Zmin, Zmax and other things ...

So I came upon $Z_{min}$ ok?

$$Z_{min} = -\frac{1}{2\beta} [\phi + (2m+1)\pi]; m = 0, 1, 2, ...$$

To find $\phi$, we'll first find the Reflection Coefficient $\Gamma$.

$$\Gamma = \frac{Z_L - Z_o}{Z_L + Z_o}$$

and,

$$\Gamma = |\Gamma| \angle\phi$$

So like, get $\phi$ that way.

Turns out, there's also a $Z_{max}$ which is

$$Z_{max} = -\frac{1}{2\beta} (\phi + 2n\pi); n=0, \pm 1, \pm 2, ...$$