The document discusses transmission lines and provides examples of calculating characteristic impedance, propagation constant, velocity of propagation, input impedance, reflection coefficient, standing wave ratio, and more for various transmission line scenarios. It also includes examples using the Smith chart to analyze transmission lines terminated with different loads.

1. Transmission Lines
Tutorial 7
1) Calculate the characteristic impedance, propagation constant and velocity of propagation at frequency
of 400KC/s for a transmission line having L=0.5mH/Km, C= 0.08μF and negligible R and G.
2) A lossless transmission line is 100cm long and operates at a frequency of 700MHz. The line
parameters are L= 0.3μH/m and C= 120pF/m. Find the characteristics impedance, the phase constant, the
velocity of the wave in line and the input impedance for ZL= 150 .
3) In a lossless transmission line, the velocity of propagation is 2.5x108
m/s. The capacitance of the line is
30PF/m, find (i) inductance of the line (ii) Phase constant at 100MHz (iii) Characteristics impedance of
the line.
4) 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:
(i) Characteristics impedance.
(ii) The Phase constant.
(iii) The velocity of the line.
(iv) The input impedance for ZL = 100.
5) A transmission line has the following primary constants per Km. [R=70,L=3mH, C=0.2μH]
Calculate the :
(i) Characteristics impedance and propagation coefficient at ω=4000rad/sec.
(ii) Current at 20Km from the sending end of the transmission line when the input voltage is 40<0˚ volts.
(iii) Phase difference between the received and sent currents.
(iv) Inductance of the loading coil at 30meters spacing to ensure distortion less transmission.
6)A lossless transmission line with Z0=60 is 400m long. It is terminated with load ZL=40+j80 and
operated at a frequency of 1MHz. Let the velocity v=0.8C on the line where C=3x108m/s. Find
a) The reflection Coefficient ().
b) The standing wave Ratio (SWR)
c) The input impedance (Zin)
7) Assume a two wire 300 lossless-line (Z0=300) such as the lead in wire form the antenna to TV.
Suppose the length of the line to be 2m and the value of L and C such that the velocity on line is
2.5x108m/s. Also suppose that the line is terminated with a receiver an input resistance of 300 &
represent the antenna by its Thevenin equivalent Z=300 in series with voltage source (Vs) =60V at
100MHz. Determine the load voltage, load current and power delivered to the load by the line.

2. 8)A 300 transmission line is lossless, 0.25λ long and is terminated by ZL=500. The line has the
generator with 90<0 in series with 100 connected to the input find
a) Load Voltage
b) Voltage at the midpoint of the line.
9) If a transmission line having characteristics impedance Z0=200 is operating at frequency 15MHz with
propagation constant =j0.5m-1, then determine;
a) Velocity of Propagation
b) Wavelength
c) Inductance
d) Capacitance
10) A transmission line has the following primary constants per Km: R=60, L=2mH, C=0.1μF, G=80μS
a) Calculate the characteristic impedance and propagation coefficient at ω=5000 rad/s
b) Calculate the current at 10Km from the sending end of the transmission line when the input voltage is
20<30 volts.
c) Calculate phase difference between the received and sent currents.
d) Determine the inductance of loading coils at 200m spacing to ensure distortionless transmission.
e) Determine the velocity if propagation when the loading coils in circuit.
11) A lossless 50 line is 1.5λ long & is terminated with a pure resistance of 60. The load voltage is
20<40 volts. Find
a) Average power delivered to the load.
b) The magnitude of minimum voltage on the line.
12) A transmission line with a Z0=300 is terminated in a purely resistive load. While making SWR
measurements, the meter reads a maximum voltage of 7.5μV and a minimum of 5μV. What should be the
load resistance?
13) Calculate the value of impedance of Quarter-Wave transformer to match the load impedance of 150
Swith line impedance of 100.
14) At an operating radian frequency of 500Mrad/s, typical circuit values for a certain transmission line
are: R=0.2/m, L=0.25μH/m, G=10μS/m and C=100pF/m. Find (a) ; (b) ; (c) λ;(d) Vp;(e)Z0
Ans:- 2.25mNp/m; 2.5rad/m; 2.51m; 2x108m/s; 50-j0.0350
15)Determine the value of L,C,R,G, per Km, Z0at 1MHz for a copper coaxial cable in which the inner
diameter of the outer conductor (2b) is 10mm and the ratio b/a is 3.6 for, Air dielectric.(Cu=5.8x107
S/m)

3. 16) A (75+j125) load is connected to 72 lossless line.
Find
i) 
ii) VSWR
iii) The load admittance, YL.
iv) Zin at 0.3 from the load (using smith chart).
17) A line with negligible losses having characteristics impedance of 200 Ohms is terminated in a load
impedance of (100 + j180) Ohm. Find using Smith chart
i) Standing wave ratio
ii) Reflection coefficient
iii) Position of maximum voltage from load
18) A transmission line of RC = 100 is terminated at a load ZL = 150 + j 200 find (i) VSWR (ii) shortest
distance of 1s maxima & 1st
minima from load. (iii) Reflection coefficient with the help of smith’s chart.
19) A single stub tuner is to match the lossless line of 400ohm to a load of 800-j400ohm. The frequency
is 3Ghz. Find the position and length of the short circuited stub from the load end (using Smith Chart)
20) A load ZL = 60 + j80  terminates a 60  lossless transmission line. If the wavelength on the line is
18 cm.
i. How far form the load should the shortest possible short circuited 60  stub should be
located?
ii.What is the stub length?
21) A load of 100+j150 ohm is connected to a 75 lossless line, find using smith chart
a) Reflection coefficient b) VSWR c)Load admittance d) Zin at 0.4λ from load
e) Zin at generator if line is 0.6λ long.