M-derived filters or m-type filters are a type of electronic filter designed using the imaging method. They were invented by Otto Zobel in the early twenties. This type of filter was originally designed for use with telephone multiplexing and was an improvement on the existing constant k type filter. The main problem addressed was the need to achieve a better adaptation of the filter at termination impedances. In general, all filters designed by the image method do not give an exact match, but the filter of type m is a great improvement with the appropriate choice of parameter m. The m-type filter section has an additional advantage because there is a rapid transition from the cutoff frequency of the passband to an attenuation pole just inside the stopband. Despite these advantages, there is a drawback with m-type filters; At frequencies beyond the attenuation pole, the response begins to rise again, and types m have a poor rejection of the stop band. For this reason, filters designed with m-type sections are often designed as composite filters with a mixture of k- and m-type sections and different m-values at different points to obtain optimum performance of both types.
Zobel patented an impedance matching network in 1920 that essentially used the topology of what are now called m-type filters, but Zobel did not name them as such or analyze them by the imaging method. This earlier George Campbell publication of its constant k-type design in 1922 in which the m-type filter is based. Zobel published the theory of image analysis of m type filters in 1923. Once popular, M-type filters and filters designed with general image parameters are now rarely designed, having been replaced by more network synthesis methods Advanced.