Low pass filters with poles located on elliptic and parabolic contours revisited

Transfer functions of low pass filters with parabolic and elliptic distribution of poles and all transmission zers at infinity are discussed and three new classes of those filters are introduced. They are referred to as the Transitional Butterworth-Scanlan (TBS) filters. the Transitional Mullick (TM) filters and the Transitional Chebyshev-Scanlan (TCS) filters. All these filter functions depend on one variable parameter which entails a tradeoff between the frequency and time-domain characteristics. This enables a large variety of filter specifications to be met in practical design by a single class of transfer functions. In particular, the Transitional Chebyshev-Scalan (TCS) filters are shown not only to cover the widest range of specifications but also to provide better frequency and time domain characteristics than any other transitional class of filters so far described. The pole locations of the now classes of TM and TCS filters are tabulated for n = 3 - 7 together with some moat relevant parameters of the transient responses to a unit step input. The most common techniques of the frequency and gain normalization employed when comparing different classes of pulse forming networks are critically reviewed and a figure of merit is defined for evaluating the relative effectiveness of various systems.