2.1: Introduction

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Analog circuits at frequencies up to a few tens of megahertz are characterized by admittances, impedances, voltages, and currents. Above these frequencies it is not possible to measure voltage, current, or impedance directly. One reason for this is that measurement equipment is separated from the device by lengths of transmission line that are electrically long (i.e., at least an appreciable fraction of a wavelength long). It is better to use quantities such as voltage reflection and transmission coefficients that can be quite readily measured and are related to power flow. As well, in RF and microwave circuit design the power of signals and of noise is always of interest. Thus there is a predisposition to focus on measurement parameters that are related to the reflection and transmission of power.

Scattering parameters, \(S\) parameters, embody the effects of reflection and transmission. As will be seen, it is easy to convert these to more familiar network parameters such as admittance and impedance parameters. In this chapter \(S\) parameters will be defined and related to impedance and admittance parameters, then it will be demonstrated that the use of \(S\) parameters helps in the design and interpretation of RF circuits. \(S\) parameters have become the most important parameters for RF and microwave engineers and many design methodologies have been developed around them.

Figure \(\PageIndex{1}\): A two-port network: (a) port voltages; and (b) with transmission lines at the ports.

This chapter presents microwave circuit theory which is based on the representation of distributed structures that are too large to be considered to be dimensionless, by lumped element circuits. The origins of microwave circuit theory were in the 1940s, 1950s and 1960s [1, 2, 3] with extensions for networks with lossy transmission lines [4, 5].