Microwave Filters for Communication Systems: Fundamentals, Design and Applications

CHAPTER 7

SYNTHESIS OF NETWORK–CIRCUIT APPROACH

In the previous chapters, methods were established to derive the transfer and reflection polynomials for a broad class of lowpass prototype filter functions. The next step in the design process is to translate these polynomials into a prototype electrical circuit from which a real microwave filter may be developed. Two methods for doing this are available: the classical circuit synthesis method and the direct coupling matrix synthesis approach. In this chapter, the circuit synthesis approach, based on the [ABCD] transfer matrix, or the “chain” matrix, as it is sometimes known, is described.

There are many excellent and comprehensive contributions to the subject of circuit synthesis techniques in the literature [1–6]. It is not the intention to repeat the works here, but rather to utilize the theories to develop a general microwave filter synthesis technique. The techniques described here include both, the symmetric as well as asymmetric lowpass prototype alters. As described in Sections 3.10 and 6.1, such prototype networks require the hypothetical frequency-invariant reactive elements, referred to by the acronym FIR [7]. Inclusion of such elements leads to transfer and reflection polynomials to have complex coefficients. In bandpass or bandstop alters, FIR elements appear as frequency offsets to the resonant circuits. The various components used in the microwave synthesis process include the following:

• Frequency-dependent reactive ...