A New Equivalent Circuit Extraction Method A New Equivalent Circuit Extraction Method For Quasi-static RegionsFor Quasi-static Regions

Benjamin D. BraatenBenjamin D. BraatenDr. Robert M. NelsonDr. Robert M. NelsonYuxin FengYuxin Feng

North Dakota State UniversityNorth Dakota State University

TopicsTopics

IntroductionIntroduction Computing the equivalent circuitComputing the equivalent circuit ValidationValidation ConclusionConclusion

North Dakota State UniversityNorth Dakota State University

IntroductionIntroduction

Recently, Electric Field Integral Equations (EFIE) were Recently, Electric Field Integral Equations (EFIE) were developed for evaluating problems with [1]developed for evaluating problems with [1] electrically large regions (full-wave regions)electrically large regions (full-wave regions) electrically small regions (quasi-static regions)electrically small regions (quasi-static regions) geometrically complex quasi-static regionsgeometrically complex quasi-static regions thin-wire full-wave regionsthin-wire full-wave regions

But, problems with a large number of quasi-static regions But, problems with a large number of quasi-static regions (>4) have resulted in a long computation time [1].(>4) have resulted in a long computation time [1].

North Dakota State UniversityNorth Dakota State University

[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

IntroductionIntroduction

This has lead to the development of modeling these This has lead to the development of modeling these quasi-static regions as equivalent circuits [1],[2].quasi-static regions as equivalent circuits [1],[2].

This will allow the quasi-static regions to be This will allow the quasi-static regions to be represented as equivalent circuits in fast efficient full-represented as equivalent circuits in fast efficient full-wave solvers such as Mininec [3]. wave solvers such as Mininec [3].

North Dakota State UniversityNorth Dakota State University

[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 full-wave 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.

IntroductionIntroduction

In this work we introduce a method for determining the In this work we introduce a method for determining the equivalent circuit of a quasi-static region based on equivalent circuit of a quasi-static region based on

work by Mayhan et.al. [4].work by Mayhan et.al. [4]. This method can then be used to determine the This method can then be used to determine the

equivalent circuit of a quasi-static region that may not equivalent circuit of a quasi-static region that may not have a convenient analytical method for evaluating the have a convenient analytical method for evaluating the

equivalent circuit.equivalent circuit.

North Dakota State UniversityNorth Dakota State University

[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.

Computing the equivalent circuitComputing the equivalent circuit

First, consider the following equation:First, consider the following equation:

North Dakota State UniversityNorth Dakota State University

antenna antenna

admittanceadmittance scattered field from scattered field from open circuitopen circuit

known loadknown load

admittanceadmittance

scattered fieldscattered field

from known loadfrom known loadscattered field from scattered field from

short circuitshort circuit

(1)(1)

Computing the equivalent circuitComputing the equivalent circuit

Rearranging (1) and using impedance values we get:Rearranging (1) and using impedance values we get:

North Dakota State UniversityNorth Dakota State University

impedance attached to impedance attached to the port of the the port of the antennaantenna

scattered field from scattered field from open circuitopen circuit

known antenna known antenna input impedanceinput impedance

scattered fieldscattered field

from unknown from unknown loadload

scattered field from scattered field from short circuitshort circuit

(2)(2)

Computing the equivalent circuitComputing the equivalent circuit

Step 1: Redefine the quasi-static region at the port of Step 1: Redefine the quasi-static region at the port of a test dipole with a known input impedance and a test dipole with a known input impedance and calculate .calculate .

Computing the equivalent circuitComputing the equivalent circuit

Step 2: Remove the Step 2: Remove the quasi-static region at quasi-static region at the port of the test dipole the port of the test dipole with a known input with a known input impedance impedance and short the terminals and short the terminals to calculate .to calculate .

North Dakota State UniversityNorth Dakota State University

Computing the equivalent circuitComputing the equivalent circuit Step 3: Remove the Step 3: Remove the short at the port of the short at the port of the test dipole and opentest dipole and openthe terminals to the terminals to calculate . calculate . Then use (2) to calculateThen use (2) to calculatethe equivalent circuitthe equivalent circuitof the quasi-static region.of the quasi-static region. All computations can be All computations can be performed in QUICNEC [1]. performed in QUICNEC [1].

North Dakota State UniversityNorth Dakota State University

ValidationValidation The first problem chosen to validate the method The first problem chosen to validate the method

presented here was a capacitively dominant quasi-presented here was a capacitively dominant quasi-static region.static region.

North Dakota State UniversityNorth Dakota State University

ValidationValidation

Using the scattered Using the scattered field method an field method an equivalent circuit of equivalent circuit of RRoo=0 and C=0 and Coo=.32pF =.32pF was calculated.was calculated.

This problem also This problem also results in an analytical results in an analytical equivalent circuit equivalent circuit approximation approximation of .28pF (epsilon A/d).of .28pF (epsilon A/d).

North Dakota State UniversityNorth Dakota State University

ValidationValidation

North Dakota State UniversityNorth Dakota State University

The following two The following two problems were then problems were then defined in QUICNEC defined in QUICNEC and Mininec for and Mininec for validation.validation.

ValidationValidation

North Dakota State UniversityNorth Dakota State University

This resulted in the following input reactance.This resulted in the following input reactance.

ValidationValidation

The second problem The second problem used to validate the used to validate the method was a two method was a two insulator wire insulator wire problem.problem.

This problem was This problem was chosen because is chosen because is may not be very may not be very easy to calculate an easy to calculate an equivalent circuit equivalent circuit analytically.analytically.

North Dakota State UniversityNorth Dakota State University

ValidationValidation

North Dakota State UniversityNorth Dakota State University

Using the method Using the method described here an described here an equivalent circuit of equivalent circuit of RRoo=1251 Ohms and =1251 Ohms and CCoo=.00692pF was =.00692pF was calculated.calculated.

This resulted in the This resulted in the following induced following induced current at 1340 KHz.current at 1340 KHz.

The equivalent circuit The equivalent circuit was defined in was defined in Mininec.Mininec.

Computation timeComputation time

North Dakota State UniversityNorth Dakota State University

First problem: QUICNEC 57 seconds and First problem: QUICNEC 57 seconds and Mininec <1 second.Mininec <1 second.

Second problem: QUICNEC 6 minutes Second problem: QUICNEC 6 minutes and Mininec < 1 second.and Mininec < 1 second.

ConclusionConclusion

North Dakota State UniversityNorth Dakota State University

A method for determining the equivalent circuit A method for determining the equivalent circuit based on various scattered fields has been based on various scattered fields has been presented.presented.

Two problems have been chosen to validate the Two problems have been chosen to validate the methodmethod a capacitively dominant quasi-static regiona capacitively dominant quasi-static region a quasi-static insulator a quasi-static insulator

It has been shown that this method can be used to It has been shown that this method can be used to accurately model quasi-static regions in Mininec.accurately model quasi-static regions in Mininec.

Finally, a significant savings in computation time is Finally, a significant savings in computation time is observed.observed.

QuestionsQuestions

Thank you for listeningThank you for listening

North Dakota State UniversityNorth Dakota State University