Microwave Filters for Communication Systems: Fundamentals, Design and Applications

CHAPTER 8

COUPLING MATRIX SYNTHESIS OF FILTER NETWORKS

In this chapter, we examine the coupling matrix representation of microwave filter circuits. Modeling the circuit in matrix form is particularly useful because matrix operations can then be applied, such as inversion, similarity transformation, and partitioning. Such operations simplify the synthesis, reconfiguration of the topology, and performance simulation of complex circuits. Moreover, the coupling matrix is able to include some of the real-world properties of the elements of the filter. Each dement in the matrix can be identified uniquely with an element in the finished microwave device. This enables us to account for the attributions of electrical characteristics of each dement, such as the Q_u values for each resonator cavity, different dispersion characteristics for the various types of mainline coupling and cross-coupling within the filter. This is difficult or impossible to achieve with a polynomial representation of the filter's characteristics.

The basic circuit that the coupling matrix represents is reviewed, and the method used to construct the matrix directly from a lowpass prototype circuit, synthesized in Chapter 7, is outlined. This is followed by the presentation of two methods for synthesis of the coupling matrix directly from the filter's transfer and the reflection polynomials, the N × N and the N + 2 matrices.

8.1 COUPLING MATRIX

In the early 1970s, Atia and Williams introduced the concept of the coupling ...