AWR eBooks

CHAPTER 3 - Foundations of RF & Microwave Circuit Characterisation 146 3.8 Two-Port Networks and S-parameters In section 3.2 we saw how the reflection coefficient may be expressed as the ratio of incident and reflected voltages or incident and reflected currents. These are not always easy to measure at RF and microwave frequencies in particular when the line is terminated with open or short circuits! However there is a quantity which is much more easily measured at high frequency and that is power. Now our reflection coefficient may also be expressed in terms of incident and reflected power as shown in (3.8-1) √ We can easily see how this equation is equivalent to the one which we worked out for the voltage (3.2-3). √ √ √ ⁄ ⁄ √ ⁄ √ ⁄ In (3.8-2), is the normalised incident voltage wave and is the normalised reflected voltage wave. These are defined as shown in (3.8-3) and allow us to make voltage waves independent of the characteristic impedance of the line. √ √ So far we have been looking at one port systems like that depicted in Figure 3.2-1 however we often deal with two port networks such as filters and amplifiers. It would be good therefore to define two sets of parameters, one for each port, which would allow us to understand what voltage and current are doing at each port. We can therefore define and waves at both input ( , ) and output ports ( , ) as shown in Figure 3.8-1. We can then work out a set of equations which shows how the reflected wave at port 1, , depends on both incident wave at port 1, , and incident wave at port 2, . We can do the same for the reflected wave at port 2, . [ ] [ ] [ ] (3.8-1) (3.8-2) (3.8-3) (3.8-4) (3.8-5) Conquer Radio Frequency 146 www.cadence.com/go/awr

• Cover