5.2 Review of the Smith Chart 1035.2 Review of the Smith ChartThe reflection coefficient is a very common figure of merit used to determine how well matched two impedances are. It is related to the ratio of power transmitted to power reflected from the load. A plot of the reflection coefficient is the basis of the Smith chart, which is a very useful way to plot the impedances graphically. The reflection coefficient G can be defined in terms of the load impedance ZL and the characteristic impedance of the system Zo as follows: 11LoLoZZzZZz--G ==++ (5.1)where z = ZL/Zo is the normalized impedance. Alternatively, given G, one can find ZL or z as follows: 11LoZZ+ G=- G (5.2)or 11z+ G=- G (5.3)For any impedance with a positive real part, it can be shown that: 01£ G £ (5.4)The reflection coefficient can be plotted on the x-y plane and its value for any impedance will always fall somewhere in the unit circle. Note that for the case where ZL = Zo, G = 0. This means that the center of the Smith chart is the point Figure 5.3 Example of a very simple matching network.Figure 5.4 A possible impedance matching network.