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
WiP, 13-18 April 2008, Paris
I.Vendik
Content
IntroductionTunable componentsCommutation quality factor (CQF) of tunable componentsFigure of merit of tunable devices:Tunable resonatorTunable filterPhase shifterComments and conclusions
WiP, 13-18 April 2008, Paris
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
WiP, 13-18 April 2008, Paris
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
WiP, 13-18 April 2008, Paris
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
WiP, 13-18 April 2008, Paris
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
WiP, 13-18 April 2008, Paris
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
WiP, 13-18 April 2008, Paris
I.VendikControlling the magnetic resonance frequency of SNG material
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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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I.Vendik
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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I.Vendik
Tunable components
P-i-n diodeMEMSFETSemiconductor varactorFerroelectric varactor(Piezoelectric components)
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I.Vendik
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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I.Vendik
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
WiP, 13-18 April 2008, Paris
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
WiP, 13-18 April 2008, Paris
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
WiP, 13-18 April 2008, Paris
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
−+ = + +
WiP, 13-18 April 2008, Paris
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
WiP, 13-18 April 2008, Paris
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:
WiP, 13-18 April 2008, Paris
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
WiP, 13-18 April 2008, Paris
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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I.Vendik
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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I.Vendik
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)
WiP, 13-18 April 2008, Paris
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
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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
WiP, 13-18 April 2008, Paris
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
WiP, 13-18 April 2008, Paris
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
WiP, 13-18 April 2008, Paris
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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I.Vendik
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
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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
WiP, 13-18 April 2008, Paris
I.VendikReconfigurable varactor loaded SRR transmission line
I. Gil
et
al. Elect. Lett, October2004.
WiP, 13-18 April 2008, Paris
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!
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I.VendikTunable RH/LH TL 3-dB directional coupler
Varactor diodes
WiP, 13-18 April 2008, Paris
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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I.Vendik
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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I.Vendik
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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I.Vendik
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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I.Vendik
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
=
WiP, 13-18 April 2008, Paris
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
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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
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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
WiP, 13-18 April 2008, Paris
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
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I.VendikTunable dual-band filter on RH/LH TL sections
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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
WiP, 13-18 April 2008, Paris
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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I.Vendik
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
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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