PHY 2001 Applied Electromagnetics (Fall 2020-21)
Assignment 6 (Impedance Matching)
(Use Smith Chart to solve problems 1-4)
1) Normalize the following impedance with respect to 50 Ω and locate them on
the Smith chart
a) Z a  80
b) Z b  60  j 40
c) Z c  30  j120
2) A 75 Ω lossless transmission line is 132 cm long with a dielectric constant
 r  3.62 . If the line operates at 400 MHz with an input impedance of
Z in  40  j 65
Use the Smith chart to determine the terminating load
3) An antenna connected to a 150 Ω lossless line, produces a standing wave ratio
of 2.6. If measurements indicate that voltage maxima are 120 cm apart and that
the last maximum is 40 cm from the antenna, calculate
a) The operating frequency
b) The antenna impedance
c) The reflection coefficient (Assume u=c)
4) An 80 Ω lossless line has Z L  j60 Ω and Z in  j 40 Ω
a) Determine the shortest length of the line
b) Calculate standing wave ratio
c) Calculate reflection coefficient
5) A quarter-wave lossless 100 Ω line is terminated by a load Z L  210 Ω. If the
voltage at the receiving end is 80 V, what is the voltage at the sending end?
6) Two λ/4 transformers in tandem are to connect a 50 Ω line to 75 Ω load as
shown in Figure. Determine the characteristic impedance Z 01 if Z 02 = 30 Ω and
there is no reflected wave to the left of A
7) Consider the three lossless lines shown in Figure. If Z 0  50 , calculate
a) Z in looking into line 1
b) Z in looking into line 2
c) Z in looking into line 3
8) A 50 Ω lossless transmission line that is 20 m long is terminated into a
120  j 220 Ω load. To perfectly match, what should be the length and location
of a short circuited stub line? Assume an operating frequency of 10 MHz.