Mm'-type filter

The mm'-type section has two independent parameters (m and m') that the designer can adjust. It is arrived at by double application of the m-derivation process. Its chief advantage is that it rather better at matching in to resistive end terminations than the k-type or m-type. The image impedance of a half-section is Zim on one side and a different impedance, Zimm' on the other. Like the m-type, this section can be constructed as a series or shunt section and the image impedances will come in T and Π flavours. Either a series construction is applied to a shunt m-type or a shunt construction is applied to a series m-type. The advantages of the mm'-type filter are achieved at the expense of greater circuit complexity so it would normally only be used where it is needed for impedance matching purposes and not in the body of the filter.

The transfer function of an mm'-type is the same as an m-type with m set to the product mm'. To choose values of m and m' for best impedance match requires the designer to choose two frequencies at which the match is to be exact, at other frequencies there will be some deviation. There is thus some leeway in the choice but Zobel suggests the values m=0.7230 and m'=0.4134 which give a deviation of the impedance of less than 2% over the useful part of the band. Since mm'=0.3, this section will also have a much faster cut-off than an m-type of m=0.6 which is an alternative for impedance matching.

It is possible to continue the m-derivation process ad-infinitum and produce mm'm"-types etcetera. However, the improvements obtained diminish at each iteration and are not usually worth the increase in complexity.