Design of generalized Chebyshev filters with asymmetrically located transmission zeros

A simple design technique is introduced for generalized Chebyshev filters with asymmetrically located transmission zeros. The efficient and exact procedure is given for the calculation of transmission zeros for a class of generalized Chebyshev low-pass prototype filters with a maximum of four asymmetrically located transmission zeros of any multiplicity. This technique is based on obtaining the frequencies of magnitude characteristic extreme values in closed form, and after this, transmission zeros can be calculated by solving a system of nonlinear equations. Novel formulas for orders of zeros of maximally selective filters with equiripple characteristics in the passband and stopband are deduced. The obtained results are verified and illustrated by given examples.