Finite Difference Time Domain Calculations

of Antenna Mutual Coupling

by

Raymond Luebbers and Karl Kunz

Electrical Engineering DepartmentThe Pennsylvania State University

University Park, PA 16802

April 1991

Abstract

The Finite Difference Time Domain (FDTD) technique has beenapplied to a wide variety of electromagnetic analysis problems,including shielding and scattering. However, the method has notbeen extensively applied to antennas. In this short papercalculations of self and mutual admittances between wire antennasare made using FDTD and compared with results obtained using theMethod of Moments. The agreement is quite good, indicating thepossibilities for FDTD application to antenna impedance andcoupling.

I Introduction

The Finite Difference Time Domain (FDTD) technique has had onlylimited application to antennas. This is somewhat surprising,since the geometrical and material generality of the methodsuggests that it might have significant application to antennaanalysis, especially in situations where other structures,especially electromagnetically penetrable ones, are nearby. Thisis due to the relative ease with which the FDTD methodaccommodates modeling of volumetric electromagnetic interactionswith materials as compared to the Method of Moments.

'̂

Earlier work [1] has shown that the FDTD method could compute theself impedance of a wire antenna in three dimensions, however,the approach used in [1], plane wave incidence, did not lenditself to mutual coupling calculations. Accurate self-admittanceFDTD results for two-dimensional antenna geometries werepresented in [2]. In this paper we demonstrate both self andmutual admittance FDTD calculations for three dimensional wireantennas.

n ' FINITE DIFFERENCE TIME N92-2Q442DOMAIN CALCULATIONS OF ANTENNA MUTUALCOUPLING (Pennsylvania State Univ.) 15 p

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https://ntrs.nasa.gov/search.jsp?R=19920011200 2018-07-11T10:23:57+00:00Z

II Approach

The test problem geometry is shown in Figure 1. Two wire dipolesof length 57 and 43 cm are parallel and separated by 10.5 cm.Both are center fed, and are symmetrically positioned. The goalis to determine the self admittance of the driven dipole and themutual admittance between the two dipoles.

The FDTD computations were made using a three dimensionalcomputer code based on the Yee [3] cell, with second order Mur[4] absorbing boundaries. The problem space was chosen as61x51x80 cells, with the cell dimensions Ax=Ay=0.5 cm, Az=1.0 cm.Making the two transverse dimensions smaller results in a greaterlength to diameter ratio, so that a thin wire Moment Method codemay be used to provide comparison results over a wider band offrequencies. Thinner wires may be modeled in FDTD using sub-cellmethods [5,6].

For the FDTD calculations the longer dipole is fed at the centerwith a Gaussian pulse of 100 volts maximum amplitude that reachedits 1/e amplitude in 16 time steps. The time steps were 11.11picoseconds, the Courant stability limit for the cell sizechosen.

During the progress of the FDTD calculations the currents at thecenter of each dipole were saved for each time step. They werecomputed by evaluating the line integral of the magnetic fieldaround the dipoles at the center. Along with the appliedGaussian voltage pulse the currents were Fourier transformed tothe frequency domain. Then, based on the admittance parameterequations

I = V Y + V Y•h V1 X11 V2 X12

= V1 *21 + V2 Y22

d^ taking V1 to be the driven dipole voltage and V2 zero, weeas'ily obtain the self admittance of dipole 1 and the mutualadmittance (since Y12 = Y?1) between the dipoles by dividing theappropriate complex Fourier transforms of V1r I,,, and I2.

The Moment Method results were obtained using the ElectromagneticSurface Patch Version 4 [7] computer code. The wire radius forthe Moment Method calculations was taken as 0.281 cm, providingthe same cross section area as the 0.5 cm square FDTD cells.While the FDTD calculations should be valid up to approximately 3GHz based on having 10 FDTD cells per wavelength, the thin wireapproximation for the Moment Method code becomes questionable at

approximately 1 GHz and this was taken as the upper frequencylimit for comparison of results.

III Results

Figure 2 shows the Gaussian pulse voltage applied to the 1 cellgap at the center of the longer, driven dipole. Figures 3 and 4show the current flowing in the center cell of the driven andpassive dipole respectively. All are plotted on the same timescale, corresponding to 8,192 time steps. This calculationrequired approximately 7 hours on a 25 MHz 486-based personalcomputer.

Figures 5-7 show the magnitude of the Fourier transforms of thevoltage and current results of Figures 2-4. The current resultsindicate the complicated frequency domain behavior of the coupleddipole system.

The self admittance was obtained by dividing the complex Fouriertransform of the driven dipole current by that of the Gaussianvoltage pulse at each frequency. The results are shown inmagnitude and phase in Figures 8 and 9 and compared with ESP4Moment Method results. Considering the differences in how thefeed region is modeled (a 1 cm gap in the FDTD calculations vs aninfinitesimal gap in ESP4) the agreement is quite good.

The mutual admittance was obtained in a similar manner, dividingthe complex passive dipole current by that of the Gaussian pulse.The results are shown in Figures 9 and 10. Again the agreementis quite good considering the different approximations andassumptions made in the FDTD approach relative to the ESP4computer code.

IV Conclusions

The capability of the FDTD method to predict mutual couplingbetween antennas was demonstrated. The test case was twoparallel wire dipoles of different lengths, with one driven by aGaussian pulse. The complex self and mutual admittance resultsobtained using FDTD showed good agreement with results obtainedusing the Method of Moments.

V References

1. K. Kunz, R. Luebbers, F. Hunsberger, "A Thin Dipole AntennaDemonstration of the Antenna Modeling Capabilities of theFinite Difference Time Domain Technique", AppliedComputational Electromagnetics Society Journal. Summer 1990.

2. J. G. Maloney, G. S. Smith, and W. R. Scott, Jr., "Accuratecomputation of the Radiation from Simple Antennas using theFinite-Difference Time Domain Method," IEEE Trans. Antennasand Propagat. . vol. AP-38, pp 1059-1068, July 1990.

3. K. S. Yee, "Numerical solution of initial boundary valueproblems involving Maxwell's equations in isotropic media,"IEEE Trans. Antennas and Propagat., vol. AP-14, pp 302-307,May 1966. /

4. G. Mur, "Absorbing boundary conditions for the FiniteDifference Approximation of the Time-Domain ElectromagneticField Equations," IEEE Trans, on ElectromagneticCompatibility, vol. EMC-23, pp 377-382, November 1981.

5. R. Holland and L. Simpson, "Finite-difference analysis ofBMP coupling to thin struts and wires," IEEE Trans, onElectromagnetic Compatibility, vol. EMC-23, May 1981.

6. K. Umashankar, A. Taflove, and B. Beker, "Calculation andexperimental validation of induced currents on coupled wiresin an arbitrary shaped cavity," IEEE Trans. Antennas andPropaaat.. vol. AP-35, pp 1248-1257, November 1987.

7. E. Newman, "A user's manual for the electromagnetic surfacepatch code: ESP Version IV," The Ohio State UniversityResearch Foundation, ElectroScience Laboratory, Departmentof Electrical Engineering, Columbus, Ohio 43212.

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