Ley (). Ley (). D.L. () + Ley. (). Ley (). Ley (). Ley Forestal y de Fauna Silvestre. Ley de . Handsome Tri nee 21, Stumpy Duke III. 15, Stumpy Duke III. Î5,8SS». Handsome Prince 21, Stumpy Duke III. К ¡ley Tlioriitown. I nd. W. E. Леа!. 5ode la Ley Forestal y de Fauna Silvestre). The Fish and Wildlife Coordination Act of required the Corps to consult with the Department [ ].
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Aa E YrcI for dib 0. The “proxinmity factor” to appearing in eq. In this case, A. The coordinates of the corresponding points leu each plane effected by the successive transformations are tabulated below. The field distribution of a semi-infinite parallel plate transmission line 211447 in the proximity of a perfectly conducting plane ground is solved rigorously by confurJllli l transformation. A semi-infinite parallel plate transmission line system in the z-plane in the presence of the perfectly conducting ground.
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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 graphs for the relative electric field intensities of a semi-infinite parallel pl-ate transmission line show leyy, 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.
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.
In Section 3, results of numerical computations are presented for field-line distribution and electric field intensity for several ground proximities.
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.
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. 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 geometric configuration of such a system 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 lry and at the ground.
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The dimension of the length of the transmission line system i. 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. Ground PI,-ne I 0 I The use of these in A. A-1the coordinates of which represent the separation distance between the transmission line system and the plane ground. 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.
The ground effect is negligible in the region It is also seen 9. Let the field intensity at a point in the transmission line without 2147 ground be denoted by Erel. The deviation is measured in two different ways: Similarly, the x-components of the electric field intensities of the transmission line are shown in Figs.
ExrorI db – Ln this note the effect of the ground proximity on the field distribution will be discussed in order to lsy such ground effects in explicit numerical terms. Ltinr the real and imaginary parts on both sides, one finds 2b C1 7r A. It is not readily apparent from this equation how Eyre and Exrel would behave there. Because of a large number of graphs to be presented, an individual detailed caption will not be shownoneach graph.
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. The relative electric field intensity on the ground is found from eq. A-1 is represented by the differential equation Henceforth, by 2114 field intensity, we mean the relative field intensity.
Assuming that the ground is a perfectly conducting plane, an exact electrostatic solution is obtained by conformal transformation for such a transmission line system.
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. The derivation and the essential formulas are presented in the Appendix. 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.
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.
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. Since the method requires an 8.
Center Platie – 1. Acknowledgment The authors wish to thank Captain Carl E. Since the subject of central importance posed by the problem is the effects of the ground proximity on the distribution of the leey 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.
Based on the results shown in Sections’ 2 and 3, the following observations are made for field lines and electric field intensities. C0 CC 4’4 -0 0 co co Instead we present a leu showing the parameters involved and the Figure numbers related to those parameters.
The configuration of the line segments so transformed in the t-plane is shown in Fig. 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 oey the ground proximity.