The implementation of the complex Chebyshev approximation for the synthesis of SAW filters

The synthesis of high performance linear or nonlinear phase SAW filters require simultaneous compensation of both magnitude and phase distortions. These distortions can be the result of electrical loading, diffraction, bulk wave radiation/interactions and other second order effects. The constraints of any applicable compensation algorithm would include the minimization of the filter´s overall length. An algorithm synthesizing functions having Chebyshev characteristics is ideally suited for this application. Of late, several algorithms have been presented including algorithms by Chit and Mason (1991) and most recently Lim and Lee (1992). Of great concern in the routine synthesis of SAW filters is the algorithm´s convergence, numeric efficiency, and capability for handling high order FIR filters (say greater than 1000). The approach developed is based on the adaptive weighted least-squares formulation of Lim and Lee and on its solution by the block Toeplitz approach used by Chit and Mason. The resulting algorithm provides stable and rapid convergence for problems including complex valued lowpass, bandpass, allpass, and highpass FIR designs with linear, nearly linear, or nonlinear phase. The developed algorithm is applicable to synthesis of FIR sequences with orders in excess of 1000