Next: Measurement of S-parameter Up: MSc Module: RF Systems Previous: Smith charts


Let's insert a two-port network into the transmission line as shown in Figure 7. Looking at text_wrap_inline2835, we see that it is made up of that portion of text_wrap_inline2837 reflected from the output port as well as that portion of text_wrap_inline2839 that is transmitted through the network.

Figure 7: 2-port network inserted in to a transmission line

It should be possible to relate these four traveling wave by a set of parameters. For example,


By substituting the expression for a total voltage and total current on a transmission line into this parameter set, we can rearrange these equations such that the incident traveling voltage waves are the independent variables; and the reflected traveling waves are the dependent variables
The functions text_wrap_inline2841 and text_wrap_inline2843 represent a new set of network parameters relating traveling voltage waves rather than total voltages and total currents. In this case, these functions are expressed in terms of y-parameters. They could have been derived from any other parameter set. We call this new parameter set "scattering parameter" or S-parameter. We can divide both sides of the above equations by text_wrap_inline2845, the characteristic impedance of the transmission line, the parameter set will not change. It will, however, give us a set of new variables:

Notice that the square of the magnitude of these new variables has the dimension of power. text_wrap_inline2847 can then be thought of as the incident power on port one. text_wrap_inline2849 can then be thought of as the reflected power on port one. These new waves can be called traveling power waves rather than traveling voltage waves. Throughout this notes, we will simply refer to these waves as traveling waves.

Finally, we see that the S-parameter relate these four waves in this fashion