A New Equivalent Circuit Extraction Method
For Quasi-static Regions
Benjamin D. Braaten
Dr. Robert M. Nelson
Yuxin Feng
North Dakota State University
Topics




Introduction
Computing the equivalent circuit
Validation
Conclusion
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Introduction
 Recently, Electric Field Integral Equations (EFIE) were
developed for evaluating problems with [1]
 electrically large regions (full-wave regions)
 electrically small regions (quasi-static regions)
 geometrically complex quasi-static regions
 thin-wire full-wave regions
 But, problems with a large number of quasi-static regions
(>4) have resulted in a long computation time [1].
[1] B.D. Braaten, R.M. Nelson and M.A. Mohammed, “Electric field integral equations for
electromagnetic scattering problems with electrically small and electrically large regions,” IEEE
Transactions on Antennas and Propagation, Vol. 56, No. 1, January 2008, pp. 142-150
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Introduction
 This has lead to the development of modeling these
quasi-static regions as equivalent circuits [1],[2].
 This will allow the quasi-static regions to be
represented as equivalent circuits in fast efficient fullwave solvers such as Mininec [3].
[1] B.D. Braaten, R.M. Nelson and M.A. Mohammed, “Electric field integral Equations for
electromagnetic scattering problems with electrically small and electrically large regions,” IEEE
Transactions on Antennas and Propagation, Vol. 56, No. 1, January 2008, pp. 142-150
[2] R.G. Olsen, G.L. Hower and P.D. Mannikko, “A hybrid method for combining Quasi-static and fullwave techniques for electromagnetic scattering problems,”IEEE Transactions on Antennas and
Propagation, Vol. 36, No. 8, pp. 1180-1184,August 1988.
[3] J.W. Rockway and J.C. Logan, “The New MININEC (Version 3): A Mini-numerical
Electromagnetics code,” U.S. Department of Commerce National Technical Information Service,
Springfield, VA September 1986, pp. 1-21.
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Introduction
 In this work we introduce a method for determining the
equivalent circuit of a quasi-static region based on
work by Mayhan et.al. [4].
 This method can then be used to determine the
equivalent circuit of a quasi-static region that may not
have a convenient analytical method for evaluating the
equivalent circuit.
[4] J.T. Mayhan, A.R. Dion and A.J. Simmons, “A technique for measuring antenna drive port
Impedance using backscatter data,” IEEE Transactions on Antennas and Propagation, Vol. 42, No. 4,
April 1994, pp. 526-533.
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Computing the equivalent circuit
First, consider the following equation:
scattered field from
short circuit
antenna
admittance
scattered field
from known load
(1)
known load
admittance
scattered field from
open circuit
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Computing the equivalent circuit
Rearranging (1) and using impedance values we get:
scattered field from
short circuit
scattered field
from unknown
load
(2)
known antenna
impedance attached to
input impedance
the port of the
scattered field from
antenna
open circuit
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Computing the equivalent circuit
Step 1: Redefine the quasi-static region at the port of
a test dipole with a known input impedance
and
calculate .
Computing the equivalent circuit
Step 2: Remove the
quasi-static region at
the port of the test dipole
with a known input
impedance
and short the terminals
to calculate
.
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Computing the equivalent circuit
 Step 3: Remove the
short at the port of the
test dipole and open
the terminals to
calculate
.
 Then use (2) to calculate
the equivalent circuit
of the quasi-static region.
 All computations can be
performed in QUICNEC [1].
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Validation
 The first problem chosen to validate the method
presented here was a capacitively dominant quasistatic region.
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Validation
 Using the scattered
field method an
equivalent circuit of
Ro=0 and Co=.32pF
was calculated.
 This problem also
results in an analytical
equivalent circuit
approximation of
.28pF (epsilon A/d).
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Validation
The following two
problems were then
defined in QUICNEC
and Mininec for
validation.
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Validation
This resulted in the following input reactance.
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Validation
 The second problem
used to validate the
method was a two
insulator wire
problem.
 This problem was
chosen because is
may not be very
easy to calculate an
equivalent circuit
analytically.
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Validation
 Using the method
described here an
equivalent circuit of
Ro=1251 Ohms and
Co=.00692pF was
calculated.
 This resulted in the
following induced
current at 1340 KHz.
 The equivalent circuit
was defined in
Mininec.
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Computation time
 First problem: QUICNEC 57 seconds and
Mininec <1 second.
 Second problem: QUICNEC 6 minutes
and Mininec < 1 second.
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Conclusion
 A method for determining the equivalent circuit
based on various scattered fields has been
presented.
 Two problems have been chosen to validate the
method
 a capacitively dominant quasi-static region
 a quasi-static insulator
 It has been shown that this method can be used to
accurately model quasi-static regions in Mininec.
 Finally, a significant savings in computation time is
observed.
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Questions
Thank you for listening
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