Microwave Filter Analysis and Design

Microwave Filter Analysis and Design

DOI: 10.4018/978-1-7998-2084-0.ch003

Abstract

A microwave filter is a two-port component usually employed when there is a need to control the frequency response at any given point in a microwave system. They provide transmission at certain frequencies, which are known as the passband frequencies, and attenuation at other frequencies, which are referred to as the stopband frequencies. The frequencies outside the passband are attenuated or reflected. Microwave filter is often named after the polynomial used to form its transfer function (i.e., Chebyshev, Butterworth [or maximally flat], Elliptical, etc.). The filter can be further sub-divided into four categorises (i.e., lowpass, highpass, bandstop, and bandpass filters) according to its frequency responses. This chapter gives a detailed discussion on filter classification and transfer function. It also covers the analysis, design, and implementation of a test microwave filter using the 21st century SIW transmission line. The simulation and measurement results of the test filter is also presented, compared, and discussed.
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Filters Classification

Microwave filters can be categorised into lowpass, highpass, bandstop, and bandpass filters depending on the characteristic of their passband responses. This section presents an overview of these four categories of filters and their frequency and elemental design transformations.

Lowpass Filter

A lowpass filter (LPF) is any filter that passes or transmits all signals between zero frequency and its cut-off frequency, and attenuates all signals above its cut-off frequency. The frequency response, i.e. selectivity, roll-off, etc., of a lowpass filter depends on the filter transfer function itself. This type of filter can be used in conjunction with a highpass filter to produce a bandpass filter. A diagram of a lowpass filter characteristic is shown in Figure 1, where f is the frequency and f0 is the cut-off frequency.

Figure 1.

Lowpass filter characteristic

978-1-7998-2084-0.ch003.f01

A practical lowpass filter can be determined from a normalised lowpass prototype by re-mapping the normalised lowpass frequency domain using Eqn. (1) (Hong & Lancaster, 2001). Where Ω is the normalised lowpass prototype angular frequency domain, Ωc is the normalised lowpass prototype angular cut-off frequency, ω is the new angular frequency domain and ωc is the new angular cut-off frequency. If the normalised lowpass filter has an inductance, Lp and a capacitance, Cp, in its circuitry, these elements will transform into LLPF and CLPF after the re-mapping of the frequency domain and are given in Eqn. (2). The normalised lowpass prototype to practical lowpass element transformation is shown in Figure 2 (Hong & Lancaster, 2001).

978-1-7998-2084-0.ch003.m01
(1)
978-1-7998-2084-0.ch003.m02
(2a)
978-1-7998-2084-0.ch003.m03
(2b)
Figure 2.

Normalised lowpass prototype to practical lowpass element transformation

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