Non-Foster Reactances for ElectricallySmall 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
Outline of Presentation
• What Does “Non-Foster” Mean?
• Possible Applications of Non-Foster
Reactances
– Electrically Small Antennas
– High-Impedance Surfaces
– Artificial High-Permeability Materials
• Realization of Non-Foster Reactances
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
2
Outline of Presentation
• What Does “Non-Foster” Mean?
• Possible Applications of Non-Foster
Reactances
– Electrically Small Antennas
– High-Impedance Surfaces
– Artificial High-Permeability Materials
• Realization of Non-Foster Reactances
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
3
Foster’s Reactance Theorem
• The theorem is a consequence of
conservation of energy.
• The slope of the input reactance
(susceptance) of a lossless passive oneport is always positive.
• All zeros and poles of the impedance
(admittance) function are simple, and a
zero must lie between any two poles, and
a pole between any two zeros.
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
4
Consequences of Foster’s
Reactance Theorem
• Impedances (admittances) of passive oneport networks rotate clockwise on the
Smith Chart as frequency increases.
• There is no such thing as a negative
capacitor or a negative inductor (for
passive circuits).
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
5
Foster Network
L
L2
L=40 nH
R=
Term
Term1
Num=1
Z=50 Ohm
L
C
L1
C1
L=40 nH
C=30 pF R=
R
R1
R=50 Ohm
60
20
S(1,1)
imag(Zin1)
real(Zin1)
40
0
-20
0
50
100
150
200
250
300
freq, MHz
freq (10.00MHz to 300.0MHz)
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
6
Non-Foster Network
Term
Term1
Num=1
Z=50 Ohm
L
L2
L=40 nH
R=
L
L
L1
L3
L=40 nH
L=-40 nH R=
R=
R
R1
R=50 Ohm
120
80
S(1,1)
imag(Zin1)
real(Zin1)
100
60
40
20
0
-20
0
50
100
150
200
250
300
f req, MHz
f req (10.00MHz to 300.0MHz)
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
7
Outline of Presentation
• What Does “Non-Foster” Mean?
• Possible Applications of Non-Foster
Reactances
–Electrically Small Antennas
– High-Impedance Surfaces
– Artificial High-Permeability Materials
• Realization of Non-Foster Reactances
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
8
VHF Whip: A Canonical ESA
•Geometry of monopole
antenna as modeled in
Antenna Model software.
The monopole is a copper
cylinder 0.6 meters in
length and 0.010 meters in
diameter, mounted on an
infinite perfect ground
plane.
•Frequency range is 30 to
90 MHz.
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
9
Input Impedance of VHF Whip From Simulation
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10
Two Tools to Help With Analysis
• Exact two-port representation of antenna
in frequency domain in terms of sparameters.
• Approximate lumped equivalent circuit
model of antenna over frequency range of
interest.
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
11
Two-Port Representation of Antenna
Z0
jX a
Rl
N :1
Z0
The quantities in this box are re-evaluated
at every frequency for which we have data.
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
12
Two-Port Representation of Antenna
Z a = Ra + jX a = Rr + Rl + jX a
Rr = ecd Ra = radiation resistance
R/ = (1 − ecd ) Ra = dissipative loss resistance
X a = antenna reactance
N=
Rr
Z0
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
13
Two-Port Representation of Antenna
• Antenna impedance and radiation efficiency are
used to produce a Touchstone *.s2p file for use
in 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 for
considering the use of non-Foster reactances in
antenna matching networks.
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
14
Approximate Equivalent Circuit of the Antenna
• To model the antenna, we assume that the real
part of the antenna impedance varies as the
square of frequency, and the imaginary part
behaves as a series LC.
2
ω 

1 

Z a = R0   + j  ωLa −
ωC a 
 ω0 

Impedance produced by equivalent circuit
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
15
Approximate Equivalent Circuit of the Antenna
• Evaluation of the model parameters (R0, La and
Ca):
R0 = ℜ{Z a (ω0 )}

ω1

ω
2

− 1   La 
 ℑ{Z a (ω1 )}



ω1   

  = 

− 1 1
  ℑ{Z a (ω2 )}
ω2   Ca 
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
16
Approximate Equivalent Circuit of the Antenna
R0 = 4.30 Ω
La = 194 nH
Term
Term1
Num=1
Z=50 Ohm
Ca = 8.69 pF
Z1P_Eqn
Z1P1
Z[1,1]=4.30*(freq/52e6)**2
C
Ca
C=8.69 pF
0
imag(VHF_Whip_S2P..Zin1)
imag(Zin1)
real(VHF_Whip_S2P..Zin1)
real(Zin1)
20
L
La
L=194 nH
R=
15
10
5
0
30
40
50
60
70
80
90
-100
-200
-300
-400
-500
-600
30
freq, MHz
40
50
60
70
80
90
freq, MHz
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
17
Matching Network Concept
Γ
Z0
Matching
Network
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
ZL
18
Points to Consider
• A real passive matching network can only
approach and never exceed the performance
predicted by the Bode-Fano criterion.
• The matchable bandwidth is limited by the Q of
the load.
• The matchable bandwidth can only be increased
by de-Qing the load – that is by intentional
introduction of dissipative losses into the
matching network – and concomitant reduction
in radiation efficiency.
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
19
Bode-Fano Criterion
∆f
≤
f0
π
Maximum
allowable
reflection
coefficient
 1 
Q ⋅ ln 
 Γm 
Q of the load
Maximum value of fractional
bandwidth that can be achieved with
any passive, lossless matching
network.
∆f
1
Q = 81.9, Γm = ⇒
≤ 0.035
3
f0
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
20
Single-Tuned Mid-band Match
Term
Term1
Num=1
Z=4.30 Ohm
m1
freq=51.80MHz
S(1,1)=-10.409 / -73.141
impedance = Z0 * (0.992 - j0.630)
L
Le
L=884 nH
R=
C
Ca
C=8.69 pF
m2
freq=52.20MHz
S(1,1)=-10.477 / 71.883
impedance = Z0 * (1.008 + j0.630)
∆f 52.2 − 51.8
≈
= 0.008
f0
52
m2
S(1,1)
L
La
L=194 nH
R=
Z1P_Eqn
Z1P1
Z[1,1]=4.30*(freq/52e6)**2
m1
freq (30.00MHz to 90.00MHz)
Analytical:
∆f
1
=
= 0.009
f0
2Q
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
21
Wheeler-Lopez Double-Tuned Matching
A.R. Lopez, “Wheeler and Fano Impedance
Matching”, IEEE Antennas and Propagation
Magazine, Vol. 49, No. 4, August 2007
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
22
Wheeler-Lopez Double-Tuned Matching
A.R. Lopez, “Wheeler and Fano Impedance
Matching”, IEEE Antennas and Propagation
Magazine, Vol. 49, No. 4, August 2007
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
23
Wheeler-Lopez Double-Tuned Matching with
Antenna De-Qing
N
S-PARAMETERS
Zin
S_Param
SP1
Start=30 MHz
Stop=90 MHz
Step=1 MHz
Zin
Zin1
Zin1=zin(S11,PortZ1)
1
Term
Term1
Num=1
Z=50 Ohm
L
L2
L=177 nH
R=
C
C2
C=53.0 pF
R
RD
R=200 Ohm
L
Le
L=884 nH
R=
2
Re f
Term
Term2
Num=2
Z=50 Ohm
S2P
SNP1
File="VHF_whip.s2p"
TF
TF1
T=0.354
-6
-12
-14
dB(S(2,1))
S(1,1)
dB(S(1,1))
-8
-10
-16
-18
-20
-12
-22
-14
-24
30
40
50
60
70
80
90
freq, MHz
30
40
50
60
70
80
90
freq, MHz
Decent match, poor efficiency
freq (30.00MHz to 90.00MHz)
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
24
Matching Network with Non-Foster Reactances
L
L1
T erm
L=-44.9 nH
T erm1
R=
Num=1
Z=50 Ohm
L
L3
L=44.9 nH
R=
L
L2
L=-44.9 nH
R=
C
Ca1
C=-8.69 pF
L
La1
L=-194 nH
R=
Z1P_Eqn
Z1P1
Z[1,1]=4.30*(freq/52e6)**2
L
La
L=194 nH
R=
C
Ca
C=8.69 pF
Dualizer
Antenna
m1
S(1,1)
Cancels frequency squared
dependence of radiation resistance.
m1
freq= 90.00MHz
S(1,1)=4.843E-4 / -3.517E-5
impedance = Z0 * (1.001 - j5.952E-10)
Van Der Pol, Proc, IRE, Feb. 1930
freq (30.00MHz to 90.00MHz)
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
25
Antenna with More Practical Matching Network
using Non-Foster Reactances.
Z0
− (La + Lm )
− Ca
Lm
Z0
Active matching network
Two-port model of
antenna
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
26
Optimized Non-Foster Matching Network
1
Term
Term1
Num=1
Z=50 Ohm
L
L2
L=-Lneg nH
R=
L
L3
L=Lm nH
R=
Var
Eqn
2
Ref
C
Ca1
C=-Cneg pF
VAR
VAR1
Lm=49.5959 {o}
Lneg=226.588 {o}
Cneg=8.72637 {o}
-16
0.0
-0.1
-20
dB(S(2,1))
dB(S(1,1))
-18
S(1,1)
Term
Term2
Num=2
Z=50 Ohm
S2P
SNP1
File="VHF_whip.s2p"
-22
-24
-0.2
-0.3
-0.4
-26
-28
-0.5
30
40
50
60
70
80
90
freq, MHz
30
40
50
60
70
80
90
freq, MHz
freq (30.00MHz to 90.00MHz)
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
27
Outline of Presentation
• What Does “Non-Foster” Mean?
• Possible Applications of Non-Foster
Reactances
– Electrically Small Antennas
– High-Impedance Surfaces
– Artificial High-Permeability Materials
• Realization of Non-Foster Reactances
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
28
High-Impedance Ground Plane
Capacitive
FSS
Low
Permittivity
Spacer
Metal Vias
Metal Backplane
10”
Coaxial Feed
Bent Wire
Element
Sievenpiper, et. al, IEEE Trans. MTT, Nov. 1999
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
29
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 not
supported (thus can be called an
electromagnetic bandgap structure).
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
30
Model for Surface Impedance of Sievenpiper HIS
Zin
d
ηo
C
Zo, β
Short
Γ
Zstub
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.
Shunt Capacitance
180o
2β
βd
Short
Γ
Zin
Open
θ
Phase Angle, θ
Zstub
90o
BW ~ 10% to 20% of fo.
0o
-90o
-180o
fo
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
Frequency
31
Reflection Phase Bandwidth of
Sievenpiper HIS
FSS layer
µr
Spacer layer
h
Ground plane
∆ω
ω0
= 2πµr
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
h
λ0
32
Electrically-Thin Broadband HighImpedance Surface
• In principle, one could realize an electrically-thin
broadband HIS by using a high-permeability
spacer layer.
• A high-permeability meta-material can be
realized using artificial magnetic molecules
(AMMs) implement with negative inductance
circuits.
• Unfortunately, AMM performance is very
sensitive to component tolerances.
• But, there is a better way …
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
33
Electrically-Thin Broadband
High-Impedance Surface
Kern, Werner, Wilhelm, APS 2003
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
34
Electrically-Thin Conventional HIS
0.062 in Rogers
Duroid 5880
m1
m2
freq=2.308GHz
freq=2.502GHz
phase(S(1,1))=90.015 phase(S(1,1))=-90.204
C
C1
C=2.17 pF
TLINP
TL1
Z=377/sqrt(2.2) Ohm
L=1.6 mm
K=2.2
A=0.0
F=1 GHz
TanD=0.0009
Mur=1
TanM=0
Sigma=0
200
m1
phase(S(1,1))
Term
Term1
Num=1
Z=377 Ohm
m3
freq=2.403GHz
phase(S(1,1))=-0.139
100
m3
0
m2
-100
-200
1.0
∆f
= 8%
f0
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
1.5
2.0
2.5
3.0
3.5
4.0
freq, GHz
35
Electrically-Thin HIS with Negative Inductance
L
Lneg
L=-2.02 nH
R=
TLINP
TL1
Z=377/sqrt(2.2) Ohm
L=1.6 mm
K=2.2
A=0.0
F=1 GHz
TanD=0.0009
Mur=1
TanM=0
Sigma=0
phase(S(1,1))
Term
Term1
Num=1
Z=377 Ohm
15
10
5
0
-5
-10
1.0
1.5
2.0
2.5
3.0
3.5
4.0
freq, GHz
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
36
Unit Cell of Sievenpiper HIGP
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
37
Reflection Phase Response of
Sievenpiper HIGP
40
Reflection Coefficient Phase (deg)
20
0
-20
-40
-60
-80
-100
-120
-140
12
13
14
15
Frequency (GHz)
16
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
17
18
38
Unit Cell of Sievenpiper HIGP with Reactive Loading
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
39
Equivalent Circuit of Loaded HIGP for
Normally Incident Plane Wave
Zload
E
Zload
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
40
Reflection Phase of Capacitively
Loaded HIGP
200
Reflection Coefficient Phase (deg)
150
100
50
0
-50
-100
-150
-200
0.5
1
1.5
2
2.5
Frequency (GHz)
3
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
3.5
4
41
Reflection Phase of Negative-Inductor
Loaded HIGP
40
Reflection Coefficient Phase (deg)
30
Lneg = -2.2nH
20
10
0
-10
-20
-30
-40
0.5
1
1.5
2
2.5
Frequency (GHz)
3
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
3.5
4
42
Outline of Presentation
• What Does “Non-Foster” Mean?
• Possible Applications of Non-Foster
Reactances
– Electrically Small Antennas
– High-Impedance Surfaces
– Artificial High-Permeability Materials
• Realization of Non-Foster Reactances
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
43
What is an Artificial Material?
• An artificial material is a large-scale emulation of an actual
material, obtained by embedding a large number of electrically
small inclusions (“artificial molecules”) within a host medium.
• Like natural molecules, the electrically small inclusions exhibit
electric and/or magnetic dipole moments.
• As a result of these dipole moments, the macroscopic
electromagnetic constitutive parameters (εr and µr) are altered
with respect to the host medium.
D = ε • ε0 E
B = µ • µ0 H
IEEE Waves and Devices 19 Feb 2010
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44
Why Create an Artificial
Magnetic Material?
• “Naturally” occurring magnetic materials
(ferrites) are heavy, fragile and expensive, and
they also exhibit relatively high magnetic losses
and dielectric constant.
• Available ferrite materials provide a limited
selection of relative permeabilities.
• The permeability tensor of the ferrite is
controlled by applying a static magnetic field –
permanent magnets and/or electromagnets are
required.
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
45
Artificial Magnetic Metamaterial
W
dy
dz
ZL
z
dx
dz
a
y
dy
•A 3-dimensional lattice of artificial
molecules.
•Electrically small loop with a load
impedance
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
46
Simple Circuit Model for Artificial Magnetic Molecule (AMM)
Relative
permeability
Rrad
µ xx = 1 + Nα
Lloop
Number of
AMMs per
unit volume
I
VH
+
-
ZL
− jωµ 0 a 4
m
α= =
H Rloss + jωLloop + Z L
Magnetic
polarizability of
each AMM
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
47
Broadband, High Permeability Requires Negative Inductance
18
16
real
Relative Permeability
14
Circuit Theory Model
12
10
W
8
6
ZL= -jω Ld
4
a
2
imag
0
0
1
2
3
4
5
6
Frequency, GHz
7
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
8
9
10
48
How to Extract Material Properties
(TEM waveguide containing material sample)
PMC walls
wave port 1
wave port 2
material sample
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
49
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 ABCD
parameters.
-Calculation of propagation constant and
characteristic impedance of equivalent
transmission line.
-Evaluation of the material properties.
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
50
How to Extract Material Properties
(Loop Configuration)
lumped element
copper loop
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
51
Negative Inductance is Modeled as a Frequency-Dependent
Capacitance
Cequiv =
1
(2πf )2 Lneg
IEEE Waves and Devices 19 Feb 2010
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52
Cancellation of Parasitic
Capacitance Using NIC
To remove the resonance, the parasitic capacitance of the loop should be
compensated by a negative capacitance.
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
53
Remedy for Snoek-Like Phenomenon: Add Negative Capacitance in
Shunt with Negative Inductance
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
54
Outline of Presentation
• What Does “Non-Foster” Mean?
• Possible Applications of Non-Foster
Reactances
– Electrically Small Antennas
– High-Impedance Surfaces
– Artificial High-Permeability Materials
• Realization of Non-Foster Reactances
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
55
Negative Impedance Converter (NIC)
• An ideal NIC is a two-port network such that when a
load impedance is attached to the output terminal, the
input impedance is the (possibly scaled) negative
value of the load impedance.
Zin=-kZL (k>0)
Ideal
NIC
ZL
Canonical NIC
R
+
Z in = − Z
-
Z
R
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
57
Simple Op-Amp Test Circuit
S-PARAMETERS
S_Param
SP1
Start=1 MHz
Stop=4000 MHz
Step=1 MHz
Term
Term1
Num=1
Z=50 Ohm
R
R1
R=1 kOhm
R
R4
R=100 Ohm
R
R3
R=50 Ohm
OpAmp
AMP2
Gain=100 dB
BW=500 MHz
R
R2
R=1 kOhm
Can specify DC
gain and unity gain
BW.
FOM: RL > 15 dB
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
58
Unity-gain BW = 500 MHz
0
m1
dB(S(1,1))
-10
m1
freq=7.000MHz
dB(S(1,1))=-14.883
-20
-30
-40
1E6
1E7
1E8
1E9
4E9
freq, Hz
IEEE Waves and Devices 19 Feb 2010
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59
NIC Return Loss BW vs. Op-Amp Unity Gain BW
NIC Return Loss BW (MHz)
30
25
20
15
10
5
500
Op-amp based NICs
contra-indicated for
applications above 30 MHz
1000
1500
Op-Amp Unity-Gain BW (MHz)
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
2000
60
Fabricated OPA690 NIC Evaluation
Board
IEEE Waves and Devices 19 Feb 2010
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61
Circuit for evaluating the performance
of a grounded negative impedance
Rg
Vin
Vg
Rin
Vneg
NIC
Iin
ZL
Signal
Generator
Zin
-ZL
Stability requires that
Rin > Z L
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
62
Schematic captured from Agilent ADS of the circuit
for evaluating the performance of the OPA690 NIC
T R A N S IE N T
T ra n
T ra n 1
S to p T im e = 5 u s e c
M a xT im e S te p = 0 . 5 n s e c
Vg
Va r
Eqn
VAR
VAR1
R s c a le = 2 5 0
R s c a le 2 = 2 5 0
V in
R
Rg
R =50 O hm
V t S in e
Vg
V dc=0 m V
A m p lit u d e = 1 0 0 m V
F re q = 0 .5 M H z
D e la y = 0 n s e c
D a m p in g = 0
P hase=0
R
R7
R = R s c a le
V neg
R
R in
R =100 O hm
O P A 6 9 0 _ p o rt
X1
R
R3
R = R s c a le 2
R
R 10
R =50 O hm
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
63
dB(Return_Loss_Measured)
dB(Return_Loss_Simulated)
Simulated and measured return loss for
the OPA690 NIC evaluation circuit
0
-10
-20
-30
-40
-50
0
2
4
6
8
10
12
14
16
18
20
freq, MHz
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
64
Ground Negative Impedance Versus
Floating Negative Impedance
• Canonical NIC and most other NIC circuits in the literature produce
grounded negative impedance
-Z
• But for the applications we are considering here, we need floating
negative impedance
-Z
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
65
Floating NIC Realized Using Two Op-Amps
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
66
Op-Amp FNIC Test Circuit
S-PARAMETERS
Mu
S_Param
SP1
Start=0.1 MHz
Stop=100 MHz
Step=0.1 MHz
Mu
Mu1
Mu1=mu(S)
OpAmp
AMP1
Gain=100 dB
BW=500 MHz
Term
Term1
Num=1
Z=50 Ohm
MuPrime
R
R3
R=1k Ohm
R
R4
R=1k Ohm
R
Rneg
R=50 Ohm
R
R1
R=1k Ohm
R
R2
R=1k Ohm
MuPrime
MuPrime1
MuPrime1=mu_prime(S)
R
RL
R=50 Ohm
Term
Term2
Num=2
Z=50 Ohm
OpAmp
AMP2
Gain=100 dB
BW=500 MHz
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
67
Unity-gain BW = 500 MHz
0
0
-20
-30
m1
freq=3.600MHz
dB(S(1,1))=-15.048
-40
-50
-5
-10
-15
1E5
1E6
1E7
1E8
1E5
1E6
freq, Hz
1E7
1E8
freq, Hz
1.010
1.008
MuPrime1
Mu1
dB(S(1,1))
dB(S(2,1))
m1
-10
1.006
1.004
1.002
1.000
0.998
0
20
40
60
80
100
freq, MHz
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
68
NIC Return Loss BW vs. Op-Amp Unity Gain BW
Op Amp BW
15 dB RL NIC BW
500 MHz
3.6 MHz
1000 MHz
7.2 MHz
2000 MHz
14.5 MHz
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
69
Floating NIC Circuit Using Two Transistors
v3
i1
ZL
Q1
v3′
i2
Q2
+
+
v1
v2
-
-
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
70
NIC “All-Pass” Test Circuit
Z0
ZL
− ZL
Z0
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
71
High-Frequency BJT Device Model
C
Cc
C=Cc pF
R
Rb
R=Rb Ohm
Port
P1
Num=1
Var
Eqn
VAR
VAR1
Rpi=110
fT=32
gm=900
Rb=7
Cc=Cpi/10
Cpi=gm/(2*pi*fT)
C
Cpi
C=Cpi pF
Port
P2
Num=2
VCCS
SRC1
G=gm mS
R1=Rpi Ohm
R2=1e100 Ohm
Port
P3
Num=3
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
72
Test Circuit Results (fT = 32 GHz)
-15
-0.2
-0.3
dB(S(2,1))
-20
-25
-0.4
-0.5
-0.6
-0.7
-0.8
-30
0.0
0.2
0.4
0.6
0.8
-0.9
1.0
0.0
0.2
freq, GHz
m1
freq=502.0MHz
dB(S(1,1))=-19.995
0.4
0.6
0.8
1.0
freq, GHz
1.0000000
1.0000000
MuPrime1
Mu1
dB(S(1,1))
m1
1.0000000
1.0000000
1.0000000
0.0
0.2
0.4
0.6
0.8
1.0
freq, GHz
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
73
All-Pass -20 dB RL BW v. fT
600
All-pass bandwidth in MHz
500
400
300
200
100
0
0
5
10
15
20
Transistor fT in GHz
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
25
30
35
74
Fabricated Two Transistor Floating
NIC Using 2N2222 Devices
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
75
Measured Results for Two Transistor FNIC
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
76
Summary of NIC Developments
• We’ve 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.
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
77
How Best to Use a NIC to Make
a Non-Foster Reactance?
• Direct negation:
−Z
NIC
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
Z
78
How Best to Use a NIC to Make
a Non-Foster Reactance?
• Using a certain transformation:
Verman, Proc. IRE, Apr. 1931
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
79
Negative Impedance Transformation
R
R
Zin(s)
-R
ZL(s)
Grounded
R/2
R/2
-R
Floating
R/2
Z in
• Can develop an NIC that
needs to work for only one
value of real impedance
• Also suggests the possibility
of using negative resistance
diodes (Tunnel, Gunn, etc.) for
NIC realization
ZL(s)
R/2
R + Z L ( s ) )( − R )
(
(s) =
+R=
Z L (s)
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
−R2
Z L ( s)
80
Negative Impedance Transformation
Z L (s)
sL
Z in ( s )
−1
sCneg
1
sC
− sLneg
1
sL +
sC
1
1
sC +
1
sL
− sCneg
1
−
sLneg
− sLneg
1
−
sCneg
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
Lneg = R 2C
Cneg = L
R2
81
Schematic captured from Agilent ADS of
VHF monopole with active matching network
S-PARAMETERS
N
OPTIM
Zin
S_Param
SP1
Start=30 MHz
Stop=90 MHz
Step=1 MHz
Mu
Zin
Zin1
Zin1=zin(S11,PortZ1)
MuPrime
Mu
Mu1
Mu1=mu(S)
Optim
Optim1
OptimTy pe=Gradient
MaxIters=250
DesiredError=0.0
StatusLev el=4
FinalAnaly sis="None"
NormalizeGoals=no
SetBestValues=y es
Sav eSolns=y es
Sav eGoals=y es
Sav eOptimVars=no
UpdateDataset=y es
Sav eNominal=no
Sav eAllIterations=no
UseAllOptVars=y es
UseAllGoals=y es
MuPrime
MuPrime1
MuPrime1=mu_prime(S)
GOAL
Goal
OptimGoal1
Expr="abs(imag(Zin1))"
SimInstanceName="SP1"
Min=
Max=20
Weight=
RangeVar[1]=
RangeMin[1]=
RangeMax[1]=
CAPQ
Cneg
C=Cneg pF
Q=100.0
F=60.0 MHz
Mode=proportional to f req
INDQ
Lneg
L=Lneg nH
Q=100.0
F=60.0 MHz
Mode=proportional to f req
Rdc=0.0 Ohm
sp_nec_NE85630_7_19940401
SNP3
Bias="Bjt: Vce=10V Ic=30mA"
Frequency ="{0.05 - 3.60} GHz"
GOAL
sp_nec_NE85630_7_19940401
SNP2
Bias="Bjt: Vce=10V Ic=30mA"
Frequency ="{0.05 - 3.60} GHz"
Goal
OptimGoal2
Expr="abs(real(Zin1)-50)"
SimInstanceName="SP1"
Min=
Max=10
Weight=
RangeVar[1]=
RangeMin[1]=
RangeMax[1]=
Var
Eqn
Term
Term1
Num=1
Z=50 Ohm
INDQ
Lm
L=Lm nH
Q=100.0
F=60.0 MHz
Mode=proportional to f req
Rdc=0.0 Ohm
Sav eCurrentEF=no
VAR
VAR1
Lm=55.1849 {o}
Lneg=291.922 {o}
Cneg=7.6146 {o}
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
1
2
Re f
S2P
SNP1
Term
Term2
Num=2
Z=50 Ohm
82
Simulated return loss at input of optimized active
matching network and antenna
Return Loss (dB)
-10
dB(S(1,1))
-15
-20
-25
-30
30
40
50
60
70
80
90
freq, MHz
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
83
Overall efficiency (in percent) of optimized active matching
network and antenna
Overall Efficiency (%)
mag(S(2,1))*100
95
90
85
80
75
70
30
40
50
60
70
80
90
freq, MHz
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
84
Small-signal geometrically-derived stability factor for the
optimized active matching network and antenna
1.01
MuPrime1
Mu1
1.00
0.99
0.98
0.97
30
40
50
60
70
80
90
freq, MHz
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
85
Outline of Presentation
• What Does “Non-Foster” Mean?
• Possible Applications of Non-Foster
Reactances
– Electrically Small Antennas
– High-Impedance Surfaces
– Artificial High-Permeability Materials
• Realization of Non-Foster Reactances
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
86
Summary
• 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 in
circuits as well as field theory and sufficient
funding is needed to realize reliable high
frequency non-Foster reactances and to
integrate them into electromagnetic devices.
IEEE Waves and Devices 19 Feb 2010
Copyright © 2010James T. Aberle
87