A real-frequency approach to the design of a Butterworth diplexer

A real-frequency approach to the design of a diplexer having Butterworth response is presented. The real parts of two minimum reactance functions are preassigned from the given transducer power gains. Their imaginary parts are derived by means of the rational Hilbert transform. Using the least pth method to implement the solution process, we greatly reduce the highly nonlinear combinations of the objective functions and the independent variables, resulting in a successful design of a diplexer approximating the Butterworth response, both in the low-pass and the high-pass channels