Questions
1. Why an ordinary extension cord is not usually considered a transmission line, while a television
antenna cable of the same length would be?
2. Explain the difference between balance and unbalanced lines, and give an example of each.
3. Draw the equivalent circuit for a short section of transmission line, and explain the physical
meaning of each circuit element.
4. What is meant by the characteristic impedance of a transmission line?
5. Define the velocity factor for a transmission line and explain why it can never be greater than
one.
6. Explain what is meant by the SWR on a line. What is its value when a line is perfectly matched?
7. Why is a high SWR generally undesirable?
8. Why are shorted stubs preferred to open ones for impedance matching?
9. Draw a sketch showing how the impedance varies with distance along a lossless shorted line.
10. What would be the effect of placing a shorted, half-wave stub across a matched line?
11. What are the major contributors to transmission line loss?
12. How does transmission line loss vary with frequency? Why?
13. How does the SWR at the source differ from that on the load with a lossy line? Why?
14. Draw circuits for a balun using a transformer and one using a transmission line segment.
Which of there has greater bandwidth? Which is likely to have a larger ratio of power handling
capacity to the cost?
15. Draw a sketch showing how a quarter-wave transformer can be used for impedance matching.
Is the transformer itself matched?
16. Compare single- and double-stub matching, giving one advantage of each.
17. Why is a smith chart circular?
18. Why are admittances rather than impedances used for sub-matching calculations?
19. Explain how TDR can be used to find a defect in an underground cable.
20. Describe two ways in which the standing- wave ratio no the transmission line can be measured.
Section 14.3
21. A 12 V dc source is connected to a 93 Ω lossless line through a 93 Ω source resistance at t = 0.
The line is 85 m long and is terminated in a resistance.
a) What is the voltage across the input of the line immediately after t = 0?
b) At time t = 1.0 µs, the voltage at the input end of the line changes to 7.5 V, with
the same polarity as before. What is the resistance that terminates the line?
c) What is the velocity factor of the line?
22. A 2 V dc source is connected through a 50 Ω resistor to one end of a 50 Ωline at time t = 0. The
line is 100 m long and lossless, with a velocity factor of 0.8. Draw a sketch showing how the
voltage at the source end of the line varies with time, if the line has 20 Ω load.
23. A 10 V positive-going pulse is sent down 50 m of lossless 50 Ω cable with a velocity factor of
0.8. the cable is terminated with a 150 Ω resistor. Calculate the length of time it will take the
reflected pulse to return to the start and the amplitude of the reflect pulse.
24. Calculate the characteristic impedance of an open-wire transmission line consisting of two
wires with a diameter 1mm and separation 1cm.
25. An open-wire transmission line is made from two tires, each with a diameter of 2mm, located
15 mm apart
a) Calculate the characteristic impedance of the line.
b) What happens to the impedance if the wire spacing is increased?
26. Calculate the characteristic impedance of a coaxial line with a polyethylene dielectric if the
diameter of the inner conductor is 3 mm and the inside diameter of the outer conductor is 10
mm.
Section 14.4
27. A transmitter delivers 50 W into a 600 Ω lossless line that is terminated with an antenna that
has an impedance of 275 Ω, resistive.
a) What is the coefficient of reflection?
b) How much of the power actually reaches the antenna?
28. A 75 Ω lossless line is terminated in error with a 93 Ω resistor. A generator sends 100 mW
down the line
a) What is the SWR on the line?
b) What is the reflection coefficient?
c) How much power is dissipated at the load?
d) What happens to the rest of the power?
29. A generator is connected to short-circuited line 1.25 wave-lengths long.
a) Sketch the waveforms for the incident, reflected, and resultant voltages at the instant
the generator is at its maximum positive voltage
b) Sketch the pattern of voltage standing waves on the line.
c) Sketch the variation of impedance along the line. Be sure to note whether the
impedance is capacitive, inductive, or resistive at each point.
30. A transmission line is to be used to shift the phase of a 10 MHz signal by 90°. If RG-8/U with
solid polyethylene di-electric is used how long should the line be?
31. An open- circuited line is 0.75 wavelengths long.
a) Sketch the incident, reflected, and resultant voltage waveforms at the instant the
generator is at its peak negative voltage
b) Draw a sketch showing how RMS voltage varies with position along the line.
32. A 75 Ω source is connected to a 50 Ω load (a spectrum analyzer) with a length of 75 Ω line. The
source produces 10 mW. All impedances are resistive
a) Calculate the SWR.
b) Calculate the voltage reflection coefficient
c) How much power will be reflected from the load?
Section 14.5
33. A properly matched transmission line has a loss of 1.5 dB/100 m, if 10 W is supplied to one end
of the line, how may watt reach the load, 27 m away?
34. A transmitter sends 100 watts down 13 m of matched line with a loss of 2 dB/100 m.
a) How much power is dissipated at the load?
b) What happens to the rest of the power?
35. A receiver requires 0.5 µV of signal for satisfactory reception. How strong (in microvolts)
must the signal be at the antenna if the receiver is connected to the antenna by 25 m of
matched line having an attenuation of 6 dB per 100m?
36. A transmitter with an output power of 50 W is connected to a matched load by 32 m of
matched coaxial cable. It is found that only 35 of power is dissipated in the load. Calculate the
loss in the cable in decibels per 100 meters.
Section 14.6
37. A 75 Ω transmission line is terminated with a load having an impedance of 45 – j30 Ω. Use the
Smith chart to find:
a) The distance (in wavelengths) from the load to the closest place at which a quarterwave transformer would be used to match the line.
b) The characteristic impedance that should be used for the quarter-wave transformer.
38. Draw a dimensioned sketch of a transmission line balun that could be used to match RG-59/U
type coaxial cable, with foam dielectric, to television twin-lead. Design it to work in the center
of the FM broadcast band (98 MHz).
39. Find the length and position of the transformer in problem 37, given that the operating
frequency is 20 MHz and the velocity factor for both lines is 0.66
40. A transmitter supplies 100 W to a 50 Ω lossless line that is 5.65 wavelengths long. The other
end of the line is connected to an antenna with a characteristic impedance of 150 + j25 Ω.
a) Use the Smith chart to find the SWR and the magnitude of the reflection coefficient.
b) How much of the transmitter power reaches the antenna?
c) Use the smith chart to find the best place to insert a shorted matching stub on the
line.( give the answer in wavelengths from the load.)
d) Use the smith chart to find the proper length for the stub( in wave lengths).
41. Use the Smith chart to solve this problem. A 75 Ω transmission line has a load impedance of 40
+j30 Ω. Find a suitable place for a shorted stub to match this line, and calculate the length of
the stub. The frequency is 45 MHz, and the line has a velocity factor of 0.95.
42. A 50 Ω transmission line is terminated with a resistive load of 120 Ω impedance. A generator
puts a signal with a frequency of 70 MHz and a power level of 20 dBm into the other end of
the line. The line has a velocity factor of 0.8
a) Calculate the reflection coefficient at the load
b) Calculate the voltage standing –wave ration at the load.
c) How much power is dissipated by the load?
d) Design a quarter-wave transformer that could be installed at the load to match it to
the line. Sketch the transformer and calculate its length and characteristic impedance.
43. A 50 Ω coaxial transmission line with a velocity factor of 0.8 is connected to a load of 89 – j47
Ω. The system operates at 300MHz. fid the proper position and component value to match this
line using:
a) A series capacitor
b) A series inductor
c) A transformer
44. Find the SWR for each setup of problem 43, at a frequency of 350 MHz.
Section 14.7
45. A slotted line having an impedance of 50 Ω and a velocity facto of 0.95 is used to conduct
measurements with a generator and a resistive load, which is known to be more that 50 Ω. It is
found that the maximum voltage on the line is 10 V and the minimum is 3 V. the distance
between two minima is measured as 75 cm.
a) What is the wavelength of the line?
b) What is the frequency of the generator?
c) What is the standing wave ratio?
d) What is the load resistance?
46. A time-domain reflectometer produces a 1 V step input. Sketch the signal that would be
viewed if the line is lossless, is 50 m in length, has a velocity factor of 0.8, and is terminated in
an open circuit.
Systems
47. A transmission line of unknown impedance is terminated with two different resistances, and
the SWR is measured each time. With a 75 Ω termination, the SWR measures 1.5. With a 300
Ω termination it measures 2.26. What is the impedance of the line?
48. Lumped constants can be used instead of transmission-line stubs to match lines. Solve
problem 40 in this way, by calculating the correct value of inductance or capacitance that
could be place across the line, instead of using a shorted stub. The frequency is 20 MHz.
Frenzel
1.
Calculate the L and C values of an L network that is to match a 9 Ω transistor power amplifier to
a 75 Ω antenna at 122 MHz.
2. Calculate what L network components will match a 4 Ω internal resistance in series with an
internal inductance of 9nH to a 72 Ω load impedance in parallel with a stray capacitance of 24 pF
at a frequency of 46 MHz
3. Design an LCC T network that will match 5 Ω internal resistances to a 52 Ω load at 54 MHz.
Assume a Q of 12.
4. A transformer has 6 turns on the primary and 18 turns on the secondary. If the generator
(source) impedance is 50 Ω, what should the load impedance be?
5. A transformer must match a 2500 Ω generator to a 50 Ω load. What must the turn’s ratio be?