CHAPTER SEVEN
Coupled-Resonator Circuits
Coupled-resonator circuits are of importance for design of RF/microwave filters, in particular, the narrow-band bandpass filters that play a significant role in many applications. There is a general technique for designing coupled-resonator filters in the sense that it can be applied to any type of resonator despite its physical structure. It has been applied to the design of waveguide filters [1,2], dielectric resonator filters [3], ceramic combline filters [4], microstrip filters [5–7], superconducting filters [8], and micromachined filters [9]. This design method is based on coupling coefficients of intercoupled resonators and the external quality factors of the input and output resonators. We actually saw some examples in Chapter 5 when we discussed the design of hairpin-resonator filters and combline filters. We will discuss more applications for designing various filters through the remainder of this book. Since this design technique is so useful and flexible, it would be desirable to have a extensive understanding of not only the approach, but also the theory behind it. For this purpose, this chapter will present a comprehensive treatment of relevant subjects.
The general coupling matrix is of importance for representing a wide range of coupled-resonator filter topologies. Section 7.1 shows how it can be formulated either from a set of loop equations or from a set of node equations. This leads to a very useful formula for analysis ...