By Randall W. Rhea
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Extra resources for HF Filter Design and Computer Simulation
The horizontal axis of the complex-frequency diagram represents the real portion of roots and the vertical axis represents the Poles are indicated on the imaginary portion of roots. ” For realizable passive networks, the poles of H(s) occur in the left half of the complex-frequency plane, or on the imaginary axis, while zeros may occur in either half. Poles and zeros occur in complex-conjugate pairs unless they lie on the real axis, in which case they may exist singly For lossless ladder networks with no mutual inductors, P(s) has only imaginary axis roots and is either purely even or purely odd.
The generator (input) termination resistance is universally normalized to 1 ohm, that is g(0) = 1, so it is not included in the tables. The form of all-pole prototypes is shown in Figure 2-6 and the form of elliptic prototypes is shown in Figure 2-11. O. O. 0432 dB, R. L. 4 dB, G(O)=l. O. O. O. O. O. O.
The class of filters with equiripple in the passband, LAr and equal minimum attenuation, Amin, in the stopband is referred to as Cauer-Chebyshev. The attenuation of Cauer-Chebyshev is given by LA = lOlog[ 1 +&~(o,)] (74) where OI, is the frequency normalized to the cutoff, E is from the equation (54) and q (0, > are elliptic functions of order 2v. The evaluation of & (0,) and the attenuation expression above is involved and closed form solutions are unknown. The lowpass prototype structure and the alternative form of the elliptic Cauer-Chebyshev are given in Figure 2-11.
HF Filter Design and Computer Simulation by Randall W. Rhea