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
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).
(1)(2a)(2b)Figure 2. Normalised lowpass prototype to practical lowpass element transformation