Determination of transmission zeros is important in synthesis of cross-coupled filter.A novel method to determine the general Chebyshev filter degree and transmission zeros at the same time is proposed according to the extreme characteristic of the general Chebyshev function and the relationship between the filter degree and the number of transmission zeros.On the condition of the given filter specifications

the least filter degree and the optimum positions of transmission zeros are realized.Several simulation examples illustrate the procedure and the validity in the filter design of the proposed method.