Ten-element bandpass filter section and its derivatives

Explicit formulas are derived for a 10-element bandpass filter section. This is a halfsection having image impedances of class d and f, and an image transfer function of class 2. The entire design is carried out in the z plane (which is obtained by means of a bilinear transformation of the squared frequency variable), and the resulting network is defined by four parameters m1, m2, m3, m4, which are constants in the z plane. As one or more of these parameters is allowed to assume its limiting value, consistent with physical realisability, the 10-element section degenerates into a total of 40 distinct filter sections. These include the 6-element classical and zigzag sections due to Zobel and Laurent, respectively, the crystal-filter sections given by Poschenrieder, and others not previously described. The 10-element section is of interest in supplying a unified treatment of a very large number of band-pass sections. The prime application of the results is in the design of filters employing quartz crystals.