6.10: Summary

This chapter presented techniques for impedance matching that achieve maximum power transfer from a source to a load. The simplest matching network uses a series and a shunt element, a two-element matching network, to realize a single-frequency match. This type of impedance matching network uses lumped elements and can be used up to a few gigahertz. Performance is limited by the self-resonant frequency of lumped elements and by their loss, particularly that of inductors. The shunt element can be replaced by a shunt stub, but in most transmission line technologies, including microstrip, the series element cannot be implemented as a stub. Matching networks can also be realized using transmission line segments only, principally shunt stubs and cascaded transmission lines. A tunable double-stub matching network, which uses two stubs separated by a transmission line, is standard equipment in microwave laboratories and facilitates matching of a circuit under development.

The bandwidth of a matching network is set by the maximum allowable reflection coefficient of the terminated network. Two-element matching nearly always results in a narrow match and for typical communications applications often achieves acceptable matching over bandwidths of only \(1\%–3\%\). The most significant determinant of the quality of the match that can be achieved is the ratio of the source and load resistances, as well as the reactive energy storage of the source and load. Clearly if the load and source are resistances of the same value, the bandwidth of the matching network is infinite, as it is no more than a wired connection.

An important concept in matching network design is a technique for controlling bandwidth. The concept is based on matching to an intermediate resistance \(R_{v}\). Increased bandwidth is obtained if \(R_{v}\) is the geometric mean of the source and load resistances. This new network consists of two two-element matching networks. If \(R_{v}\) is greater or less than both the source and load resistances, then the bandwidth of the matching network is reduced. Matching network synthesis can also be addressed using filter design techniques, enabling simultaneous control over the quality and bandwidth of the match. It is always a good idea to have no more bandwidth in the system than is needed, as this minimizes the propagation of noise.

A powerful graphical matching tool is the Smith chart on which the load and source can be plotted. The design objective is then to determine the path, subject to constraints, from the load back to an input, which is the complex conjugate of the source, a task that a human is particularly adept at performing. Alternatively the perspective could be flipped and the role of the source and load interchanged.

Design becomes increasingly more difficult as the required bandwidth increases. Many times it is sufficient to have small-to-moderate bandwidths that can be tuned rather than providing one large instantaneous bandwidth. Also many of the evolving wireless systems require multiple functionality, which in turn requires adjustability of a matching network. In some applications the matching network may require adjustment to match a variable load impedance. A good example is dealing with a cell phone antenna where the user may put his or her hand over the antenna and alter the load seen by the RF frontend. Some types of matching network designs are more adjustable than others. Such designs require variable components, so matching design can be a source of competitive advantage.