By Raj Mittra
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I i (b) (a ) Numerical approximation Ideal FiG. 8. Incident and scattered fields on axis for a plane wave incident on a straight wire (courtesy of R. Turpin). 01l ~ 200 7 O c ~~ L I50 o 6— 100 Point matching ~R„=e2. 1 ill I - - - - - - - "ii11 11 3 `, i 2 IPI -150 2 3 4 5 6 No. of equations deleted from end of dipole FIG. 9. Curves showing effects of equation deletion near ends of dipole. WIRE ANTENNAS 29 certain distance, d (Fig. e. the equations corresponding to these points are deleted from the set of equations) a better solution results as has been shown by Turpin (1969).
A similar interpretation applies to Z36 , Z45 , and Z46 . Thus submatrices SQr , q r , represent the interaction between elements q and r. If all the directors are of the same length, then SQr = Srq for director submatrices. Further, for uniform director spacing there will be several interdirector spacings or distances that will be the same. Consider the four-director Yagi in Fig. 17. The distance between directors 1 and 3 is the same as that between 2 and 4, for instance. Hence 513 = S24, assuming the directors are of the same length.
This is accomplished by applying two reaction tests on the true current I(z). One equation is obtained by reacting 1(z) with a test dipole centered on the antenna axis as in Fig. 11. This test dipole has arm length h/2. The dipole is then moved to the right a distance h/2 and reacted with I(z). This yields a pair of simultaneous linear equations. 114) I1Z11 + 12 Z 12 = V1 ~ I1Z21 + 12 Z22 = O. 115) 711 and Z22 represent the mutual impedance between parallel filamentary dipoles with sideways displacement a and no stagger.