INTRODUCTION

In Chapter 8 we noted the central role two-port theory plays in RF circuit design, and especially the role of reflection coefficients in determining the stability and gain of two-ports. Reflection coefficients were introduced as surrogates for source and load impedance (recall Equations (8.32) and (8.37)), facilitating the use of scattering parameters. In this chapter we consider impedance matching, which is the process of converting impedances (equivalently, embedded reflection coefficients) from a given value to some other value.

Applications for impedance matching include (1) maximizing power transfer between twoports, (2) eliminating reflections (not the same thing!), and (3) converting from a given impedance to another impedance necessary for setting the stability and/or gain of a two-port. In each of these cases, the problem is essentially as shown in Figure 9.1: We wish to design a passive two-port that converts the output impedance of the source, ZS = RS + jXS , into the desired input impedance for the load, ZL = RL + jXL . Usually we would like to achieve this with a TPG as close to 1 as possible, and often there is a frequency span over which a minimum TPG which must be achieved. At the design frequency, the nominal embedded input impedance Zin of the matching two-port is either for maximum power transfer or ZS for reflectionless matching. Similarly, the nominal embedded output impedance Zout of the matching two-port is either or ZL at the design frequency.

The organization of this chapter is as follows. In Section 9.2 we consider some rudimentary approaches to impedance matching, including resistive matching, transformer matching, and reactance canceling. Section 9.3 introduces narrowband matching using two discrete reactances in an “L” configuration, which is useful both as a standalone technique as well as a building block for more sophisticated techniques. Section 9.4 considers the issue of bandwidth, and introduces the concept of quality factor to provide some insight into how the bandwidth of matching circuits is determined and can be manipulated. In Section 9.5 we combine the concepts of previous sections to develop impedance matching circuits having bandwidth which can be wider or narrower than that obtained by using discrete two-reactance matching. Section 9.6 explains how to obtain differential versions of the single-ended circuits developed in earlier sections.