TABLE OF CONTENTS The previous chapters have concentrated on the theory and design of lumped element filters. By definition lumped elements are zero-dimensional, i.e. they have no physical dimensions which are significant with respect to the wavelength at the operating frequency. One of the great advantages of restricting oneself to lumped elements is that circuits may be completely described in terms of one complex frequency variable.
As we increase frequency into the microwave spectrum it is easy to see that lumped element theories will not suffice, e.g. the wavelength at 10 GHz is only 3 cm and circuit elements may easily have dimensions in excess of a quarter wavelength. Furthermore, as we have already seen, narrowband filters with low insertion loss require high Q resonators. This implies physically large resonators, again meaning that dimensions become significant fractions of a wavelength. It is thus necessary to have design theories which are pertinent to these 'distributed' circuits.
In general, networks consisting of arbitrary connections of distributed circuit elements do not have a unified design theory. Although analysis of such circuits may be accomplished by solving Maxwell's equations using, for example, finite element analysis, this is not the same as having a design theory. As an example a circuit consisting of an interconnection of transmission lines of different lengths would require a theoretical approach using more than one complex variable. Work in this area has been extremely limited. To simplify the design theories we usually restrict ourselves to the case where...
