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This paper proposes a new approach to the optimal design of a minimum mismatch network, when operating between three given terminating impedances, yields a best transmission characteristic. First, we use the voltage and current to construct a scattering matrix, and then present two definitions which state that if there exists a set of numbers such that the scatting matrix satisfies the transmission function maximizes the smallest input reflectance, the problem is solvable. As an example, a fifth band-pass filter is designed in the center frequency 70 MHz. Explicit formulas for the element values of a band-pass filter having Butterworth, Chebyshev and Elliptic responses are given by using ADS. When load impedance is varying, experimental results on this filter are cited showing excellent agreement with theory. The simulation results demonstrated the optimal approach of minimum mismatch network is feasible.