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Electronic Communications: A Systems Approach

Jeffrey S. Beasley

Chapter 12

TRANSMISSION LINES - all with Video Answers

Educators

Chapter Questions

Problem 1

Define transmission line. If a simple wire connection can be a transmission line, why is an entire chapter of study devoted to it?

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Problem 2

In general terms, discuss the various types of transmission lines. Include the advantages and disadvantages of each type.

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Problem 3

What would be the considerations in choosing a solid dielectric cable over a hollow pressurized cable for use as a transmission line?

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Problem 4

Why is an inert gas sometimes placed within concentric radio-frequency transmission cables?

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Problem 5

Where are twisted-pair cables often used?

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Problem 6

What is meant by the CAT6/5e designation?

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Problem 8

Describe three additional test considerations for twisted-pair cable with the enhanced data capabilities.

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Problem 9

Explain how an unbalanced line differs from a balanced line.

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00:53

Problem 10

Explain how the pickup of unwanted signals on a balanced transmission line is attenuated when converted to an unbalanced signal.

Keshav Singh
Keshav Singh
Numerade Educator
02:30

Problem 11

A balanced transmission line picks up an undesired signal with a $5-\mathrm{mW}$ level. After conversion to an unbalanced signal using a center-tapped transformer, the undesired signal is $0.011 \mu \mathrm{W}$. Calculate the common mode rejection ratio (CMRR). ( $56.6 \mathrm{~dB}$ )

Narayan Hari
Narayan Hari
Numerade Educator
02:57

Problem 12

Draw an equivalent circuit for a transmission line, and explain the physical significance of each element.

Surendra Kumar
Surendra Kumar
Numerade Educator
01:51

Problem 13

Provide a physical explanation for the meaning of a line's characteristic impedance $\left(\mathrm{Z}_0\right)$.

Surendra Kumar
Surendra Kumar
Numerade Educator

Problem 14

Calculate $\mathrm{Z}_0$ for a line that exhibits an inductance of $4 \mathrm{nH} / \mathrm{m}$ and $1.5 \mathrm{pF} / \mathrm{m}$. ( $51.6 \Omega$ )

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01:47

Problem 15

Calculate the capacitance per meter of a $50-\Omega$ cable that has an inductance of $55 \mathrm{nH} / \mathrm{m}$. (22 pF/m)

Kai Chen
Kai Chen
Princeton University
01:57

Problem 16

In detail, explain how an impedance bridge can be used to determine $\mathrm{Z}_0$ for a piece of transmission line.

Surendra Kumar
Surendra Kumar
Numerade Educator
02:48

Problem 17

If the spacing of the conductors in a two-wire radio-frequency transmission line is doubled, what change takes place in the surge impedance $\left(\mathrm{Z}_0\right)$ of the line?

Vishal Gupta
Vishal Gupta
Numerade Educator

Problem 18

If the conductors in a two-wire radio-frequency transmission are replaced by larger conductors, how is the surge impedance affected, assuming no change in the center-to-center spacing of the conductor?

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Problem 19

What determines the surge impedance of a two-wire radio-frequency transmission line?

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Problem 20

Determine $Z_0$ for the following transmission lines:
(a) Parallel wire, air dielectric with $D / d=3 .(215 \Omega)$
(b) Coaxial line, air dielectric with $D / d=1.5 \cdot(24.3 \Omega)$
(c) Coaxial line, polyethylene dielectric with $D / d=2.5 .(36.2 \Omega)$

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Problem 21

List and explain the various types of transmission line losses.

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01:38

Problem 22

A long transmission line delivers $10 \mathrm{~kW}$ into an antenna; at the transmitter end, the line current is $5 \mathrm{~A}$, and at the coupling house (load) it is $4.8 \mathrm{~A}$. Assuming the line to be properly terminated and the losses in the coupling system to be negligible, what is the power lost in the line? $(850 \mathrm{~W})$

Narayan Hari
Narayan Hari
Numerade Educator

Problem 23

Define surge impedance.

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03:48

Problem 24

Derive the equation for the time required for energy to propagate through a transmission line [Equation (12-19)].

Surendra Kumar
Surendra Kumar
Numerade Educator
01:15

Problem 25

What is the velocity of propagation for radio-frequency waves in space?

Mayukh Banik
Mayukh Banik
Numerade Educator

Problem 26

A delay line using RG-8A/U cable is to exhibit a 5-ns delay. Calculate the required length of this cable. $(3.39 \mathrm{ft}$ )

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00:34

Problem 27

Explain the significance of the velocity factor for a transmission line.

Hast Aggarwal
Hast Aggarwal
Numerade Educator

Problem 28

Determine the velocity of propagation of a $20-\mathrm{km}$ line if the LC product is $7.5 \times 10^{-12} \mathrm{~s}^2$. $\left(7.3 \times 10^9 \mathrm{~m} / \mathrm{s}\right)$

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01:56

Problem 29

What is the wavelength of the signal in Problem 28 if the signal's frequency is $500 \mathrm{GHz}$ ? (0.0146)

Meghan Miholics
Meghan Miholics
Numerade Educator

Problem 30

If the velocity of propagation of a 20 - $\mathrm{ft}$ transmission line is $600 \mathrm{ft} / \mathrm{s}$, how long will it take for the signal to get to the end of the line? $(33.3 \mathrm{~ms})$

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Problem 31

Define a nonresonant transmission line, and explain what its traveling waves are and how they behave.

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01:38

Problem 32

An antenna is being fed by a properly terminated two-wire transmission line. The current in the line at the input end is $3 \mathrm{~A}$. The surge impedance of the line is $500 \Omega$. How much power is being supplied to the line? $(4.5 \mathrm{~kW})$

Narayan Hari
Narayan Hari
Numerade Educator
11:45

Problem 33

With the help of Figure 12-15, provide a charging analysis of a nonresonant line with an ac signal applied.

NT
Nikhil Tiwari
Numerade Educator

Problem 34

Explain the properties of a resonant transmission line. What happens to the energy reaching the end of a resonant line? Are reflections a generally desired result?

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Problem 35

A de voltage from a $20-\mathrm{V}$ battery with $R_{\mathrm{s}}=75 \Omega$ is applied to a $75-\Omega$ transmission line at $t=0$. It takes the battery's energy $10 \mu$ to reach the load, which is an open circuit. Sketch current and voltage waveforms at the line's input and load.

Manish Kumar ( Iit K )
Manish Kumar ( Iit K )
Numerade Educator

Problem 36

Repeat Problem 35 for a short-circuited load.

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Problem 37

What are standing waves, standing wave ratio (SWR), and characteristic impedance, in reference to transmission lines? How can standing waves be minimized?

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01:04

Problem 38

With the help of Figure 12-19, explain how standing waves develop on a resonant line.

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
00:51

Problem 39

If the period of one complete cycle of a radio wave is $0.000001 \mathrm{~s}$, what is the wavelength? $(300 \mathrm{~m})$

Devon Burke
Devon Burke
Numerade Educator
02:16

Problem 40

If the two towers of a $950-\mathrm{kHz}$ antenna are separated by 120 electrical degrees, what is the tower separation in feet? ( $345 \mathrm{ft}$ )

AG
Ankit Gupta
Numerade Educator
01:07

Problem 41

Define reflection coefficient, $\Gamma$, in terms of incident and reflected voltage and also in terms of a line's load and characteristic impedances.

Surendra Kumar
Surendra Kumar
Numerade Educator
03:52

Problem 42

Express standing wave ration (SWR) in terms of
(a) Voltage maximums and minimums.
(b) Current maximums and minimums.
(c) The reflection coefficient.
(d) The line's load resistance and $Z_{\text {or }}$.

Kai Chen
Kai Chen
Princeton University

Problem 43

Explain the disadvantages of a mismatched transmission line.

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Problem 44

What is the primary reason for terminating a transmission line in an impedance equal to the characteristic impedance of the line?

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Problem 45

What is the ratio between the currents at the opposite ends of a transmission line one-quarter wavelength long and terminated in an impedance equal to its surge impedance?

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Problem 46

An single sideband (SSB) transmitter at $2.27 \mathrm{MHz}$ and $200 \mathrm{~W}$ output is connected to an antenna $\left(R_{\mathrm{in}}=150 \Omega\right)$ via $75 \mathrm{ft}$ of $\mathrm{RG}-8 \mathrm{~A} / \mathrm{U}$ cable. Determine
(a) The reflection coefficient.
(b) The electrical cable length in wavelengths.
(c) The SWR.
(d) The amount of power absorbed by the antenna.

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Problem 47

What should be the approximate surge impedance of a quarter-wavelength matching line used to match a $600-\Omega$ feeder to a $70-\Omega$ (resistive) antenna?

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Problem 48

Calculate the impedance of a line 675 electrical degrees long. $Z_0=75 \Omega$ and $Z_L=50 \Omega+j 75 \Omega$. Use the Smith chart and Equation (12-30) as separate solutions, and compare the results.

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Problem 49

Convert an impedance, $62.5 \Omega-j 90 \Omega$, to admittance mathematically and with the Smith chart. Compare the results.

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Problem 50

Find the input impedance of a $100-\Omega$ line, $5.35 \lambda$ long, and with $Z_L=200 \Omega+j 300 \Omega$.

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02:31

Problem 51

Why is the impedance of a transmission line an important factor with respect to matching "out of a transmitter" into an antenna?

Surendra Kumar
Surendra Kumar
Numerade Educator

Problem 52

What is stub tuning?

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Problem 53

The antenna load on a $150-\Omega$ transmission line is $225 \Omega-j 300 \Omega$. Determine the length and position of a short-circuited stub necessary to provide a match.

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02:21

Problem 54

Repeat Problem 53 for a $50-\Omega$ line and an antenna of $25 \Omega+j 75 \Omega$.

Sanjeev Kumar
Sanjeev Kumar
Numerade Educator
03:26

Problem 55

Calculate the length of a short-circuited $50-\Omega$ line necessary to simulate an inductance of $2 \mathrm{nH}$ at $1 \mathrm{GHz}$.

Vishal Gupta
Vishal Gupta
Numerade Educator

Problem 56

Calculate the length of a short-circuited $50-\Omega$ line necessary to simulate a capacitance of $50 \mathrm{pF}$ at $500 \mathrm{MHz}$.

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Problem 57

Describe two types of baluns, and explain their function.

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Problem 58

How may harmonic radiation of a transmitter be prevented?

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Problem 59

Describe three methods for reducing harmonic emission of a transmitter.

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Problem 60

Draw a simple schematic diagram showing a method of coupling the radio-frequency output of the final power amplifier stage of a transmitter to a two-wire transmission line, with a method of suppression of second and third harmonic energy.

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Problem 61

Explain the construction of a slotted line and some of its uses.

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02:24

Problem 62

Explain the principle of time-domain reflectometry (TDR) and some uses for this technique.

Ajay Singhal
Ajay Singhal
Numerade Educator

Problem 63

A pulse is sent down a transmission line that is not functioning properly. It has a propagation velocity of $2.1 \times 10^8 \mathrm{~m} / \mathrm{s}$, and an inverted reflected pulse (equal in magnitude to the incident pulse) is returned in $0.731 \mathrm{~ms}$. What is wrong with the line, and how far from the generator does the fault exist?

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Problem 64

A fast-rise-time $10-\mathrm{V}$ step voltage is applied to a $50-\Omega$ line terminated with an $80-\Omega$ resistive load. Determine $\Gamma, E_R$ and $E_r(0.231,12.3 \mathrm{~V}, 2.3 \mathrm{~V})$

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11:45

Problem 65

With the help of Figure 12-12, provide a step-by-step explanation of how a dc voltage propagates through a transmission line.

NT
Nikhil Tiwari
Numerade Educator
01:57

Problem 66

An open-circuited line is $1.75 \lambda$. Sketch the incident, reflected, and resultant waveforms for both voltage and current at the instant the generator is at its peak negative value. Sketch and compare the waveforms for a short-circuited line.

Surendra Kumar
Surendra Kumar
Numerade Educator

Problem 67

You are asked to design a line "free of transmission line effects." You design one that is $\lambda / 16$ long. How would you justify this design?

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Problem 68

Match a load of $25 \Omega+j 75 \Omega$ to a $50-\Omega$ line using a quarter-wavelength matching section. Determine the proper location and characteristic impedance of the matching section. Repeat this problem for a $Z_L=110 \Omega-j 50 \Omega$ load. Provide two separate solutions.

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