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					  Design and Measurement of Frequency Tunable Metamaterials                  January 4th, 2008

         URSI 2008 National Radio Science Meeting
Design and Measurement of Frequency
        Tunable Metamaterials
                Thomas H. Hand and Steven A. Cummer
                   Department of Electrical Engineering
                                 Duke University
                          Friday, January 4th, 2008

                                              Friday, January 4th, 2008




                                                                                           1
T. Hand and S.A. Cummer     Department of Electrical Engineering, Duke University     URSI 2008
  Design and Measurement of Frequency Tunable Metamaterials                  January 4th, 2008


                                     Outline
  Motivation:
       - Externally Tunable SRRs for Real-Time Control of
         magnetic permeability

  Realizing Frequency Tunable Metamaterials:
       - Using varactor diode loaded SRRs

       - Using ferroelectric-loaded SRRs for frequency
         tunability [Hand and Cummer, In Review, 2007]

       - Using MEMS switches to realize a dual-state particle
         [Hand and Cummer, IEEE AWPL, 2007]
                                                                                           2
T. Hand and S.A. Cummer     Department of Electrical Engineering, Duke University     URSI 2008
  Design and Measurement of Frequency Tunable Metamaterials                  January 4th, 2008


                                 Motivation

    Exploring tunable metamaterials: expanding achievable
    effective medium properties of artificial electromagnetic
    structures

    Tunability allows for real-time control of electromagnetic
    parameters, expanding the uses and applications of
    metamaterials.

    Allows for interesting applications such as tunable phase
    shifters, beam-steerable antennas, etc.


                                                                                           3
T. Hand and S.A. Cummer     Department of Electrical Engineering, Duke University     URSI 2008
   Design and Measurement of Frequency Tunable Metamaterials                  January 4th, 2008


Externally Tunable SRRs for Real-Time Control of
             Magnetic Permeability
 SRRs known to produce a resonant response [Pendry, 1999], where magnetic
 permeability of the medium is described by [cite]:

                             F 2                      F = oscillator strength
                 r  1  2
                         0   2  j                 Γ = loss term

 Fixed SRR design limits values the magnetic permeability can achieve.

 Embedding a bias-tunable capacitance into the SRRs allows the resonant
 frequency and magnetic permeability to tune:

                                F 2                            ( V )   0 ( V ) / Q
        r ( V )  1  2
                      0 ( V )   2  j( V )                 0 ( V )  ( LC ( V )) 1/ 2
                                   V = Bias Field Strength                                    4
 T. Hand and S.A. Cummer     Department of Electrical Engineering, Duke University     URSI 2008
  Design and Measurement of Frequency Tunable Metamaterials                  January 4th, 2008

        Recent Work on Tunable Metamaterials
Tunable metamaterials using varactor diodes:
 - [Shadrivov, Opt. Exp. 2006] examined a single SRR
 particle loaded with a varactor diode

Report of tunable magnetic medium using SRRs immersed in liquid crystal
[Zhao, et. al., APL 90, 2007]:

 - Tunable range of two percent was achieved
 - Requires SRR array be enclosed in leak-proof packaging

Tunable negative index medium reported [He, et. al., JMMM, 2007]
 - Used copper wires and ferrite sheets

 - NIM band dependent on ferrimagnetic resonance

 - External coil or magnetic needed to bias the ferrite sheets for tuning
                                                                                           5
T. Hand and S.A. Cummer     Department of Electrical Engineering, Duke University     URSI 2008
  Design and Measurement of Frequency Tunable Metamaterials                  January 4th, 2008

    Tunable Magnetic Response Using Varactor Diode
                     loaded SRRs
   Realizing tunable metamaterials with varactor diode-loaded SRRs

   Particle-Particle variance of the tunable SRRs makes tuning a single
   resonant frequency difficult

   Lorentz model assumes all resonators tuned identically

   Recent work [Gollub, Hand, et. al. APL, 2007] verifies experimentally increasing
   loss with increasing disorder.

                                    Simply loading
                                    SRRs with varactor
                                    diodes for tuning
                                    the resonant
                                    frequency of the
                                    medium leads to
                                    messy response, as
                                    shown in the right
                                    figure.
                                                                                           6
T. Hand and S.A. Cummer     Department of Electrical Engineering, Duke University     URSI 2008
   Design and Measurement of Frequency Tunable Metamaterials                          January 4th, 2008

Using BST Elements to Realize the Tunable Medium
  [Hand, Cummer, In Review, 2007]
Loading SRR gaps with Barium Strontium Titanate (BST)
thin films permits external tuning of SRR resonance

Large-scale printed circuit board fabrication of structures is
simple and practical.

Precise control of effective permeability state by biasing
BST.
Tunable range of medium expressed in terms of the
properties of an individual unit cell by [Hand and
Cummer, In Review, 2007]:

                                    L: Self Inductance of ring (~ 45 nH)
                                    C: Gap Capacitance (C~ 0.24 pF)
     1        1           1
δ                                 CBST: Zero-bias capacitance of BST thin
                                                                               Top: Individual tunable SRR.
   2π LC     CBST       CBST Δ      film (~ 1.84 pF)
                                                                               Bottom: Nine-cell tunable SRR
                                                                               medium
            CBST  C   CBST Δ  C   Δ: Tunability parameter of BST capacitor
                                    (~ 0.5)                                                           7
 T. Hand and S.A. Cummer     Department of Electrical Engineering, Duke University              URSI 2008
  Design and Measurement of Frequency Tunable Metamaterials                  January 4th, 2008

Medium measured in microstrip waveguide,
which permits retrieval of effective magnetic
permeability.                                          Port 1                          Port 2


One distinct resonance that tunes over a 140
MHz bandwidth (8% tunable range) for biases
from 0-5 V.

Magnetic Loss Tangent tan(δm) ~ 0.6 for 0V
bias.




                                                                                            8
T. Hand and S.A. Cummer     Department of Electrical Engineering, Duke University     URSI 2008
  Design and Measurement of Frequency Tunable Metamaterials                  January 4th, 2008


Exploring Tunability Using MEMS-loaded SRRs [Hand
          and Cummer, IEEE AWPL, 2007]

   - Design ring resonant between 2-3 GHz with low loss.

   - WR-340 rectangular waveguide (TE10 cutoff frequency 1.77
     GHz) used for measurements.

   - Determine MEMS switch parasitics to characterize ring
     response.
   - Analysis of two switch topologies to understand how switch
     position affects SRR tunability and loss


                                                                                           9
T. Hand and S.A. Cummer     Department of Electrical Engineering, Duke University     URSI 2008
  Design and Measurement of Frequency Tunable Metamaterials                      January 4th, 2008

  Experimental Setup:

  MEMS-loaded SRR placed in
  the middle of a WR-340
  waveguide (operable between
  2-3 GHz)

  Holes drilled in the top of the
  waveguide to bias the
  Teravicta MEMS switch




                                                Unloaded SRR design for resonance
                                                between 2-3 GHz.

                                                Copper ring on low-loss Duroid
                                                substrate (εr = 2.2, tanδe ~ 0.0009)

                                                a = 16 mm, d = 2.5 mm, g = 0.3 mm


                                                                                              10
T. Hand and S.A. Cummer        Department of Electrical Engineering, Duke University      URSI 2008
      Design and Measurement of Frequency Tunable Metamaterials                        January 4th, 2008


    127 kΩ
                                    Series Configuration
    isolation                                                MEMS Switch Equivalent Circuit:
                         Teravicta 7 GHz RF
    resistor
                         MEMS Switch
                                            Lring ~ 22 nH
                                            R ~ 0.3 Ω



                                                                   Open State           Closed State


Pads for DC     Gap capacitance C ~ 0.24 pF to
bias (~ 68 V)   excite resonance within 2-3 GHz.


  Deducing MEMS Switch Parasitics:


                            (Ceff due to series C and Cs)




                                                                                                    11
   T. Hand and S.A. Cummer            Department of Electrical Engineering, Duke University     URSI 2008
     Design and Measurement of Frequency Tunable Metamaterials                     January 4th, 2008

                                Parallel Configuration
In this configuration, MEMS
switch in parallel with ring:
                                   Thicker ring trace to   MEMS Switch Equivalent Circuit:
                                   decrease effective
                                   inductance and
                                   increase resonant
                                   frequency for
                                   operation in the WR-
                                   340 waveguide.
                     5.5 mm
                                                                Open State           Closed State

    Need C to be comparable to Cs to excite resonance
    within WR-340 passband.

    Widen trace width to raise resonance

    Parallel configuration more useful at lower
    frequencies where Cs<< C

    Tight control of switch parasitics makes this
    configuration useful at higher frequencies.
                                                                                                12
  T. Hand and S.A. Cummer         Department of Electrical Engineering, Duke University     URSI 2008
  Design and Measurement of Frequency Tunable Metamaterials                  January 4th, 2008


                                  Conclusions
    - Varactor diode-loaded SRR medium difficult to realize

    - Tight tolerance of BST thin films allows us to build a
      magnetic medium that tunes with a distinct resonance
    - Achievable loss tangent of BST medium completely
      determined by loss of BST thin films

    - MEMS-loaded SRR realizes a state-switchable
      magnetic particle

    - Two switch topologies of MEMS SRR allows for greater
      design flexibility:
      Series: better suited for higher frequencies
      Parallel: better suited for lower frequencies (lower loss)
                                                                                          13
T. Hand and S.A. Cummer     Department of Electrical Engineering, Duke University     URSI 2008

				
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