CHAPTER THREE

Impedance Matching

3.1 INTRODUCTION

A major part of RF design is matching one part of a circuit to another to provide maximum power transfer between the two parts. Even antenna design can be thought of as matching impedance of free space to a transmitter or receiver. This chapter describes a few techniques that can be used to match between two real impedance levels. While some comments will be made relative to matching to a complex load, the emphasis will be on real impedance matching. The first part of this chapter will discuss the circuit quality factor, Q. The Q factor is useful in certain matching circuit designs.

3.2 THE Q FACTOR

The circuit Q factor is defined as the ratio of stored to dissipated power in the following form:

(3.1) c03e001

For a typical parallel RLC circuit, the Q becomes

(3.2) c03e002

where G is 1/R. For a series RLC circuit,

(3.3) c03e003

It should be emphasized that Q is defined at circuit resonance. If the circuit reactance is plotted as a function of frequency, the slope of the reactance at resonance is a measure of Q (Fig. 3.1). This is explicitly given as

(3.4) c03e004

where ...

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