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WiP, 13-18 April 2008, Paris

I.Vendik

Dynamically controllable metamaterials

Irina

VendikSt. Petersburg Electrotechnical

University

E-mail: [email protected]

Women in Photonics (WiP) School on Photonic MetamaterialsParis, April 13-18, 2008


I.Vendik

Content

IntroductionTunable componentsCommutation quality factor (CQF) of tunable componentsFigure of merit of tunable devices:Tunable resonatorTunable filterPhase shifterComments and conclusions


I.Vendik

Introduction

•

Metamaterials are artificial structures designed to exhibit specific electromagnetic properties not commonly found in nature.

•

Double-negative (DNG) metamaterials are characterized by simultaneously negative permittivity (ε

< 0) and

permeability (μ

< 0)•

Single-negative (SNG) metamaterials are characterized by the negative permeability μ

< 0 or by the negative

permittivity ε

< 0•

The DNG and SNG properties are realized in a limited frequency range, which is conditioned by the resonance nature of the constituents of the metamaterial


I.Vendik

First experimental DNG structures

D.R. Smith, W.J. Padilla et al. “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett., V. 84, p. 4184, May 2000R.A. Shelby, D.R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science, V. 292, p. 77, April 2001

a) b)

y

z

xx


I.VendikResonant nature of artificial particles in metamaterials

•

SRR is a resonant “particle”

generating an equivalent magnetic dipole; resonance is used for providing effective negative permeability

•

DNG medium can be formed as a regular lattice of magnetic and electric dipoles generated by resonant “particles”

•

DNG medium can be formed as a regular lattice of magnetic dipoles generated by resonant “particles”

placed in the medium with effective negative dielectric permittivity in the frequency range below the electric plasma frequency or cut-off frequency of the guiding structure


I.VendikEffective ε

and μ

of the

SRR/wire medium

( )ωζω

ωωε

ipe

r +−= 2

2

1

( )ωζωω

ωωμi

F

mr +−

−= 20

2

2

1

Effective dielectric permittivity of the thin-wire regular structure: ωpe is the electric plasma frequency depending on the geometry; ζ

is the loss factor

Effective magnetic permeability of the SRR regular structure: ωom is the magnetic resonance frequency depending on the geometry; ζ

is the loss factor

The magnetic resonance frequency ωom depends on the gap dimension and the dielectric constant of the substrate


I.VendikCut-off parallel-plate waveguide loaded with 2D lattice of dielectric resonators

2-D lattice structure for the DR array in the cutoff waveguide; εd,r can be tuned

Tetsuya Ueda, Anthony Lai, and Tatsuo Itoh, Negative Refraction in a Cut-Off Parallel-Plate Waveguide Loaded with Two-Dimensional Lattice of Dielectric Resonators, Proc. EuMC36, Manchester 2006, pp. 435-438

The effective permittivity for the parallel-plate TEn mode is

2,

, , 1 c nef n d r

ωε ε

ω

⎡ ⎤⎛ ⎞⎢ ⎥= − ⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

,,

c nd r

n cd

πωε

⋅ ⋅=

Y

X

xZ

,y xE H

TE1 resonance in the dielectric resonators provides the effective negative magnetic permittivity


I.VendikControlling the magnetic resonance frequency of SNG material


I.Vendik

Electrically tunable impedance surface

Daniel

F. Sievenpiper, James

H. Schaffner

et al, Two-Dimensional

Beam

Steering

Using

an

Electrically

Tunable

Impedance

Surface, IEEE TRANS.

AP, VOL. 51, NO. 10, 2003, p. 2713


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How to control the metamaterial parameters?

•

To change the capacitance as the constitutive component of the metamaterial particle

•

To change the dielectric permittivity of the material used for a design of the metamaterial


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Tunable components

P-i-n diodeMEMSFETSemiconductor varactorFerroelectric varactor(Piezoelectric components)


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p-i-n diode

RonRoff

Coff

Typical parameters:Ron = 1 Ohm;Roff = 1 Ohm;Coff = 0.05-0.5 pF.

U ≤

0 V U > 0

U


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MEMS

U

U = 0 V U = Umax

C1

R=1R

C2

2Cωδtan

+R=2R

Typical:tanδ

= 0.001;

R = 0.5 Ohm;C1 = 1.4 pF; C2 = 3.0 pF


I.VendikDevices based on a tunable capacitor: FET, semiconductor or ferroelectric

varactor

U = 0 V U = Umax

C1

1Cω1δtan

=1R

C2

2Cω2δtan

=2RU

Ferroelectric:Ferroelectric:tanδ1 = 0.01 tanδ2 = 0.005C1 = 1.0 pFC2 = 0.5-0.7 pF

X>>R

Semiconductor:Semiconductor:R1~R2 = 0.5-0.8 OhmC1 = 1.5 pFC2 = 0.3 pF

FET:FET:R1 = 1- 5 OhmC1 = 0.3 pFR2 = 1.0 Ohm


I.VendikEstimation of quality of tunable components

The commutation quality factor (CQF) is the generalized criterion for estimation of quality of tunable components

The following components are compared by the CQF:p-i-n diodeMEMSFETSemiconductor varactorFerroelectric varactor


I.VendikCommutation quality factor (CQF)

of tunable components (definition)

Generally CQF is denoted K and determined as .

⎩⎨⎧

=2,IN

1,ININ R

RZ

⎩⎨⎧

+=

+==

222

111L iXRZ

iXRZZ

A BC D

,1

,2

in

in

RK

R=

The commutation quality factor (CQF) is defined as the ratio of the input impedances of a lossless reciprocal two-port

terminated in the impedance pair Z1 and Z2 under condition Im Zin,1,2 =0

( )21 21 2

2 1 1 2

1 X XR RKK R R R R

−+ = + +


I.VendikCommutation quality factor (CQF)

of tunable components

Z1

= R1

+ jX1

State 1 State 2

Z2

= R2

+ jX2

( )22 1

1 2

-X XK

R R=

⋅

X>>R

I. B. Vendik, O. G. Vendik, E. L. Kollberg, “Commutation quality factor of two-state switching devices”, IEEE Trans. on Microwave Theory and Tech., Vol. 48, No. 5, May 2000, pp. 802-808.

The CQF is used for a comparison of different tunable components


I.VendikMore convenient form of the CQF

for tunable capacitors

U = 0 V U = Umax

C1

1Cω1δtan

=1R

C2

2Cω2δtan

=2R

1 2n C C=

( )2

1 2

-1tan tan

nK

n δ δ=

⋅

Tunability of the capacitor:


I.VendikDefinitions of the tunability of a tunable dielectric material

( )2

1 2

-1tan tan

nK

n δ δ=

⋅Tunability Relative tunability

max max

(0) (0)( ) ( )

1

CnU C U

n

εε

= =

≥

max(0) ( )* 100%,(0)

* 100%

Un

n

ε εε−

= ⋅

<

*1 (1 0.01 )n n= −

n 1.11 1.25 1.43 1.67 2.0 n*, % 10 20 30 40 50


I.VendikCommutation quality factor of a tunable capacitor

6

2 3 41

2

3

4

5

1TUNABILITY OF THE COMPONENT (n)

1

tan δ = 0.003

tan δ = 0.01

tan δ = 0.03

tan δ = 0.1

K = 2000

log

K(n

)


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f, GHz5 10 15 20 25 30

log(

K)

1

2

3

4

5

6

7

8

9

p-i-ndiode ferroelectric

capacitor

varactordiodeFET

MEMScapacitor

Comparison of the CQF (2003)

V.V.Pleskachev, I.B. Vendik, The Commutation Quality Factor of Electrically Controlled Microwave Device Components, Tech. Phys. Letters, Vol. 29, No. 12, pp. 1018-

1020, 2003.


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Frequency, GHz

0.1 1 10 100

K

100

101

102

103

104

105

106

107

Varactor diode

MEMS capacitor

Ferroelectriccapacitor

Comparison of the CQF (2006)


I.VendikUsing of ferroelectric capacitor as a tunable component

Electrodes

Dielectric substrate

Ferroelectric film

Biasing voltage (V)

0 100 200

0.01

0.02

0

tanδ(U)

C(U), pF

0 100 200

0.5

1.0

1.5

2.0

0


I.Vendik

Dielectric constant ε depends on the temperature T and the biasing field E

Loss factor tanδ depends on the temperature T and the biasing field E

Using of ferroelectric capacitor as a tunable component


I.VendikCharacteristics of ferroelectric material:dielectric permittivity

0 50 100 150 200 250 3000

500

1000

1500

2000

(T,E)ε1. E = 0 kV/cm2. E = 10 kV/cm3. E = 30 kV/cm4. E = 100 kV/cm

1

2

3

4

TEMPERATURE (K)

0 100 200 3000

25

20

15

10

5

1- E = 0 kV/cm2- E = 2 kV/cm3- E = 5 kV/cm4- E = 15 kV/cm

1

2

34

TEMPERATURE, K

Dielectric constant of single crystal SrTiO3

(STO) (ξS = 0.018)Dielectric constant of STO polycrystalline film (ξS = 0.7 )

ε(T,E) x10-3


I.VendikCharacteristics of ferroelectric material:loss tangent

0 100 200 3000.0001

0.001

0.01

0.1

ξS = 0.02

tanδ(Τ)

TEMPERATURE, K

ξS = 1.0 E = 0

0.1

0 100 200 3000.0001

0.001

0.01

tanδ(E)

ξS = 0.5

ξS = 0.02

ξS = 1.0

ξS = 1.5 T = 78 K

BIASING FIELD, kV/cm

f = 10 GHz; ξ

= 0.02 corresponds to single crystal STO.

Parameter ξ characterizes the material quality: the lower ξ , the lower is tanδ


I.VendikCQF of BSTO capacitor as a function of Ba

concentration (x) and the film structural quality (ξs

)

0 0.2 0.4 0.6 0.8 1102

103

104

ξS = 0.3

105K(x,ξ)

ξS = 1.0

ξS = 0.5

ξS = 1.5

x

Emax = 200 kV/cm,

T = 300 K, f = 3 GHz

ξs is the statistical dispersion of the built- in-field in the sample: the smaller ξs , the higher is the CQF

O. G. Vendik, S. P. Zubko, and

M. A. Nikol’ski, “Microwave loss-factor

of

BSTO”, Journal of Applied Physics, Vol. 92, No. 12, pp. 7448-7452, Dec., 2002

Bax Sr1-x TiO3


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Ferroelectric (BSTO) varactor

A. Vorobiev, P. Rundqvist, K. Khamchane, S.Gevorgian, “Silicon substrate integrated high Q-factor parallel-plate ferroelectric varactors for microwave/millimeterwave

applications”, Appl. Phys. Letters, Vol.83, pp. 1344-1346, 2003


I.VendikTunable and switchable devices based

on left/right-handed transmission lines

Tunable resonators using semiconductor or ferroelectric varactors Reconfigurable filtersSwitchable

and tunable phase shifters


I.VendikReconfigurable varactor loaded SRR transmission line

I. Gil

et

al. Elect. Lett, October2004.


I.VendikArtificial LH TL with separately tunable phase and line impedance

Varactors

Inductive stubs

Christian

Damm,Martin

Schu.ler,Jens

Freese,and

Rolf

Jakoby, Artificial Line Phase Shifter with separately tunable phase and line Impedance, Proc. EuMC, Manchester 2006

( )

( )

0 0

00

0

1 1 1xxL xC

xLZ xxC

ϕω

= − ⋅

=

In the tunability range the matching is kept constant!


I.VendikTunable RH/LH TL 3-dB directional coupler

Varactor diodes


I.VendikEstimation of quality of tunable

devices (Figure of Merit)

•

The quality of the devices is estimated by the figure of merit (FM) determined by a combination of general parameters of the device.

•

The FM is defined for¤ Tunable resonator¤ Tunable filter¤ Phase shifter


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21S

ωω02ω01

Δω

02 01 1 2LC LC nγ ω ω= = =

0 0Q ω ω= Δ

Tunability of the resonator:

Q-factor of the resonator (depends on loss):

Tunable resonator

L C


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Figure of merit of a tunable resonator

( )02 010 01F Qω ω γ

ω−

= = − ⋅Δ

0,max 0.5F K≈ ⋅

If the Q-factor depends on the loss in the FE tunable capacitor only, the FM is determined by the commutation quality factor K and is defined as

For K = 5000, F = 35


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What is the filter?

The ideal filter is a passive lossless and perfectly matched 2-port providing electromagnetic wave transmission in a limited frequency range and full reflection outside this range.There are four main filters: low-pass (LP), high-pass HP), band-pass (BP), and band-stop (BS)The filter design is based on using lumped or distributed componentsTunable filters are supposed to be able to change the width of the frequency band or to shift the characteristic as a whole over the frequency range


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Tunable filter (LP) characteristics

The transmission coefficient S21 of the LP filter versus frequency ω

ωc±Δω

ω ωc

S21

The cut-off frequency ωc

is shifted while tuning; at the same time the pass band is changed

0

1

21out

in

USU

=


I.VendikTunable filter (BP) characteristics

(two versions)

Δω

ω ω1

S21

ω2

The transmission coefficient S21 of the BP filter versus frequency ω

The central frequency ω1

is shifted to ω2

while tuning; at the same time the pass band remains the same

Δω1

ω ω1

S21 Δω2

The central frequency ω1

is kept constant; at the same time the pass band is changed


I.Vendik

Figure of merit of a tunable N-pole filter

0 00

0 0

-up low

up lowF

ω ω

ω ω=

Δ ⋅ ΔGeneral definition:

L, dB

ΔωlowLlow Lupω0

low

ωω0

up

Δωup


I.Vendik

43 84 843 84 8

2.3 2.35 2.4 2.45 2.5 2.55 2.6 2.65 2.7 2.75 2.8 2.85Frequency

(GHz)

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

MS

(dB

)

U=200 VU=0 V

BST capacitors:C(0 V) = 0.941 pFC(200 V) = 0.655 pFn = 1.44tan δ

= 0.01Substrate:Arlon 25N (εr = 3.38)

C

1 MΩ

30 x 20 mm2

f0 = 2.45 – 2.7 GHz; Δf = 25 MHz (1%)

3-pole tunable filter

10000 =

Δ−

=ωωω lowup

F


I.VendikAdvanced definition of the figure of merit of the N-pole filter

dB-10up low

FFL L

=⋅

V. Pleskachev, I. Vendik, Figure of merit of tunable ferroelectric planar filters, Proc. 33rd

EuMC, Vol. 1, pp. 191- 194, October 2003.

max 8.68KF

N=

⋅dB-1

K is the commutation quality factor

N is the number of the resonators


I.VendikTunable dual-band filter on RH/LH TL sections


I.Vendik

What is the phase shifter?

•

The phase shifter is the device, which provides continuous or digital change of the phase of transmitted or reflected electromagnetic wave under the control signal and is characterized by the differential

phase shift:

1 2ϕ ϕ ϕΔ = −


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2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4Frequency

(GHz)

-180

-135

-90

-45

0

45

90

135

180

PS

21 (d

eg) State2 (EM)

State1 (EM)

Δφ

(EM)

2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4Frequency

(GHz)

-50

-40

-30

-20

-10

0

MS

11 (d

B)

State2 (EM)

State1 (EM)

State2 (LC)

State1 State2

90°

phase shifter on switchable RH/LH TL sections


I.VendikCoplanar design of the180о

phase shifter (switchable

TLs)SP

DT

SPD

TIn

LH TL

RH TL

Out

State 22 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4Frequency

(GHz)-180-135-90-45

04590

135180225

Phas

eSh

ift(d

eg)

Δϕ

State 1

State 2

2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4Frequency

(GHz)-40-35-30-25-20-15-10-50

MS

(dB

)

MS 11

MS 21

State 1

State 2


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deg ree dBF / L= ΔϕFor a digital reflection type one-bit phase shifter

1

F 6.6 sin K2 2

−Δϕ Δϕ⎛ ⎞= ⋅⎜ ⎟⎝ ⎠

K is the commutation quality factor (CQF)

Figure of merit of a phase shifter


I.Vendik

The characteristics of metamaterial can be controlled by a variation of the dielectric permittivity of the host material and/or constitutive resonant inclusions The characteristics of TL metamaterial can be controlled by a variation of parameters of capacitive componentsThe control of the dielectric permittivity can be performed by the temperature or dc biasing electric field (optical control is possible)The quality of tunable material/component can be estimated by the CQF, which is determined by the tunability and the loss factor of the tunable material/componentThe quality of tunable devices based on tunable matamaterial is determined by the figure of merit FM, which is fully determined by the CQF

Comments and conclusions

dynamically controllable metamaterialsesperia.iesl.forth.gr › ~wip › lectures › pdfs ›...

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