Synthesis of coupling matrix for lossy filter networks

A generalized method for the synthesis of lossy microwave filters is given in this paper. An equation on the polynomials of S parameters is given to replace the power conservation. When the polynomials of S parameters satisfy a given condition, it is guaranteed that the admittance parameters as well as the coupling matrix (CM) can be derived from the S parameters. Two special cases are discussed for solving the refection function from a prescribed transfer function. In the first case, F11 (the numerator of S11) equals to F22 (the numerator of S22). This is the case that is equivalent to the even/odd mode analysis but is extended to be applied for asymmetric filter responses. In the second case, the loss distribution among a filter network is given. A method of iteration is applied to derive the CM with the prescribed loss distribution. The method is an extension to the conventional method of predistortion with nonuniform resonator Qs and lossy invertors.