6.11 Finding zl

Let's move on to some other Smith Chart applications. Suppose, somehow, we can obtain a plot of $V(s)$ on a line with some unknown load on it. The data might look like . What can we tell from this plot? Well, $V(\max )=1.7$ and $V(\min )=0.3$ which means

Secondly, we note that there is a voltage minima at about 2.5 cm away from the load. Where on would we expect to find a voltage minima? It would be where $r(s)$ has a phase angle of ${180}^{°}$ or point "A" shown in here . The voltage minima is always where the VSWR circle passes through the real axis on the left hand side. (Conversely a voltagemaxima is where the circle goes through the real axis on the right hand side.) We don't really care about $\frac{Z(s)}{Z_0}$ at a voltage minima, what we want is $\frac{Z(s=0)}{Z_0}$ , the normalized load impedance. This should be easy! If we start at "A" and go $\frac{2.5}{20}=0.125\lambda$ towards the load we should end up at the point corresponding to $\frac{Z_L}{Z_0}$ . The arrow on the mini-Smith Chart says "Wavelengths towards generator" If we start at A, and want to go towards the load , we had better go around the opposite direction from the arrow. (Actually, as you can see on a real Smith Chart, there are arrows pointing in both directions, and they are appropriately marked for yourconvenience.)