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    Non-Foster Reactances for Electrically-Small Antennas, High-Impedance

    Surfaces, and Engineered Materials

    James T. Aberle

    Associate Professor of Electrical Engineering

    School of Electrical, Computer and Energy Engineering

    Arizona State University

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    Outline of Presentation What Does Non-Foster Mean?

    Possible Applications of Non-FosterReactances

    Electrically Small Antennas High-Impedance Surfaces

    Artificial High-Permeability Materials

    Realization of Non-Foster Reactances

    2IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Outline of Presentation

    What Does Non-Foster Mean?

    Possible Applications of Non-FosterReactances

    Electrically Small Antennas High-Impedance Surfaces

    Artificial High-Permeability Materials

    Realization of Non-Foster Reactances

    3IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Fosters Reactance Theorem The theorem is a consequence of

    conservation of energy.

    The slope of the input reactance

    (susceptance) of a lossless passive one-port is always positive.

    All zeros and poles of the impedance

    (admittance) function are simple, and azero must lie between any two poles, anda pole between any two zeros.

    4IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Consequences of Fosters

    Reactance Theorem

    Impedances (admittances) of passive one-

    port networks rotate clockwise on theSmith Chart as frequency increases.

    There is no such thing as a negativecapacitor or a negative inductor (forpassive circuits).

    5IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Foster NetworkC

    C1

    C=30 pF

    L

    L1

    R=

    L=40 nH

    L

    L2

    R=

    L=40 nH

    Term

    Term1

    Z=50 Ohm

    Num=1

    R

    R1

    R=50 Ohm

    50 100 150 200 2500 300

    0

    20

    40

    -20

    60

    freq, MHz

    real(Zin1)

    imag(Zin1)

    freq (10.00MHz to 300.0MHz)

    S(1,1

    )

    6IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Non-Foster NetworkL

    L3

    R=

    L=-40 nH

    L

    L1

    R=

    L=40 nH

    L

    L2

    R=

    L=40 nH

    Term

    Term1

    Z=50 Ohm

    Num=1

    R

    R1

    R=50 Ohm

    50 100 150 200 2500 300

    0

    20

    40

    60

    80

    100

    -20

    120

    f req, MHz

    real(Zin1)

    imag(Zin1)

    f req (10.00MHz to 300.0MHz)

    S(1,1

    )

    7IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Outline of Presentation What Does Non-Foster Mean?

    Possible Applications of Non-FosterReactances

    Electrically Small Antennas High-Impedance Surfaces

    Artificial High-Permeability Materials Realization of Non-Foster Reactances

    8IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    VHF Whip: A Canonical ESA

    Geometry of monopole

    antenna as modeled inAntenna Model software.The monopole is a coppercylinder 0.6 meters in

    length and 0.010 meters indiameter, mounted on aninfinite perfect groundplane.

    Frequency range is 30 to90 MHz.

    9IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Input Impedance of VHF Whip From Simulation

    10IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Two Tools to Help With Analysis Exact two-portrepresentation of antenna

    in frequency domain in terms of s-parameters.

    Approximate lumped equivalent circuitmodel of antenna over frequency range ofinterest.

    11IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    ajXlR 1:N0Z

    0Z

    Two-Port Representation of Antenna

    The quantities in this box are re-evaluatedat every frequency for which we have data.

    12IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Two-Port Representation of Antenna

    /

    radiation resistance

    (1 ) dissipative loss resistanceantenna reactance

    a a a r l a

    r cd a

    cd a

    a

    Z R jX R R jXR e R

    R e RX

    = + = + += =

    = ==

    0Z

    RN r=

    13IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Two-Port Representation of Antenna

    Antenna impedance and radiation efficiency are

    used to produce a Touchstone *.s2p file for usein circuit simulation the exact two-port

    representation of the antenna at each frequency

    for which we have data. Allows concepts like transducer power gain and

    stability measures to be applied to antennas.

    The latter being particularly important forconsidering the use of non-Foster reactances in

    antenna matching networks.

    14IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Approximate Equivalent Circuit of the Antenna

    To model the antenna, we assume that the real

    part of the antenna impedance varies as thesquare of frequency, and the imaginary part

    behaves as a series LC.

    +

    =

    a

    aaC

    LjRZ

    12

    0

    0

    Impedance produced by equivalent circuit

    15IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Approximate Equivalent Circuit of the Antenna

    Evaluation of the model parameters (R0,La and

    Ca):( ){ }

    ( ){ }

    ( ){ }

    =

    =

    2

    1

    2

    2

    1

    1

    00

    11

    1

    a

    a

    a

    a

    a

    Z

    Z

    C

    L

    ZR

    16IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Approximate Equivalent Circuit of the Antenna

    pF69.8

    nH194

    30.40

    =

    =

    =

    a

    a

    C

    L

    RL

    La

    R=

    L=194 nHZ1P_Eqn

    Z1P1

    Z[1,1]=4.30*(freq/52e6)**2

    C

    Ca

    C=8.69 pF

    Term

    Term1

    Z=50 OhmNum=1

    40 50 60 70 8030 90

    -500

    -400

    -300

    -200

    -100

    -600

    0

    freq, MHz

    imag

    (Zin1)

    imag

    (VH

    F_

    Whip

    _S2P

    ..Zin1)

    40 50 60 70 8030 90

    5

    10

    15

    0

    20

    freq, MHz

    rea

    l(Zin1)

    rea

    l(VH

    F_

    Whip

    _S2P

    ..Zin1)

    17IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    LZ

    0Z

    MatchingNetwork

    Matching Network Concept

    18IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Points to Consider A real passive matching network can only

    approach and never exceed the performancepredicted by the Bode-Fano criterion.

    The matchable bandwidth is limited by the Qofthe load.

    The matchable bandwidth can only be increasedby de-Qing the load that is by intentionalintroduction of dissipative losses into thematching network and concomitant reduction

    in radiation efficiency.

    19IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Bode-Fano Criterion

    mQ

    f

    f

    1ln

    0

    Maximum value of fractionalbandwidth that can be achieved withany passive, lossless matching

    network.

    Q of the load

    Maximumallowable

    reflectioncoefficient

    035.03

    1,9.81

    0

    ==f

    fQ m

    20IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Single-Tuned Mid-band Match

    TermTerm1

    Z=4.30 Ohm

    Num=1

    L

    Le

    R=

    L=884 nHCCa

    C=8.69 pF

    Z1P_Eqn

    Z1P1Z[1,1]=4.30*(freq/52e6)**2

    L

    La

    R=

    L=194 nH

    freq (30 .00MHz to 90 .00MHz)

    S(1

    ,1)

    m1

    m2

    m1freq=

    S(1,1)=-10.409 / -73.141impedance = Z0 * (0.992 - j0.630)

    51.80MHzm2freq=

    S(1,1)=-10.477 / 71.883impedance = Z0 * (1.008 + j0.630)

    52.20MHz

    008.0

    52

    8.512.52

    0

    =

    f

    f

    009.02

    1

    0

    ==

    Qf

    fAnalytical:

    21IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Wheeler-Lopez Double-Tuned Matching

    A.R. Lopez, Wheeler and Fano ImpedanceMatching, IEEE Antennas and PropagationMagazine, Vol. 49, No. 4, August 2007

    22IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Wheeler-Lopez Double-Tuned Matching

    A.R. Lopez, Wheeler and Fano ImpedanceMatching, IEEE Antennas and PropagationMagazine, Vol. 49, No. 4, August 2007

    23IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Wheeler-Lopez Double-Tuned Matching with

    Antenna De-Qing

    Term

    Term2

    Z=50 Ohm

    Num=2

    R

    RD

    R=200 Ohm

    C

    C2

    C=53.0 pF

    TF

    TF1

    T=0.354

    L

    L2

    R=

    L=177 nH

    L

    Le

    R=

    L=884 nHTerm

    Term1

    Z=50 Ohm

    Num=1

    Zin

    Zin1

    Zin1=zin(S11,PortZ1)

    Zin

    N

    S_Param

    SP1

    Step=1 MHz

    Stop=90 MHz

    Start=30 MHz

    S-PARAMETERS

    S2P

    SNP1

    File="VHF_whip.s2p"

    21

    Ref

    freq (30.00MHz to 90.00MHz)

    S(1

    ,1)

    40 50 60 70 8030 90

    -12

    -10

    -8

    -14

    -6

    freq, MHz

    dB(S(1

    ,1))

    40 50 60 70 8030 90

    -22

    -20

    -18

    -16

    -14

    -24

    -12

    freq, MHz

    dB(S(2

    ,1))

    Decent match, poor efficiency

    24IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Matching Network with Non-Foster Reactances

    Z1P_EqnZ1P1

    Z[1,1]=4.30*(freq/52e6)**2

    LLa

    R=

    L=194 nHC

    Ca

    C=8.69 pF

    LLa1

    R=

    L=-194 nH

    C

    Ca1C=-8.69 pF

    Term

    Term1

    Z=50 Ohm

    Num=1

    LL2

    R=

    L=-44.9 nH

    LL1

    R=

    L=-44.9 nH LL3

    R=

    L=44.9 nH

    AntennaDualizer

    freq (30.00MHz to 90.00MHz)

    S(1,1

    ) m1m1freq=S(1,1)=4.843E-4 / -3.517E-5impedance = Z0 * (1.001 - j5.952E-10)

    90.00MHzCancels frequency squareddependence of radiation resistance.

    Van Der Pol, Proc, IRE, Feb. 1930

    25IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    0Z

    0ZmL

    ( )ma LL +

    aC

    Two-port model ofantenna

    Active matching network

    Antenna with More Practical Matching Network

    using Non-Foster Reactances.

    26IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Optimized Non-Foster Matching Network

    VAR

    VAR1

    Cneg=8.72637 {o}

    Lneg=226.588 {o}

    Lm=49.5959 {o}

    EqnVar

    C

    Ca1

    C=-Cneg pF

    L

    L2

    R=

    L=-Lneg nHL

    L3

    R=

    L=Lm nH

    Term

    Term1

    Z=50 OhmNum=1

    Term

    Term2

    Z=50 Ohm

    Num=2S2P

    SNP1File="VHF_whip.s2p"

    21

    Ref

    freq (30.00MHz to 90.00MHz)

    S(1,1

    )

    40 50 60 70 8030 90

    -26

    -24

    -22

    -20

    -18

    -28

    -16

    freq, MHz

    dB(S(1

    ,1))

    40 50 60 70 8030 90

    -0.4

    -0.3

    -0.2

    -0.1

    -0.5

    0.0

    freq, MHz

    dB(S(2,1

    ))

    27IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Outline of Presentation What Does Non-Foster Mean?

    Possible Applications of Non-FosterReactances

    Electrically Small AntennasHigh-Impedance Surfaces

    Artificial High-Permeability Materials

    Realization of Non-Foster Reactances

    28IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    High-Impedance Ground Plane

    Sievenpiper, et. al, IEEE Trans. MTT, Nov. 1999

    Capacitive

    FSS

    Low

    Permittivity

    Spacer

    Metal BackplaneMetal Vias

    10

    Coaxial Feed

    Bent Wire

    Element

    29IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    EM Properties of the Sievenpiper

    High-Impedance Ground Plane

    Surface impedance is (ideally) an open-circuit(emulating a PMC rather than a PEC like a

    conventional ground plane).

    Propagation of TM and TE surface waves is notsupported (thus can be called an

    electromagnetic bandgap structure).

    30IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Model for Surface Impedance of Sievenpiper HIS

    For plane waves at normal incidence, the substrate may be understood as an electrically short length of

    shorted transmission line in parallel with a shunt capacitance at the reference plane of the outer surface.

    Open

    Short

    Zstub

    Zin

    Shunt Capacitance

    2d

    PhaseAngle,

    Frequency

    180o

    90o

    0o

    -90o

    -180o

    fo

    BW ~ 10% to 20% of fo.

    Co Zo, Short

    Zstub

    Zind

    31IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Reflection Phase Bandwidth of

    Sievenpiper HIS

    00 2

    h

    r=

    hr

    Spacer layer

    FSS layer

    Ground plane

    32IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Electrically-Thin Broadband High-

    Impedance Surface In principle, one could realize an electrically-thin

    broadband HIS by using a high-permeabilityspacer layer.

    A high-permeability meta-material can be

    realized using artificial magnetic molecules(AMMs) implement with negative inductance

    circuits.

    Unfortunately, AMM performance is verysensitive to component tolerances.

    But, there is a better way

    33IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Electrically-Thin Broadband

    High-Impedance Surface

    Kern, Werner, Wilhelm, APS 2003

    34IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Electrically-Thin Conventional HIS

    Term

    Term1

    Z=377 Ohm

    Num=1

    C

    C1

    C=2.17 pF

    TLINP

    TL1

    Sigma=0

    TanM=0

    Mur=1

    TanD=0.0009

    F=1 GHz

    A=0.0K=2.2

    L=1.6 mm

    Z=377/sqrt(2.2) Ohm

    m1

    freq=phase(S(1,1))=90.015

    2.308GHz

    m2

    freq=phase(S(1,1))=-90.204

    2.502GHz

    m3freq=phase(S(1,1))=-0.139

    2.403GHz

    1.5 2.0 2.5 3.0 3.51.0 4.0

    -100

    0

    100

    -200

    200

    freq, GHz

    phase(S(1,1))

    m1

    m2

    m3

    m1

    freq=phase(S(1,1))=90.015

    2.308GHz

    m2

    freq=phase(S(1,1))=-90.204

    2.502GHz

    m3freq=phase(S(1,1))=-0.139

    2.403GHz

    %80

    =

    f

    f

    0.062 in RogersDuroid 5880

    35IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Electrically-Thin HIS with Negative Inductance

    L

    Lneg

    R=

    L=-2.02 nH

    TLINP

    TL1

    Sigma=0TanM=0

    Mur=1

    TanD=0.0009

    F=1 GHz

    A=0.0K=2.2

    L=1.6 mm

    Z=377/sqrt(2.2) Ohm

    Term

    Term1

    Z=377 Ohm

    Num=1

    1.5 2.0 2.5 3.0 3.51.0 4.0

    -5

    0

    5

    10

    -10

    15

    freq, GHz

    phase

    (S(1

    ,1))

    36IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Unit Cell of Sievenpiper HIGP

    37IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Reflection Phase Response of

    Sievenpiper HIGP

    12 13 14 15 16 17 18-140

    -120

    -100

    -80

    -60

    -40

    -20

    0

    20

    40

    Frequency (GHz)

    Re

    flec

    tion

    Coeffic

    ien

    tPhase

    (deg

    )

    38IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Unit Cell of Sievenpiper HIGP with Reactive Loading

    39IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Equivalent Circuit of Loaded HIGP for

    Normally Incident Plane Wave

    E

    Zload

    Zload

    40IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Reflection Phase of Capacitively

    Loaded HIGP

    0.5 1 1.5 2 2.5 3 3.5 4-200

    -150

    -100

    -50

    0

    50

    100

    150

    200

    Frequency (GHz)

    Re

    flec

    tion

    Coef

    fic

    ien

    tPhase

    (deg

    )

    41IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

    R fl i Ph f N i I d

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    Reflection Phase of Negative-Inductor

    Loaded HIGP

    0.5 1 1.5 2 2.5 3 3.5 4-40

    -30

    -20

    -10

    0

    10

    20

    30

    40

    Frequency (GHz)

    Re

    flec

    tion

    Coe

    fficien

    tPhase

    (deg

    ) Lneg = -2.2nH

    42IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Outline of Presentation What Does Non-Foster Mean?

    Possible Applications of Non-FosterReactances

    Electrically Small Antennas High-Impedance Surfaces

    Artificial High-Permeability Materials

    Realization of Non-Foster Reactances

    43IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    What is an Artificial Material? An artificial material is a large-scale emulation of an actualmaterial, obtained by embedding a large number of electricallysmall inclusions (artificial molecules) within a host medium.

    Like natural molecules, the electrically small inclusions exhibitelectric and/or magnetic dipole moments.

    As a result of these dipole moments, the macroscopic

    electromagnetic constitutive parameters (r and r) are altered

    with respect to the host medium.

    HB

    ED

    0

    0

    ==

    44IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

    Why Create an Artificial

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    Why Create an Artificial

    Magnetic Material? Naturally occurring magnetic materials

    (ferrites) are heavy, fragile and expensive, andthey also exhibit relatively high magnetic losses

    and dielectric constant.

    Available ferrite materials provide a limitedselection of relative permeabilities.

    The permeability tensor of the ferrite is

    controlled by applying a static magnetic field permanent magnets and/or electromagnets are

    required.

    45IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Artificial Magnetic Metamaterial

    A 3-dimensional lattice of artificialmolecules.

    Electrically small loop with a loadimpedance

    dx

    dy

    dz

    dz

    dy

    a

    W

    ZL

    y

    z

    46IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Simple Circuit Model for Artificial Magnetic Molecule (AMM)

    Llooploss

    xx

    ZLjR

    aj

    H

    m

    N

    ++==

    +=

    40

    1

    VH

    Rrad

    Lloop

    +

    -ZL

    I

    Relative

    permeabilityNumber ofAMMs per

    unit volume

    Magneticpolarizability of

    each AMM

    47IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

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    Broadband, High Permeability Requires Negative Inductance

    0 1 2 3 4 5 6 7 8 9 10

    0

    2

    4

    6

    8

    10

    12

    14

    16

    18

    Frequency, GHz

    RelativePermeability

    imag

    real

    a

    W

    ZL= -j Ld

    0 1 2 3 4 5 6 7 8 9 10

    0

    2

    4

    6

    8

    10

    12

    14

    16

    18

    Frequency, GHz

    RelativePermeability

    imag

    real

    a

    W

    ZL= -j Ld

    Circuit Theory Model

    48IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

    H t E t t M t i l P ti

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    How to Extract Material Properties(TEM waveguide containing material sample)

    wave port 1wave port 2

    material sample

    PMC walls

    49IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    How to Extract Material

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    How to Extract Material

    Properties HFSS

    -Two port S parameters calculation of TEM

    waveguide containing material sample.

    MATLAB

    -Shifting of the reference planes.

    -Conversion of S-parameters to ABCDparameters.

    -Calculation of propagation constant and

    characteristic impedance of equivalenttransmission line.

    -Evaluation of the material properties.

    50IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    How to Extract Material Properties

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    How to Extract Material Properties(Loop Configuration)

    lumped element

    copper loop

    51IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    N i I d i M d l d F D d

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    Negative Inductance is Modeled as a Frequency-Dependent

    Capacitance

    ( ) negequiv

    Lf

    C2

    2

    1

    =

    52IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Cancellation of Parasitic

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    Cancellation of Parasitic

    Capacitance Using NIC

    To remove the resonance, the parasitic capacitance of the loop should be

    compensated by a negative capacitance.

    53IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

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    Remedy for Snoek-Like Phenomenon: Add Negative Capacitance in

    Shunt with Negative Inductance

    54IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

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    Outline of Presentation What Does Non-Foster Mean?

    Possible Applications of Non-FosterReactances

    Electrically Small Antennas

    High-Impedance Surfaces

    Artificial High-Permeability Materials

    Realization of Non-Foster Reactances

    55IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    N ti I d C t (NIC)

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    Negative Impedance Converter (NIC)

    An ideal NIC is a two-port network such that when aload impedance is attached to the output terminal, the

    input impedance is the (possibly scaled) negativevalue of the load impedance.

    IdealNIC

    ZL

    Zin=-kZL (k>0)

    IdealNIC

    ZL

    Zin=-kZL (k>0)

    C i l NIC

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    Canonical NIC

    R

    RZ

    +

    -ZZin =

    57IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Simple Op Amp Test Circuit

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    S_Param

    SP1

    Step=1 MHz

    Stop=4000 MHz

    Start=1 MHz

    S-PARAMETERS

    OpAmp

    AMP2

    BW=500 MHz

    Gain=100 dB

    R

    R4

    R=100 OhmTerm

    Term1

    Z=50 Ohm

    Num=1

    RR3

    R=50 Ohm

    R

    R2

    R=1 kOhm

    R

    R1R=1 kOhm

    Simple Op-Amp Test Circuit

    Can specify DC

    gain and unity gainBW.FOM: RL > 15 dB

    58IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Unity-gain BW = 500 MHz

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    1E7 1E8 1E91E6 4E9

    -30

    -20

    -10

    -40

    0

    freq, Hz

    dB(S(1,1

    )) m1

    m1freq=dB(S(1,1))=-14.883

    7.000MHz

    y g

    59IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    NIC R t L BW O A U it G i BW

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    NIC Return Loss BW vs. Op-Amp Unity Gain BW

    500 1000 1500 20005

    10

    15

    20

    25

    30

    Op-Amp Unity-Gain BW (MHz)

    NICRe

    turnL

    oss

    BW

    (MHz)

    Op-amp based NICscontra-indicated for

    applications above 30 MHz

    60IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Fabricated OPA690 NIC Evaluation

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    Board

    61IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Circuit for evaluating the performance

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    NIC ZL

    Rin

    SignalGenerator

    Vin Vneg

    Iin

    -ZL

    Vg

    Rg

    Zin

    g p

    of a grounded negative impedance

    Lin ZR >

    Stability requires that

    62IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Schematic captured from Agilent ADS of the circuit

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    V g V in V n e g

    V t S i n e

    V g

    P h a s e = 0

    D a m p i n g = 0

    D e l a y = 0 n s e c

    F r eq = 0 . 5 M H z

    A m p lit u d e = 1 0 0 m V

    V d c = 0 m V

    Tran

    T ran1

    M a x Ti m e S te p = 0 . 5 n s e c

    S t o p Tim e = 5 u s e c

    T R A N S I E N T

    R

    R in

    R = 1 0 0 O h m

    RR 7

    R = R s c a l e

    O P A 6 9 0 _ p o r t

    X 1

    R

    R 1 0

    R = 5 0 O h m

    R

    R 3

    R = R s c a l e 2

    V A R

    V A R 1

    R s c a l e 2 = 2 5 0

    R s c a l e = 2 5 0

    E q nVa r

    R

    R g

    R = 5 0 O h m

    p g

    for evaluating the performance of the OPA690 NIC

    63IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Simulated and measured return loss for

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    2 4 6 8 10 12 14 16 180 20

    -40

    -30

    -20

    -10

    -50

    0

    freq, MHz

    dB(Return_

    Loss_

    Simulate

    d)

    dB(Return_

    Loss_

    Measure

    d)

    the OPA690 NIC evaluation circuit

    64IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Ground Negative Impedance Versus

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    Canonical NIC and most other NIC circuits in the literature producegrounded negative impedance

    But for the applications we are considering here, we need floatingnegative impedance

    Floating Negative Impedance

    -Z

    -Z

    65

    IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Floating NIC Realized Using Two Op-Amps

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    Floating NIC Realized Using Two Op-Amps

    66

    IEEE Waves and Devices 19 Feb 2010

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    Op-Amp FNIC Test Circuit

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    S_ParamSP1

    Step=0.1 MHzStop=100 MHzStart=0.1 MHz

    S-PARAMETERS

    MuPrime

    MuPrime1MuPrime1=mu_prime(S)

    MuPrime

    Mu

    Mu1Mu1=mu(S)

    Mu

    TermTerm2

    Z=50 OhmNum=2

    TermTerm1

    Z=50 OhmNum=1

    RR2R=1k Ohm

    RR1R=1k Ohm

    RR4R=1k Ohm

    RR3R=1k Ohm

    RRLR=50 Ohm

    RRnegR=50 Ohm

    OpAmpAMP2

    BW=500 MHzGain=100 dB

    OpAmpAMP1

    BW=500 MHz

    Gain=100 dB

    67IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

    Unity-gain BW = 500 MHz

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    m1freq=dB(S(1,1))=-15.048

    3.600MHz

    1E6 1E71E5 1E8

    -40

    -30

    -20

    -10

    -50

    0

    freq, Hz

    dB(S

    (1,1

    ))m1

    m1freq=dB(S(1,1))=-15.048

    3.600MHz

    1E6 1E71E5 1E8

    -10

    -5

    -15

    0

    freq, Hz

    dB(S(

    2,1

    ))

    20 40 60 800 100

    1.000

    1.002

    1.004

    1.006

    1.008

    0.998

    1.010

    freq, MHz

    Mu1

    MuPrime1

    68IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

    NIC Return Loss BW vs. Op-Amp Unity Gain BW

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    Op Amp BW 15 dB RL NIC BW

    500 MHz 3.6 MHz

    1000 MHz 7.2 MHz

    2000 MHz 14.5 MHz

    C etu oss s Op p U ty Ga

    69IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

    Floating NIC Circuit Using Two Transistors

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    1i

    1v

    +

    -

    LZ

    2i

    2v

    +

    -

    1Q 2Q

    3v 3v

    Floating NIC Circuit Using Two Transistors

    70IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

    NIC All-Pass Test Circuit

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    NIC All Pass Test Circuit

    0Z

    LZ0Z L

    Z

    71IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

    High-Frequency BJT Device Model

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    High Frequency BJT Device Model

    VAR

    VAR1

    Cpi=gm/(2*pi*fT)

    Cc=Cpi/10

    Rb=7

    gm=900

    fT=32

    Rpi=110

    EqnVar

    Port

    P3

    Num=3

    Port

    P2

    Num=2

    Port

    P1

    Num=1

    C

    Cc

    C=Cc pF

    R

    Rb

    R=Rb Ohm

    CCpi

    C=Cpi pF

    VCCS

    SRC1

    R2=1e100 Ohm

    R1=Rpi Ohm

    G=gm mS

    72IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

    Test Circuit Results (f = 32 GHz)

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    Test Circuit Results (fT

    32 GHz)

    0.2 0.4 0.6 0.80.0 1.0

    -0.8

    -0.7

    -0.6

    -0.5

    -0.4

    -0.3

    -0.9

    -0.2

    freq, GHz

    dB(S(2

    ,1))

    0.2 0.4 0.6 0.80.0 1.0

    -25

    -20

    -30

    -15

    freq, GHz

    dB(S(1

    ,1))

    m1

    m1freq=dB(S(1,1))=-19.995

    502.0MHz

    0.2 0.4 0.6 0.80.0 1.0

    1.0000000

    1.0000000

    1.0000000

    1.0000000

    1.0000000

    freq, GHz

    Mu

    1

    Mu

    Prime

    1

    73IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

    All-Pass -20 dB RL BW v. fT

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    All Pass 20 dB RL BW v. fT

    0 5 10 15 20 25 30 350

    100

    200

    300

    400

    500

    600

    Transistor fT in GHz

    All-passb

    an

    dw

    idthinMHz

    74IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

    Fabricated Two Transistor Floating

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    NIC Using 2N2222 Devices

    75IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

    Measured Results for Two Transistor FNIC

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    76IEEE Waves and Devices 19 Feb 2010Copyright 2010James T. Aberle

    Summary of NIC Developments

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    y p

    Weve had some successes in fabricating NICs

    that work up to about 50 MHz.

    We have had many more failures.

    The main issue concerns stability small and

    large signal stability. We are making progress, albeit very slowly

    Someday, someone will make a reliable FNIC

    that works into the 100s of MHz range.

    77IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    How Best to Use a NIC to Make

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    a Non-Foster Reactance?

    Direct negation:

    ZZ NIC

    78IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    How Best to Use a NIC to Make

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    a Non-Foster Reactance?

    Using a certain transformation:

    Verman, Proc. IRE, Apr. 1931

    79IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Negative Impedance Transformation

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    R R

    -R ZL(s)

    Zin(s)

    ( )( ) 2( )( )

    ( ) ( )

    L

    in

    L L

    R Z s R RZ s R

    Z s Z s

    + = + =

    ZL(s)

    R/2 R/2

    R/2 R/2

    -R

    Can develop an NIC thatneeds to work for only one

    value of real impedance Also suggests the possibilityof using negative resistancediodes (Tunnel, Gunn, etc.) forNIC realization

    Grounded

    Floating

    80IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Negative Impedance Transformation

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    ( )( )

    1

    1

    1 11

    1 11

    L in

    neg

    neg

    neg

    neg

    neg

    neg

    Z s Z s

    sL

    sC

    sLsC

    sLsC

    sCsL

    sLsC

    sCsL

    +

    +

    2

    2

    neg

    neg

    L R C

    LCR

    =

    =

    81IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Schematic captured from Agilent ADS of

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    Optim

    Optim1

    SaveCurrentEF=no

    UseAllGoals=yes

    UseAllOptVars=yes

    SaveAllIterations=no

    SaveNominal=no

    UpdateDataset=yes

    SaveOptimVars=noSaveGoals=yes

    SaveSolns=yes

    SetBestValues=yes

    NormalizeGoals=noFinalAnalys is="None"

    StatusLevel=4

    DesiredError=0.0

    MaxIters=250

    OptimTy pe=Gradient

    OPTIM

    VAR

    VAR1

    Cneg=7.6146 {o}

    Lneg=291.922 {o}Lm=55.1849 {o}

    EqnVar

    Goal

    OptimGoal2

    RangeMax[1]=RangeMin[1]=

    RangeVar[1]=

    Weight=

    Max=10

    Min=

    SimInstanceName="SP1"

    Expr="abs(real(Zin1)-50)"

    GOAL

    Goal

    OptimGoal1

    RangeMax[1]=

    RangeMin[1]=

    RangeVar[1]=

    Weight=

    Max=20

    Min=

    SimInstanceName="SP1"

    Expr="abs(imag(Zin1))"

    GOAL

    sp_nec_NE85630_7_19940401

    SNP3

    Frequency ="{0.05 - 3.60} GHz"

    Bias="Bjt: Vce=10V Ic=30mA"sp_nec_NE85630_7_19940401

    SNP2

    Frequency ="{0.05 - 3.60} GHz"

    Bias="Bjt: Vce=10V Ic=30mA"

    CAPQ

    Cneg

    Mode=proportional to f req

    F=60.0 MHz

    Q=100.0

    C=Cneg pF

    INDQ

    Lm

    Rdc=0.0 Ohm

    Mode=proportional to f req

    F=60.0 MHz

    Q=100.0

    L=Lm nH

    INDQ

    Lneg

    Rdc=0.0 Ohm

    Mode=proportional to f reqF=60.0 MHz

    Q=100.0

    L=Lneg nH

    MuPrime

    MuPrime1

    MuPrime1=mu_prime(S)

    MuPrime

    Mu

    Mu1

    Mu1=mu(S)

    Mu

    Zin

    Zin1

    Zin1=zin(S11,PortZ1)

    Zin

    N

    S2P

    SNP1

    21

    Ref

    Term

    Term2

    Z=50 Ohm

    Num=2

    Term

    Term1

    Z=50 Ohm

    Num=1

    S_Param

    SP1

    Step=1 MHz

    Stop=90 MHz

    Start=30 MHz

    S-PARAMETERS

    VHF monopole with active matching network

    82IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Simulated return loss at input of optimized active

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    40 50 60 70 8030 90

    -25

    -20

    -15

    -30

    -10

    freq, MHz

    dB(S(1

    ,1))

    Return Loss (dB)

    matching network and antenna

    83IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Overall efficiency (in percent) of optimized active matchingnetwork and antenna

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    40 50 60 70 8030 90

    75

    80

    85

    90

    70

    95

    freq, MHz

    mag(S(2,1

    ))*100

    Overall Efficiency (%)

    84IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Small-signal geometrically-derived stability factor for theoptimized active matching network and antenna

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    40 50 60 70 8030 90

    0.98

    0.99

    1.00

    0.97

    1.01

    freq, MHz

    Mu1

    Mu

    Prime1

    85IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Outline of Presentation

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    What Does Non-Foster Mean?

    Possible Applications of Non-FosterReactances

    Electrically Small Antennas

    High-Impedance Surfaces

    Artificial High-Permeability Materials

    Realization of Non-Foster Reactances

    86IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle

    Summary

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    The use of non-Foster reactances could improve

    the performance of ESAs and HIGPs

    dramatically. Some hard-won successes have been achieved

    in the development of the requisite NICs.

    But an interdisciplinary team with expertise incircuits as well as field theory and sufficient

    funding is needed to realize reliable high

    frequency non-Foster reactances and tointegrate them into electromagnetic devices.

    87IEEE Waves and Devices 19 Feb 2010

    Copyright 2010James T. Aberle