MURI Teleconference 5/28/04
30
MURI Teleconference 5/28/04 Electrical Engineering Department University of California, Los Angeles Professor Tatsuo Itoh
description
MURI Teleconference 5/28/04. Professor Tatsuo Itoh. Electrical Engineering Department University of California, Los Angeles. Agenda. Voltage scanned Leaky Wave Antenna Near Field Focusing using Non-uniform Leaky Wave Antenna 2D Mushroom Structure Planar Lens Surface Plasmon - PowerPoint PPT Presentation
Transcript of MURI Teleconference 5/28/04
MURI Teleconference 5/28/04
Electrical Engineering Department
University of California, Los Angeles
Professor Tatsuo Itoh
Agenda
• Voltage scanned Leaky Wave Antenna
• Near Field Focusing using Non-uniform Leaky Wave
Antenna
• 2D Mushroom Structure
• Planar Lens
• Surface Plasmon
• Leaky Wave Antenna
• Generalized Transmission Matrix Method
Composite Right / Left-Handed (CRLH) TL
0, Z
d
RL
RC LL
LC
H m
F m
H m
F m
0z
Infinitesimal Circuit Model Transmission Line Representation
22
, where
1 1,
1
R RL L
R RR R
L L L L
j Z Y
Z j L Y j Cj C j L
L Cs L C
L C L C
22
12
1
R RL L
R R
L L
RH LH
L CL C
L CL C
Balanced CasePropagation Constant
Definition: R L L RL C L C L C
1 2
1 1 1 11if min , and 1 if max ,
R L L R R L L R
sL C L C L C L C
RL
RCLL
LC
Motivation of Electronically-Scanned LW AntennaMotivation of Electronically-Scanned LW Antenna
Conventional LWA Frequency dependent scanning
Conventional Electrically-Scanned LWA Frequency independent scanning Only two discrete states are possible Waveguide configuration with PIN diode
Novel Electronically Scanned LWAFrequency independent scanning Efficient ChannelizationContinuous scanning capabilityMicrostrip technology Low profile
Conventional Magnetically-Scanned LWA Frequency independent scanning Biasing DC magnetic field NOT practical Waveguide configuration
R. E. Horn, et. al, “Electronic modulated beam steerable silicon waveguide array antenna,” IEEE Tran. Microwave Theory Tech.H. Maheri, et. al, “Experimental studies of magnetically scannable leaky-wave antennas having a corrugated ferrite slab/dielectric layer structure,” IEEE Trans. AP.L. Huang, et. al, “An electronically switchable leaky wave antenna,” IEEE Trans. AP.
The Principle of the Proposed Idea : Radiation Angle ControlThe Principle of the Proposed Idea : Radiation Angle Control
Scanning angle is dependent on inductances and capacitances Introducing varactor diodes
Capacitive parameters are controlled by voltages Dispersion curves are shifted vertically as bias voltages are varied Radiating angle becomes a function of the varactor diode’s voltages
Scanning angle is dependent on inductances and capacitances Introducing varactor diodes
Capacitive parameters are controlled by voltages Dispersion curves are shifted vertically as bias voltages are varied Radiating angle becomes a function of the varactor diode’s voltages
0
0RH 0LH 0
0( )
c
k
1V
1V2V
2V
3V
3V
0k
1
0
( )( ) sin
VV
k
1
0
( ) sinVk
Series and Shunt Varactors Fairly constant characteristic impedance Additional degree of freedom for wider scanning range
Reverse biasing to Varactors Anodes of varactors : GND Cathodes of varactors: Biasing
Series and Shunt Varactors Fairly constant characteristic impedance Additional degree of freedom for wider scanning range
Reverse biasing to Varactors Anodes of varactors : GND Cathodes of varactors: Biasing
stub (via) shorted :B
capacitor alinterdigit :A
`
Z Z
L2CL2CRL 2RL 2
LLRC
Y
A B
var,RLvar,LC var,LC var,RL
1,RL 1,LC 1,LC 1,RL
1,LL
var,RC 1,RC 2,LLDCL
DCV
Z Z
Y
A B
A
B
varactor
GND
GND inductor
Modified Layout of a Microstirp CRLH TL Unit cellsModified Layout of a Microstirp CRLH TL Unit cells
Dispersion diagramDispersion diagram
1( ) cos (1 '( ) '( )) /V Z V Y V d
dCj
LjVCj
LjVZL
RL
R
1,1,
var,var,
1||
)(
1)('
dLLVCC
VCLCLVCLCLj
RRLL
LRLRLRLR
)()(
1)()(
var,1,2
var,1,
2var,var,1,1,2
var,var,1,1,
dLj
CjVCjLj
VYL
RRL
2,1,var,
1,
1)(||
1)('
dLj
CjVCL
j
LR
RL
2,1,
var,1,2
1
)(/1
0/ k
Voltages
Parameters0 V 5 V 10 V
LR,var [nH] 1.840 2.029 1.768
C R, var (=C L,var) [pF] 2.544 0.916 0.765
LL1 [nH] 5.168 6.165 6.524
CR1 [pF] 1.230 1.018 0.900
LL2 [nH] 4.597
CL1 [pF] 0.485
LR1 [nH] 2.027
Prototype of 30 Cell Proposed TLPrototype of 30 Cell Proposed TL
The cathodes of three varactors in the same direction Efficient biasing: Only one bias circuitry in unit cell
Back to back configuration of two series varactors Fundamental signals : in phase and add up Harmonic signals: out of phase and cancel
Port 1 : Excitation Port 2: Terminated with 50 ohms Suppress undesired spurious beams
Shunt varactor
Series varactors3.02 (0.46 )strip
effcm
DC
Bias Configuration
Shunt varactor
varactorsSeries
-+
Via
Feed) (DCInductor
)(V GND, b
Via
- ++
)(V bias DC b
LZinP
38.34 (5.87 )stripeffcm
3.02 (0.46 )stripeffcm
1.2 (0.18 )stripeffd cm
1Port 2Port
Continuous Scanning Capability at 3.33 GHzContinuous Scanning Capability at 3.33 GHz
01020100
0
30
6060
30
01020100
030
6060
30
01020100
0
30
6060
30
V = 18 VLH ( β < 0)
V = 3.5 VBroadside ( β = 0 )
V = 1.5 VRH ( β > 0)
Scanning Range Δθ = 99º (-49º to +50º) Backward, forward, and broadside
Biasing Range ΔV = 21 V ( 0 to 21 V)
Fixed operating frequency : 3.33 GHz
Good agreement with theoretical and experimental results
Scanning Range Δθ = 99º (-49º to +50º) Backward, forward, and broadside
Biasing Range ΔV = 21 V ( 0 to 21 V)
Fixed operating frequency : 3.33 GHz
Good agreement with theoretical and experimental results
Performance as a LW AntennaPerformance as a LW Antenna
High directivity : One of attractive characteristic of LW antennas Achieved by increasing the number of cells Large radiation aperture
Antenna dimension : Maximum Gain : 18 dBi at broadside ( V = 3.5 V )
High directivity : One of attractive characteristic of LW antennas Achieved by increasing the number of cells Large radiation aperture
Antenna dimension : Maximum Gain : 18 dBi at broadside ( V = 3.5 V )
38.34 (5.87 )stripeffcm
Focusing by a Planar Non-Uniform LW InterfacePrinciple Dipole array model for the TX antenna
x
z
focus
d0
TXˆ
iRi
yL
ˆFFr x
iFR
iz
ˆ ˆiF z iFR x z
01
( ) exp( ) ( )N
z i i zii
E I j E
F iFr R
E-Field Maximization
d0 = 0/2 F = 6
0
0
0 20 0
0 2
0
1 1 ˆ( ) 1 sin
1 ˆ2 cos
ˆ ˆ ˆ( ) ( ) ( )
jk
i
jk
i
xi yi zi
eE j
jk k
j eE
k
E E E
iF
iF
R
i iF i
iF iFiF
R
i
iF iFiF
iF iF iF
E R θR RR
RR RR
x R y R z R
E-Field of a Dipole
F
z
Fx
RX
TX
source
focus
0 θ i
F
z
Fx
RX
TX
source
focus
0 θ i
zi(RiF+Ez(rF) ~ k0|RiF|+constant~
0 2 4 6 8 10 12-18
-16
-14
-12
-10
-8
-6
-4
-2
0
x(z
No
rmal
ized
Ele
ctri
c F
ield
(d
B)
Effects of Different Array Length.
z(
z(z
z(
No
rmal
ized
Ele
ctri
c F
ield
(d
B)
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
L=12L=30
L=12L=30
4 -2 0 2 4
F = 60
dB
L = 300L = 120
Piece-Wise Linear Approximation
0 2 4 6 8 10 12-18
-16
-14
-12
-10
-8
-6
-4
-2
0
x (0) (z=0)
Nor
ma
lized
Ele
ctri
c F
ield
(d
B)
2 Groups6 GroupsContinuous
2 Groups6 GroupsContinuous
-4 -2 0 2 4-30
-25
-20
-15
-10
-5
0
z (0) (x=F=60)
Nor
mal
ized
Ele
ctric
Fie
ld (
dB)
2 Groups6 GroupsContinuous
-4 -2 0 2 4-30
-25
-20
-15
-10
-5
0
z (0) (x=F=60)
Nor
mal
ized
Ele
ctric
Fie
ld (
dB)
2 Groups6 GroupsContinuous
z(0)
-15 -10 -5 0 5 10 152000
3000
4000
5000
6000
2000
3000
4000
5000
z (0)
phas
e of
exc
itatio
n (d
eg) 2 Groups
6 GroupsContinuous
F = 60
~
k 0|RiF|+
cons
tant
~
dB
L = 300
Effects of Leakage Factor
Willkinson power dividerNon-uniform LW antennax x
Prototype
0 2 4 6 8 10 12-18
-16
-14
-12
-10
-8
-6
-4
-2
0
x (0) (z=0)
Nor
mal
ized
Ele
ctric
Fie
ld (
dB)
=0 (1/m)=1 (1/m)=4 (1/m)
0 2 4 6 8 10 12-18
-16
-14
-12
-10
-8
-6
-4
-2
0
x (0) (z=0)
Nor
mal
ized
Ele
ctric
Fie
ld (
dB)
=0 (1/m)=1 (1/m)=4 (1/m)
-4 -2 0 2 4-40
-35
-30
-25
-20
-15
-10
-5
0
z (0) (x=F=60)
Nor
ma
lized
Ele
ctri
c F
ield
(d
B)
=0 (1/m)=1 (1/m)=4 (1/m)
-4 -2 0 2 4-40
-35
-30
-25
-20
-15
-10
-5
0
z (0) (x=F=60)
Nor
ma
lized
Ele
ctri
c F
ield
(d
B)
=0 (1/m)=1 (1/m)=4 (1/m)
F = 60 L = 300
•Passive, planar and non-uniform LW focusing interface
•Simplified phased-array model of the non-uniform LW structure
•Optimized phase distribution for focusing•Focusing by a thin planar passive interface instead of a bulk of LH material or active components
Realization of 2D Metamaterials
2.5D Textured Structure: Meta-Surface (“open”)
2D Lumped Element Structure: Meta-Circuit (“closed”) RH
yz
x
RC
2RL
2RL2RL
2RL
LH
LL
2 LC
2 LC
2 LC2 LC
yz
x
2D interconnection
y
x
Chip Implementation
Enhanced Mushroom Structure Uniplanar Interdigital Structure
top patch
ground plane
capspost
Unit cell
top patch
sub-patches
ground plane
via
Analysis of the Periodic 2D TL
Unit cell representation and parameters
ixA
ixBi
xCixD
iyA
iyB
iyC
iyD
zA zB
zC zD
oxA
oxBo
xCoxD
oyA
oyB
oyC
oyD
ix xI I
ix xV V
iy yI I
iy yV V
xjk aox xI I e
xjk aox xV V e
yjk aoy yI I e
yjk aoy yV V e
0V
izI
x
yz
0ixV
0iyV 0o
xV
0oyV
1I
2I3I
4I
5I
Transmissionor [ABCD]Matrixes:
relate In/out I/V
Ingredients:
Kirchoff’sVoltage/Currents
Laws:Linear HomogeneousSystem in , , ,x x y yV I V I
NB: can be solved numerically (fast) or analytically (insight)
Bloch-FloquetTheorem:
relates in/out phases,Brillouin zone resolution
→ dispersion diagram:, BZx yk k
det , 0x yM k k
Negative Refractive Index of Mushroom Structure
source
refocus
focus
Electric field distribution, | E |
Positive / negative refractive index
Ab
solu
te r
efra
ctiv
e in
dex
0
5
10
–1.0 –0.5 0 0.5 1.0
–
M
n= c0
/
Fre
qu
ency
(G
Hz)
– X
–5
–10
–15
a
MX
strong C (MIM) mixed RH / LH
air linedielectric line
quasi-TEM
quasi-TE
Open
ground plane
top
caps
vias
dispersion diagramTM0
TEM
if h/<<1
Parameter Extraction Method
L
LL C
LZ
X M
RH
LH
CRLH1
2
0
1X
2X
2M
cM 1
HIGH-PASS GAP
10
(GHz) f
2
8
M
X xk
yk
0
a
a
a
a
How to determine: LR, CR, LL, CL
- Full-wave analysis: ωΓ1, ωX1, ωM1
- Compute ωse, ωL, ωR, ωsh, ωLωR = ωsh ωse
- Compute Bloch impedance ZB= fct(ωX1)
- Insert ZB(ωX1) to determine
- Finally, using ,
1L B XZ Z
222
1,
1,
1,
RRR
seLR
LLL
L
LL L
CC
LL
CZ
L
L L LZ L C
2 2 2 21 1 1 12
2 2 2 21 1 1 12 2 2 2
1 1 1 1
24
1 1 1 1
M X
L
M XX M
2 2
2 1 1
22 2
1 1
1 14
XR
LX
R L se sh
1se
Paraboloidal “Refractor”
Plane Wave to Cylindrical WavePrinciple
Mushroom ImplementationEffective Medium Full-Wave Demonstration
nI > nII: HyperbolanI < nII: EllipsenI = -nII: Parabola
III
III
IIIIII
nn
nnfr
frABDC
fnDCnrnABn
cos
)(
...
)cos(
Full-Wave Demonstration of Microwave Surface Plasmon
Constitutive Parameters and Dispersion
ATR-Type Setup (PPWG)
Effective Medium Demonstration
2D CRLH Metamaterial
2
20
1R L
r
C L
p
2
20
1R L
r
L C
p
2D Mushroom-Structure Leaky-Wave
Unit cell
a
Equivalent CRLH circuit
2RL2 LC
RLLC
Dispersion Diagram
Γ ΓX M
LH
RH
fΓ1
ΓX
M
fΓ2
2D Mushroom-Structure Leaky-Wave cont’d
Γ ΓX M
LH
RH
fΓ1
ΓX
M
β = 0.1π/a
fΓ2
2D Dispersion Diagram
xkyk
,n x yk k
0LH
RH
radiationcone
Brillouin Zone
XX
M
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
kx (/a)
k y ( /
a)
11.7448
14.175816.606919.0379
21.469
21.469
21.469
21.4
69
Γ
LH-1 -0.5 0 0.5 1
-1
-0.5
0
0.5
1
kx (/a)
k y ( /
a)
14.169417.338920.5083
23.6777
26.8472
26.8472
26.8472
26.8472
Γ
RH
Isotropy
Conical Beam OperationPrototype (top view)
β β
vp
vp
vp
vp
LH
RHθ θ
θ
β β
θ
Radiation Principle
center excitation
RH
0
45
90
135
180
225
270
315
-35
-35
-40
-40
-45
-45
-50
-50
-55
-55-60
11.0 GHz13.0 GHz15.0 GHz
0
45
90
135
180
225
270
315
-30
-30
-35
-35
-40
-40
-45
-45
-50
-50
-55
-55-60
9.0 GHz9.6 GHz10.1 GHz
LH
Measured Radiation Patterns
Radiation Angle vs Frequency
Full-Scanning Edge-Excited 2D-LW Antenna
E.g. Hexagonal 3-ports antenna surface
each port scans
from backfire-to-endfire
N-ports = N-edges/2
P1=90
P2=45
P3=0
P3=135
Array Factor Approach of LW Structures
Phased Array Leaky-Wave Structure
1 sin0
1
Nj n kp
n
AF I e
• linear phase:
• constant magnitude:
• excitation: feed at each element
• array factor:
0n n
0 ,nI I n
DISCRETE EFFECTIVELY HOMOGENEOUS
1 sin
1
Nj n kp
nn
AF I e
• linear phase : uniform structure
• exponentially decaying magnitude:
• excitation: induced by propagation
• array factor:
10with n p
nI I e
directivity N
x
z
p
1 1,I
2 3 40
0I 0I 0I 0I 0I
2 2,I 3 3,I 4 4,I 5 5,I
0I 01 sinn n kp
x
z
p 2 3 40
0I
0nxI e
0I
01 sinn n kp
Generalized Transmission Matrix Method (GTMM)
• 2D network decomposed into N columns of M unit cells
• each column column transmission matrix [T]; [T]tot = [T]N
• unit cell parameters known from extraction
CRLH
[T]
[T]tot
GTMM – Global S-Parameters: Examples
CRLH unit cell
PortP4Num=4
PortP3Num=3
PortP2Num=2
PortP1Num=1
PLCPLC1
C=CR FL=LL H
SLCSLC4
C=CL2 FL=LR2 H
SLCSLC3
C=CL2 FL=LR2 H
SLCSLC2
C=CL2 FL=LR2 H
SLCSLC1
C=CL2 FL=LR2 H
CRLH_ucX1
4
2
3
1
Test parameters
0
2.5 nH
1.0 pF
Z 50
50 ,
R L
R L
R L
R L
th tv
L L
C C
L L
C C
Z Z
RR24R=Ztv Ohm
RR23R=Ztv Ohm
RR22R=Ztv Ohm
RR21R=Ztv Ohm
RR20R=Ztv Ohm
RR19R=Ztv Ohm
RR18R=Ztv Ohm
RR17R=Ztv Ohm
RR16R=Ztv Ohm
RR15R=Ztv Ohm
RR14R=Ztv Ohm
RR13R=Ztv Ohm
RR12R=Ztv Ohm
RR11R=Ztv Ohm
RR10R=Ztv Ohm
RR9R=Ztv Ohm
RR8R=Ztv Ohm
RR7R=Ztv Ohm
RR6R=Ztv Ohm
RR5R=Ztv Ohm
RR4R=Ztv Ohm
RR3R=Ztv Ohm
RR2R=Ztv Ohm
RR1R=Ztv Ohm
TermTerm1Num=1
CRLH_ucX1
4
2
3
1
CRLH_ucX2
4
2
3
1
CRLH_ucX6
4
2
3
1
CRLH_ucX5
4
2
3
1
CRLH_ucX4
4
2
3
1
CRLH_ucX3
4
2
3
1
CRLH_ucX7
4
2
3
1
CRLH_ucX8
4
2
3
1
CRLH_ucX9
4
2
3
1
CRLH_ucX10
4
2
3
1
CRLH_ucX11
4
2
3
1
CRLH_ucX12
4
2
3
1
CRLH_ucX24
4
2
3
1
CRLH_ucX23
4
2
3
1
CRLH_ucX22
4
2
3
1
CRLH_ucX21
4
2
3
1
CRLH_ucX20
4
2
3
1
CRLH_ucX19
4
2
3
1
CRLH_ucX18
4
2
3
1
CRLH_ucX17
4
2
3
1
CRLH_ucX16
4
2
3
1
CRLH_ucX15
4
2
3
1
CRLH_ucX14
4
2
3
1
CRLH_ucX13
4
2
3
1
CRLH_ucX36
4
2
3
1
CRLH_ucX35
4
2
3
1
CRLH_ucX34
4
2
3
1
CRLH_ucX33
4
2
3
1
CRLH_ucX32
4
2
3
1
CRLH_ucX31
4
2
3
1
CRLH_ucX30
4
2
3
1
CRLH_ucX29
4
2
3
1
CRLH_ucX28
4
2
3
1
CRLH_ucX27
4
2
3
1
CRLH_ucX26
4
2
3
1
CRLH_ucX25
4
2
3
1
CRLH_ucX48
4
2
3
1
CRLH_ucX47
4
2
3
1
CRLH_ucX46
4
2
3
1
CRLH_ucX45
4
2
3
1
CRLH_ucX44
4
2
3
1
CRLH_ucX43
4
2
3
1
CRLH_ucX42
4
2
3
1
CRLH_ucX41
4
2
3
1
CRLH_ucX40
4
2
3
1
CRLH_ucX39
4
2
3
1
CRLH_ucX38
4
2
3
1
CRLH_ucX37
4
2
3
1
CRLH_ucX60
4
2
3
1
CRLH_ucX59
4
2
3
1
CRLH_ucX58
4
2
3
1
CRLH_ucX57
4
2
3
1
CRLH_ucX56
4
2
3
1
CRLH_ucX55
4
2
3
1
CRLH_ucX54
4
2
3
1
CRLH_ucX53
4
2
3
1
CRLH_ucX52
4
2
3
1
CRLH_ucX51
4
2
3
1
CRLH_ucX50
4
2
3
1
CRLH_ucX49
4
2
3
1
CRLH_ucX72
4
2
3
1
CRLH_ucX71
4
2
3
1
CRLH_ucX70
4
2
3
1
CRLH_ucX69
4
2
3
1
CRLH_ucX68
4
2
3
1
CRLH_ucX67
4
2
3
1
CRLH_ucX66
4
2
3
1
CRLH_ucX65
4
2
3
1
CRLH_ucX64
4
2
3
1
CRLH_ucX63
4
2
3
1
CRLH_ucX62
4
2
3
1
CRLH_ucX61
4
2
3
1
CRLH_ucX73
4
2
3
1
CRLH_ucX74
4
2
3
1
CRLH_ucX75
4
2
3
1
CRLH_ucX76
4
2
3
1
CRLH_ucX77
4
2
3
1
CRLH_ucX78
4
2
3
1
CRLH_ucX79
4
2
3
1
CRLH_ucX80
4
2
3
1
CRLH_ucX81
4
2
3
1
CRLH_ucX82
4
2
3
1
CRLH_ucX83
4
2
3
1
CRLH_ucX84
4
2
3
1
CRLH_ucX96
4
2
3
1
CRLH_ucX95
4
2
3
1
CRLH_ucX94
4
2
3
1
CRLH_ucX93
4
2
3
1
CRLH_ucX92
4
2
3
1
CRLH_ucX91
4
2
3
1
CRLH_ucX90
4
2
3
1
CRLH_ucX89
4
2
3
1
CRLH_ucX88
4
2
3
1
CRLH_ucX87
4
2
3
1
CRLH_ucX86
4
2
3
1
CRLH_ucX85
4
2
3
1
CRLH_ucX108
4
2
3
1
CRLH_ucX107
4
2
3
1
CRLH_ucX106
4
2
3
1
CRLH_ucX105
4
2
3
1
CRLH_ucX104
4
2
3
1
CRLH_ucX103
4
2
3
1
CRLH_ucX102
4
2
3
1
CRLH_ucX101
4
2
3
1
CRLH_ucX100
4
2
3
1
CRLH_ucX99
4
2
3
1
CRLH_ucX98
4
2
3
1
CRLH_ucX97
4
2
3
1
CRLH_ucX120
4
2
3
1
CRLH_ucX119
4
2
3
1
CRLH_ucX118
4
2
3
1
CRLH_ucX117
4
2
3
1
CRLH_ucX116
4
2
3
1
CRLH_ucX115
4
2
3
1
CRLH_ucX114
4
2
3
1
CRLH_ucX113
4
2
3
1
CRLH_ucX112
4
2
3
1
CRLH_ucX111
4
2
3
1
CRLH_ucX110
4
2
3
1
CRLH_ucX121
4
2
3
1
CRLH_ucX122
4
2
3
1
CRLH_ucX123
4
2
3
1
CRLH_ucX124
4
2
3
1
CRLH_ucX125
4
2
3
1
CRLH_ucX126
4
2
3
1
CRLH_ucX127
4
2
3
1
CRLH_ucX128
4
2
3
1
CRLH_ucX129
4
2
3
1
CRLH_ucX130
4
2
3
1
CRLH_ucX131
4
2
3
1
CRLH_ucX132
4
2
3
1
CRLH_ucX109
4
2
3
1
CRLH_ucX133
4
2
3
1
CRLH_ucX134
4
2
3
1
CRLH_ucX135
4
2
3
1
CRLH_ucX136
4
2
3
1
CRLH_ucX137
4
2
3
1
CRLH_ucX138
4
2
3
1
CRLH_ucX139
4
2
3
1
CRLH_ucX140
4
2
3
1
CRLH_ucX141
4
2
3
1
CRLH_ucX142
4
2
3
1
CRLH_ucX143
4
2
3
1
CRLH_ucX144
4
2
3
1
TermTerm24Num=24
TermTerm23Num=23
TermTerm22Num=22
TermTerm21Num=21
TermTerm20Num=20
TermTerm19Num=19
TermTerm18Num=18
TermTerm17Num=17
TermTerm16Num=16
TermTerm15Num=15
TermTerm14Num=14
TermTerm13Num=13
TermTerm12Num=12
TermTerm11Num=11
TermTerm10Num=10
TermTerm9Num=9
TermTerm8Num=8
TermTerm7Num=7
TermTerm6Num=6
TermTerm5Num=5
TermTerm4Num=4
TermTerm3Num=3
TermTerm2Num=2
12 12 network
1
2
12
13
14
24
6
3
4
5
7
8
9
10
11
15
16
17
18
19
20
21
22
23
GTMM – Global S-Parameters: Example cont’d
1,1S
3,9S
6,6S
6,24S
GTMMADS
GTMM – Fields Distributions, Example, 2D, g
1.0 GHzf 1.5 GHzf 2.0 GHzf
2.5 GHzf
Dispersion Diagram
Fre
qu
en
cy
(G
Hz)
3.0 GHzf 3.13 GHzf
4.0 GHzf 5.0 GHzf 6.0 GHzf 7.0 GHzf
8.0 GHzf 9.0 GHzf 10.0 GHzf 12.0 GHzf
Cu
rren
ts d
istr
ibu
tio
ns
21
21
net
wo
rk
2.5 GHzf
