Theoretical Minimum Insertion Loss of the Butterworth and Chebyshev Bandpass Filters

This paper presents an analytical approach that makes it possible to find an ultimate theoretical minimum of insertion loss for the Butterworth and Chebyshev filters. This minimum is achieved, if the filters are designed for the optimum bandwidth. The difference between the minimum of insertion loss for a practical case of the integer number of resonators and for the theoretical case, when the number of resonators can be fractional, is discussed. A criterion suitable to characterize quality of a practical filter design in terms of insertion loss related to its theoretical minimum is proposed.