LEY 21147 PDF

LEY 21147 PDF

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The dotted lines superimposed on each figure represent the field lines of the similar transmission line without the ground in the Figs. A semi-infinite parallel plate transmission line system in the z-plane in the presence of the perfectly conducting ground.

If the ground and the plates are assumed to be perfectly conducting, the line can support 1.

Theoretical Results In oey 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. A-1 is represented by the differential equation The configuration of the line segments so transformed in the t-plane is shown in Fig.

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 deviation is measured in two different ways: The theoretical results so obtained are discussed in Section 2. ExrorI db – Aa E YrcI for dib 0. The derivation and the essential formulas are presented in the Appendix. A-1the coordinates of which represent the separation distance between the transmission line system and the plane ground.

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. 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.

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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. Henceforth, by the field intensity, we mean the relative field intensity. 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.

Based on the results shown in Sections’ 2 and 3, the following observations are made for field lines and electric field intensities. Center Platie – 1.

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. I Exreil without ground. Ground PI,-ne I 0 I The plate separation distance is designated by 2b and the distance between the near edge of the plates to the ground by d.

It is also seen 9. 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 dimension of the length of the transmission line system i. Upper Plate y b 0.

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In particular, the pey distribution and line impedance of a parallel plate transmission has been examined in detail by Baum and extended by Lfy and Granzow. Assuming that the ground is a perfectly conducting plane, an exact electrostatic solution is obtained by conformal transformation for such a transmission line system.

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 point to in the t-plane corresponds to the point C in the z-plane Fig. The use of these in A. In Section 3, results of numerical computations are presented for field-line distribution and electric field intensity for several ground proximities.

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. Similarly, the x-components of the electric field intensities of the transmission line are shown in Figs. Conclusions The primary objective of this work lye to investigate the effect of the ground proximity on the field distribution of a semi-infinite parallel plate transmission line.

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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 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.

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. Acknowledgment The authors wish to thank Captain Carl E.

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. It is not readily apparent from this equation how Eyre and Exrel would behave there. Let the field intensity at a point in the transmission line without the ground be denoted by Erel. Detailed numerical calculations are presented in this note.

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 pey be modified to a greater or lesser extent, depending on the degree of the ground proximity. Since the method requires an 8. This basic structure can be considered as the proto-type of simulators considered in other notes 3 4.

C0 Leh 4’4 -0 0 co co The coordinates of the corresponding points in each plane effected by the successive transformations are tabulated below.