Problem 5:

Case (a)

Case (b)

Comments: As expected, the inductor behaves like a short for DC and the impedance increases with

increase in frequency becoming a nearly open circuit element at high frequencies. The S(1,1) plot for a

lumped inductor element in case(b) shows a movement in the clockwise direction, clearly shows this

behavior. However, the transmission shows a periodic behavior and continues around the smith chart

twice. The length of the line at 414.9 GHz is λ, which shows that the rotation around the smith chart is

periodic for every λ/2. This is why a lumped element can only be used as an approximation when the

length of the transmission line is much less than λ/4.

Comments: As expected, the capacitor behaves like an open for DC and the impedance decreases with

increase in frequency becoming a nearly short circuit element at high frequencies. The S(1,1) plot for a

lumped capacitor element in case(b) shows a movement in the anti-clockwise direction starting at

open(S(1,1) = Г = 1), clearly shows this behavior. The periodic behavior mentioned in problem (5) applies

here too.