By Raj Mittra
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Extra resources for Computer Techniques for Electromagnetics
102) P — i Re n=1 where I and E„ are the current and the total electric field intensity at the N match points. 01l. Note that a very significant improvement is obtained by simply deleting the point nearest each end. This is usually true for most situations. Note further that this is not the optimum for the dipole being considered. The optimum distance depends on the wire radius and on the accuracy of the numerical impedance matrix. The impedance matrix [Z~] used to obtain these solutions was derived by a transformation from a piecewise uniform basis of dimension N = 80 to a cosine basis where M = 20.
From the equivalence principle of Schelkunoff, J and K generate the true field outside S and a null field in the interior region. For perfectly conducting antennas, such as we will consider here, K vanishes except in the gap region. The next step is to place a filamentary electric line source on the axis of the antenna and "react" this "test source" with the true source. By react we mean apply the reciprocity theorem. That is, if source distributions J(a) and K(a) generate fields E(a) and K(a) in the presence of source b acting as a receiver (and vice versa), then a complex number defined as the reaction between sources a and b is given by [J(a) • E(b) — 1(a) • H(b)] (a, b) = V d Va .
116) The integration is carried out on tn the coordinate along the arms of the nth true dipole filaments. The symbol dmn is the standard Kronecker delta. Let the assumed form of In(tn) for the true dipole be inserted into eqn. 116) and define a mutual impedance term as Zmn — ~ m. In-1 sin k (ln — 1) sin kdn _ 1 „_1•E m dl— 1 `n+ sin k (1 — l n) f • Em d l . 117) The dummy variable 1 is the coordinate along a particular segment where do _ 1 and do are the lengths of the (n — 1)th and nth segments, respectively.
Computer Techniques for Electromagnetics by Raj Mittra