Example 4-9: Input impedance computation of a transmission line

Example C.S1.1 Input impedance computation of a transmission line based on the
use of the signal flow chart
A lossless transmission line system with characteristic line impedance Z0 and
length l is terminated into a load impedance ZL and attached to a source voltage VG and
source impedance ZG, as shown in Figure C.S1.1.1. (a) Draw the signal flow chart and (b)
derive the input impedance formula at port I from the signal flow chart representation.
Figure C.S1.1.1 Transmission line attached to a voltage source and terminated by a load
a) Consistent with our previously established signal flow chart notation, we can readily
convert Figure 4-26 into the form seen in Figure C.S1.1.2.
Figure C.S1.1.2 Signal flow chart diagram for transmission line system in Figure 4-26
b) The input reflection coefficient at port 1 is given by
b1  L e  j2l a 1
in (l)  L e 2 jl 
Zin  Z 0
Zin  Z 0
Solving for Zin yields the final result
Zin  Z0
1  L e 2 jl
1  L e 2 jl
This example shows how the input impedance of a transmission line can be found quickly
and elegantly by using signal flowchart concept.