AUTOMATED DESIGN OF TWO-ZERO RATIONAL CHEBYCHEV FILTERS

Abstract

The Rational Chebyshev Function was first introduced by Bernstein (1926), used by Sharpe (1953), then later by Heldman (1955) to design elliptic-characteristic filters. Namely for a filter of order N, we have N/2 equal ripples in the passband and N/2 equal ripples in the stopband of the magnitude response. Here, the same mechanics are used but are now producing a new and different type of response. It has N/2 ripples in the passband but only one ripple in the stopband for all orders. As N increases from three, the result is a substantial saving in number of capacitors in the passive ladder realization of the above function as compared to that of traditional elliptic filters of the same order N. It also has been discovered that the above ladder's element values can be expressed as explicit expressions involving only the coefficients of the transfer function. These expressions can also be used for other types of filters. Numerically, the design can be carried out by a Fortran program or a set of programs on a programmable calculator. The design is termed automated because the user needs only to give the three specifications: the filter order N, the stopband zeros Z, and the passband ripple amount R(p). The program automatically selects the starting point for the given case and proceeds. The numerical results of the above programs over a range of specifications has led to a surprising and simple expression relating the above specifications to the minimum stopband attenuation. This is a useful relationship for the designer to estimate the zero position when using the programs.