Passivity enforcement in the synthesis of lossy filters

A recent paper introduced an algorithm concerning the synthesis of lossy filters which allows to exploit some degrees of freedom available in a lossy design. In the original formulation, though, the passivity of the network is not enforced beforehand and requires a check a posteriori. In the present paper we propose an analytical procedure which can be used in conjunction with that algorithm in order to obtain a more robust synthesis technique for lossy filters. This theoretical improvement allows to avoid the trial-and-error method initially suggested and provides a simple way to identify some additional constraints introduced by the passivity condition on the available degrees of freedom. The approach described here also allows to derive some guidelines to relate the choice of these degrees of freedom to the maximum quality factor required in the synthesis and to the expected behavior of the synthesizable reflection functions under the assumptions originally required by the algorithm.