Design of Unsymmetrical Band-Pass Filters

The paper presents a new approach to the synthesis of band-pass filters, in particular of filters with electrical characteristics which are not symmetrical with respect to their center frequency when plotted on an arithmetic frequency scale. The synthesis proceeds in three steps: approximation, representation by means of fictitious network elements in the low-pass domain, and subsequent low-pass, band-pass transformation. The approximation process leads to network functions defined by polynomials containing complex coefficients. It is shown that these functions can be handled with available synthesis procedures, if suitable modifications are made. This technique is based upon the properties of quasi-Hurwitz polynomials, treated in the Appendix. These procedures then lead to a network representation in the low-pass domain, which includes two fictitious network elements, namely constant positive or negative imaginary quantities. After a low-pass, band-pass transformation has been applied the network becomes physically realizable. It is shown that unsymmetrical lossless networks can be developed into canonic forms in the low-pass domain. A practical example is given.