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The graphs for the relative electric field intensities of 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 is significant, as far as in the region between the upper plate 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.

I Exreil without ground. Ln this note the effect of the ground proximity on the field distribution will be discussed in order to establish such ground effects in explicit numerical terms. The “proxinmity factor” to appearing in eq. Center Platie – 1. The coordinates of the corresponding points in each plane effected by the successive transformations are tabulated below.

It is also seen 9. A-1the coordinates of which represent the separation distance between the transmission line system and the plane ground.

C0 CC 4’4 -0 0 co co The deviation is measured in two different ways: Instead we present a table showing the parameters involved and the Figure numbers related to those parameters. Ltinr the real and imaginary parts on both sides, one finds 2b C1 7r A.

Let the field intensity at a point in the transmission line without the ground be denoted by Erel.

This basic structure can be considered as the proto-type of simulators considered in other notes 3 4. U ppe, —r 1.

A semi-infinite parallel plate transmission line system in 211477 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. The field distribution of a semi-infinite parallel plate transmission line placed in the proximity of a perfectly conducting plane ground is solved rigorously by confurJllli l transformation.

This was done solely for the sake of graphical clarity.

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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. In this case, A.

A third computer program was developed to calculate the field intensities at a set of predetermined points in the transmission line system by use of the Newton-Raphson method for the complex function. Henceforth, by the field intensity, we mean the relative field intensity.

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Theoretical Results In this section we present a theoretical discussion on field lines and electric field intnsiLies in lej semi-infinite parallel plate transmission line system in the proximity of a perfectly conducting plane ground.

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.

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. The derivation and the essential formulas are presented in the Appendix.

leg When a semi-infinite parallel plate transmission line is in the proximity of a perfectly conducting 2147 ground, one expects the field distribution and impedance of a transmission 211147 to be modified to a greater or lesser extent, depending on the degree of the ground proximity. The theoretical results so obtained are discussed in Section 2. The dimension of the length of the transmission line system i. Ground PI,-ne I 0 I The configuration of the line segments so transformed in the t-plane is shown in Fig.

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. 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.

The use of these in A.

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The point to in the t-plane corresponds to the point C in the z-plane Fig. The ground effect is negligible in the region In order to examine the behavior of the x- and y-component of Erel in a close neighborhood of the singular point, one needs to combine the eqs. If the ground and the plates are assumed to be perfectly conducting, 211147 line can support 1.

It is not readily apparent from this equation how Eyre and Exrel would behave there. 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.

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.