ABSTRACT
Gain versus frequency specifications were translated at the outset into a gain versus frequency rational function from which, through the machinery of spectral factorization, a rational Positive Real (PR) impedance Z was calculated and finally realized according to Darlington's Theorem as a lossless two-port terminated on a resistor. In the case of filters doubly terminated by resistors, there are no special constraints on the transfer function other than those imposed by losslessness, and the analytically defined gain functions, example, Butterworth, Chebyshev, elliptic, lead to general solutions which are practical and readily implemented. The Real Frequency Technique (RFT), on the other hand, is a numerical method, and generates the rational PR function Z, which is the input impedance to the equalizer, directly from the approximation process. No rational transfer function is prescribed. The optimization can directly impose objectives, such as the minimization of maximum loss in the passband.
