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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.
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.
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The configuration of the line segments so transformed in lfy t-plane is shown in Fig. Thus E E 1 uniform b Yuniform It seems appiropriate, therefore, to normalize the field intensity of the tr-ansmission line with respect to the uniform field. It is also seen 9.
The relative electric field intensity on the ground is found from eq. The “proxinmity factor” to appearing in eq.
The geometric configuration of such a system is shown in Fig. 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. A semi-infinite parallel plate transmission line system in the z-plane in the presence of the perfectly conducting ground.
I Exreil without ground. U ppe, —r 1. A systematic numerical computation of the electric field intensity of the transmission line has been carried out and the results are presented in Section 3. Upper Plate y b 0. The dotted lines superimposed on each figure represent the field lines of the similar transmission line without the ground in the Figs.
C0 CC 4’4 -0 0 co co The derivation and the essential formulas are presented in the Appendix. The plate separation distance is designated by 2b and the distance between the near edge of the plates to the ground by d.
In this case, A. Ground PI,-ne I 0 I The field distribution of a semi-infinite parallel plate transmission line placed in the 221147 of a perfectly conducting plane ground is solved rigorously by confurJllli l transformation.
The theoretical results so obtained are discussed in Section 2. This basic structure can be considered as the proto-type of simulators considered in other notes 3 4. Graphical Representation In Section 2, a mathematical discussion was presented for a semi-infinite parallel plate transmission line placed in the proximity of a perfectly conducting plane ground.
A-1the coordinates of which represent the separation distance between the 21417 line system and the plane ground. Acknowledgment The authors wish to thank Captain Carl E.
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The ground effect is negligible in the region 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. Assuming that the ground is a perfectly conducting plane, an exact electrostatic solution is obtained by conformal transformation for such a transmission line system. The point to lry the t-plane corresponds to the point C in the z-plane Fig.
Similarly, the x-components of the electric field intensities of the transmission line are shown in Figs. The deviation is measured in two different ways: The mapping of the flux functions were also computVlr-CLdCl1latud by feeding as an input to a program a set of appropriate 21417 of u and v. 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.
ExrorI db – From the contour plots, it is observed that, as a whole, the presence of a perfectly conducting plane ground causes the field strength to be enhanced in a neighborhood of the upper edge and to be weakened in a region where the center plane intersects the ground plane. A third computer program was developed to calculate the field intensities at a set of predetermined points in the transmission line system by use lej the Newton-Raphson method for the complex let.
Center Platie – 1.