microwave applications of metamaterial structures ieee...

Microwave Electronics Lab

Microwave Applicationsof

Metamaterial StructuresIEEE MTT DML Talk

Tatsuo Itoh

Electrical Engineering DepartmentUniversity of California, Los Angeles


Plan

1. Left-Handed (LH) Metamaterials andTransmission Line Approach

2. Composite Right / Left-Handed (CRLH)Metamaterials

3. Applications:Guided WavesRadiated WavesRefracted Waves2D Leaky-Waves

4. Summary and Prospects


1. Left-Handed (LH) Metamaterialsand Transmission Line Approach


Different Approaches of LH Metamaterials

UCSD, 2D-LH

Historical Milestones• 1968 : theoretical analysis of hypothetical LH materials by Veselago• 1996/9 : introduction of electric (ε<0) / magnetic (µ<0) plasmon by Pendry• 2000 : experimental demonstration of LH structure by Smith

• approach: no simple/rigorous analysis& no design method

• structures: RESONANTlossy & narrow bandwidth& highly dispersive

LH definition: → materials with→ unit-cell << λ effective / macroscopic / homogeneous

0 and 0 0 and || p gn v vε µ< < ⇒ < −

• approach: Transmission line analysis& circuit design methods

• structures: NON-RESONANTlow loss & broad bandwidth& moderate dispersion

“BACKWARD WAVES”(e.g. Brillouin, Pierce)

( )CjZ ′=′ ω1

high-pass( )LjY ′=′ ω1

Resonant Structure Approach Transmission Line Approach

- L. Brillouin, “Wave Propagation in Periodic Structures”, Mc Graw Hill, 1946- J. R. Pierce, “Traveling-Wave Tubes”, D. Van Nostrand Company, 1950


β

kC/∆z

L/∆z

β

kL∆z

C∆z

Distributed Model of transmission Line LH structure

∆z→0

∆z→0

vp>0, vg>0

vp>0, vg<0


Anti-parallel Phase / Group Velocities

0 0

, ,

,

,

Then, the triad becomes

, if 0 (RH),

, if ,

, i

0 (LH

f 0 ( H)

Maxwell:

Plane Wave:

, i

)

,

E H k

E j B H j Djk r jk rE E e H H e

HB

H

E RD

E

k E

k H

ω ω

ω µ µω

ω µ

ω ε εω

ω ε

µ

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

⎧⎪⎪⎪⎨⎪⎪⎪⎩

∗ ∇× =− ∇× =− ⋅ − ⋅∗ = =

∗

+ >= =

− >= =

− <

+−

×

×

rr r

r r r r

r rr rr r r r

rr

r

rr

r

r r

r r

Poynting Vec

0 (L

tor: ( )

)

Hf .

S E H RH

ε

⎧⎪⎪⎪⎨⎪⎪⎪⎩

∗ ∗= ×

<r r r

an0 0dε µ< <• Definition of LHMs:

Er

Hr

(dir. )k vϕ

r r

Er

Hr

(dir. )k vϕ

r r

(dir. )grS vr r

(dir. )grS vr r

(RH)

(LH)

||p gv v=−or


General Classifications of Material Based on (ε,µ)

conventionalplasma

wire structure

split rings structureferrites

LHMs

0, 0n εµε µ> >

=+

0, 0ε µ> <

0, 0ε µ< <

0, 0ε µ< >

ε

µ

No transmission

No transmissionn εµ=−

(RH)air air

air air

(Permittivity)


Rectangular WG Loaded with a LHM: vp = -||vg

kr

kr

kr

Sr

Sr

Sr

Output

Input

Perfect matching for nL= -nR

0.4 0.6 0.8 1 1.2 1.4 1.6Frequency (GHz)

-40

-35

-30

-25

-20

-15

-10

-5

0

5

S-pa

ram

eter

s (d

B)

S11S21

0.4 0.6 0.8 1 1.2 1.4 1.6Frequency (GHz)

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

S-pa

ram

eter

s (d

B)

S21S11

0.4 0.6 0.8 1 1.2 1.4 1.6Frequency (GHz)

-120

-100

-80

-60

-40

-20

0

S-pa

ram

eter

s (d

B)

S11S21

: Poynting vecto: wave v

rectork

S

r

ur

0, 0ε µ> < 0, 0ε µ< >

0, 0ε µ< <

Only one negative parameter → No transmission

E-field magnitude contour

cf

WR-650: 6.5x3.25 in, TE10 fc = 0.908 GHz


LH TL Material Constitutive Parameters

Zj

µω′

=• Mapping Maxwell toTelegrapher’s eqs :

• LH TL parameters:

• Dispersive ε & µ:non-resonant

( )21 0 !Cµ ω ′= − <

• Dispersive n:

• EntropyConditions:

( ) ( )( )

( )2 2

1 00

1 0

LW E H

C

ωεωε ωµ ωω ω ωµ

ω

⎧∂= >⎪⎫∂ ∂ ⎪ ′∂= + > ⇒⎬ ⎨∂ ∂ ∂⎭ ⎪ = >⎪ ′∂⎩

( )1Y j Lω′ ′=

Yj

εω′

=

( )1Z j Cω′ ′=

( )21 0 !Lε ω ′= − <

0 0 02

0 !r rc c cZ Yn

j L Cε µ β

ω ω ω′ ′

= = = = − <′ ′

losslessj Z Yγ β ′ ′= =L′C ′

[ ]H m⋅

[ ]F m⋅


Realization of 1D LH TLsLumped Element Implementation

Distributed Implementation (Microstrip)

microstripline

seriesinterdigitalcapacitor

shuntspiral

inductorT-junction

via toground

unit cell

interdigitalcapacitors

shorted stubinductors

Ideal Elements Chip Components

Interdigital C & spiral / stub L Interdigital C & stub L

MIM-C

GP

shortedstub

MIM-C

GP

shortedstub

Multilayer → LTCC


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 LC2 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


2. Composite Right / Left-Handed (CRLH)Metamaterials


Ideal Composite Right / Left-Handed (CRLH) TL

0, Zβ

d

RL′

RC′ LL′

LC′

[ ]H m

[ ]F m[ ]H m⋅

[ ]F m⋅

0z∆ →

Infinitesimal Circuit Model Transmission Line Representation

( ) 22

, where1 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 CL C L C

γ β

ω ωω ω

β ω ωω

′ ′= =

′ ′ ′ ′= + = +′ ′

⇓

⎛ ⎞′ ′′ ′= + − +⎜ ⎟′ ′ ′ ′⎝ ⎠

22

1 2

1

R RL L

R RL L

RH LH

L CL C

L CL C

β ωω

ω

β βω

′ ′= + −′ ′

′ ′= −′ ′

= +

Balanced CasePropagation Constant

Definition: R L L RL C L C L C′ ′ ′ ′ ′ ′= =

↓

( ) 1 21 1 1 11 if min , and 1 if max ,R L L R R L L R

sL C L C L C L C

ω ω ω ω ωΓ Γ

⎛ ⎞ ⎛ ⎞= − < = + > =⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

RL′

RC′LL′

LC′


Phase/Group Velocities: No Physical Law ViolationPure LH TL

2

1L C

βω

= −′ ′

LL ′

LC ′

0z∆ →

Balanced CRLH TL Unbalanced CRLH TLRL′

RC′ LL′

LC′

[ ]H m

[ ]F m[ ]H m⋅

[ ]F m⋅

0z∆ →

RL′

RC′LL′

LC′

[ ]H m⋅

[ ]F m⋅

[ ]F m

[ ]H m

0z∆ →

22

1LC

CL

ωβω

= −′

′′

′ 22 1

L L L L

R RR R L C L C

L CL Cω

ωβ⎛ ⎞

= + −′

′ ′′ ′

′+

′⎜⎝ ′ ⎟

⎠

( ) : not physical!gv ω → ∞ = ∞( ) 0gv c nω → ∞ =

( ) ( )0 0 2gv c nω ω→ =( ) 0gv c nω → ∞ =

-10-8-6-4-202468

10

vp/(nc0) vg/(nc0)

ω -2.0-1.5-1.0-0.50.00.51.01.52.0

vp/(nc0) vg/(nc0)

ω-2.0-1.5-1.0-0.50.00.51.01.52.0

vp/(nc0) vg/(nc0)

ω

GAP

0ω 1ωΓ 2ωΓ

0gnv c0pnv c

0gnv c0pnv c

0gnv c0pnv c

balanced: R L L RL C L C L C′ ′ ′ ′ ′ ′= =


Dispersion Diagram and Group Velocity (CRLH)

1 21 1: ,R L L RL C L C

ω ωΓ ΓΓ = =1

2 22 2 2 2 22 2 2 21 01 02 01 02R R 01 022

2

: 2 22 2

X

X

Xω ω ω ω ωω ω ω ωω

⎧ ⎫⎫ ⎛ ⎞+ +⎪ ⎪= + + −⎬ ⎨ ⎬⎜ ⎟⎝ ⎠⎭ ⎪ ⎪⎩ ⎭

m

( ) 22

1 1cos 12

R RR R

L L L L

L Ca L CL C L C

β ωω

⎧ ⎫⎛ ⎞⎪ ⎪= − + − +⎨ ⎬⎜ ⎟⎪ ⎪⎝ ⎠⎩ ⎭

( )2

3

sin1g

R RL L

a av

L CL C

β

ωω

= −⎛ ⎞

−⎜ ⎟⎝ ⎠

balanced: 1 0 !2R L L R g

R R

L C L C va L CΓ= → = ≠unbalanced: 0R L L R gL C L C v Γ≠ → =

,β α

ω

1ωΓ

2ωΓ

aπ+aπ− 0

2Xω

1Xω

Γ XX

GAP

RH/+zRH/ z−

LH/+z LH/ z−,β α

ω

1 2 0ω ω ωΓ Γ= =

2Xω

1Xω

aπ+aπ− 0Γ XX

RH/+zRH/ z−

LH/+z LH/ z−

matching

0aλ Γ

⎤ =⎥⎦homogeneous

isotropic

0R L

R L

L LZC C

= =


Guided Wavelength along a CRLH-TLFull-wave simulations (HFSS)

1.0 1.35 1.70 2.05 2.20 2.70 3.402.30

0fLH ← RH→ fcf

( )2

2 1R Ra LC

λ π β

π ω ω

= =

∝2

2 !L La L C

λ π β

πω ω

=

= ∝

LH RHGAP

Characteristics• LH / RH range: backward / forward

propagation verified• λg proportional ω in LH range and

to 1/ω in RH range verified

interdigitalcapacitors

shorted stubinductors

24-cells prototype


3a. Guided-WavesApplications


Microstrip CRLH Coupled-Line Couplers

-40-35-30-25-20-15-10

-50

1 1.5 2 2.5 3 3.5 4 4.5 5frequency (GHz)

S-pa

ram

eter

s (dB

)

S11

S21

S31

S41

LH RH

COUPLEDTHROUGH

-40-35-30-25-20-15-10-50

1 1.5 2 2.5 3 3.5 4 4.5 5frequency (GHz)

S-pa

ram

eter

s (dB

)

S11

S21

S31

S41

THROUGH COUPLED

Magnitude characteristics (meas.)

LH RH

SYMMETRIC ~ 0dB prototype

Characteristics:• ARBITRARY TIGHT COUPLING & BROAD BANDWIDTH• novel type of backward coupler:

coupling depending on attenuation length• quadrature outputs (90 deg)

ASSYMMETRIC ~ 0dB prototype

βS

Characteristics:• ARBITRARY TIGHT COUPLING & BROAD BANDWIDTH• novel type of backward coupler:

LH range only, forward-type phenomenon• more compact

Magnitude characteristics (meas.)


Unit Cell Circuits and Even/Odd Decomposition

RL

RLRC

RC

LL

LLLC

LC

mCmL

RL

2R mC C+LL

LC

E EH H

PEC

E = 0

ei

2R mL L+

RCLL

LCE EH H

PMC

H = 0

mi

RL

RLRC

RC

LL

LLLC

LC

2 mC2 mL

2 mCPMCEL

open

+

+ 2 mL

EVEN

PECEL

short

RL

RLRC

RC

LL

LLLC

LC

2 mC2 mL

2 mC

+

− 2 mL

ODD

( )2

0 2

1 21

R m LLe

L L R

L L CLZC L C

ωω

− += ⋅

−

( )2

0 2

11 2

L R Lo

L L R m

L L CZC L C C

ωω

−= ⋅

− +

0 fct( )eZ ω=REIM

e e

e e

jγ βγ α

⇒ =⇒ =

0 fct( )oZ ω=REIM

o o

o o

jγ βγ α

⇒ =⇒ =

COUPLER

Like CRLH !

Like CRLH !


Tight Coupling( ) ( )

( ) ( )0 0

0 0 0

tanh2 tanh

e oBWD

e o

Z Z jC

Z Z Z jα β

α β

⎡ ⎤− +⎣ ⎦=⎡ ⎤+ + +⎣ ⎦

l

l

( )( )

0 0 0 0

0 0 0 0

coupling range 021

e oBWD

e o

Z Z Z ZC

Z Z Z Zβ

α

⎫⇒ = −⎪ ⇒ ≅⎬ + +> ⎪⎭l

( )( )

0 0 0 020 0 0

0 0 0 02e e

e o BWDe e

Z Z Z ZZ Z Z C

Z Z Z Z−

= ⇒ ≅+ +

( )( )

im im0 0 0 0im

0 0 im im0 0 0 0

100% COUPLING!!!1: 2

e ee e BWD

e e

j Z Z Z ZZ jZ C

j Z Z Z Z

+= ⇒ ≅ =

+ −

( )( ) ( ) ( )

1 1 1

1 2 21 1trick: 1

2 4BWD

jC

j

ξ ξ ξ ξ ξ ξξ ξ ξ ξ ξ ξ

− − −

−− −

+ + +≅ = = =

+ − + − +


CRLH Asymmetric Coupler

Prototype

Unit cell circuit model

1 2

3 4

in through

isolatedcoupled

Sβ

c sL µ

RLRC

c sC µ

LLLC

mCmL

conventional µstrip (cµs) TL

CRLH-TL

1 2

3 4

Principle

( )

m ax

m ax

2sin ,

1 2

w ith

coherence length:

w eak coupling

very sm all

cFW D

c

c

C RLH S

dpC

p

RpR

d

d

π

π

π

µ

β β

πβ β

πβ β

⎡ ⎤−= ⎢ ⎥+ ⎣ ⎦

= −

=−

↓

= →+

, : ratios of the voltages on the tw o lines for c and m odescR Rπ π


Dual-Band Components, E.g.: Quadrature Hybrid

Characteristics:

• dual-band functionality for anarbitrary pair of frequencies f1, f2

• principle: transition freq. (LH-RH)provides DC offset additional degreeof freedom with respect to thephase slope

• BW does not become narrower!• applications in multi-band systems• can be extended to many components

( ) ( )2131 SS ϕϕ −

CRLH / CRLH hybrid

CRLH

CRLH

CRLH CRLH

1 2

34

( )2 1 90nϕ

°

∆ =

− + ⋅

0

90−

180−

270−

360−

90

180

270

360

1fCRLH

2f conv2 13f f=

f

( ) ( )31 21 (deg)S Sϕ ϕ ϕ∆ = −

NB: Conventional quadrature:restricted to odd harmonicsbecause only control on slope

conv. RHCRLH

DC offset

1LH R R

L L

L CL C

ϕ ωω

⎛ ⎞′ ′∆ = − +⎜ ⎟⎜ ⎟′ ′⎝ ⎠

l

0f

RH R RL Cϕ ω ′ ′∆ = − l

01

2 R R L L

fL C L Cπ

=


Dual-Band Couplers

Band # 1:

0.92 GHz

Band # 2:

1.74 GHz

0.6 0.8 1 1.2 1.4 1.6 1.8 2frequency (GHz)

-25

-20

-15

-10

-5

0

S-p

aram

eter

s (d

B)

S11S21S31S41

Magnitude Measurements

Band # 1:

1.5 GHz

Band # 2:

3.0 GHz

-40

-35

-30

-25

-20

-15

-10

-5

0

dB

S11MeasS21MeasS31MeasS41Meas

1 1.5 2 2.5 3 3.5 4frequency(GHz)

Magnitude Measurements (∆ in)

2

1

1.89ff

=

2

1

2.0ff

=

Rat Race

LHTLs

1 2

3 4

∆- in Σ- in

out out

LHTLs

0Z 0Z0

2Z

0

2Z

Branch Linein

isolated out

out


Broadband Microstrip-to-CPS Transition and its Antenna Application

+90º0º

0f02 f

03 f-90º

CRLH-TL

Microstrip

-180º-270º

Microstrip line

CRLH-TL

10L 11L

1W

1W3W

Lump Elements

4/gλ

1W

1W

2W

1L

2L

3L

4L 6L

7L

via12L

8L

5L

Using unique phase slope and phase control prosperities of CRLH TL. to have broadband out of phase characteristic.85% back-to-back transition.65% bandwidth of Quasi-Yagiantenna (~15% enhancement)

Lumped Elements

4/gλ

1W

1W

2W3W1L

2L

3L

4L

5L

7L 8L

1WLC

LL

power divider

CRLH Transmission line

CPS

1W

via

6L

Microstrip ground


CRLH Ring Resonators

-2π

-4π

-6π

0f1 2f1 3f1

2π

Microstrip Line

CRLH 1

CRLH 2

Frequency

Increasedf1, > 2f1CRLH 1

Decreasedf1, < 2f1CRLH 2

f1, 2f1, 3f1…Microstrip

BandwidthResonant Frequencies

• Resonates when

• Bandwidth dependent on

• Use CRLH phase response to tune mode spacing and

bandwidth

( ) 2ring f nφ π= −

( )ring ff

φ∂

∂


CRLH Harmonic Tuning Approach

Class F

f=2.4 GHz

24 dBm

P1dB

63%

P.A.E

• Single CRLH-TL for two harmonics

• Reduced number of stubs leads to: Compact circuit size, Reduced associated loss

+180 deg @f0-90 deg @2f0-270 deg @3f0

90 deg @f0

2 3 4 5 6 71 8

-200

0

200

400

600

-400

800

freq, GHz

unw

rap(

phas

e(S

(2,1

)))+

720

unw

rap(

phas

e(S(

4,3)

))

-270 deg @3f0

+180 deg @f0 -90 deg

@2f0

RH-TL

CRLH-TL


Compact Enhanced-Bandwidth Rat-Race Coupler

0.5 1 1.5 2 2.5 3 3.5frequency (GHz)

-10-9-8-7-6-5-4-3-2-10

inse

rtion

loss

(dB

)

S34 LHS24 LHS34 conv.S24 conv.

Magnitude Measurements (∆ in)

150

160

170

180

190

200

210

0.5 1 1.5 2 2.5 3 3.5frequency [G H z]

phase balance (S24-S

34) [deg]

proposed conventionalPhase Balance Measurements (∆ in)

Prototype

3

4

1

2L

C2

C3

C4

r L

C1

L

L

w1

CRLH-TL

∆ in

out

out

Σ in

Σ input Δ input Σ input Δ input

output [dB ] -3.14±0.25 -3.15±0.25 -3.19±0.25 -3.28±0.25

frequency range [G H z] 1.73 - 2.32 1.73 - 2.32 1.67 - 2.59 1.65 -2.62

bandw idth [% ] 29 29 43 46

phase balance [deg] 0±10 -180±10 0±10 180±10

frequency range [G H z] 1.68 - 2.40 1.67 - 2.33 1.36 - (3.5) 1.68 - (3.5)

bandw idth [% ] 35 33 >88 >70

isolation [dB ]

frequency range [G H z]

bandw idth [% ]

return loss [dB ]

frequency range [G H z]

bandw idth [% ]

>78

1.54 - (3.5)

<-20

1.69 - 2.38

conventional proposed

47 39

<-15 <-15

1.53 - 2.48 1.72 - 2.54

<-20

34


ZeroZerothth Order CRLH ResonatorOrder CRLH Resonator

Resonant modes

β±1 = kc / (N – 1)

β0 = 0

…

ω1,ω−1

ω2, ω−2

ωΝ, ω−Ν

ω0

β±2 = 2 kc/ (N – 1)

β±N = kc

Dispersion diagramω

ωc

βkc− kc 0

ωΓ1

ωΓ2

ωX

ω0

ω1

ω2

ω3

ωN – 1

…

ω−1ω−2ω−3ω−N +1

…

Nπ

Nπ2

Nπ

−… …

7 cell CRLH resonator

• n=0: no dependence on physical sizesupercompact resonator

• Initial prototype: more than 2x sizereduction and experimental Q0 = 290 !

–2 n = 0–1 –3

2 4Frequency (GHz)

–60

1 5

0

–20

–40

|S21

| (dB

)–80

|S21||S11|

3

Survives with increasing loss!!

–11 2 3 4 5 6n = 0

–2–3

–4

–6

–5

10 Ω1 Ω

R = 0 Ω

2 4Frequency (GHz)

–60

1 5

0

–20

–40

|S21

| (dB

)–80

|S21||S11|

3

Survives with increasing loss!!

–11 2 3 4 5 6n = 0

–2–3

–4

–6

–5

10 Ω1 Ω

R = 0 Ω

10 Ω1 Ω

R = 0 Ω

Resonance characteristicsField distribution


N-Port In-Phase Series Divider Based on Infinite Wavelength

Experimental Results

f∞=2.37 GHz1

2 3 4 5 6

13 Cells, 5 Output Ports


Power Dividing (APMC 2005)

10.33dBm

~

5 dBm

4.83 dBm

4.83 dBm

0.67 dBmloss

P1

P2 P3 P4

1 2 3 4Port number

-80

-70

-60

-50

-40

-30

-20

-10

Rel

ativ

e ph

ase

nois

e po

wer

[dB

c]

PN@10 KHz offsetPN@100 KHz offsetPN@1 MHz offset

Single osc.

Phase noise measurement

1 2 3 4Port number

-70

-60

-50

-40

-30

-20

Rel

ativ

e ha

rmon

ic p

ower

[dB

c]

2nd Harmonic3rd Harmonic4th Harmonic

Single osc.

Harmonic measurement

• Equal amplitude distribution observed

• Harmonic suppression observed

• Reduction in phase noise


Power Combining (APMC 2005)Combiner 1 (22 mm spacing) Combiner 2 (99 mm spacing)

2.35874 2.35899 2.35924 2.35949 2.35974Frequency [GHz]

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

P

• Pout: 12 dBm (73% combining efficiency)• Phase noise: -23 dBc @10KHz offset, -44 dBc @100KHz offset, -68 dBc @1 MHz offset, • Improvement in phase noise at 10 KHz offset compared to single osc.

Results for both combiner 1 and 2

Single oscillator

• Pout: 10.33 dBm

• Phase noise: -13 dBc @10KHz offset, -42 dBc @100KHz offset, -68 dBc @1 MHz offset,

Spectrum from combiner 2


3b. Radiated WavesApplications


Backfire-to-Endfire Leaky-Wave AntennaAntenna Configuration

x

z

ysource

bwd

fwd

broadside

θ

longitudinalpolarization

Main beam θ versus ω (meas.)

2 3 4 5 6 7-90

-60

-30

0

30

60

90

Sca

nnin

g A

ngle

(deg

)Frequency (GHz)

II.LW-LH

III.LW-RH

0f0 2c β π maxf

x y

z

θ

I.Guided

-LH

0

30

60

90

120

150

180

α / β diagram (meas.)

2 3 4 5 6 7-4

-3

-2

-1

0

1

2

β / k0 α / k0

Frequency (GHz)

β / k

0

0.00

0.02

0.04

0.06

0.08

0.10

0.12

α / k

0

II.LW-LH

III. LW-RH

0f0 2c β π maxf

I. Guided

-LH

CRLH dispersion diagram

β

ω0cβω −=

ILH

GUIDANCE

IVRH

GUIDANCE

IILH

RAD.

IIIRH

RAD.

0cβω +=

0ω

( )rad 0asin kθ β=

0k

β

θ 2 20k k β⊥ = −

-30

-20

-10

0

0

30

6090

120

150

180

210

240270

300

330

-30

-20

-10

0

3.4 GHz 3.9 GHz 4.3 GHz

ωω

Radiation Patterns (meas.)

Main Beam Radiation


Electronically Scanned LW Antenna

( )

( )

0

22

0

asin

1 1cos 12

R RR R

L L L L

R L

R L

k

L Ca L CL C L C

L LZC C

θ β

β ωω

=

⎫⎧ ⎛ ⎞⎪= − + − +⎨ ⎬⎜ ⎟⎪⎩ ⎝ ⎠⎭

′ ′= =

′ ′0ω

2

0V

β =1

0RHV

β >3

0LHV

β <

3V

2V

1Vβ

cω β=

ω

biaswires

ZL

−

shuntvaractor

seriesvaractors

Pin

DC feedvia

via

Vb (+)

Vb (-)

-10

-5

0

0

30

60

90

120

150

180-10

0 V 5 V 15 V

0°-30° +30°

-60°

+90°

+60°

dB-10

-5

0

0

30

60

90

120

150

180-10

0 V 5 V 15 V

0°-30° +30°

-60°

+90°

+60°

dB


BeamwidthBeamwidth Control Capability: PrincipleControl Capability: Principle

1U 2U 3U 4U 5U 6U

0V 0V 0V 0V 0V 0V

Beamwidth

1U 2U 3U 4U 5U 6U

1V 2V 3V 4V 5V 6V

Beamwidth

Uniform biasing Non-uniform biasing

Uniformly biased periodic TLEach unit cell radiates toward the same angleHigh directivity

Non-Uniformly biased periodic TLEach unit cell radiates toward different anglesBeamwidth is determined by the superposition of each cellBroader beamwidth

Uniformly biased periodic TLEach unit cell radiates toward the same angleHigh directivity

Non-Uniformly biased periodic TLEach unit cell radiates toward different anglesBeamwidth is determined by the superposition of each cellBroader beamwidth


BeamwidthBeamwidth Control Capability: PredictionControl Capability: Prediction

N: the number of elementsd: the distance of unit cellfn (θV): the normalized beam pattern functionAn: the attenuation factorwn(θV): the weighting factorαn: the attenuation constant at the nth cellSince the amplitude factor exponentially decreases as n increases, θv,n’s from the onset cells are dominant factors.

N: the number of elementsd: the distance of unit cellfn (θV): the normalized beam pattern functionAn: the attenuation factorwn(θV): the weighting factorαn: the attenuation constant at the nth cellSince the amplitude factor exponentially decreases as n increases, θv,n’s from the onset cells are dominant factors.

Approximation methodSuperposition of each beam pattern

( )11

1

; ; ( ) ( )

( ) ( )

n n n

n

n n

N

total V V n n V n VnN

ndn V n V

n

f A w f

e w fα

θ θ θ θ

θ θ

=

−

=

⋅ ⋅

= ⋅ ⋅

∑

∑

L

Beam pattern at the applied bias of Vn

Exponentially decreasing as n is increasing

0 2 4 6 8 10 12 14 16 18 20 22-60

-50

-40

-30

-20

-10

0

0 2 4 6 8 10 12 14 16 18 20 22-30

-25

-20

-15

-10

-5

0

S21

[dB]

S21

S11

& S

22 [d

B]

Reverse bias voltage [V]

S11 S22

0.90920

0.92615

0.94410

0.9645

0.9740

Insertion loss per a single varactor [dB]Voltage [V]

Insertion Loss Versus Reverse Voltage


BeamwidthBeamwidth Tuning Capability: MeasurementTuning Capability: Measurement

Less power is radiated at the end of LW antennaThe first row becomes dominant

48º (43 to 200 % increased)33.5º @ 1 V16º @ 0V

HPBWHPBW maxHPBW min

Non-Uniform biasing( 0 V to 2 V, 6 V to 10 V)

Uniform biasing

37º (48 to 80 % increased)24.95º @ 5 V20.61º @ 8 V

HPBWHPBW maxHPBW min

Non-Uniform biasing(5 V to 10 V, 10 V to 15 V)

Uniform biasing

1099988877666555

151414141313131212121111111010

2221.51.51.51110.50.50.5000

101010999888777666

-90 -60 -30 0 30 60 90Angle [degree]

-60

-50

-40

-30

-20

-10

0

(Nor

mal

ized

) Rec

eive

d Po

wer

[dB

m (d

B)]

Normalized, non-uniform, measurementNormalized, non-uniform, theoryUniform 5VUniform 8VUniform10V

-90 -60 -30 0 30 60 90Angle [degree]

-60

-50

-40

-30

-20

-10

0

(Nor

mal

ized

) Rec

eive

d Po

wer

[dB

m (d

B)]

Normalized, non-uniform, measurementNormalized nonuniform distribution from theoryUniform 0VUniform 1VUniform 2VLH RH


ZeroZerothth Order CRLH Resonator AntennaOrder CRLH Resonator Antenna

frequency (GHz)2 4 6 8 10 12-20

-10

0

S 11[

dB]

LH

RH

n = 0

–1–2

–3

1

2

Return Loss

Radiation Patterns

Exp. Copolar

Sim. Copolar

Exp. Crosspolar

Sim. Crosspolar

f0=4.88 GHz f0=4.90 GHz

10 mm20.6 mm

Unit-cell

50 ΩInterdigital capacitor

Virtual groundcapacitor

Meander-lineinductor


Electrically Small Antenna using CRLH TL (AP-S 05)

0 1

βρ/π

0

1

2

3

4

5

6

7

8

Freq

uenc

y (G

Hz)

ω−1 ω−2 ω−3 ω−Νω−Ν−1

ω+1ω+2

ω+3

ω+Ν−1ω+ΝRH

region

LH region

N1

N2

N3

NN 2−

NN 1−

Physical antenna size depends on the unit cell size of CRLH TL.β becomes larger as frequency decreases. Antenna size can be reduced and the field distribution remains the same. Using MIM capacitance and CPW stub to increase CL and LL , respectively, and lower the operation frequency.Physical dimension : 1/19λ0 x 1/23λ0 x 1/83λ0

98% area size reduction compared to the conventional microstrip patch antenna built on the sub1.

15 mm

12.2 mm

CPW feed

MIM Capacitance

ground

CPW stub

via

sub1

sub2


Electrically Small Circular polarized Antenna using CRLH TL

Using 3x3 enhanced mushroom structure. Zero field at the center.90% area size reduction compared to the patch antenna.116° 3dB axial ratio bandwidth & 2.2 dB gain

-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90

observation angle (degree)

1

2

3

4

5

6

7

8

9

AR

(dB

)

116º 3dB bandwidth


Backward Wave Dual-Mode Antenna (APMC 2005)

-30

-20

-10

0

030

60

90

120

150180

210

240

270

300

330

-30

-20

-10

0

Phi=0° Phi=90°

-30

-20

-10

0

030

60

90

120

150180

210

240

270

300

330

-30

-20

-10

0

Phi=0° Phi=90°

f0=4.015 GHzgain=2.3 dBiefficiency=75.0%size: λo/5 x λo/5 x λo/50

f-1 =3.560 GHzgain=-2.5 dBiefficiency=22.5%size: λo/5.7 x λo/5.7 x λo/54


3c. Refracted-WaveApplications


Typical 2D-CRLH Dispersion Diagram

( ) ( )2

3

sin1

xXg x

R RL L

a k av k

L CL C

ωω

Γ− = −⎛ ⎞

−⎜ ⎟⎝ ⎠

group velocity

0

:unbalanced

=→≠

≠

Γg

LLRR

RLLR

vCLCL

CLCL

LRCL11 =Γω RLCL12 =Γω

balanced:

12g

R R

R L L R

R R L L

L C L C LC

L C L C

va L CΓ

= =

=

→ =

LC1021 === ΓΓ ωωω2ga λ=2ga λ=0=ga λ

Γ ΓX M

0=ga λ

RH

LH

CRLH

1Γω

2Γω

0ω

1Xω

2Xω

2Mω

cM ωω =1

HIGH-PASS GAP

10

β

(GHz) f

2

8

12

14

16

4Xga λ=

Bragglong λ

Γ

M

X xk

yk

0

aπ

aπ

aπ−

aπ−

refraction scatteringlumped distrib.

balanced: 1 , 1 , 1, 1; unbalanced: 0.55 , 2 , 1.82, 0.5L L R L R L L L R L R LL nH C pF L L C C L nH C pF L L C C= = = = = = = =


Focusing: Experimental Demonstration

PPWGPPWG

PPWGPPWG

SourceSource(Coax.)(Coax.)

2D CRLH 2D CRLH StructureStructure

Magnitude Phase

source source

Measured E⊥

Full-wave simulation

Unit cell: 5.0x5.0mm2

CRLH Structure:

20x6 cells

100 x 30mm2

nLH = 3.14

f = 3.95GHz

Magnitude Phase

2D CRLH Structure

f = 3.731GHz


Measured Results

SourceMagnitude Phase

SourceSourceMagnitude Phase

Source

Magnitude PhaseSourceSource

Magnitude Phase

~ Mushrooms (23x16 cells) in outlined area* Entire structure built on εR=10.2 substrate

Mushrooms (21x10 cells)* Entire structure built on εR=10.2 substrate

f0 =3.79 GHz

f0 =3.77 GHz


3d. 2D Leaky-WaveApplications


Interdigital 2D Leaky-Wave Textured Surface

Measured Frequency Scanning

Initial Prototype (top view)

source

0 (endfire)θ = o

180 (backfire)θ = o

90 (broadside)θ = o

0 30 60 90 120 150 180 210 240 270 300 330 360angle (degrees)

-25

-20

-15

-10

-5

0

Nor

mal

ized

Pow

er (d

B)

2.5GHz2.7 GHz3 GHz

ground plane

via

interdigitalcapacitor

x

y

Structure

Dispersion diagram

xkΓ ,X Y→,X Y ←

ωLC

LL

RL

RC

0ω RHRH

LH LH

TM


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

9 10 11 12 13 14 15 16 17 18Frequency (GHz)

0102030405060708090

θ

MeasuredTheoretical

RH LH

LH

Measured Radiation Patterns

Radiation Angle vs Frequency


2D Edge Excited CRLH Leaky Wave Antenna

2.25 cm

0

45

90

135

180

225

270

315

-5

-5

-10

-10

-15

-15

-20

-20

-25

-25-30

0

45

90

135

180

225

270

315

-5

-5

-10

-10

-15

-15

-20

-20

-25

-25-30

0

45

90

135

180

225

270

315

-5

-5

-10

-10

-15

-15

-20

-20

-25

-25-30

6.40 GHz 7.40 GHz5.76 GHz

Passive 2Dscanning

possible if excited from

different edges


4. Conclusions and Prospects


Conclusions - Novelties

Transmission line approach of metamaterialsNonresonant structureswith low losses and broad bandwidthConcept of composite right/left-handed (CRLH) material Unusual Phenomena:

λg increasing → ∞ → decreasing as ω↑Radiation LW backfire → broadside → endfireSlope + DC Offset2D Leaky WavesAmplification of evanescent waves (couplers)Anisotropic RH / LH structures Negative refraction (focusing)Meta-Interface (phase conjugation / LW)Microwave surface plasmons


Conclusions – Applications

Radiated Waves and 2D Leaky WavesBackfire-to-endfire frequency-scanned leaky-wave antennaElectronically-scanned leaky-wave antennaArbitrary-angle reflecto-directive systems2D conical-beam antenna

Guided WavesArbitrary-coupling directive couplersDual-band componentsMiniaturized and bandwidth-enhanced componentsZeroth order compact / high-Q resonator

Refracted WavesPlanar distributed negative “lens”Microwave surface plasmons


Prospects

Antennas and ReflectorsIntegration of leaky-wave antennas/reflectors real applicationsFrequency / electronically-scanned functional systemsLow cost 2D full-space scanning antennas(e.g. radar, anti-collision, millimeter-wave imaging)

Microwave ComponentsOptimization (e.g. resonator)Technological implementation (e.g. MMIC / LTCC)Industrial applictions (e.g. dual-band: IEEE 802.11)Other concepts and applications

TheorySynthesis, quasi-effective media theory, approximate methods

Metamaterials and MetastructuresConcepts → ApplicationsNovel metamaterials (semiconductors, nanotech, nature)Focusing & anisotropic structures: quasi-optical beam-formingPhase shifting by material: phased array antennasSurface plasmons → miniaturized devices

microwave applications of metamaterial structures ieee...

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