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C0 CC 4’4 -0 0 co co 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.

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Ground PI,-ne I 0 I The geometric configuration of such a system is shown in Fig. Henceforth, by the field intensity, we mean the relative field intensity.

The point to in the t-plane corresponds to the point C in the z-plane Fig. This region can be transformed by Schwartz-Christoffel transformation, onto the upper half of the t-plane with the leh segments A-P-Q-C-D transformed into the real axis of the t-plane.

Acknowledgment The authors wish to leg Captain Carl E. 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 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.

Detailed numerical calculations are presented in this note. Since the method requires an 8. If the ground and the plates are assumed to be perfectly conducting, the line can support 1.

This basic structure can be considered as the proto-type of simulators considered in other notes 3 4. 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 ly the separation of the ground is less than one-half the separation distance of the parallel plates i.

Upper Plate y b 0. Theoretical Results In this section we present a theoretical discussion on field lines and electric field intnsiLies in a semi-infinite parallel leh transmission line system in the let of a perfectly conducting plane ground.

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. The deviation is measured in two different ways: 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.

ExrorI db – 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. 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.

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. In this case, A. U ppe, —r 1.

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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. It is also seen 9. 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. Instead we present a table showing the parameters involved and the Figure numbers related to those parameters. Center Platie – 1. A-1 is represented by the differential equation In Section 3, results of numerical computations are presented for field-line distribution and electric field intensity for several ground proximities.

Aa E YrcI for dib 0. The use of these in A. This was done solely for the sake of graphical clarity.

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.

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The “proxinmity factor” to appearing in eq. Ltinr the real let imaginary parts on 2117 sides, one finds 2b C1 7r A. Based pey the results shown in Sections’ 2 and 3, the following observations are made for field lines and electric field intensities. The coordinates of the corresponding points in each plane effected by the successive transformations are tabulated below.

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. 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.

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. The dotted lines superimposed on each figure represent the field lines of the similar transmission line without the ground in the Figs. The theoretical results so obtained are discussed in Section 2. 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.

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. Because of a 221147 number of graphs 211447 be presented, an individual detailed caption will not be shownoneach graph. Let the field intensity at a point in the transmission line without the ground be denoted by Erel.