Microwave Filters for Communication Systems: Fundamentals, Design and Applications

CHAPTER 12

WAVEGUIDE AND COAXIAL LOWPASS FILTERS

Synthesis methods presented in Chapters 7, 8, and 9 are based on lossless, lumped-element prototype filters. Such a model is suitable for realizing practical narrowband (typically < 2% bandwidth) filters at microwave frequencies. The bulk of filter applications in a communication system is for bandpass filters with bandwidths of less than 2%. The lumped-element model serves well to satisfy this need. However, communication systems also require lowpass filters. The bandwidth requirement for lowpass filters is much higher (typically in the GHz range), and therefore, prototype models based on lumped elements are not suitable for realization at microwave frequencies. It requires use of distributed elements for the prototype filters and, as a consequence, modification of the synthesis techniques.

In this chapter, we study the methods for synthesizing the transfer and reflection polynomials, suitable for two important classes of lowpass filter (LPF): the distributed stepped impedance (SI) filter and the mixed lumped distributed filter. The theory behind the synthesis and realization of lowpass filters is due mainly to Levy [1–5], who produced a series of papers in the 1960s and 1970s. He introduced a class of prototype polynomials that is suitable for representing the LPF transfer and reflection performance, and from which a lowpass prototype circuit may then be synthesized. These include the al1-pole Chebyshev function, the Chebyshev ...