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Lines In this section we present the electric and magnetic field lines of a semiinfinite parallel plate transmission line near a perfectly conducting plane ground, i.
Acknowledgment The authors wish to thank Captain Carl E. When a semi-infinite parallel plate transmission line is in the proximity of a perfectly conducting plane ground, one expects the field distribution and impedance of a transmission line to be modified to a greater or lesser extent, depending on the degree of the ground proximity. Detailed numerical calculations are presented in this note. The theoretical results so obtained are discussed in Section 2.
The point to in the t-plane corresponds to the point C in the z-plane Fig.
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This region can be transformed by Schwartz-Christoffel transformation, onto the upper half of the t-plane with the line segments A-P-Q-C-D transformed into the real axis of the t-plane. The ground effect is negligible in the region Based on the theoretical and numerical results presented in Sections 2 and 3, conclusions are drawn in Section 4 on the effects of the perfectly conducting plane on the distribution of the field lines and electric field intensities.
In particular, the field distribution and line impedance of a parallel plate transmission has been examined in detail by Baum and extended by Brown and Granzow.
Ltinr the real and imaginary parts on both sides, one finds 2b C1 7r A. A-1 is represented by the differential equation Since the subject of central importance posed by the problem is the effects of the ground proximity on the distribution of the field lines and electric field intensities, these quantities are presented in this section in graphical form with a view to showing the parametric effects on the field distributions.
The derivation leyy the essential formulas are presented in the Appendix. Assuming that the ground is a perfectly conducting plane, an exact electrostatic solution is obtained by conformal transformation for such a transmission line system. It may be instructive, however, to consider briefly some special cases of interest such as field variations on the upper plate, on the center plane and at the ground.
Instead we present a table showing the parameters involved and the Figure numbers related to those parameters. Ground PI,-ne I 0 I C0 CC 4’4 -0 0 co co U ppe, —r 1. The graphs for the relative electric field intensities key a semi-infinite parallel pl-ate transmission line show that, as a whole, the effect of the presence of a perfectly conducting ground on the field intensity leh significant, as far as in the region between the upper 211147 and the center plane is concerned, only when the separation of the ground is less than one-half the separation distance of the parallel plates i.
APPENDLX – The Conformal Transformation Our aim is to find the distribution of electric field and magnetic field lines of a semi-infinite parallel plate transmission line system which is placed at some arbitrary distance above the perfectly conducting plane ground as illustrated in Fig.
In this case, A. A-1the coordinates of which represent the separation distance between the transmission line 221147 and the plane ground. The use of these in A.
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ExrorI db – A semi-infinite parallel plate transmission line system in the z-plane in the presence of the perfectly conducting ground. The mapping of the flux functions were also computVlr-CLdCl1latud by feeding as an input to a program a set of appropriate values of u and v. Conclusions The primary objective of this work is to investigate the effect of the ground proximity on the field distribution of a semi-infinite parallel plate transmission line. The dimension of the length of the transmission line system i.
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Theoretical Results In this section we present a theoretical discussion on field lines and electric field intnsiLies in a semi-infinite parallel plate transmission line system in the proximity of a perfectly conducting plane ground. The coordinates of the corresponding points in each plane effected by the successive transformations are tabulated below. Center Platie – 1.
Similarly, the x-components of the electric field intensities of the transmission line are shown in Figs. Since the method requires an 8. Henceforth, by the field intensity, we mean the relative field intensity.
The configuration of the line segments so transformed in the t-plane is shown in Fig.