TABLE OF CONTENTS S-parameters and transmission lines are the main tools utilized in microwave amplifier design. Before we can design our own circuits, however, we need to study some methods of analysis. In this chapter, we will use mathematical and graphical tools to analyze circuits. These circuits will be networks composed of one or more elements. The methods shown in this chapter assume that the S-parameters of a one or two-port have been found or measured. We will concentrate on analyzing the circuit response of a network and groups of interconnected networks. The tools presented in this chapter as well as in Chapter 3 lay the groundwork for the following chapters on synthesizing microwave circuits and amplifiers.
Section 4.2 introduces complex mapping functions. Complex mapping functions are often needed when using transmission lines and S-parameters and are essential in identifying zones of acceptable or unacceptable impedance loads that can be placed on a transistor. As a casual observer, you can always turn to formulas in this book or other books without having to understand their origin. However, behind the scenes, it is important to understand the functions, properties, and theorems used to develop these formulas. Mapping functions are a way to analyze how a complex function affects a complex variable. For example, in this chapter, we will be discussing how an impedance is changed by connecting various circuits, such as a transistor, to it. One way to determine this is to investigate how the impedance plane is distorted, or mapped, onto...
