In this chapter an attempt has been made to summarise various network theoretical concepts which are relevant to modern filter design. The book is concerned entirely with linear passive time-invariant networks and so these properties have been precisely defined. The concept of the input impedance of a network in terms of the complex frequency variable has led to the properties of positive real and bounded real functions. The synthesis of lossless one-port networks has led on to Darlington synthesis of terminated two-port networks, with lowpass ladder networks being one particular case. Various analysis techniques in terms of ABCD matrices, S parameters, even and odd-mode networks and image parameters have been discussed.

Starting from lowpass prototype networks a series of transformations are used to convert to arbitrary cut-off frequency lowpass, highpass, bandpass and bandstop filters with arbitrary impedance terminations. Procedures are developed for narrowband bandpass and bandstop filters where the inverters are approximated by pi sections of capacitors and quarter wave transmission lines respectively. These procedures are illustrated by design examples which also introduce the concept of nodal admittance matrix scaling. The effect of losses in filters is described with particular emphasis on bandpass filters so that the designer can compute the midband insertion loss of a particular design. Finally various practical procedures for measuring resonator couplings and Q factors are described.

This chapter is concerned with the design of waveguide filters to realise various transfer functions. Initially a review of the basic theory of rectangular and circular waveguides and waveguide resonators is presented. Next a design procedure for waveguide bandpass filters with all-pole transfer functions is developed, and supported with an example. More complex transfer functions require either cross-coupled or extracted pole filters. The former enable realisation of transfer functions with real-axis transmission zeros, i.e. prototypes with all positive couplings. The development of design procedures for these generalised waveguide filters is presented. The restriction of transmission zero locations in the real axis is removed by the use of extracted pole waveguide filters, the design theory of which is developed and again supported by an example. Finally techniques for the design of dual-mode filters are presented. It is important to note that the extracted pole and dual-mode techniques are relevant to the dielectric resonator filters described in the next chapter.

Various techniques for the miniaturisation of filters are reviewed. A brief discussion on dielectric resonators points out the limitations in terms of increasing the dielectric constant or the number of degenerate modes. Superconducting filters offer near infinite Q in small physical size, but at the expense of complex cooling systems and poor intermodulation performance. SAW filters offer high levels of miniaturisation with relatively modest performance. Active filters exhibit near infinite Q when considered as small signal devices but suffer from poor large signal performance and have an associated noise figure. An alternative approach for receiver filters is to use predistorted lossy filters. High selectivity can be achieved in a small physical size provided the filter is preceded by a high intercept low noise amplifier. An intermodulation analysis is used to justify this approach and the details of the required filter synthesis procedure are presented.