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
•
Leaky Wave Antenna
Generalized Transmission Matrix Method
Composite Right / Left-Handed (CRLH) TL
Infinitesimal Circuit Model
Transmission Line Representation
CL F  m
 , Z0
LR
 H m
LL H  m
CR
 F m
d
z  0
Propagation Constant
  j   Z Y  , where
Z   j LR 
1
1
, Y   jCR 
jCL
j LL

  s    2 LR CR 

s    1 if   1  min 


Balanced Case
Definition: LR CL  LL CR  LC 

1
2
2
 LL CL
L
1
  LR CR 
 LL CL
C
  RH   LH
   2 LR CR 
R
 LR CR 
1

   
2


 LLCL  LL CL 
1
,
LR CL
1
LL CR


 and  1 if    2  max 




R
1
,
LR CL
1
LLCR




CL
LL
Motivation 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
Conventional Magnetically-Scanned LWA
 Frequency independent scanning
 Biasing DC magnetic field  NOT practical
 Waveguide configuration
Novel Electronically Scanned LWA
Frequency independent scanning  Efficient Channelization
Continuous scanning capability
Microstrip technology  Low profile
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 Control

V3
V2
V1
  c
(   k0 )

(V )  sin  
 k0 
1
0
 (V ) 
(V )  sin 

k
 0 
1
  0  RH  0  LH  0
V2
V1
V3
 k0
 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
Modified Layout of a Microstirp CRLH TL Unit cells
A : interdigit al capacitor
`

A
B
LR 2
2C L
2C L LR 2
Z
B
Z
GND
LL
CR
B : shorted (via) stub

Y
A
varactor
B
Z
 Series and Shunt Varactors
 Fairly constant characteristic impedance
 Additional degree of freedom
for wider scanning range
Z
LR ,v ar C L ,v ar
L R ,1 C L ,1
C L ,v ar LR ,v ar
C L ,1
L L ,1
 Reverse biasing to Varactors
 Anodes of varactors : GND
 Cathodes of varactors: Biasing
C R ,v ar
A
Y
GND
inductor
C R ,1 L L , 2
L R ,1
LDC
V DC
Dispersion diagram
 (V )  cos 1 (1  Z '(V )Y '(V )) / d
3.9

 

1

 ||  jLR ,1  1 
Z ' (V )   jLR ,var 
 d
jCL ,var (V )  
jCL ,1 



Frequency [GHz]

1 

2
 j   L R ,1C L ,1  L R , var C L , var (V )   L R ,1C L ,1 L R , var C L , var (V )  2  
 




2
C L ,1  C L , var (V )   ( L R ,1  L R , var )




3.6
d


1 
 1

Y ' (V )  
|| jC R ,var (V )   jC R ,1 
 d
j

L
j

L


L
,
1
L
,
2





j
1 
 

j

C

R
,
1
2
 d


L

1
/
C
(
V
)
j

L
L
,
1
R
,
var
L
,
2


Voltages
3.3
3.0
2.7
0V
5V
10 V
2.4
0.0
0.1
0.2
0.3
0.4
0.5
 / k0
0V
5V
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
Parameters
LL2 [nH]
4.597
CL1 [pF]
0.485
LR1 [nH]
2.027
0.6
0.7
0.8
0.9
1.0
Prototype of 30 Cell Proposed TL
 The cathodes of three varactors in the same direction
 Efficient biasing: Only one bias circuitry in unit cell
Bias Configuration
 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
Shunt varactor
Port 2: Terminated with 50 ohms
Shunt varactor
 Suppress undesired spurious beams
+
DC
 strip
d  1.2 cm (0.18eff
)
GND, Vb ()
 strip
3.02 cm (0.46eff
)
Series varactors
 strip
3.02 cm (0.46eff
)
Series varactors
+
-
+
Via
Via
Inductor (DC Feed)
DC bias Vb ()
Port 1
Port 2
Pin
 strip
38.34 cm (5.87eff
)
ZL
Continuous Scanning Capability at 3.33 GHz
0
0
30
30
30
0
30
60 60
60
10
0
20
10
0
30
30
60 60
10
0
V = 18 V
LH ( β < 0)
20
10
V = 3.5 V
Broadside ( β = 0 )
0
0
60
10
20
10
V = 1.5 V
RH ( β > 0)
Scanning angle [degree]
60
Theory
Measurement
40
 Scanning Range Δθ = 99º (-49º to +50º)
 Backward, forward, and broadside
20
 Biasing Range ΔV = 21 V ( 0 to 21 V)
0
 Fixed operating frequency : 3.33 GHz
-20
-40
 Good agreement with theoretical and
experimental results
-60
0
2
4
6
8
10
12
14
16
Reverse bias voltage [V]
18
20
22
0
Performance as a LW Antenna
30
25
Gain [dBi]
20
15
10
5
0
-5
-10
-50
-40
-30
-20
-10
0
10
20
30
40
50
Scanning Angle [degree]
 High directivity : One of attractive characteristic of LW antennas
Achieved by increasing the number of cells  Large radiation aperture
 Antenna dimension :
 strip
38.34 cm (5.87eff
)
 Maximum Gain : 18 dBi at broadside ( V = 3.5 V )
Focusing by a Planar Non-Uniform LW Interface
Principle
Dipole array model for the TX antenna
F
source
RX
x
z
R iF  Fxˆ  zizˆ
TX
TX
 0
F
x
θi
focus
E-Field of a Dipole

1
1
Ei (R iF )  E0 j 1 


jk0 R iF
k0 R iF


R iF
zi
i
focus
rF  Fxˆ
ˆ
R
i
y
L
d0 = 0/2
d0
F = 60.
E-Field Maximization

  jk0 RiF
e
sin i θˆ i
2
R iF


  jk0 RiF
1
j
ˆ
e
2 E0 

cos i R
i
2
 R iF k R  R iF
0
iF 

 xˆ Exi (R iF )  yˆ E yi (R iF )  zˆ Ezi (R iF )
Ez (rF ) 
N
I
i 1
i0
exp( ji ) Ezi (R iF )
iEzi(RiF+Ez(rF) ~
~ k0|RiF|+constant
z
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
Normalized Electric Field (dB)
Normalized Electric Field (dB)
Effects of Different Array Length.
L=120
L=300
0
2
4
6
8
x(0z0
10
12
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
L=120
L=300
4
-2
0
z(0z0
2
4
F = 60
L = 120
z(0
L = 300
z(0
dB
Normalized Electric Field (dB)
Piece-Wise Linear Approximation
phase of excitation (deg)
2 Groups
6 Groups
Continuous
4000
3000
2000
6000
2 Groups
6 Groups
Continuous
-2
-4
-6
-8
-12
4000
-14
-16
3000
2000
-15
0
-10
5000
Normalized Electric Field (dB)
i~~ k0|RiF|+constant
5000
-10
-5
0
z (0)
5
10
15
-18
0
2
4
6
x (0) (z=0)
0
-5
-15
-20
-25
-2
10
12
F = 60
L = 300
2 Groups
6 Groups
Continuous
-10
-30
-4
8
0
2
z (0) (x=F=60)
4
z(0)
dB
Normalized Electric Field (dB)
Normalized Electric Field (dB)
Effects of Leakage Factor
0
-2
-4
=0 (1/m)
=1 (1/m)
=4 (1/m)
-5
-10
-6
-15
-8
-20
-10
-25
 =0 (1/m)
 =1 (1/m)
 =4 (1/m)
-12
-14
-16
-18
0
0
2
4
6
-30
-35
8
x (0) (z=0)
10
12
-40
-4
F = 60 L = 300
-2
0
2
z (0) (x=F=60)
4
Prototype
Non-uniform LW antenna
    x
Willkinson power divider
x
• Passive, planar and non-uniform LW
focusing interface
• Simplified phased-array model of the nonuniform 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
2D Lumped Element Structure: Meta-Circuit (“closed”)
LR 2
RH
LH
LR 2
2CL
2D interconnection Chip Implementation
2CL
LR 2
LR 2
2CL
CR
z
y
2CL
LL z
y
y
x
x
x
2.5D Textured Structure: Meta-Surface (“open”)
Enhanced Mushroom Structure
Uniplanar Interdigital Structure
top patch
top patch
caps
post
via
sub-patches
ground plane
ground Unit
plane
cell
Analysis of the Periodic 2D TL
Ingredients:
Transmission
or [ABCD]
Matrixes:
relate In/out I/V
Kirchoff’s
Voltage/Currents
Laws:
Linear Homogeneous
System in Vx , I x , Vy , I y
Bloch-Floquet
Theorem:
relates in/out phases,
Brillouin zone resolution
k x , k y  BZ
→ dispersion diagram:
I  Ix
i
x
Unit cell representation and parameters
I yo  I y e
 jk y a
z
V  Vx
i
x
y
i
x
i
x
A
i
C Bx
Dxi
x
V
i0
x
I1
I3
I5
I yi  I y
Vyi  Vy
B
i
Ay D
Cyi
i
y
i
y
Vyi 0
I4
I2
Vyo 0
o
y
o
y
B
A D
C
o
y
o
y
Vyo  Vy e
 jk y a
V0
Vxo 0
Az Bz
Cz Dz
Axo
o
oB
x
Cx o
Dx
I zi
det  M  k x , k y   0
NB: can be solved numerically (fast) or analytically (insight)
I xo  I x e  jk x a
Vxo  Vx e  jk x a
Negative Refractive Index of Mushroom Structure
Positive / negative refractive index
Absolute refractive index
top
caps
vias
10
5
0
n = c0 
/
–5
–M
–10
dispersion diagram
TM0
TEM
dielectric line
air line
if h/<<1
–1.0
–0.5
–X
–15
0
a 
source
quasi-TEM

focus

X
M
0.5
1.0
Electric field distribution, | E |
quasi-TE

Frequency (GHz)
Open

strong C (MIM)  mixed RH / LH
refocus
Parameter Extraction Method
How to determine: LR, CR, LL, CL
- Full-wave analysis: ωΓ1, ωX1, ωM1
f (GHz)
- Compute ωse, ωL, ωR, ωsh, ωLωR = ωsh ωse
M 2
L2  4
X 2
ky
10
 a
8 RH
 a
 2
0 CRLH
1
2 LH

M
 a
X
0
 
2
R
kx
L
Z L a L
CL
X1
M 1  c
X

M

2
M1
2
M1
 1
 21  2
 X 1

 
1 

  

 21  2  X2 1  21
 X2 1  21
 1
1 
4  L2  2  2 
  X 1 1 
2
1

2
X1

 1
1 
 21  2  2 
 M 1 1 

se  1
RL  sesh
- Compute Bloch impedance ZB= fct(ωX1)
HIGH-PASS GAP



- Insert ZB(ωX1) to determine Z L  Z B  X 1  
- Finally, using Z L  LL CL ,
Z
1
1
1
LL  L , C L 
,
L

,
C

R
R
L
LL L2
C Lse2
LR R2
Paraboloidal “Refractor”
Principle
nI AB  nII r  nI DC  nII f
Plane Wave to Cylindrical Wave
 DC  AB  (r cos   f )
...
f (nI  nII )
r
nI cos   nII
nI > nII: Hyperbola
nI < nII: Ellipse
nI = -nII: Parabola
Effective Medium Full-Wave Demonstration
Mushroom Implementation
Full-Wave Demonstration of Microwave Surface
ATR-Type Setup (PPWG)
2D CRLH Metamaterial Plasmon
 r 2   

CR  1  2 LL
p 0

 r 2   

LR  1  2CL

p 0
Constitutive Parameters and Dispersion
Effective Medium Demonstration
2D Mushroom-Structure Leaky-Wave
Equivalent CRLH circuit
Unit cell
2CL LR 2
CL
LR
a
Dispersion Diagram
30
Frequency (GHz)
25
20
M
15
X
Γ
fΓ2
fΓ1
10
LH
5
0

Γ

X


M
Γ
2D Mushroom-Structure Leaky-Wave cont’d
2D Dispersion Diagram
Isotropy
1
26
.8
RH 472
n  k x , k y 
.
26
RH
k (/a)
y
14.
.3
-0.5
X
M
kx
Γ
17
LH
Brillouin Zone
0
ky
1
-1
-1
169
38
0
kx (/a)
k (/a)
y
M
15
0
L
H

Γ
Γ
14
16. .1758
-0.5 21
606
1
.46 9.0
9
9
37
9
21
5
0
8
fΓ2
fΓ1
1
44
Γ
10
0.5
.7
X
469
11
Frequency (GHz)
20
2
69
25
21.
47
.4
0.5
2
8
6.
21
LH
-0.5
30
β = 0.1π/a
4
9
23 20
.
5
.
083
26 67
7
.8
47 7
2
69
radiation
cone

X
0.5
.4
0
47
2
8

X


M

Γ
-1
-1
-0.5
0
kx (/a)
0.5
1
Conical Beam Operation
Prototype (top view)
Measured Radiation Patterns
90
90
-35
-30
135
135
45
-35
45
-40
-40
-45
-45
-50
-50
-55
-55
-60 -55 -50 -45 -40 -35 -30
180
-60 -55
9.0 GHz
9.6 GHz
10.1 GHz
225
Radiation Principle
β
RH
vp
LH
vp
θ
-40
11.0 GHz
13.0 GHz
15.0 GHz
225
315
315
270
270

vp
β
θ
vp
Radiation Angle vs Frequency
90
80
70
60
50
40
30
20
10
0
LH
RH
Measured
Theoretical
9
-35
0
β
θ θ
β
-45
RH
LH
center excitation
-50
0 180
10
11
12
13
14
Frequency (GHz)
15
16
17
18
Full-Scanning Edge-Excited 2D-LW Antenna
E.g. Hexagonal 3-ports antenna surface
P3
 =135
each port scans
from backfire-to-endfire

N-ports = N-edges/2
P3
 =0
P2
 =45
P1
 =90
Array Factor Approach of LW Structures
Phased Array
Leaky-Wave Structure
DISCRETE
EFFECTIVELY HOMOGENEOUS
z
n    n  1 kp sin 0
z

0
I0
I1 , 1
I0
p 
I0
I 2 , 2
• linear phase:
2
3
4
I0
I0
I0
I 3 , 3
I 4 , 4
I 5 , 5
x
0
p 
2
3
4
x
• linear phase  : uniform structure
• exponentially decaying magnitude:
I n  I 0 , n
N
AF    I 0  e

• excitation: induced by propagation
• excitation: feed at each element
• array factor:

I 0 e  nx
I0
n  0  n
• constant magnitude:
n    n  1 kp sin 0
I0
j  n 1 kp sin   
N
• array factor:
AF     I n e
j  n 1 kp sin   
n 1
n 1
directivity  N
with
I n  I 0e
  n 1 p
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
[T]
[T]tot
CRLH
GTMM – Global S-Parameters: Examples
12  12 network
CRLH unit cell

Test parameters
LR  LL  2.5 nH
CR  CL  1.0 pF
Z0 
LR
LL

 50 
CR
CL
Zth  50 , Ztv  
1
13
2
14
3
15
4
16
5
17
6
18
7
19
8
9
20
21
10
22
11
23
24
12
GTMM – Global S-Parameters: Example cont’d
S3,9
S1,1
GTMM
ADS
S6,24
S6,6
GTMM – Fields Distributions, Example, 2D, g
f  1.0 GHz
f  1.5 GHz
f  2.0 GHz
f  2.5 GHz
f  3.0 GHz
f  3.13 GHz
f  4.0 GHz
2.5 GHz
GHz
ff  5.0
f  6.0 GHz
f  7.0 GHz
f  8.0 GHz
f  9.0 GHz
f  10.0 GHz
f  12.0 GHz
Frequency (GHz)
Dispersion Diagram


21  21 network
Currents distributions
