Narrowband Microwave Bandpass Filter Design by Coupling Matrix Synthesis

In recent years, advances within two fields have had a major impact on how filters are designed today. One is the advent of powerful electromagnetic (EM) software, which provides results that are close to measurements. However, analysis and optimization of complete filters is often too resource and time consuming to be useable in practice. Therefore, methods that separate the entire structure into discrete components for individual EM analysis are often employed.¹

The other field that has had a major impact on filter design methods is advances within the coupling matrix representation of microwave filter circuits. The coupling matrix concept was introduced in the 1970s, but general methods have recently been introduced for its synthesis.² The coupling matrix concept has also been reformulated to accommodate couplings directly from the source and the load to internal resonators.³

The coupling matrix representation of bandpass filters is convenient since, with matrix operations, it is possible to transform between topologies whereby the best suited topology for a given problem may be found. The recent coupling matrix formulation leads to more accurate determination of practical filter characteristics; highly complex filters with multiple non-adjacent couplings are now easily synthesized.

Even though a large number of articles dealing with coupling matrix synthesis have recently been published, almost none of them go into details about how to convert the synthesized matrices into physical filters. In this article, practical filter design using the coupling matrix synthesis and simple 3-D EM simulation techniques is demonstrated. Even though EM solvers in this article are used for the designs, the adopted methods may be applied even without EM solvers available. In that case a couple of test circuits must be manufactured. Emphasis is made on practical approaches and it is demonstrated that even fairly complex x-coupled filters can be made in just one iteration. The methods are validated through measurements on manufactured coaxial cavity filters. It is also demonstrated how coupling matrix synthesis may be used to better understand and explain differences between calculated and measured filter responses.

Coupling

To design microwave filters a basic understanding of coupling and coupling mechanisms is necessary. In this section the coupling mechanisms in bandpass filters are investigated. It is shown how coupling coefficients can be measured.