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A-1the coordinates of which represent the separation distance between the transmission line system and the plane ground.
Acknowledgment The authors wish to thank Captain Carl E. 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: 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. Center Platie – 1. The coordinates of the corresponding points in each plane effected by the successive transformations are tabulated below.
Let the field intensity at a point in the transmission line without the ground be denoted by Erel.
Theoretical Results In this section we present a theoretical discussion on field lines and electric field intnsiLies 2147 a semi-infinite parallel plate transmission line system in the proximity of a perfectly conducting plane ground.
The “proxinmity factor” to appearing in eq. 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. This basic structure can be considered as the proto-type of simulators considered in other notes 3 4. 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.
Instead we present a table showing the parameters involved and the Figure numbers related to those parameters. The geometric configuration of such a system is shown in Fig. In Section 3, results of numerical computations are presented for field-line distribution and electric field intensity for several ground proximities.
C0 CC 4’4 -0 0 co co Ln this note leey effect of 2147 ground proximity on the field distribution will be discussed in order to establish such ground effects in explicit numerical terms.
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Since the method requires an 8. Based on the results shown in Sections’ 2 and 3, the following observations are made for field lines and electric field intensities. 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.
Ltinr the real and imaginary parts on both sides, one finds 2b C1 7r A.
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Aa E YrcI for dib 0. If the ground and the plates are assumed to be perfectly conducting, the line can support 1.
A semi-infinite parallel plate transmission line system in the z-plane in the presence of the perfectly conducting ground. 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.
ExrorI db – 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. The point to in the t-plane corresponds to the point C in the z-plane Fig. Because of a large number of graphs to be presented, an individual detailed caption will not be shownoneach graph. The relative electric field intensity on the ground is found from eq. 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.
It is also seen 9.
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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. I Exreil without ground.
The dotted lines superimposed on each figure represent the field lines of the similar transmission line without the ground in the Figs. The ground effect is negligible in the region Ground PI,-ne I 0 I U ppe, —r 1. 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 dimension of the length of the transmission line system 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.
Upper Plate y b 0.
Detailed numerical calculations are presented in this note. A-1 is represented by the differential equation The configuration of the line segments so transformed in the t-plane is shown in Fig. The derivation and the essential formulas are presented in the Appendix.