Tutorial 6
Problem 1: A lossless transmission line is 80cm long and operates at a frequency of
600MHz. The line parameters are L=0.25μH/m, and C=100pF/m. Find the
characteristic impedance, the phase constant, and the phase velocity.
Solution:
Z  R  jL  0  j0.25  106  j0.25  106 /m
Y  G  jC  0  j100  1012  j1010 S/m
Z0 
j0.25  106
 50
j1010
Z

Y
  Z Y 
j0.25  106  j1010  j5  109    j
  5  109  2 f  109  2  600  106  5  109  18.85rad/m
vp 
 2 f 2  600  106


 2  108 m/s


18.85
Problem 2: At an operating radian frequency of 500Mrad/s, typical circuit values for
a certain transmission line are: R  0.2 / m , L  0.25 H/m , G  10S/m , and
C  100 pF/m . Find (a)  ; (b)  ; (c)  ; (d) v p ; (e) Z 0 .
Solution:
(a) (b) Z  R  jL  0.2  j500  106  0.25  106  0.2  j125/m
Y  G  jC  10  106  j500  106  100  1012  105  j0.05S/m
  Z  Y  ( R  j L)  ( R  jC )  (0.2  j125)  (105  j 0.05)
   j
m
  2.5rad/m
 2.25  103  j 2.5 1
  2.25mNp/m
(c)  
2
(d) v p 
(e) Z 0 

 2.51m

 2  108 m/s

Z
 50  j 0.035
Y
Problem 3 A 20-m length of transmission line is known to produce a 2.0-dB drop in
power from end to end.
(a) What fraction of the input power reaches the output?
(b) What fraction of the input power reaches the midpoint of the line?
(c) What exponential attenuation coefficient,  , does this represent?
Solution:
(a) 10log10
(b)
P(20m)
P(20m)
 2dB 
 100.2  0.63
P(0)
P(0)
P( z )
P(20m)
 e2 z 
 e40  0.63
P(0)
P(0)
P(10m)
 e20  e40  0.63  0.79
P(0)
(c)
Problem 4 A 50-Ω lossless transmission line is terminated by a load impedance
Z L  50  j75 . If the incident power is 100 mW, find the power dissipated by the
load.
Solution: The reflection coefficient is

Z L  Z 0 50  j 75  50

 0.36  j 0.48  0.6e j 0.93
Z L  Z 0 50  j 75  50
Pt  (1 |  |2 ) Pin  (1  0.62 )100  64mW