Two-Port Networks

HNC Engineering Assignment

TWO-PORT NETWORKS
QUESTION 1
The z-parameters in the two-port network for the given figure,
Solution
For an open circuit, current at node 2 is 0,
ZII =V 1
I 1
= ( R8 + R6 ) ( I 1 )
I 1
ZII =R8 + R6=14 Ω
For the impedance at node 2,
Z22= V 2
I 2
= R6 I 2
I 2
Z22=6 Ω
QUESTION 2
Part a
Transmission line of lengthl=0.4 λ, determine the phase change that occurs down the line.
βl− phase change of a tra nsmission line
¿ β∗( 0.4 λ ) =0.4 βλ
0.4 βλ=a
β= 2 π
λ
0.4 ( 2 π
λ ) λ=a
1

a=0.8 π=1440− phase change
Part b
Z¿=Z0
( ZL cos βl+ j Z0 sin βl )
Z0 cos βl + jsin βl
Replacing the input impedance equation with values,
Z¿=(50 Ω) ( ( 40+ j30 ) Ω∗cos 0.4 βλ+ j(50 Ω)sin 0.4 βλ )
( 50 Ω ) cos 0.4 βλ+ jsin 0.4 βλ
0.4 βλ=a
Z¿=(50 Ω) ( ( 40+ j30 ) Ω∗cos a+ j(50 Ω)sin a )
( 50 Ω ) cos a+ jsin a
Z¿=50 ( 40 cos a+ j(30 cos a+50 sin a) )
50 cos a+ jsin a
Z¿=50 ( 40 cos 0.8 π + j ( 30 cos 0.8 π +50 sin 0.8 π ) )
50 cos 0.8 π + jsin 0.8 π
¿ 50 ( 40 cos 144 + j ( 30 cos 144+50 sin 144 ) )
50 cos 144 + jsin144
Z¿=50 40∗0.87115+ j ( 30∗0.87115+50∗(−0.49102 ) )
50∗0.87115− j 0.49102
Z¿=50 34.846+ j1.5835
43.5575− j 0.49102
The input impedance is given as,
Z¿=39.97443+ j2.26834
QUESTION 3
Part a
A transmission line is said to be distortionless when there is no dispersion and the line
parameters are given in the ratio,
2