Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 52

The Smith chart, constructed on the basis of Eqs. (9-188) and (9- 189) for a Iossless transmission line, is restricted to a unit circle because| | 1. In the case of a lossy line, 2 0 is a complex quantity, and so, in genera l, is the normalized load impedance z L = Z L /Z 0.
a) Show that the phase angle of Z L , L lies between ± 3 /4.
b) Show that | | may be greater than unity.
c) Prove that max. |f| = 2.414.