electronic Scanned Array DesignAperture Taper Efficiency = -7.78 dB u (sin θ) of 255 Schelkunoff Theorems
• Theorem I: Every linear array with commensurable separations between the elements can be represented by a polynomial and every polynomial can be interpreted as a linear array. • Theorem II: There exists a linear array with a space factor equal to the product of the space factors of any two linear arrays. • Theorem III : The space factor of a linear array of n apparent elements is the product of the space factors of (n-1) virtual couplets with their √Φ null points at the zeros of : t1, t2, … tn-1
Slide 77 SCF01 Electronic Scanned Array Design of 255
Observations
• Since A ilis real, z hititddlltthas unit magnitude, and all roots must also have unit magnitude. •For 0° 3 180°, A varies by 2k"x • Roots may fall inside or outside of this range corresponding to nulls in real space or outside real space • NllNulls al ternate w ihith pea ks (idlb(sidelobes ). The pea k va lue is smaller when nulls are closer. Grouping the nulls away from the main beam direction reduces the sidelobes while broadening the peak.
Slide 78 SCF01 Electronic Scanned Array Design of 255 Sidelobe Control
• Binomial weighting – No sidelobes – Only practical for small number of elements • Dolph-Chebyshev weighting – Smallest beamwidth at first null for specified sidelobe level – All sidelobes are equal – Only practical for small number of elements • Taylor /Bayliss weighting – Specify maximum sidelobe level and rate of falloff
Slide 79 SCF01 Electronic Scanned Array Design of 255
Analyyqtic Techniques
• UifUniform W Wihtieighting • Sidelobe Control – Binomial weighting • No sidelobes • Only practical for small number of elements – Dolph-Chebyshev weighting • Smallest beamwidth at first null for specified sidelobe level • All sidelobes are equal • Only practical for small number of elements – Taylor /Bayliss weighting • Specify maximum sidelobe level and rate of falloff • Beam shaping – Fourier Synthesis – Woodward-Lawson
Slide 80 SCF01 Electronic Scanned Array Design of 255 Uniform Weiggg(ghting(unweighted)
• Simplest • Default condition for transmit • Highest gain
Slide 81 SCF01 Electronic Scanned Array Design of 255
Uniform Exampp(le (M=11)
Uniform Method Uniform Method 0 Imaginary • λ•=•3•cm Half Power λ•=•3•cm Beamwidth = 9.2° Unit•Circle -5 M•=•11 M•=•11 Δx•=•1.5•cm Δx•=•1.5•cm Roots -10 Beam•Space
-15
) -20 BB -25 •Real
AF•(d -30
-35
-40
-45 Sidelobe•at•-15° Sidelobe•is•-13•dB -50 • Aperture•Taper•Efficiency•=•100.0% -90 -60 -30 0 30 60 90 θ Aperture•Taper•Efficiency•=•0.00•dB
Uniform•Method 1 Root real imaginary magnitude angle λ•=•3•cm 090.9 M•=•11 1 0. 841 + 0 .541i | 1 .000 32 . 7° Δ 0.8 x•=•1.5•cm 2 0.841 + -0.541i | 1.000 -32.7° 0.7 3 0.415 + 0.910i | 1.000 65.5° 0.6
0.5 4 0.415 + -0.910i | 1.000 -65.5° itation cc 0.4 5 -0.959 + 0.282i|i | 1.000 163.6° Ex 0.3 6 -0.959 + -0.282i | 1.000 -163.6° 0.2 7 -0.655 + 0.756i | 1.000 130.9° 0.1 Aperture•Taper•Efficiency•=•100.0% Aperture•Taper•Efficiency•=•0.00•dB 8 -0.655 + -0.756i | 1.000 -130.9° 0 0 2 4 6 8 10 12 Element•Number 9 -0.142 + 0.990i | 1.000 98.2° 10 -0.142 + -0.990i | 1.000 -98.2° Slide 82 SCF01 Electronic Scanned Array Design of 255 Trianggggular Weighting
• Zero at edges, unity in center, linear in-between • Special case of binomial (for three element array) • Array pattern is square of linear array pattern – Autocorrelation of aperture weights
Slide 83 SCF01 Electronic Scanned Array Design of 255
Trianggp()ular Example (M=11)
Triangular Method Triangular Method 0 Imaginary λ = 3 cm Half Power λ = 3 cm Beamwidth = 12.3° Unit Circle -5 M = 11 M = 11 Δx = 1.5 cm Δx = 1.5 cm Roots -10 Beam Space
-15
) -20 BB -25 Real
AF (d -30
-35
-40
-45 Sidelobe at -29° Sidelobe is -25 dB -50 Aperture Taper Efficiency = 80.7% -90 -60 -30 0 30 60 90 θ Aperture Taper Efficiency = -0.93 dB
Triangular Method 1 Root real imaginary magnitude angle λ = 3 cm 090.9 M = 11 1 0. 500 + 0 .866i | 1 .000 60 . 0° Δ 0.8 x = 1.5 cm 2 0.500 + -0.866i | 1.000 -60.0° 0.7 3 0.500 + 0.866i | 1.000 60.0° 0.6
0.5 4 0.500 + -0.866i | 1.000 -60.0° itation cc 0.4 5 -1.000 + 0.000i|i | 1.000 180.0° Ex 0.3 6 -1.000 + 0.000i | 1.000 180.0° 0.2 7 -0.500 + 0.866i | 1.000 120.0° 0.1 Aperture Taper Efficiency = 80.7% Aperture Taper Efficiency = -0.93 dB 8 -0.500 + -0.866i | 1.000 -120.0° 0 0 2 4 6 8 10 12 Element Number 9 -0.500 + 0.866i | 1.000 120.0° 10 -0.500 + -0.866i | 1.000 -120.0° Slide 84 SCF01 Electronic Scanned Array Design of 255 Binomial Weiggghting
• Positioning all of the nulls at the edge of the scan volume, ie A=0 so that zm=1 for all m creates a beam pattern with no sidelobes. This is termed the binomial array. • Illumination factor goes to zero at the edge of the array • First proposed by John Stone Stone in United States Paaetent s 1 ,63,33a,643,323 an d 1 ,71 5,335,433
Slide 85 SCF01 Electronic Scanned Array Design of 255
Binomial Exampp(le (M=11)
Binomial Method Binomial Method 0 Imaginary λ = 3 cm Half Power λ = 3 cm Beamwidth = 19.1° Unit Circle -5 M = 11 M = 11 Δx = 1.5 cm Δx = 1.5 cm Roots -10 Beam Space
-15
) -20 BB -25 Real
AF (d -30
-35
-40
-45 Sidelobe at -81° Sidelobe is -326 dB -50 Aperture Taper Efficiency = 51.6% -90 -60 -30 0 30 60 90 θ Aperture Taper Efficiency = -2.87 dB
Binomial Method 1 Root real imaginary magnitude angle λ = 3 cm 090.9 M = 11 1 -1.046 + 0 . 000i | 1 .046 180 .0 ° Δ 0.8 x = 1.5 cm 2 -1.038 + 0.027i | 1.038 178.5° 0.7 3 -1.038 + -0.027i | 1.038 -178.5° 0.6
0.5 4 -1.015 + 0.044i | 1.016 177.5° itation cc 0.4 5 -1.015 + -0.044i|i | 1.016 -177.5° Ex 0.3 6 -0.986 + 0.045i | 0.987 177.4° 0.2 7 -0.986 + -0.045i | 0.987 -177.4° 0.1 Aperture Taper Efficiency = 51.6% Aperture Taper Efficiency = -2.87 dB 8 -0.962 + 0.028i | 0.963 178.4° 0 0 2 4 6 8 10 12 Element Number 9 -0.962 + -0.028i | 0.963 -178.4° 10 -0.953 + 0.000i | 0.953 180.0° Slide 86 SCF01 Electronic Scanned Array Design of 255 Dolph-Chebyshev
• Provides the narrowest beamwidth (at first null) for specified sidelobe level or lowest sidelobe level for specified beamwidth • This technique matches the roots of a Chebyshev polynomial with the roots of the aperture illumination function.
Slide 87 SCF01 Electronic Scanned Array Design of 255
Chebyyyshev Polynomials
2 m = 1 m = 2 1 m = 3 m = 4 m = 5 mm 0
T m = 6 m = 7 -1 m = 8 m = 9 m = 10 -2 -1.5 -1 -0.5 0 0.5 1 1.5 x
!1 Tm(x)=cos(m cos x) x 5 1 | | !1 Tm(x) =cosh(m cosh x) x>1 m !1 Tm(x) = (!1) cosh(m cosh x) x < !1 Slide 88 SCF01 Electronic Scanned Array Design of 255 Appgerture Weight Derivation
M!1 jkm"x sin 3 cos ? AF = ame m=0 X (M!1)/2
AF (3) =exp (jk0 (M + 1)/2"x sin 3) amexp(jk0m"x sin 3) ( 1) 2 ! MX! / (M !1)/2
AF (3)= amexp(jk0 m"xsin 3) ( 1) 2 ! MX! / (M!1)/2 !1 AF (3)=a0 + amcos(2m cos x) 1 X Slide 89 SCF01 Electronic Scanned Array Design of 255
Result
• For M odd M A a = T c cos i cos (mA ) m M!1 2 i i=1 3 4 X • For M even
M Ai 1 a = T c cos cos m ! A m M!1 2 2 i i=1 3 4 33 4 4 X • c is a function of the sidelobe ratio R
cosh!1(R) c =cosh M ! 1 3 4 Slide 90 SCF01 Electronic Scanned Array Design of 255 Dolph-Chebyyp()shev Example (M=11)
Chebychev Method Chebychev Method 0 Imaginary λ = 3 cm Half Power λ = 3 cm Beamwidth = 10.1° Unit Circle -5 M = 11 M = 11 R = 20 dB R = 20 dB Roots -10 Beam Space
-15
) -20 BB -25 Real
AF(d -30
-35
-40
-45 Sidelobe at -16° Sidelobe is -20 dB -50 Aperture Taper Efficiency = 96.4% -90 -60 -30 0 30 60 90 θ Aperture Taper Efficiency = -0.16 dB
Chebychev Method 1 Root real imaginary magnitude angle λ = 3 cm 090.9 M = 11 1 0. 786 + 0 .618i | 1 .000 38 . 2° 0.8 R = 20 dB 2 0.454 + 0.891i | 1.000 63.0° 0.7 3 -0.085 + 0.996i | 1.000 94.8° 0.6
0.5 4 -0.623 + 0.783i | 1.000 128.5° itation cc 0.4 5 -0.955 + 0.296i|i | 1.000 162.8° Ex 0.3 6 -0.955 + -0.296i | 1.000 -162.8° 0.2 7 -0.623 + -0.783i | 1.000 -128.5° 0.1 Aperture Taper Efficiency = 96.4% Aperture Taper Efficiency = -0.16 dB 8 0.786 + -0.618i | 1.000 -38.2° 0 0 2 4 6 8 10 12 Element Number 9 0.454 + -0.891i | 1.000 -63.0° 10 -0.085 + -0.996i | 1.000 -94.8° Slide 91 SCF01 Electronic Scanned Array Design of 255
Tayygglor Weighting
• Taylor modified the Dolph-Chebyshev, retaining the near sidelobe structure (and polynomial zeros) and modifying the far sidelobe structure (and polynomial zeros) to use the zeros of the sinx/x function which has lower far sidelobes. • The transition between the two functions is based on two parameters σ and n-bar where σ is the scale factor for the Dolph-Chebyshev function and n-bar is the number of Dolph-Chebyshev equal sidelobes. .
Slide 92 SCF01 Electronic Scanned Array Design of 255 Tayyp()lor Example (M=11)
Taylor Method Taylor Method 0 Imaginary λ = 3 cm Half Power λ = 3 cm Beamwidth = 10.1° Unit Circle -5 M = 11 M = 11 R = 20 dB R = 20 dB Roots -10 n-bar = 5 n-bar = 5 Beam Space
-15
) -20 BB -25 Real
AF(d -30
-35
-40
-45 Sidelobe at -16° Sidelobe is -20 dB -50 Aperture Taper Efficiency = 96.3% -90 -60 -30 0 30 60 90 θ Aperture Taper Efficiency = -0.16 dB
Taylor Method 1 Root real imaginary magnitude angle λ = 3 cm 090.9 M = 11 1 -0.959 + 0 . 282i | 1 .000 163 .6 ° 0.8 R = 20 dB n-bar = 5 2 -0.959 + -0.282i | 1.000 -163.6° 0.7 3 -0.630 + 0.777i | 1.000 129.0° 0.6
0.5 4 -0.630 + -0.777i | 1.000 -129.0° itation cc 0.4 5 -0.090 + 0.996i|i | 1.000 95.2° Ex 0.3 6 -0.090 + -0.996i | 1.000 -95.2° 0.2 7 0.785 + 0.619i | 1.000 38.3° 0.1 Aperture Taper Efficiency = 96.3% Aperture Taper Efficiency = -0.16 dB 8 0.785 + -0.619i | 1.000 -38.3° 0 0 2 4 6 8 10 12 Element Number 9 0.451 + 0.893i | 1.000 63.2° 10 0.451 + -0.893i | 1.000 -63.2° Slide 93 SCF01 Electronic Scanned Array Design of 255
Beam Shappging / Sp oiling
• Previous methods developed for sidelobe control • Following methods deal with main beam • General problem is to form a shaped beam – Broad beams in azimuth direction desired for SAR – Cosecant beams u sefu l for air su rv eillance radars w here range varies with elevation angle
Slide 94 SCF01 Electronic Scanned Array Design of 255 Fourier Syyqnthesis Technique
• Since the beam shape is the Fourier transform of the illumination function, take the inverse Fourier transform of the beam shape to obtain the required illumination function – However,,p this produces an illumination function infinite in extent – Possible to truncate the computed illumination function but that produces ripples in the beam shape
Slide 95 SCF01 Electronic Scanned Array Design of 255
Fourier Transform Synthesis
• TfdidbhittTransform desired beamshape into aperture p lane, y ildiielding excitation coefficients for an infinite area
6/(2dx) dx a = F (u)exp!j(2:/6)undx du n 6 !6/Z(2dx) • For rectangular beamshape, resulting excitation is a sinc function • Synthesize beam shape based on finite limits • Ripple is termed Gibbs phenomena • Aperture needs to be long enough to encompass several zeros of the sinc in order to produce an approximately rectangular beam – Efficie n cy suff er s
Slide 96 SCF01 Electronic Scanned Array Design of 255 Fourier Transform – First Null
Fourier Method Fourier Method 0 Imaginary λ = 3 cm Half Power = 3 cm Unit Circle Beamwidth = 13.6° -5 M = 14 M = 14 Roots Δx = 1.5 cm Δx = 1.5 cm Synthesized Beam -10 Beam Space -15
) -20 BB -25 Real
AF(d -30
-35
-40
-45 Sidelobe at -19° Sidelobe is -22 dB -50 Aperture Taper Efficiency = 67.3% -90 -60 -30 0 30 60 90 Aperture Taper Efficiency = -1.72 dB θ Root real imaginary magnitude angle 1 2.624 + -0.000i | 2.624 -0.0° Fourier Method 2 0.657 + 0.754i | 1.000 48.9° 1 λ = 3 cm 3 0.260 + 0.966i | 1.000 74.9° 090.9 M = 14 4 -0.196 + 0.981i | 1.000 101.3° Δ 0.8 x = 1.5 cm 5 -0.610 + 0.793i | 1.000 127.6° 0.7 6 -0.897 + 0.441i | 1.000 153.8°
0.6 7 -1.000 + -0.000i | 1.000 -180.0°
0.5 8 -0.897 + -0.441i | 1.000 -153.8° itation cc 9 -0.610 + -0.793i | 1 . 000 -127. 6° 0.4 Ex 10 -0.196 + -0.981i | 1.000 -101.3° 0.3 11 0.260 + -0.966i | 1.000 -74.9° 0.2 12 0.657 + -0.754i | 1.000 -48.9° 0.1 Aperture Taper Efficiency = 67.3% 13 0.381 + 0.000i | 0.381 0.0° Aperture Taper Efficiency = -1.72 dB 0 0 5 10 15 Element Number
Slide 97 SCF01 Electronic Scanned Array Design of 255
Fourier Transform – Second Null
Fourier Method Root real imaginary magnitude angle 0 λ = 3 cm Half Power Beamwidth = 16.9° 1 3.098 + -0.000i | 3.098 -0.0° -5 M = 25 Δx = 1.5 cm 2 1.332 + 0.000i | 1.332 0.0° -10 3 0.758 + 0.653i | 1.000 40.7° -15 4 0.573 + 0.820i | 1.000 55.1°
) -20
BB 5 0.346 + 0.938i | 1.000 69.8° -25 6 0.095 + 0.995i | 1.000 84.6°
AF (d -30 7 -0.162 + 0.987i | 1.000 99.3° -35 8 -0.407 + 0.913i | 1.000 114.0° -40 9 -0.625 + 0.780i | 1.000 128.7°
-45 Sidelobe at -15° 10 -0.803 + 0.597i | 1.000 143.4° Sidelobe is -23 dB -50 11 -0.927 + 0.374i | 1.000 158.0° -90 -60 -30 0 30 60 90 θ 12 -0.992 + 0.127i | 1.000 172.7° 13 -0.992 + -0.127i | 1.000 -172.7° 14 -0.927 + -0.374i | 1.000 -158.0° Fourier Method 1 15 -0.803 + -0.597i | 1.000 -143.4° λ = 3 cm 0.9 M = 25 16 -0.625 + -0.780i | 1.000 -128.7° Δ 0.8 x = 1.5 cm 17 -0.407 + -0.913i | 1.000 -114.0°
0.7 18 -0.162 + -0.987i | 1.000 -99.3°
0.6 19 0.095 + -0.995i | 1.000 -84.6° 20 0.346 + -0.938i | 1.000 -69.8° ation 0.5 tt 21 0.573 + -0.820i | 1.000 -55.1° 0.4 Exci 22 0.758 + -0.653i | 1.000 -40.7° 0.3 23 0.751 + 0.000i | 0.751 0.0° 0.2 24 0.323 + -0.000i | 0.323 -0.0° 0.1 Aperture Taper Efficiency = 52.5% Aperture Taper Efficiency = -2.80 dB 0 0 5 10 15 20 25 Element Number Slide 98 SCF01 Electronic Scanned Array Design of 255 Fourier Transform – Third Null
Root real imaginary magnitude angle Fourier Method 1 5.722 + 0.000i | 5.722 0.0° 0 2 1.196 + -0.234i | 1.219 -11.1° λ = 3 cm Half Power Beamwidth = 17.8° 3 1.196 + 0.234i | 1.219 11.1° -5 M = 36 Δx = 1.5 cm 4 0.792 + -0.611i | 1.000 -37.7° -10 5 0.676 + -0.737i | 1.000 -47.5° 6 0.536 + -0.844i | 1.000 -57.6° -15 7 0.378 + -0.926i | 1.000 -67.8°
) -20 8 0.208 + -0.978i | 1.000 -78.0° BB 9 0.031 + -1.000i | 1.000 -88.2° -25 10 -0.147 + -0.989i | 1.000 -98.4°
AF(d -30 11 -0.320 + -0.947i | 1.000 -108.7° 12 -0.483 + -0.876i | 1.000 -118.9° -35 13 -0.630 + -0.776i | 1.000 -129.1° -40 14 -0.758 + -0.653i | 1.000 -139.3° 15 -0.861 + -0.508i | 1.000 -149.5° -45 Sidelobe at -13° Sidelobe is -23 dB 16 -0. 938 + -0. 348i | 1. 000 -159. 6° -50 17 -0.984 + -0.177i | 1.000 -169.8° -90 -60 -30 0 30 60 90 θ 18 -1.000 + 0.000i | 1.000 180.0° 19 -0.984 + 0.177i | 1.000 169.8° 20 -0.938 + 0.348i | 1.000 159.6° 21 -0.861 + 0.508i | 1.000 149.5° Fourier Method 22 -0.758 + 0.653i | 1.000 139.3° 1 23 -0.630 + 0.77 6i | 1 .000 12 9.1° λ = 3 cm 24 -0.483 + 0.876i | 1.000 118.9° 0.9 M = 36 25 -0.320 + 0.947i | 1.000 108.7° Δx = 1.5 cm 0.8 26 -0.147 + 0.989i | 1.000 98.4°
0.7 27 0.031 + 1.000i | 1.000 88.2° 28 0.208 + 0.978i | 1.000 78.0° 0.6 29 0.378 + 0.926i | 1.000 67.8°
ation 0.5 30 0.536 + 0.844i | 1.000 57.6° tt 31 0.676 + 0.737i | 1.000 47.5° 0.4 32 0.792 + 0.611i | 1.000 37.7° Exci
0.3 33 0.805 + -0.158i | 0.820 -11.1° 34 0.805 + 0.158i | 0.820 11.1° 0.2 35 0.175 + 0.000i | 0.175 0.0°
0.1 Aperture Taper Efficiency = 43.5% Aperture Taper Efficiency = -3.62 dB 0 0 5 10 15 20 25 30 35 Element Number Slide 99 SCF01 Electronic Scanned Array Design of 255
Woodward-Lawson Synthesis
• Starts with basis functions for beam shape based on a finite aperture • BifBasis functi ons are un ifliformly we ihtdbighted beams s teere dtd at increments of 2π/M with the result that nulls coincide • This allows a direct computation of weights to approximate any desired beam shape – Technique modified by Elliot in 1968
Slide 100 SCF01 Electronic Scanned Array Design of 255 Combine Beams 5, 6 and 7
Woodward Method 12 λ = 3 cm 10 M = 11 Δx = 15cm1.5 cm Half Power 8 Beamwidth = 27.7°
) 6 ss
4 F (volt
AA 2
0
-2
-4 -1 -0.5 0 0.5 1 u(sinu (sin θ)
Slide 101 SCF01 Electronic Scanned Array Design of 255
Woodward-Lawson Example
Woodward Method Woodward Method 0 Imaginary λ = 3 cm Half Power Beam -5 λ = 3 cm Unit Circle Beamwidth = 27.7° Beam -4 -5 M = 11 M = 11 Roots Beam -3 Δx = 1.5 cm Δx = 1.5 cm Synthesized Beam -10 Beam -2 Beam -1 Beam Space Beam 0 -15 Beam 1 Beam 2
) -20 Beam 3
BB Beam 4 -25 Beam 5 Real
AF (d -30
-35
-40
-45 Sidelobe at -26° Sidelobe is -15 dB -50 -90 -60 -30 0 30 60 90 θ
Woodward Method 1 Root real imaginary magnitude angle λ = 3 cm 090.9 M = 11 1 1 .785 + 0 .000i | 1 .785 0 .0 ° Δ 0.8 x = 1.5 cm 2 -0.959 + 0.282i | 1.000 163.6° 0.7 3 -0.959 + -0.282i | 1.000 -163.6° 0.6
0.5 4 -0.655 + 0.756i | 1.000 130.9° itation cc 0.4 5 -0.655 + -0.756i|i | 1.000 -130.9° Ex 0.3 6 -0.142 + 0.990i | 1.000 98.2° 0.2 7 -0.142 + -0.990i | 1.000 -98.2° 0.1 Woodward-Larson Efficiency = 69.8% Woodward-Larson Efficiency = -1.56 dB 8 0.415 + 0.910i | 1.000 65.5° 0 0 2 4 6 8 10 12 Element Number 9 0.415 + -0.910i | 1.000 -65.5° 10 0.560 + 0.000i | 0.560 0.0° Slide 102 SCF01 Electronic Scanned Array Design of 255 Quadratic Beam Sppgoiling
• Not a synthesis technique • Apply systematic phase error at each element
Slide 103 SCF01 Electronic Scanned Array Design of 255
Additional Phase Term
Quadratic Phase Method 160 λ = 3 cm 140 M = 11 Δx = 15cm1.5 cm
120
100 egrees)
80 ngle (d
AA 60
40 Phase Phase 20 Aperture Taper Efficiency = 100.0% Aperture Taper Efficiency = 0.00 dB 0 0 2 4 6 8 10 12 Element Number
Slide 104 SCF01 Electronic Scanned Array Design of 255 Quadratic Phase Example
Quadratic Phase Method Quadratic Phase Method 0 Imaginary λ = 3 cm Half Power λ = 3 cm Beamwidth = 26.7° Unit Circle -5 M = 11 M = 11 Δx = 1.5 cm Δx = 1.5 cm Roots -10 Beam Space
-15
) -20 BB -25 Real
AF(d -30
-35
-40
-45 Sidelobe at -25° Sidelobe is -6 dB -50 Aperture Taper Efficiency = 100.0% -90 -60 -30 0 30 60 90 θ Aperture Taper Efficiency = 0.00 dB
Quadratic Phase Method 1 Root real imaginary magnitude angle λ = 3 cm 090.9 M = 11 1 1. 231 + 0 .482i | 1 .322 21 . 4° Δ 0.8 x = 1.5 cm 2 0.556 + 1.052i | 1.190 62.1° 0.7 3 -0.138 + 1.099i | 1.107 97.2° 0.6
0.5 4 -0.686 + 0.801i | 1.055 130.6° itation cc 0.4 5 -0.975 + 0.288i|i | 1.017 163.6° Ex 0.3 6 -0.943 + -0.278i | 0.984 -163.6° 0.2 7 -0.617 + -0.720i | 0.948 -130.6° 0.1 Aperture Taper Efficiency = 100.0% Aperture Taper Efficiency = 0.00 dB 8 -0.113 + -0.896i | 0.903 -97.2° 0 0 2 4 6 8 10 12 Element Number 9 0.392 + -0.743i | 0.840 -62.1° 10 0.704 + -0.276i | 0.756 -21.4° Slide 105 SCF01 Electronic Scanned Array Design of 255
Beam Shape Comparisons 11 Element* Linear Array
Methdhod Beamwidth Effic iency FiSidlbirst Sidelobe Uniform 9.2° 100% -13 dB Triangular 12.3 ° 80.7% -25 dB Binomial 19.1° 51.6% None Dolph-Chebyshev 10.1° 96.4% -20 dB Taylor (n-bar=5) 10.1° 96.3% -20 dB Fourier Reconstruction to First Null 13.6° 67.3% -22 dB Fourier Reconstruction to Second 16.9° 52.5% -23 dB Null Fourier Reconstruction to Third Null 17.8° 43.5% -23 dB Woodward-Larson 27.7° 69.8% -15 dB Quadratic Phase (maximum 150°) 26.7° 100% -6 dB * Fourier Reconstructions Required 14, 25, and 36 elements respectively Slide 106 SCF01 Electronic Scanned Array Design of 255 Summary
• The effect of taper is similar for transmit and receive and is captures in η, the aperture taper efficiency – The effect may be described as a reduction in effective area of the aperture with the provision that the sidelobes improve, rather than degrade with the smaller effective area – The beamwidth broadens however commensurate with the reduced area • Note that the examples given are one dimensional arrays – The tappyqper efficiency must be squared to represent a two dimensional array
Slide 107 SCF01 Electronic Scanned Array Design of 255
Subarray partitioning and recombination
• It i s f requentl y conveni ent t o f orm a l arge array as an array of smaller arrays (subarrays) – Think of replacing the element (pattern) with a subarray (pattern) – In the boresight (nonsteered) case the two are indistinguishable • Thinned arrays may be constructed using non-steered subarrays connected to a fewer number of tr modules – The non-steered subarray will have nulls matching the grating lobes of the array factor of the thinned array on boresight – The grating lobes will reappear as soon as the beam is steered off boresight • Subarrays may be phase steered and combined using time dldelay to ac hieve w idiider ins tan taneous ban dw idth – The steered subarray will keep its nulls (approximately) aligned with the grating lobes of the array factor of the thinned array
Slide 108 SCF01 Electronic Scanned Array Design of 255 Arrayyy of Arrays
• Some arrays are formed from a collection of smaller arrays, termed subarrays – This is a cost/complexity based design decision – The performance may be assessed by using the subarray pattern as the element pattern in the analysis – The array will have a lattice spacing >> λ/2 which would ordinarily create excessive sidelobes – The concept of pattern multiplication applies and the nulls in the element pattern tend to coincide with the grating lobes of the array
Slide 109 SCF01 Electronic Scanned Array Design of 255
Beamforming(feed networks)
• SiSeries FdFed – Path length to different elements is different introducing a frequency dependent phase shift with the result that the beam direction will change w ith frequency • Corporate – More comppqpglicated but equal path lengths to all elements eliminates beam steering with frequency • Butler Matrix – NxN inputs and output are combined and recombined to introduce phase shifts which provide multiple simultaneous orthogonal beams – Iridium uses this technique • Blass Ma tr ix – NxM inputs and output are combined and recombined to introduce path length differences which provide multiple simultaneous beams
Slide 110 SCF01 Electronic Scanned Array Design of 255 Tolerances and Errors
• Examples drawn in Matlab with ~ 16 decimal digits of precision • RlhdReal hardware accuracy is ~ 1%1 % • Need to assess effect of errors on theoretical performance – Array flatness – Electrical length of multiple paths requires calibration and possibly recalibration – Gain and Phase control errors and quantization – Deployment to final configuration
Slide 111 SCF01 Electronic Scanned Array Design of 255
Random Phase and Amplitude Errors
• The antenna designer can readily compute by means of standard synthesis methods the aperture excitation necessary for a desired radiation pattern. However, when he constructs his antenna and measures its ppppyerformance he finds that his experimental pattern only approximates the theoretical one. – John Ruze 1951
Slide 112 SCF01 Electronic Scanned Array Design of 255 Error Analyyysis by Ruze
• Separa te act ual fi eld exc ita tions i n to id ea l fie ld exc ita tion an d error field excitation • If errors are uncorrelated then the power from each excitation are additive – Error term raises the noise floor • Correlated errors are introduced by quantization – Error term introduces additional peaks (sidelobes) in the pattern •For relativelyyp small errors, the expected rms error İ is
072 = "7 2 + /2
where Δ is the amplitude error (relative) and δ is the phase error (radians)
Slide 113 SCF01 Electronic Scanned Array Design of 255
Reflector Applications
Slide 114 SCF01 Electronic Scanned Array Design of 255 Types of Reflector Systems (Optical Analogs)
PiPrimary SdSecondary Near Field Cassegrainian Parabolic Parabolic Confocal Cassegrainian Parabolic Hyperbolic Gregorian Parabolic Ellipsoidal Ritchey-Chrétien Hyperbolic Hyperbolic
• All are “perfect” on axis, different aberrations off axis • Design trades include – Focal plane – Feed position (at or off focal point) – On-axis or offset feed
Slide 115 SCF01 Electronic Scanned Array Design of 255
ESA Fed Reflector
• CbiCombines some o fthbfit(df the benefits (and some o fthf the disadvantages) of ESAs and reflectors • ESA feeds are useful with both cylindrical (1 dimensional curvature) and parabolic reflectors (2 dimensional curvature) • Basic trade-off is to exchange electronic field of regard (EFOR) for fewer t/r modules – Analogous to thinned array – Reduces cost by substituting mechanical structure (reflector) for electronics • Approach used by Thuraya communications satellite, selected for DESDynI, used in radio telescopes (receive only)
Slide 116 SCF01 Electronic Scanned Array Design of 255 Beam Steered (()Switched) Reflector
• Se lec t f eed to d e termi ne poi n ting direc tion – Used by Israeli TecSAR system – Only one element contributes power to each beam direction
Parabolic reflector
Focal Plane
Feed
Feed
Slide 117 SCF01 Electronic Scanned Array Design of 255
ESA Fed Reflector (Phased Array Fed Reflector)
• ESAfdblkESA feed blocks some o fthbf the beam re fltdffthfltflected off the reflector • Feed at focal plan uses only one element per beam • Move feed off focal plane so that multiple elements contribute to beam • Problem using all elements for all beams (efficiency) illuminating the entire reflector
Parabolic reflector
Focal Plane SA EE
Slide 118 SCF01 Electronic Scanned Array Design of 255 When is an ESA Fed Reflector useful
• Expensive T/R modules – Cost (1000 P watt modules) < Cost (100,000 P/100 watt modules) – 1000 x $2,000 = $2 million – 100,000 x $200 = $20 million • Small Electronic Field of View is all that is required – Electronic steering limited to about 10% so addressable volume lim ite d to a bout 1% • Still need to dissipate the same amount of heat since module efficiencies are comparable
Slide 119 SCF01 Electronic Scanned Array Design of 255
ESA Fed Reflector Desigggn Challenges
• Efficient use of resources – Either ESA Feed or Reflector is oversized • Side lo bes due to aper ture bloc kage • Beam quality degrades with scan • Elec tron ic fie ld o f regar d is qu ite sma ll re la tive to ESA • Thermal problems are exacerbated (unless power is limited)
Slide 120 SCF01 Electronic Scanned Array Design of 255 Geometrical Interpretation
• Unfold the reflector system and the similarity to a thinned array is obvious • Comparing a ESA fed reflector to a fully populated phased array is the wrong comparison • Take the TR cells in the ESA feed and sprea d them ou t to th e same area as the primary reflector • Then the electronic scan capabilities are similar and the costs differ only by the cost of the structure and cabling • HthltiHowever, the electronic scan capability of the thinned array is superior as it is not limited by viggggnetting or geometric distortion
Slide 121 SCF01 Electronic Scanned Array Design of 255
Gratinggy Lobe Limit of Unfolded System
• Assume feed element spacing is λ/2 • Fitzgerald’s reflector system has magnification factor of 4 • Analogous thinned array has element spacing 4•λ/2 = 2λ • Maximum scan angle is – sin θo = p·λ/(2·d) (ref slide 57) or – sin θo = 1·λ/(2· 2λ) = ¼ •So θo= 14° (considerably better (2-3X) than limit imppygg)osed by vignetting)
Slide 122 SCF01 Electronic Scanned Array Design of 255 PART THREE
Slide 123 SCF01 Electronic Scanned Array Design of 255
Practical Design
• Theory in Matlab with high precision and no errors • Need to approximate ideal components • Electronics advances have made this possible
Slide 124 SCF01 Electronic Scanned Array Design of 255 ESA Challenges
• Constituent Parts – Radiating Elements (mutual coupling) – TR Modules – Beam Control – Microwave Distribution and PWBs • Thermal Control (Active / passive) •Integr ati on an d T est • Technology Base • Cost
Slide 125 SCF01 Electronic Scanned Array Design of 255
Radiating Elements
Slide 126 SCF01 Electronic Scanned Array Design of 255 Element types for array s
• Pri mary func tion i s to ra dia te a ll app lie d power Γ – Element match (return loss or S11 is critical metric) • Current arrays use – Patch elements – Dipole elements – Notch elements – Slotted waveguides – Horns (for widely spaced arrays) • Element behavior changes when the element is installed in an array with adjacent elements due to mutual coupling – Some power coupled into adjacent elements and reradiated
Slide 127 SCF01 Electronic Scanned Array Design of 255
Mutual Couppgling Effects
• Reduces element Q (broader bandwidth) – Coupled dipole arrays offer very good performance • CtCreates unexpec tdd(ted modes (scan blid)blindness) – Coupled power can negate drive power • No general analytic solutions • Array size determines approach – Very small arrays may be modeled numerically – Infinite arrays may be modeled using periodic boundary conditions
Slide 128 SCF01 Electronic Scanned Array Design of 255 Radiatinggq Element Requirement
• Wide angle radiation pattern • Low cost • Readily arrayed • Compatibility with feed and t/r modules
Slide 129 SCF01 Electronic Scanned Array Design of 255
Efficiency
• Mutual•coupling • If•the•transmit•power•is•not•radiated•or•receive•power•is• notbt•absor bdbthbed•by•the•an tenna • Then•it•is•scattered•back•to•the•source • The•ra dia tor•sca tteri ng•paramet er•S11 •quan tifies• this• reflection
Slide 130 SCF01 Electronic Scanned Array Design of 255 Radiating Element – Open Waveguide or Horn
• Open waveguide (sometimes with a tapered horn section) is a good radiator but not often used in arrays because it is physically large and accordingly hard to arrange in a tight lattice • It i s al so too h eavy f or ai rb orne and space applications • It has utility in thinned arrays • 8.2 – 12.4 GHz where its directivity will help • λ = 3.6 – 2.4 cm control grating lobes • 15° beamwidth • Element spacing is ~1.5λ – part of the solution is the • Gain 17.4 – 20.3 dB element gain which is small at • a=6.15 cm the grating lobe location • b=4.25 cm • cc3.15=3.15 cm
Slide 131 SCF01 Electronic Scanned Array Design of 255
Horn feeds
• SAR-Lupe – Single feed horn – no electronic scanning • TecSAR – Eiggteedoht feed horn satocusos at focus of reflector – Scan by switching feed
Figure 4 from Sharav, et al (© IEEE) Slide 132 SCF01 Electronic Scanned Array Design of 255 Slotted Waveguide
• WidilldbittdithWaveguide is very low loss and can be integrated with a radiating element – Slots in waveguide allow RF to escape – Size and orientation of slot can be tailored for desired properties • Corporate Fed – No phase variation with frequency to limit bandwidth • Series feed – Feed from one end introduces frequency scanning of beam • Center feed – Two back-to-back center feeds maintain boresiggpht pointin g until beams diverge – Used by RadarSat and Terra-SAR X
Slide 133 SCF01 Electronic Scanned Array Design of 255
Radiating Element – Slotted Waveguide
• Slotted waveguides are readily combined with waveguide based corporate feed to provide low-loss RF distribution to 100’s of radiating slots • Very wide band • But not electronically scanned
Slide 134 SCF01 Electronic Scanned Array Design of 255 Apppproach
• Slots are duals of dipoles • Easy to machine at high precision • Polarization depends on slot orientation • Feed is integral to waveguide – Slots separated by one wavelength (or alternating slots at one- half wavelength ) create broadside beam – Frequency scanning is inherent – May be centerfed to avoid frequency scanning but beamwidth increases away from nominal frequency • Waveguide is low loss, light weight and inexpensive – Very popular for non-scanning arrays
Slide 135 SCF01 Electronic Scanned Array Design of 255
Dual Polarized Approach for TerraSAR- X
• Non-inclined narrow wall slots in one waveguide generate the horizontal polarisation. The slots have to extend into the neighbouring broad walls of the waveguide to be resonant. The edge slots in the narrow wall need to be excited with a pair of wires inside the waveguide and not by slot tilt in order for minimum cross polarisation generation. • Offset broad wall slots in the second waveguide generate the vertical polarisation. In order to minimise the waveguide width using longitudinal, broad wall slots, ridge loading is used. Both of the above slot types exhibit pure polarisation generation and high isolation between the ports within a subarray.
Slide 136 SCF01 Electronic Scanned Array Design of 255 Return Loss Bandwidth
• VSWR < 1.5 or ~- 15 dB S11 – Horizontal polarization bandwidth > 120 MHz – Vertical polarization bandwidth > 400 MHz
Figure 2 from Derneryd et al (© IEEE) Slide 137 SCF01 Electronic Scanned Array Design of 255
TerraSAR-X Next Generation
• European Patent EP2100348 • StiiSerpentine inner conductor alters propagation velocity so that slots are excited in phase • Propagation modes are not dispersive which broadens bandwidth
Slide 138 SCF01 Electronic Scanned Array Design of 255 Return Loss Much Improved
• VSWR < 1.5 or ~ -15 dB S11 • HiHorizon tltal po lilariza tion bandwidth > 650 MHz • Vertical polarization bandwidth > 700 MHz
Slide 139 SCF01 Electronic Scanned Array Design of 255
Radiating Element is Key to Performance
• Impedance match, power transfer • Radiation resistance, scattering • Surface waves • Load impedance • Single element • Adjacent element (function of separation) • Scattering in receive • Q (quality factor) – energy storage
Slide 140 SCF01 Electronic Scanned Array Design of 255 Radiating Element – Dipp()ole (1)
• Infinitesimal dipole has a cosine theta beam pattern – however infinitesimal dipoles are very inefficient • Quarter wave dipoles have a more complicated beam pattern (not much different from a cosine theta pattern) – Vertical polarization – complete azimuth coverage and are very efficient
90
2
120 60 Maximum gain is 1.647 or 2.2 dB
1.5
150 30 1
0.5
180 0
210 330
240 300
270
Three dimensional pattern (gain) representation Pattern cut through vertical plane Slide 141 SCF01 Electronic Scanned Array Design of 255
Coupppled Dipole Array s
• Wideband Phased Array Antenna and Associated Methods – US Patent 6,512,487 (2003) • This array approximates ideal current sheet – Potentially very broad band and well matched
Slide 142 SCF01 Electronic Scanned Array Design of 255 Radiating Element – Flared notch
• Flared no tch has the bes t performance for airborne applications – Very wide band – Near perfect aperture match • Difficult arises in fabrication and assembly – Radiator stands off the array face – Right angle interconnect from t/r module to radiating element • Use only where benefits warrant added cost
Slide 143 SCF01 Electronic Scanned Array Design of 255
SKA Alternative
• Crossed flared notch elements provide dual polarization for up to 10:1 bandwidth • Scan performance is ±45° • Radiating element match is good
Slide 144 SCF01 Electronic Scanned Array Design of 255 Patches
• Used by – Iridium – JPL L-band designs – Cosmo-Skymed – SEOSAR/PAZ • Well suited to integration with array
Slide 145 SCF01 Electronic Scanned Array Design of 255
Radiating Element – Patch (()1)
• Patch•radiating•elements•offer• goodbd•ba lance•o f•cos t•an d• performance • Planar•configuration•lends• itself• to• large• areas • Possible•to•mount•electronic• components•on•the•back•for• higher•level • integration
Illustrations•from•Byström•(©•Ericsson•Microwave•Systems) Slide 146 SCF01 Electronic Scanned Array Design of 255 Radiating Element – Patch (()2)
E-plane H-plane
• These plots present S11 (return loss) as a function of scan angle •S11 is a measure of power reflected back to the source – This power is not radiated • The radiating element is has little intrinsic loss – Allows computation of scan patterns on next page Illustrations from Byström (© Ericsson Microwave Systems) Slide 147 SCF01 Electronic Scanned Array Design of 255
Radiating Element – Patch (()3)
E-Plane Scan HPlH-Plane S can
0.00 0.00
(1.00)
(1.00) (2.00)
(2.00) (3.00) Gain
(4.00) 1.00 (3.00) 1.25 Gain (5.00) 1.50 1.75 (4. 00) 2002.00 1.00 (6.00) (60) (40) (20) 0 20 40 60 1.25 Scan Angle (5.00) 1.50 1.75 2.00 (6.00) (()60) (()40) (()20) 0204060 Scan Angle
• Element has good predicted performance across octave bandwidth • Need to do sensitivity analysis to material properties and manufacturing tolerances • Very important to validate predictions with test articles
Slide 148 SCF01 Electronic Scanned Array Design of 255 T/R Modules
Slide 149 SCF01 Electronic Scanned Array Design of 255
Transmit/Receive Modules
• T/R modules provide distributed gain and phase control, typically at each radiating element – They provide the flexibility enabling the attractive performance of the ESA • The cost of T/R modules has been the most important restriction on their wide use • Since the 1990’s, costs have declined precipitously leading to the vast increase in ESA applications – Primarily because of commercial demand for MMICs, ASICs, etc
Slide 150 SCF01 Electronic Scanned Array Design of 255 Two Types of Transmit / Receive Modules
T/R module T/R module T/R module T/R moduleT/R module T/R moduleT/R module T/RT/R module module T/RT/R module module T/RT/R module module T/R moduleT/R module T/R moduleT/R module T/RT/R module module ld T/RT/R module module dd
oo T/R module T/RT/R module module T/RT/R module module T/RT/R module module T/R moduleT/R module manif T/R moduleT/R module manifol T/R module nifold anifold T/R module manifold T/R module aa T/R module mm T/RT/R mo d moduleul e m T/R moduleT/R module T/R moduleT/R module T/RT/R module module T/RT/R module module T/RT/R module module T/R moduleT/R module T/R moT/Rd u modulel e T/RT/R module module T/RT/R module module T/RT/R module module T/R module T/R module
Slide 151 •Brick SCF01 Electronic Scanned Array Design• Tile (or Panel) of 255
Northrop-Grumman’s History of TR Modules
Illustration from R. Hendrix (© IEEE) Slide 152 SCF01 Electronic Scanned Array Design of 255 Hughes T/R Module from High Density Microwave Packaging (HDMP) Program
Illustration from George Stimson (© SciTech Publishing, Inc) Slide 153 SCF01 Electronic Scanned Array Design of 255
Raytheon T/R Module for THAAD
Left image and upper right image from Kopp (© IEEE) Lower right image © Raytheon Slide 154 SCF01 Electronic Scanned Array Design of 255 Monolithic Microwave Integrated Circuits (MMIC) Are a Fundamental Enabler for T/R Modules
• MMICs are a fund amen tal ena bler o f t/r mod ul es an d hence ESAs • At X-band, GaAs is the semiconductor material of choice. Processing geometries are 0.25μ (micrometers) or less. Facility capitalization is very expensive so the price of these components includes significant amortization, making their price very sensitive to volume. • With the advent of cell phones, production volume picked up nicely. • Most t/r modules are made by system houses and most of these utilize in-house foundries. The syygstem houses regard these capabilities as competitive discriminators and highly proprietary; accordingly they do not sell outside.
Slide 155 SCF01 Electronic Scanned Array Design of 255
M/A-Com Commercial Chip Set for T/R Modules
• The M/A-Com foundry in Roanoke, VA is one of the few independent sources of chips for t/r modules. • Their chip set provides good performance.
Image © MA-Com Slide 156 SCF01 Electronic Scanned Array Design of 255 Example of Module Efficiency (M/A- Com chip set)
• Using typical current consumption from manufacturer’s specification
Duty Ave Part Type Part Number IDD (A) Voltage Power Factor Power LNA MA01503D 0.19 5 0.95 90% 0.855 CLC MA03503D 0.325 5 1.625 100% 1.625 Driver MAAPGM0034 0.2 10 2 10% 0.2 PA MA08509D 3.9 10 39 10% 3.9
Total 6.58
10 watts peak power, 10% transmit duty RF Out 1
Efficiency 15% Important omissions: DC-DC converter efficiency Slide 157 PA Drain switch voltageSCF01 drop Electronic Scanned Array Design of 255
MMIC Die Sizes
Description Part Number Length Width Height Area mm mm mm mm2 LNA MA01503D 4.58 3.08 0.125 14.11
Gain/Phase MA03503D 5.98 3.97 0.075 23.76 CtlControl PA Amp MA08509D 4.58 4.58 0.075 20.98
DiDriver Amp MAAPGM0034 2482.48 1581.58 00750.075 3923.92
62.76
Slide 158 SCF01 Electronic Scanned Array Design of 255 Phase Shifters & Time Delay Units
• Switched • Analog – Switched lines (TDU) – Ferrite phase shifters – Reflection • UdildUsed in older sys tems – Loaded line designed before – Hi-Lo pass filters microwave integrated • Lowest cost, better in circuit revolution most performance aspects – Cannot handle high power
Slide 159 SCF01 Electronic Scanned Array Design of 255
Time Delay Units
• Coaxial cable is an obvious choice – 1000 feet is 31 pounds and $48.00 – Loss is 1 dB per 10 foot • For L= 1 meter, H=1 meter, azimuth and elevation = 60° and λ=3cm= 3 cm • We need 272 meters of cable or about 900 feet for two-dimensional time delay steering • Printed circuits are better
(L2 " sin azimuth " H2 " sin elevation)/62 =(Area2 " sin azimuth " sin elevation)/62 Slide 160 SCF01 Electronic Scanned Array Design of 255 TELA TDU Module
Slide 161 SCF01 Electronic Scanned Array Design of 255
High-pppass / Low pass Phase Shifter
• Garver was one of th e fi rst t o noti ce th at hi gh -pass andld low-pass filters ha d differen t phase shifts that maintained a constant difference for an appreciable bandwidth. • At microwave frequencies the lumped-element values are both realizable and small and very importantly compatible with MMIC devices and processing
Pi and Tee are equivalent and may be selected according to whichever is more convenient
Presentation follows Robert V. Garver’s 1972 paper Slide 162 SCF01 Electronic Scanned Array Design of 255 Tee Filter Analysis
• ABCD formulation for cascaded lumped elements V A B V 1 = 2 I CD I 5 1 6 5 6 5 2 6
• The representation for a Tee filter is one series, one shunt and one series component
AB 1 ! B X j(2X ! B X2 ) = N N N N N CD jB 1 ! B X - -N - N N N ------
Slide 163 SCF01 Electronic Scanned Array Design of 255
Transmission Characteristic
• Accordingly the transmission term (S21) is 2 S = 21 A + B + C + D •Or 2 S21 = 2 2 (1 ! BN XN ) + j (BN +2XN ! BnXN )
• And the transmission phase characteristic is
2 BN +2XN ! BN XN ? =tan!1 ! 2 (1 ! B X ) 5 N N 6 Slide 164 SCF01 Electronic Scanned Array Design of 255 Higgyh Pass Filter Analysis
• The high pass filter exchanges the series and shunt circuit elements and provides an equal phase shift with the opposite sign • The net phase shift difference between the two circuit paths is
2 BN +2XN ! BN XN "? =2tan!1 ! 2 (1 ! B X ) 5 N N 6
Slide 165 SCF01 Electronic Scanned Array Design of 255
Inpppgut and Output Matching
• EhiitiEach circuit is ma thdiftched if 2 S21 =1 S11 = 1 ! S21 | | | | | | q • Under these conditions
2 XN "? BN = X =tan X 2 +1 N 4 N 3 4 • However, an exact match is possible at only one frequency • Frequency variation of insertion phase and match is not extreme enabling octave bandwidths
Slide 166 SCF01 Electronic Scanned Array Design of 255 Impedance Match Conditions
Low Pass Tee filter 2.0 11.25 22.5 ) n
X 30 (( 45 1.0 60 90 120 actance actance ee 150 0.5 180 Series R Series
0.2 ormalized N ρ=1.1 ρ=1.0 ρ=1.1 0.1 - 0.5 - 1.0 - 2.0 - 5.0 -10.0 Normalized Shunt Reactance (B ) n
Slide 167 SCF01 Electronic Scanned Array Design of 255
Insertion Loss
Phase Shifter Loss 0 11.25 -0.1 22.5 45 -0.2 90 180 -0.3
) -040.4
-0.5 | (dB 21
|S -0.6
-0.7
-0.8
-0.9
-1 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 ω / ω 0
Slide 168 SCF01 Electronic Scanned Array Design of 255 Phase Shifter Return Loss
Phase Shifter Match 0 11.25 22.5 -5 45 90 -10 180
-15 )
-20 | (dB 11
|S -25
-30
-35
-40 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 ω / ω 0
Slide 169 SCF01 Electronic Scanned Array Design of 255
Phase Accuracyyqy over Frequency
Frequency Dependence of Phase Shift
Return Loss 11.25 22.5
180 -20 dB -25 dB -30 dB -30 dB -25 dB -20 dB 45 90 180
90 (°) tt
45 hase Shif
PP 22.5
11.25
Diamonds represent 2° error
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 ω / ω 0
Slide 170 SCF01 Electronic Scanned Array Design of 255 Benefits and Limitations
• High-pass / Low-pass phase shifters are widely used because of their combination of performance and simplicity – Easily fabricated and integrated in MMIC process • Two sources of bandwidth limitation – Beam squint – Phase shifter error – Limitation is acceptable for most applications
Slide 171 SCF01 Electronic Scanned Array Design of 255
Packaggging
• Tight lattice spacing results in component packaging challenges • BiBric k s tyl e mo du les prov ide grea tes t vo lume an d some integration challenges • Tile style modules are preferred and achievable
Slide 172 SCF01 Electronic Scanned Array Design of 255 Georgia Tech 64-Element Antenna
• Liquid Crystal Polymer substrate • PthPatch ra ditidiating e lemen ts • SiGe BiCMOS T/R modules – 7 dB gain – 3-bit phase shifter – 500 MHz bandwidth – Noise figure ~2.5 dB
Slide 173 SCF01 Electronic Scanned Array Design of 255
7-21 GHz Dual-Polarized Array
Slide 174 SCF01 Electronic Scanned Array Design of 255 Thermal Dissipation Constrains Designs
• ESAs generate a l ot o f h eat • Ground based ESAs eventually must transfer heat into air – Problem in the desert • Airborne ESAs are liquid cooled with tight temperature control – Lots of chilled airflow • Spaceborne ESAs must radiate heat, directly or transferred to dedicated thermal radiators – Direct radiation is far simpler, lighter and more reliability but imposes limit on RF power density • High operating temperatures shorten component lifetime, reduce amplifier gain , increase noise figure
Slide 175 SCF01 Electronic Scanned Array Design of 255
Technology Base and Cost
Slide 176 SCF01 Electronic Scanned Array Design of 255 DARPA and Military Manufacturing Technology Programs Initiated the Technology Base
• DARPA - Very High Speed Integrated Circuit (VHSIC) – Industry teams • DARPA - Microwave M onolithi c In tegra te d Circu it (MMIC) – Industry teams • USAF - T/R Module Manufacturing Technology (1989- 1992 ) – Westinghouse-Texas Instruments Team – Hughes Aircraft Company
Slide 177 SCF01 Electronic Scanned Array Design of 255
Consumer Products Provided Final Cost Reductions
• Personal Computers, Mobile Phones and Wireless Networking dwarfed government investment starting in the 1990’ s
Slide 178 SCF01 Electronic Scanned Array Design of 255 AESA Suppliers
• US • Northrop Grumman Electronic Systems (formerly Westinghouse) • Raytheon Systems (formerly Raytheon, Texas Instruments and Hughes) • Harris / Texas Instruments • Lockheed Martin (formerly Martin (formerly General Electric (formerly General Electric and RCA))) • ITT-Gilfillan • Europe • EADS • AtiAstrium (L -bdband space mo dl)dules) • EADS Deutschland GmbH, Ulm (SMTR used in TerraSAR-X & CAESAR) • Defense and Security (MEADS modules) • Thales • Aerospace Division (Elancourt and Crawley) RBE2 AESA for RAFALE • Thales Alenia Space Italia (for Cosmo-Skymed) • ALCATEL ESPACE,,,( Toulouse, FRANCE( ENVISAT and Radarsat)
Slide 179 SCF01 Electronic Scanned Array Design of 255
Gallium Arsenide
•US • All of the above plus • M/A-Com (acquired by Cobham plc Dorset, England in September 2008) • TriQuint (formerly Texas Instruments) • Europe • United Monolithic Semiconductors (UMS), a Franco-German enterprise owne d by EADS an d Tha les • e2v (formerly English Electric Valve) • Asian • Offshore (Win Semiconductor, …)
Slide 180 SCF01 Electronic Scanned Array Design of 255 T/R module cost has been reduced by orders of magnitude since 1980
• Actual numbers are very hard to determine being proprietary, competition sensitive and occasionally embarrassing
Slide 181 SCF01 Electronic Scanned Array Design of 255
Congggpressional Budget Office Opinion
Parame tri c C os t of G aA s MMIC s Size o f a T/R M od ul e • Chipset on described on slides 175-177 totals 63 mm2 • GaAs prices have declined because of WiFi & Mobile Phones
Slide 182 SCF01 Electronic Scanned Array Design of 255 Naval Air Warfare Center BAA Goal
• BdABroad Agency Announcemen tfMftiRt for Manufacturing Research hd and Development of X-Band Active Electronically Scanned Array Transmit/Receive Modules N68936-96-R-0282 dated July 15, 1996 • “The thrust of this effort is to create design and manufacturing innovations to achieve per element module cost of $300 after the first 20,000 modules production” – Contract N68936-97-C-0013 for $3,554,246 awarded to Hughes Aircraft Company November 22, 1996 – Contract N68936-97-C-0017 for $4,498,223 awarded to Raytheon Electronic Systems December 17, 1996
Slide 183 SCF01 Electronic Scanned Array Design of 255
ESA Fed reflectors conceived as a solution to the high cost of T/R Modules
• In 1982 , R ob ert M aill oux ana lyze d ESA fe d re flectors (w hic h he called hybrid antennas) in The Handbook of Antenna Design – “Hyyypybrid antennas would be unnecessary if phased arrays could be made very inexpensively. If the system designers’ dream of a low-cost array with thousands of little elements, each costing a few dollars and controlled by some central processor had happened or would soon happen, there would be little need to expend much time or effort in the development of hybrid antennas.” Includes not just •T/R module function But also •Frequency synthesizer •Receiver •User Interface •Power Supply
Mailloux, R. J., “Hybrid Antennas,” Ch. 5 in The Handbook of Antenna Design, Vol. 1, A. W. Rudge, Milne, Olver, Knight, eds., Peter Peregrinus, London, 1982. Slide 184 SCF01 Electronic Scanned Array Design of 255 USA Prices
• Feb 16, 2007 – Raytheon has been awarded a $212 million contract by the Missile Defense Agency for the manufacture, delivery and integration support of one Terminal High Altitude Area Defense radar, also called the AN/TPY-2 radar. – Radar contains 25,344 modules – puts a ceiling of $8,365 for each modu le pr ice (if every thing e lse was prov ide d a t no cos t)
Clearly, T/R module cost is < $ 1, 000 each
Slide 185 SCF01 Electronic Scanned Array Design of 255
European Prices
• Within the framework of the MEADS design and development programme, EADS Defense & Security Defence Electronics had been awarded a contract worth about €120 million for the production of approx. 40,000 T/R modules and associated electronic components (€3,000 each) – First 5,000 modules delivered in 2008
Slide 186 SCF01 Electronic Scanned Array Design of 255 PART FOUR
Slide 187 SCF01 Electronic Scanned Array Design of 255
ESA Examples
Slide 188 SCF01 Electronic Scanned Array Design of 255 Airborne ESA Systems
Northrop Grumman/Raytheon AN/APG-77 FF22-22 Raptor Northrop Grumman AN/APG-80 F-16E/F Block 60 Fighting Falcon Northrop Grumman AN/APG-81 F-35 Joint Strike Fighter Northrop Grumman Multi-role AESA Boeing Wedgetail (AEW&C) Northrop Grumman APY-9 E-2D Advanced Hawkeye Raytheon AN/APG-63(()V)2F-15C Eagle Raytheon AN/APG-79 F/A-18E/F Super Hornet Raytheon AN/APQ-181 B-2 Spirit bomber European GTDAR (GEC-Thomson- DASA Airborne Radar) consortium, now AMSAR (Airborne Multirole Solid State BAE Systems, Thales, and EADS Active Arrayy) Radar ) Eurofiggghter and Rafale fighter Radar Captor-E CAESAR (CAPTOR Active Electronically Scanning Array Radar) Eurofighter Typhoon RBE2-AA (Radar à Balayage Thales Electronique 2) SELEX Sensors and Airborne Systems S.p.A. created by the merger of the avionics businesses of Finmeccanica Seaspray 7000E and part of BAE Systems Vixen 500E for helicopters Mitsubishi Electric Corporation J/APG-1 Mitsubishi F-2 fighter Ericsson Erieye AEW&C and NORA AESA JAS 39 Gripen Phazotron-NIIR Zhuk-AE (FGA-29 / FGA-35 ) MiG-35 Tikhomirov NIIP Epaulet-A (or Epolet-A) Elta EL/M-2083 aerostat-mounted air search radar Elta EL/M-2052 for fighters
Elta EL/M-2075 radfthIAIPhldar for the IAI Phalcon AEW&C AEW&Ct system
Slide 189 SCF01 Electronic Scanned Array Design of 255
Ground and Naval ESA Systems
muliflti-funct ion ra dar, pr imary sensor o f Thales APAR Dutch De Zeven Provinciën and German Sachsen class frigates SELEX Sensors and Airborne Systems S.p.A. created by the merger of the EMPAR (European Multifunction Phased avionics businesses of Finmeccanica Array Radar) and part of BAE Systems EL/M-2080 Green Pine ground-based Elta early warning AESA radar EL/M-2248 MF-STAR multifunction naval Elta radar U. S. DD(X), CG(X) an d CVN- 21 next- Raytheon AN/SPY-3 generation surface vessels U.S. National Missile Defense X-Band Raytheon Radar (XBR) MEADS International (MI), MBDA Italia, Lenkflugkörpersysteme (LFK) in Multifunction Fire Control Radar (MFCR) Germany and Lockheed Martin Lockheed Martin Space Systems THAAD system fire control radar Company (Raytheon) Insyte multi-function radar for UK. Type BAE SAMPSON 45 destroyers Mitsu bis hi Electr ic Corporat ion (Me lco ) FCS-3 OPS-24 (The world's first Naval Active Mitsubishi Electric Corporation Electronically Scanned Array radar) FPS-5 Japanese ground-based next generation Missile Defense Radar CEA Technologies CEAFAR Naval Phased Array
Slide 190 SCF01 Electronic Scanned Array Design of 255 Most Radio Telescopes are Reflectors
Lovell Telescope is the third largest steerable radio telescope in the world © Credit: Jodrell Bank Centre for Astrophysics, University of Manchester Arecibo is 305 meters diameter (73,000 m2) spherical dish (fixed position) Photo courtesy of the NAIC - Arecibo Observatory, a facility of the NSF
Proposed Square Kilometer Array (SKA) will be some form of ESA Photo © Copyright CSIRO (Commonwealth Scientific and Industrial Research Organisation) Haystack is 37 meters diameter (1,075 m2) (re-positionable) Slide 191 SCF01 Electronic Scanned Array Design © MIT of 255
THAAD
Frequency X-bdband Array size (m2)9.2 T/R Modules 25, 344 Subarrays (Tx/Rx) 72/72 Scan (Az/El) 53°/53° Mechanical El 10° - 60°
Slide 192 SCF01 Electronic Scanned Array Design of 255 Slide 193 SCF01 Electronic Scanned Array Design of 255
Airborne Fighter Aircraft have Transitioned to Active ESA
• F-15 Example
• 18 F-15C aircraft retrofitted with ESA radar entered service in 2000 • EhEnhanced perf ormance and improved maintainability
Images © Boeing Corporation Slide 194 SCF01 Electronic Scanned Array Design of 255 ESAs in Space
Slide 195 SCF01 Electronic Scanned Array Design of 255
Iridium Communications Satellite
• 66 sat ellit e cons te lla tion – 5 May 1997 to 7 Mayy() 1998 (72) • Altitude 781 km • Inclination 86.4° • Frequency 1.62 GHz • Antenna boresight 50° fdifrom nadir • Antenna size 0.86m x Iridium Prototype Installed at Smithsonian Museum 188m1.88 m – 106 patch radiators • 8 x 16 Butler Matrix Feed
Slide 196 SCF01 Electronic Scanned Array Design of 255 Iridium Beams in U-V Space
Slide 197 SCF01 Electronic Scanned Array Design of 255
Iridium Beams on Globe
Slide 198 SCF01 Electronic Scanned Array Design of 255 Iridium Beam on Globe (()detail)
Slide 199 SCF01 Electronic Scanned Array Design of 255
Iridium Beams ppjrojected to Ground
Slide 200 SCF01 Electronic Scanned Array Design of 255 Some Radars On-Orbit
StilSentinel – C-bdband TerraSAR -X – GXGermany X-bdband © European Space Agency © Astrium GmbH
RadarSat-2 – Canada C-band Cosmo-SkyMed – Italy X-band Slide 201 SCF01 Electronic Scanned Array Design © Canadian Space Agency © Finmeccanica of 255
On-orbit and Planned Radar Satellites 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 000 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 USA SeaSAT / SIR / SRTM L/C/X bands Japan JERS-1, ALOS, ALOS-2 L-band Argentina SAOCOM L-band USA-India NISAR L/S-band Germany-Japan TanDEM-L (2023) L-band
UK NovaSAR S-band ww Commercial Urthecast S/X-band Canada RadarSat-1,2 / RCM C-band Time No European Space Agency ERS-1,2 / EnviSat / Sentinel C-band Germany-military SAR-Lupe / SARah X-band Germany-civilian TerraSAR-X, TanDEM-X, TerraSAR-NG, HRWS (2022) X-band Italy Cosmo-Skymed, CSG X-band Israel TecSAR reflector X-band India RISAT-2 / RISAT-1 planar array X/C bands Korea Kompsat-5, 6 ESA X-band Spain PAZ X-band Slide 202 SCF01 Electronic Scanned Array Design of 255 Some Private Enterprise Plans
• Iceye – Constellation of six microsatellites with Synthetic Aperture Radar (SAR) imaging with first launch end of 2017 – Build own satellites • UrtheCast – Plan eight SAR satellite constellation launched in 2019 and 2020 – Supplier is Surrey Satellite dual band (X and L) based on NSARNovaSAR • XpressSAR – Constellation of four satellites planned to launch beginning in 2020 – Satellite supplier unnamed
Slide 203 SCF01 Electronic Scanned Array Design of 255
Comparative Radar Satellite Performance
60 P⋅G2=130 (dBW) P⋅G=70 (dBW) P⋅G2=120 (dBW)
COSMO-SkyMed 50 P⋅G2=110 (dBW) SAR-Lupe TecSAR RADARSAT ENVISATTerraSAR-X P⋅G=60 (dBW) ERS Sentinel P⋅G2=100 (dBW) DESDynI
n (dB) 40 P⋅G2=90 (dBW) SC/SIR-C/L JERS-1 ALOS-2ALOS SEASATSIR-ASIR-B P⋅G=50 (dBW) P⋅G2=80 (dBW) um Gai 30 P⋅G2=70 (()dBW) mm P⋅G=40 (dBW) P⋅G2=60 (dBW) Maxi
20 P⋅G2=50 (dBW) P⋅G=30 (dBW) P⋅G2=40 (dBW) 100 W 1000 W 10 10 20 30 Average Transmit Power (dBW)
Slide 204 SCF01 Electronic Scanned Array Design of 255 Satellite ESAs Optimized for SAR
# of Azimuth Elevation Satellite Modules Dx (Ȝ)Dy (Ȝ) Limit Limit ALOS 80 9.42 0.61 3.0° 54° ALOS-2 180 4.19 0.68 6.8° 47° RADARSAT 512 16.56 0.83 1.7° 37° Envisat 320 17.77 0.72 1.6° 44° Sentinel 280H/280V 15.83 0.74 1.8° 43° Cosmo-Skymed 1280 9179.17 0700.70 313.1° 45° Cosmo NG 2560 TerraSAR-X 384 12.81 0.75 2.2° 42° TerraSAR-NG 1,280 9.17 0.7 3.1° 45°
• Az and El computed to exclude grating lobe Slide 205 SCF01 Electronic Scanned Array Design of 255
ESA RF Power Densities
• COSMO-SkyM ed an d SEOSAR/PAZ uses a pat ch radi a tor; the o ther satellites use waveguide which may have better thermal dissipation properties
Satellite Band (RF) Watts per m2 ALOS/PALSAR L-band 5 ALOS-2 L-band 12 RADARSAT C-band 13 ENVISAT C-bdband 25 Copernicus (Sentinel) C-band 50 COSMO-SkyMed X-band 90 SEOSAR/PAZ X-band 117 TerraSAR-X X-band 129
Slide 206 SCF01 Electronic Scanned Array Design of 255 L/C/X Band Antenna(()s)
Slide 207 Images courtesy NASA/JPL-CaltechSCF01 Electronic Scanned Array Design of 255
TerraSAR-X
Dual polarized slotted waveguide radiator and module assembly
Spacecraft structure showing location of 12 antenna panels
Module assembly including polarization switching and FPGA controller
One of 12 antenna panels composed of 32 T/R module/radiator assemblies Slide 208 SCF01 Electronic Scanned Array Design6.3 watt (38 dBm) SMTR modules Images © IEEE of 255 TerraSAR-X NG
• UdUnder s tdtudy • Wider Bandwidth – 600 MHz (WRC 2007) – -1.2 GHz (WRC 2016) • New Radiating Element – European Patent EP2100348 – Serpentine inner conductor alters propagation velocity so that slots are excited in phase – Propagation modes are not dispersive which broadens bandwidth
Slide 209 SCF01 Electronic Scanned Array Design of 255
Italy - COSMO-SkyMed
• X-bdband • ESA Design • 57mx14marray5.7m x 1.4m array • 1,900 kg • ~5 kW peak transmit • 1,280 TR modules manufactured by Thales Alenia Space Italia • Incorporates true time delay – Up to 15 wavelengths • Growth option to five phase centers (channels) for MTI
Images © e-GEOS S.p.A. Slide 210 SCF01 Electronic Scanned Array Design of 255 COSMO-Skymed Satellite Radar
• Four satellite constellation – 8 June 2007 to 5 November 2010 • Altitude 619.6 km • Inclination 97.86° • Frequency 9.6 GHz • Antenna boresight 34° from nadir • Antenna size 5.7 m x 1.4 m – 15,360 patch radiators (240x64) • Pulsewidth up to 100 μs • Duty Cycle Tx up to 30% • PRF up to 4.5 kHz Artist's rendition of a COSMO-SkyMed • Beam steering (image credit: ASI) –Elevation ±20° –Azimuth ±2° • Beamwidth – Azimuth 0.3° Slide 211 SCF01 Electronic Scanned Array– Elevation Design 1.7° to 6° of 255
Antenna Beams in U-V Space
Slide 212 SCF01 Electronic Scanned Array Design of 255 Antenna Beams on Globe
Slide 213 SCF01 Electronic Scanned Array Design of 255
Antenna Beams on Globe (()detail)
Slide 214 SCF01 Electronic Scanned Array Design of 255 Antenna Beams Projected to Ground
Slide 215 SCF01 Electronic Scanned Array Design of 255
L-Band Trade Study
Slide 216 SCF01 Electronic Scanned Array Design of 255 L-band Systems
• History – Shuttle (JPL) – JERS-1 (JAXA) – ALOS (JAXA) – ALOS-2 (()JAXA) – SAOCOM (CONAE)
• Planned/Proposed Systems – DESDynI NISAR (JPL+ISRO) – TerraSAR -L (DLR/JAXA)
Slide 217 SCF01 Electronic Scanned Array Design of 255
Geometric Relationships
θ • Angles and lengths easily h look ρ θ incident computed with trigonometric identities r e
r e
α
2 2 2 ; = re + (re + h) ! 2re(re + h) cos(,) sin(,) sin(3 ) sin(: ! 3 ) = look = incident ; re re + h Slide 218 SCF01 Electronic Scanned Array Design of 255 L-band Arrays
10.0
6.5 99 99 2. 0.
ALOS-2 TanDEM-L Feed
10.0 13.5 3.5 3.5
SAOCOM DESDyni ESA
Slide 219 SCF01 Electronic Scanned Array Design of 255
System Performance
ALOS-2 SAOCOM DESDynI DESDynI NISAR TanDEM-L
Altitude 628 km 620 km 761 km 761 km 740 km 745 km 15 m 12 m 15 m Antenna Size 2.9 x 9.9 m 3.5 x 10 m 3.5 x 15 m diameter diameter diameter Transmit 5 kW 3.9 kW 3.2 kW 3.2 kW 3.0 kW 10.9 kW Power -24 ~ -28 -24 ~ -28 NESZ (spec) -35 dB < -20 dB -20 ~ -25 dB dB dB Resolution 1 ~ 100m 10~ 100m 3m ~ 100m 3 ~ 10m 1 ~ 10 m Incidence 8° to 70° 20° to 50° 30° to 50° 30° to 50° 34° to 48° Angle Swath Width 350 km 320 km 350 km 350 km > 200 km 350 km
±30° elevation ±25° elevation ±9° elevation ±8° elevation Electronic Scan ±3.5° azimuth ±40° azimuth no azimuth scan ±2° azimuth
Slide 220 SCF01 Electronic Scanned Array Design of 255 Antenna Characteristics
ALOS-2 SAOCOM DesDYNI DesDYNI NISAR TanDEM-L
Array Size 2.9 x 9.9m 3.5 x 10.0m 3.5 x 15.0 m 0.5 x 4.0 m 0.5 x 1.5 m 1.0 x 4.6 m
Reflector Diameter 15 m 12 m 15 m
Number of Modules 180 140 1,600 64 24 192
Number of Phase 18 20 20 32 12 32 CtCenters (El)
Phase Center 0.63 lambda 0.74 lambda 0.68 lambda 0.52 lambda 0.52 lambda 0.60 lambda Spacing (El)
Number of Phase 10780226 Centers (Az)
Phase Center 4.32 lambda 6.07 lambda 0.60 lambda 1.05 lambda 1.05 lambda 0.68 lambda Spacing (Az)
T/R Module Power 34 Watts 28 Watts 2 50 Watts 125 Watts 56.6 Watts
Peak Transmit Power 6.1 kW 3.9 kW 3.2 kW 3.2 kW 3.0 kW 10.9 kW
EIRP (PG) 66 dBW 75 dBW 76 dBW 66 dBW 68 dBW 71 dBW
PG2 114 dBW 114 dBW 116 dBW 97 dBW 100 dBW 100 dBWSlide 221 SCF01 Electronic Scanned Array Design of 255
Advanced Land Observing Satellite "DAICHI" (ALOS)
• ALOS-2 – L-band – ESA design – 9.9m x 2.9m – 2,120 kg – 5 kW peak transmit power – 180 TR modules – 5.2kW (EOL) power system
Image © JAXA | Japan Aerospace Exploration Agency
Slide 222 SCF01 Electronic Scanned Array Design of 255 ALOS (Advanced Land Observing Satellite) PALSAR (Phased Array Synthetic Aperture Radar)
PALSAR Electrical Model PALSAR-2 Flight Model
Images © JAXA | Japan Aerospace Exploration Agency Slide 223 SCF01 Electronic Scanned Array Design of 255
ALOS-2 PALSAR Array
Array Width = 9.90 meters Array Height = 2.90 meters Array Area = 25.84 square meters Wavelength = 0.229 meters Number of Elements = 1080 Areal Gain (4⋅π⋅A/λ2) = 37.9 dBi Delta X = 0. 165 meters (6. 50 inches) Delta Y = 0.145 meters (5.71 inches) Number of elements = 1080 Triangular angle = 60.4 degrees Colors denote subarrays Slide 224 SCF01 Electronic Scanned Array Design of 255 Used Uniform Element Factor
10 Maximum Gain = 7.6
0
-10
-20 Gain (dB)
-30
-40 Phi=0° Phi=45° Phi=90° cos -50 -90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90 θ (°) • Aperture equal to lattice size • Compare to slide 13 of this presentation
Slide 225 SCF01 Electronic Scanned Array Design of 255
Antenna Pattern Boresight and Steered
Slide 226 SCF01 Electronic Scanned Array Design of 255 Azimuth Cut Steered in Azimuth
40
→← 3 dB Beamwidth = 6.1° 30 → ← 10 dB Beamwidth = 10.5°
20
10 Gain (dB) Gain
0
-10 Array Factor Subarray Factor Maximum Gain = 36.4 Array Factor Grating Lobes θ = 5.0°,φ = 0.0° Subarray Factor Nuls -20 -90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90 Azimuth (degrees) Slide 227 SCF01 Electronic Scanned Array Design of 255
Elevation Cut Steered in Elevation
40
→← 3 dB Beamwidth = 5.7° 30 →← 10 dB Beamwidth = 9.6°
20
10 Gain (dB) Gain
0
-10
Maximum Gain = 36.7 Array Factor θ = 40.0°,φ = 90.0° Subarray Factor -20 -90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90 Elevation (degrees) Slide 228 SCF01 Electronic Scanned Array Design of 255 ESA Beamwidth Fairly Constant with Scan
7 7 Azimuth Beamwidth Azimuth Beamwidth Elevation Beamwidth Elevation Beamwidth 6 6
5 5 ) ) ° ° 4 4
3 3 Beamwidth ( Beamwidth Beamwidth ( Beamwidth
2 2
1 1
0 0 0 1 2 3 4 5 0 10 20 30 40 AiAzimu thSth Scan (°) Eleva tion Scan (°)
• Elevation and Azimuth beamwidth change with cos-1 θ
Slide 229 SCF01 Electronic Scanned Array Design of 255
ALOS-2 Gain as a Function of Scan
40 Azimuth Scan Elevation Scan cos θ 39
38
Gain (dB) 37
36
35 0 10 20 30 40 Scan Angle (°) Slide 230 SCF01 Electronic Scanned Array Design of 255 Beam Laydown
• Elevation scan covers nadir to 20°grazing (70° incidence) angle • Individual beam includes Doppler of ±25kHz2.5 kHz
Slide 231 SCF01 Electronic Scanned Array Design of 255
Additional Features
• Split aperture to form two beams on receive • Reduce aperture width from five to three panels to bdbbroaden beam in az ithimuth
Slide 232 SCF01 Electronic Scanned Array Design of 255 OFFSET REFLECTOR
Slide 233 SCF01 Electronic Scanned Array Design of 255
Radar Satellite Geometry & Timing
Radar 600 Radar altitude = 619. 6 km 500 -3 dB swath from 421 km to 440 km -15 dB swath from 396 km to 467 km 400 20 19 18 Pulse repetition frequency = 3.00 kHz 300 17 μ 16 15 Transmit pulse width = 33 sec ude (km) 14 tt 200 13 12 Transmit duty cycle = 10% 11 10 Time = 10,000 μ sec Alti 100 Ho 9 8 rizo 7 2025° ° 38° n 6
° 50 5
0 ° 4 60
1 4 0 3
6 0 0 3 7 2 2 5 00 36 4 6 7 1 8 000 1500 Ground offset Distance (km) 2 000
250 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 4 20 0 ) 7 ° 15 2 10 rival (
rr 5 -15 dB 0 -3 dB -5 -15 dB -10 -15 Angle of A of Angle -20 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Time of Arrival (μ seconds) TanDEM-L
Diameter 15m Focal length 13.5 m Offset (elevation) 9 m Azimuth elements 6 Elevation elements 32 (or 40) Azimuth Spacing 0.6 ʄ Elevation spacing 0.6816 ʄ
Elevation Scan Approximately ±8° Slide 235 SCF01 Electronic Scanned Array Design of 255
TanDEM-L Feed Designs
5.2 6.5 0.9 0.9
• Standard feed for 7 meter • Enhanced feed shape resolution designed to capture • Performance degrades at >80% of received power near andfd far range • Shape correspon ds to o ff- • Supports three azimuth axis aberration of channels parabolic reflector
Slide 236 SCF01 Electronic Scanned Array Design of 255 Deformation, Ecosystem Structure and Dynamics of Ice DESDyni (JPL)
• A dedicated U.S. InSAR and LIDAR mission optimized for studying hazards and global environmental change. • L-ban d syn the tic aper ture ra dar (SAR) sys tem – Operated as a repeat-pass interferometer (InSAR) – Multiple polarization: single, dual, or fully polarimetric – Strip-map or scanSAR (SCORE) modes with a viewable swath of 340 km – 35 m ground resolution – Two sub-bands separated by 70 MHz for ionospheric correction
Slide 237 SCF01 Electronic Scanned Array Design of 255
DESDyni Reflector Concept
Resource Reflector Instrument Mass 600 kg Instrument Power 1600 watts Dimensions 15 meter diameter ~4 x 0.5 meter feed
desdyni.jpl.nasa.gov/files/DESDynI_RadarDes&PerfV4a.pdf Images courtesy NASA/JPL-Caltech Slide 238 SCF01 Electronic Scanned Array Design of 255 Feed Structure Also Contains Electronics and Thermal Management System
Next Generation Geodetic Imaggging with Interferometric SAR: Toward InSAR Ever ywhere , All the Time Paul A. Rosen, Jet Propulsion Laboratory, California Institute of Technology UNAVCO Workshop, Boulder, Colorado, March 10, 2010 Slide 239 SCF01 Electronic Scanned Array Design of 255
DESDynI Model
Slide 240 SCF01 Electronic Scanned Array Design of 255 DESDynI Model Parameters
• Rfltdit15tReflector diameter 15 meter pro jtdibjected in beam ditidirection (actual reflector is elliptical) • Focal Length is 10 meters • Array feed of 24 conical horns, distributed on 2.2 meter centers at focal ppplane position with 40 de gree ta per angle and 12 dB taper – Feed design would be optimized for Efficiency/Spillover during detailed design • No struts or other obstructions which tend to raise sidelobes • Used Ticra Grasp software (full version) – These cases can run on student version if each feed element is separately analyzed (24 cases) and results summed
Slide 241 SCF01 Electronic Scanned Array Design of 255
Feed Pattern Over-illuminates Reflector Spillover 1 Relative Power Spill Over (dB) 0.95
0.9
0850.85
0.8
0.75
070.7
0.65
0 5 10 15 20 25Slide 242 SCF01 Electronic Scanned Array Design Element Number of 255 Individual Beam Patterns Elevation Cut
Array Feed Element 12 Far-field Principal Plane Cuts 50 66
Elevation Cut 0.1 0. Individual Feed →←→← 40 Azimuth Cut
30
20
10
0
-10
-20
-30
-40 1.0° 3 dB beamwidth Effective Array Width (λ/θ) = 12.2 meters 101.0° 3dBb3 dB beam he ig hht Effecti ve A rray H e ig ht (λ/θ)122) = 12.2 meters -50 -50 -40 -30 -20 -10 0 10 20 30 40 50Slide 243 SCF01 Electronic Scanned Array Design of 255
Transmit Beam Comprises Sum of 24 Feeds Combined Feeds Elevation Plane Cut 50 →←Individual Feed Summation 40
30
20
10
0
-10
-20 Effective Array Width (λ/θ) = 13.6 meters 13. 9° 3dBb3 dB beam he ig hht Effecti ve A rray H e ig ht (λ/θ)09) = 0.9 meters -30 -50 -40 -30 -20 -10 0 10 20 30 40 50Slide 244 SCF01 Electronic Scanned Array Design of 255 24 Element Sum Principal Plane Cuts Combined Feeds Principal Plane Cuts 50 Elevation Cut →←→← Individual Feed Summation Azimuth Cut 40
30
20
10
0
-10
-20 0.9° 3 dB beamwidth Effective Array Width (λ/θ) = 13.6 meters 13. 9° 3dBb3 dB beam he ig hht Effecti ve A rray H e ig ht (λ/θ)09) = 0.9 meters -30 -50 -40 -30 -20 -10 0 10 20 30 40 50Slide 245 SCF01 Electronic Scanned Array Design of 255
Beam Width Variation Reflector vs ESA Individual Beam Size 6 BeamwidthBeamwidth Azimuth ReflectorAzimuth BeamwidthBeamwidth Elevation ElevationReflector Beamwidth Azimuth ALOS-2 5 Beamwidth Elevation ALOS-2
4 )) °°
3 BB size size ( ( dddd 3-3-
2
1
0 -40 -10 -30 -20 -5 -10 0 10 5 20 30 10 40Slide 246 SCF01 Electronic Scanned Array Design Scan Angle (°) of 255 Reflector Beam Gain Variation
Array Feed Elements Far-field Pattern Contour Elemental Beam Gain 0.3 46 15° 42 dB 39 dB 0.2 36 dB 44 10° 33 dB 30 dB
42 0.1 5°
0° 40 V 0 Gain (dB) Gain
-5° -0.1 38
-10° 36.536.5 -0.2 Individual Feed Patterns 36 20141215Job_03 offset_reflector_array -15° -15° -10° -5° 0° 5° 10° 15° 34 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0 5 10 15 20 25 U Element Number
• Beam broadening and gain reduction are directly related
Slide 247 SCF01 Electronic Scanned Array Design of 255
Eqqpuivalent Aperture Sizes for Reflector
Array Feed Element 24 Reflector Current Contour
-3 dB width = 8.7 meters -34 dB 6 -3 dB height = 8.0 meters -38 dB -41 dB -46 dB 4
2 -31.2
0 Y (m)
-2
-4 Feed 24 20141215Job_03 -6 offset_reflector_array
-6 -4 -2 0 2 4 6 Slide 248 SCF01 Electronic Scanned Array Design X (m) of 255 Currents in Reflector
Array Feed Total Contour
-3 dB width = 8.5 meters -13 dB 6 -3 dB height = 3.5 meters -17 dB -20 dB -25 dB 4 -30 dB
2
0 Y (m) -10.3 -2
-4
Individual Feed -6 20141215Job_03 offset_reflector _ array
-6 -4 -2 0 2 4 6 Slide 249 SCF01 Electronic Scanned Array Design X (m) of 255
L-band Summary
• Array size – Array height of 4 meters matches Tx requirement well – Array height of > 4 meters advantageous for Rx – Array length of ~ 10 meters compatible with azimuth resolution of ~ 3 - 10 meters • Scan Capability – Elevation beam agility required for good area coverage (SSARSweepSAR/SCORE, SSARScanSAR, etc) – Azimuth beam agility enables additional modes (TOPSAR) – Beam agility required for spotlight modes – Reflectors have limited azimuth steering
Slide 250 SCF01 Electronic Scanned Array Design of 255 Feeds
• Feed for reflector needs beam shaping to for acceptable efficiency in both Rx and Tx • Array f eed s h ave cons idera bly hig her power dens ity than ESAs complicating cooling • Large number of TRM’ s in ESA provides degrees-of- freedom necessary for advanced beam control
Slide 251 SCF01 Electronic Scanned Array Design of 255
Launch Constraints
• Reflector antennas are more amenable to folding required for launch – Provide higher gain in receive • ESA antennas up to 3.5 x 10 meters have been designed for folding
Slide 252 SCF01 Electronic Scanned Array Design of 255 References
• Phased A rray A nt enna H andb ook , S econd Editi on b y Ro ber t J. Ma illoux, 508 pages, Ar tec h House, 2nd edition (March 31, 2005) (originally published in 1994) • “Electronically scanned array” in Synthesis Lecture on Antennas, R. J. Mailloux, Morgan & Claypool Publishers, 2007. • Radar Handbook, Third Edition by Merrill Skolnik, 1328 pages, McGraw-Hill Professional, 3rd edition (January 22, 2008) (originally published 1970) – Chapter 12 Reflector Antennas by Michael Cooley and Daniel Davis – Chapter 13 Phased Array Radar Antennas by Joe Frank and John D. Richards • Antenna Theory Analysis and Design by Constantine Balanis, 790 pages, Harper & Row 1982 • Practical Phased Array Antenna Systems (Artech House Antenna Library) (Paperback) by Eli Brookner, 320 pages Artech House (December 1, 1991) • Phased Array Antennas (Wiley Series in Microwave and Optical Engineering) (Hardcover) by R. C. Hansen (Author) 504 pages Wiley-Interscience (January 19, 1998) (originally published in 1966) • Introduction to Airborne Radar by George W. Stimson, 584 pages, SciTech Publishing, 2nd Edition (January 1, 1998) (originally published in 1983) • Electronically Scanned Arrays MATLAB® Modeling and Simulation by Arik D. Brown, 224 pages, CRC Press , (May 3 , 2012) • Antenna Arrays: A Computational Approach by Randy L. Haupt, 534 pages, Wiley-IEEE Press Slide 253 (April 12, 2010) SCF01 Electronic Scanned Array Design of 255
Web Based References
• EW and Radar Handbook – https://ewhdbks.mugu.navy.mil/home.htm • Dr. Dav id C. Jenn lec ture s lides an d Ma tLa b co de – http://www.nps.navy.mil/Faculty/jenn/ • Jet Propulsion Laboratories – http://southport.jpl.nasa.gov/ • Microwave 101 – http://www.microwaves101.com/index.cfm • Electromagnetic Waves and Antennas – Sophocles J. Orfanidis – http://www.ece.rutgers.edu/~orfanidi/ewa
Slide 254 SCF01 Electronic Scanned Array Design of 255 Thank you for your attention
Slide 255 SCF01 Electronic Scanned Array Design of 255