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ADAMSON UNIVERSITY
COLLEGE OF ENGINEERING
ECE DEPARTMENT
TRANSMISSION LINE REVIEWER- MULTIPLE CHOICE
REFERENCE: Review Book (2009) by
Cuervo Santos
Communication System by
Blake
Submitted By:
Caldejon Ashley Q.
Calamucha, Xiareen Taye C.
Casantusan, Genielyn
Bernadeth B. Zari, PECE
Instructor
TRANSMISSION LINE
Identification:
1. A device for coupling balanced and unbalanced lines.a. Balunb. Transmission Linec. Coaxial Lined. Open-wire Line
Answer: A
2. The ratio between voltage and current on an infinitely long transmission line.a. Balunb. Characteristic Impedancec. Propagation Velocityd. Reflection Coefficient
Answer: B
3. A transmission line containing concentric conductors.a. Transmission Lineb. Quarter-wave Transformerc. Coaxial Lined. Stub
Answer: C
4. A transmission line containing parallel conductors separated by spacers.a. Balunb. Transmission Linec. Coaxial Lined. Open-wire Line
Answer: D
5. The speed at which signals travel down a transmission line.
a. Propagation Velocityb. Stubc. Smith Chartd. Surge Impedance
Answer: A
6. A section of transmission line, electrically a quarter-wavelength in length, that is used to change impedances on a transmission line.a. Propagation Velocityb. Quarter-wave transformerc. Stubd. Smith Chart
Answer: B
7. The ratio of reflected to incident voltage on a transmission line.a. Smith Chartb. Standing-wave Ratioc. Reflection Coefficientd. Velocity Factor
Answer: C
8. A graphical transmission line calculator.a. Stubb. Velocity Factorc. Reflection coefficientd. Smith Chart
Answer: D
9. The ratio of maximum to minimum voltage on a transmission line.a. Stubb. Balunc. Velocity Factord. Surge Impedance
Answer: A
10. Any pair of conductors used to conduct electrical energy.a. Stubb. Transmission Linec. Balund. Coaxial Line
Answer: B
11. Ratio of the speed of propagation on a line to that of light in free space.a. Balunb. Coaxial Linec. Velocity Factord. Reflection Coefficient
Answer: C
12. Transmission media with some form of conductor that provides a conduit in which electromagnetic signals are contained.a. Transmission line input
impedanceb. Reflection Coefficientc. Unguided transmission mediad. Guided transmission media
Answer: D
13. Transport signals using electrical current.a. Copper wiresb. Optical fibersc. Stubd. Balun
Answer: A
14. Transport signals by propagating electromagnetic waves through a nonconductive material.a. Copper wires
b. Optical fibersc. Stubd. Balun
Answer: B
15. Emitted then radiated through air or a vacuum or sometimes water.a. Balunb. Stubc. Unguided signalsd. Guided signals
Answer: C
16. Transmission media that are wireless systems (i.e., those without a physical conductor)a. Guided transmission mediab. Copper wiresc. Optical fibersd. Unguided transmission media
Answer: D
17. A guided transmission medium and can be any physical facility used to propagate electromagnetic signals between two locations in a communications system.a. Cable transmission mediumb. Guided transmission mediumc. Unguided transmission mediumd. Optical transmission medium
Answer: A
18. The most common means of interconnecting devices in local area networks because cable transmission systems are the only transmission medium suitable for the transmission of digital signals.
a. Cable transmission mediumb. Cable transmission systemsc. Transmission Lined. Balun
Answer: B
19. A metallic conductor system used to transfer electrical energy from one point to another using electrical current flow.a. Copper wireb. Optical fiberc. Transmission Lined. Cable
Answer: C
20. Type of transmission where one conductor carries the signal, and the other conductor is the return path.a. Unbalanced transmission linesb. Regular transmission linesc. Irregular transmission linesd. Balanced signal transmission
Answer: D
21. Type of transmission where one wire is at ground potential, whereas the other wire is at signal potential.a. Unbalanced signal transmissionb. Balanced signal transmissionc. Regular signal transmissiond. Irregular signal transmission
Answer: A
22. Most common type of balun is __________.a. Cable balunb. Narrowband balunc. Shield
d. Stub
Answer: B
23. Comprised of two or more metallic conductors.a. Series-wire transmission linesb. Open-wire transmission linesc. Parallel-wire transmission linesd. Closed-wire transmission lines
Answer: C
24. Nonconductive insulating material.a. Metalb. Twin leadc. Silverd. Dielectric
Answer: D
25. Consist of two parallel wires, closely spaced and separated by air.a. Open-wire transmission linesb. Closed-wire transmission linesc. Series-wire transmission linesd. Parallel-wire transmission lines
Answer: A
26. Essentially the same with open-wire transmission line except that the spacers between the two conductors are replaced with a continuous solid dielectric that ensures uniform spacing along the entire cable.a. Open-wire transmission linesb. Twin leadc. Closed-wire transmission linesd. Parallel-wire transmission lines
Answer: B
27. Formed by twisting two insulated conductors around each other and often stranded in units, and the units are then cabled into cores containing up to 3000 pairs of wire.a. Open-wire transmission linesb. Parallel-wire transmission linesc. Twisted-pair transmission linesd. Twin lead
Answer: C
28. Consists of two copper wires where each wire is separately encapsulated in PVC insulation.a. Shielded wireb. Shielded twisted pairc. Stranded wired. Unshielded twisted pair cable
Answer: D
29. A parallel two-wire transmission line consisting of two copper conductors separated by a solid dielectric material.a. Shielded-twisted pair cableb. Unshielded-twisted pair cablec. Shielded wired. Stranded wire
Answer: A
30. The name given to the area between the ceiling and the roof in a single-story-building or between the ceiling and the floor of the next higher level in a multistory building.a. Stubb. Plenumc. Wired. Platinum
Answer: B
31. Often used for high data transmission rates to reduce losses and isolate transmission paths.a. Plenumb. Stubc. Coaxial cablesd. Optical fibers
Answer: C
32. A coaxial cable with one layer of foil insulation and one layer of braided shielding is referred to as ____ shielded.a. Singleb. Triplec. Quadrupled. Dual
Answer: D
33. Consists of two layers of foil insulation and two layers of braided metal shielding.a. Quad shieldingb. Dual shieldingc. Single shieldingd. Triple shielding
Answer: A
34. Relatively expensive to manufacture, and to minimize losses, the air insulator must be relatively free of moisture.a. Water-filled coaxial cablesb. Rigid air-filled coaxial cablesc. Optical fibersd. Shielded wires
Answer: B
35. Used to express the attenuation and the phase shift per unit length of a transmission line.a. Reflection coefficientb. Velocity constantc. Propagation constantd. Velocity factor
Answer: C
36. Other name for propagation constant.a. Reflection coefficientb. Velocity constantc. Velocity factord. Propagation coefficient
Answer: D
37. Defined as the ratio of the actual velocity of propagation of an electromagnetic wave through a given medium to the velocity of propagation through a vacuum.a. Velocity factorb. Reflection coefficientc. Propagation coefficientd. Stub
Answer: A
38. Other name for velocity factora. Propagation factorb. Velocity constantc. Propagation valued. Propagation constant
Answer: B
39. The relative permittivity of a material.a. Velocityb. Acceleration constantc. Dielectric constant
d. Shielded wire
Answer: C
40. The ratio of the ac resistance to the dc resistance of a conductor is called __________ ratio.a. Capacitorb. Diodec. LEDd. Resistance
Answer: D
41. Also directly proportional to frequency.a. Radiation lossb. Radiance lossc. Copper lossd. Capacitor loss
Answer: A
42. Occurs whenever a connection is made to or form a transmission line or when two sections of transmission line are connected together.a. Radiation lossb. Coupling lossc. Capacitor lossd. Resistance loss
Answer: B
43. A luminous discharge that occurs between the two conductors of a transmission line when the difference of potential between them exceeds the breakdown voltage of the dielectric insulator.a. Radiation lossb. Coupling lossc. Corona
d. Copper loss
Answer: C
44. A transmission line with no reflected power.a. Coaxial transmission lineb. Optical transmission linec. Copper transmission lined. Nonresonant line
Answer: D
45. Other name for nonresonant line.a. Flatb. Roundc. Coupledd. Single
Answer: A
46. Defined as the ratio of the maximum voltage to the minimum voltage or the maximum current to the minimum current of a standing wave on a transmission line.a. Round-wave ratiob. Standing-wave ratioc. Single-wave ratiod. Double-wave ratio
Answer: B
47. SWR stands for:a. Shorted Wave Radiation b. Sine Wave Response c. Shorted Wire Regiond. none of the above
ANS: D
47. TDR stands for:a. Total Distance of Reflection b. Time-Domain Reflectometerc. Time-Domain Responsed. Transmission Delay Ratio
ANS: B
48. An example of an unbalanced line is:a. a coaxial cable b. 300-ohm twin-lead TV cable c. an open-wire-line cabled. all of the above
ANS: A
49. When analyzing a transmission line, its inductance and capacitance are considered to be:a. lumped b. distributed c. equal reactances d. ideal elements
ANS: B
50. As frequency increases, the resistance of a wire:a. increases b. decreasesc. stays the same d. changes periodically
ANS: A
51. The effect of frequency on the resistance of a wire is called:a. I2R loss b. the Ohmic effectc. the skin effect
d.there is no such effect
ANS: C
51. As frequency increases, the loss in a cable's dielectric:a. increases b. decreasesc. stays the same d. there is no loss in a dielectric
ANS: A
52. The characteristic impedance of a cable depends on:
a. the resistance per foot of the wire used
b. the resistance per foot and the inductance per foot
c. the resistance per foot and the capacitance per foot
d. the inductance per foot and the capacitance per foot
ANS: D
54. For best matching, the load on a cable should be:a. lower than Z0 b. higher than Z0 c. equal to Z0d. 50 ohms
ANS: C
55. The characteristic impedance of a cable:a. increases with length b. increases with frequencyc. increases with voltage
d. none of the above
ANS: D
56. The velocity factor of a cable depends mostly on:a. the wire resistance b. the dielectric constantc. the inductance per foot d. all of the above
ANS: B
57. A positive voltage pulse sent down a transmission line terminated in a short-circuit:a. would reflect as a positive pulseb. would reflect as a negative pulsec. would reflect as a positive pulse followed by a negative pulsed. would not reflect at all
ANS: B
58. A positive voltage pulse sent down a transmission line terminated with its characteristic impedance:a. would reflect as a positive pulseb. would reflect as a negative pulsec. would reflect as a positive pulse followed by a negative pulsed. would not reflect at all
ANS: D
59. A positive voltage-pulse sent down a transmission line terminated in an open-circuit:a. would reflect as a positive pulseb. would reflect as a negative pulsec. would reflect as a positive pulse followed by a negative pulse
d. would not reflect at all
ANS: A
60. The optimum value for SWR is:a. zero b. onec. as large as possibled. there is no optimum value
ANS: B
61. A non-optimum value for SWR will cause:a. standing waves b. loss of power to loadc. higher voltage peaks on cable d. all of the above
ANS: D
62. VSWR stands for:a. variable SWR b. vacuum SWRc. voltage SWR d. none of the above
ANS: C
63. The impedance "looking into" a matched line:a. is infinite b. is zero c. is the characteristic impedance
d. 50 ohms
ANS: C
64. A Smith Chart is used to calculate:a. transmission line impedances
b. propagation velocity c. optimum length of a transmission lined. transmission line losses
ANS: A
65. Compared to a 300-ohm line, the loss of a 50-ohm cable carrying the same power:a. would be less b. would be more c. would be the samed. cannot be compared
ANS: B
66. A balanced load can be connected to an unbalanced cable:a. directly b. by using a filter c. by using a "balun"d. cannot be connected
ANS: C
67. On a Smith Chart, you "normalize" the impedance by:a. assuming it to be zero b. dividing it by 2p c. multiplying it by 2pd. dividing it by Z0
ANS: D
68. The radius of the circle you draw on a Smith Chart represents:a. the voltage b. the currentc. the impedanced. none of the above
ANS: D
69. The center of the Smith Chart always represents:a. zero b. one c. the characteristic impedanced. none of the above
ANS: C
70. A TDR is commonly used to:a. measure the characteristic impedance of a cableb. find the position of a defect in a cablec. replace a slotted-lined. all of the above
ANS: B
II. PROBLEM SOLVING
71.A parallel-wire line spaced at 1.27 cm has a diameter of 0.21 cm. What is the characteristic impedance?
a. 304 Ωb. 303 Ωc. 301 Ωd. 300 Ω
Solution:
Zo = 276 log 2 Dd
Zo = 276 log 2(1.27)
0.21
Zo= 298.8 Ω ≈ 300 Ω
72. In a coaxial line if the inner diameter is 0.51 cm and the center conductor has a diameter of 0.22 cm. What is the characteristic impedance?
a. 50.1 Ωb. 50.2 Ωc. 50.4 Ωd. 50.5 Ω
Solution:
Zo= 138 log Dd
Zo= 138 log ( 0.510.22
)
Zo= 50.4 Ω
73. A stripline is formed using a multilayer board (dielectric constant =2). The center track is 0.15 inch wide and 0.005 inch thick and the PC board first- layer thickness is 0.05 inch thick., with an overall board thickness of twice the single layer. What is its characteristic impedance?
a. 14.7 Ω b. 14.8Ωc. 14.9Ω
d. 15.1Ω
Solution:
Zo= 60√∈
ln (4 t
0.67 πb (0.8+ch))
Zo= 602
ln (
4 (0.05∗2)
0.67 π (0.15)(0.8+ 0.0050.0525
))
Zo = 14.7Ω
74. In an improperly loaded transmission line, determine the power reflected from the load if the incident power at the load is 500 W and the reflection coefficient is 0.71.
a. 252.05Ω b. 252.06Ωc. 253.4Ωd. 254Ω
Solution:Pref = t2 PincPref = (0.71)2 (500)Pref = 252.05Ω
75. In wire communications system,calculate the return loss in dB, if the load impedance is 600 ohms and the characteristics impedance of the line is 300 ohms.
a. 9.60Ωb. 9.56Ωc. 9.54Ω d. 9.52Ω
Solution:
Return Loss (dB)= 20 log(Zl+ZcZl−Zc
)
Return Loss (dB)= 20 log( Zl+ZcZl−Zc
)
Return Loss (dB)= 20 log( 600+300600−300
)
Return Loss (dB) = 9.54dB
76. The VSWR on a loss- free line of 50 ohm characteristic impedance is 4.2. Determine the value of the purely resistive load impedance which is known to be larger than 50 ohms.
a. 211Ωb. 210Ω c. 209Ωd. 208Ω
Solution:
VSWR = RlZo
RL = (VSWR)(Zo)RL= (4.2)(50)RL= 210 Ω
77. A microstrip lie is formed using a 0.095 inch thick PC board (dielectric constant = 1.8) with a bottom grounds plane and a single 0.15 inch wide, 0.008 inch thick track on the top. What is its characteristic impedance?
a. 72.8Ωb. 72.6Ωc. 72.4Ω d. 72.2Ω
Solution:
Zo= 87
√∈ t+1.41 ln (
5.98h0.8 b+c
)
Zo= 87
√1.8+1.41 ln (
5.98 (0.095)0.8(0.095)+0.008
)
Zo= 72.4 Ω
78. Determine the impedance of a balanced 2-wire with unequal diameters d1 = 12 mm and d2= 10mm. The spacing between wires is 30mm.
a. 35.56MΩ b. 35.57MΩc. 35.55MΩd. 35.58MΩ
Solution:
Zo = 60
√∈ tcosh−1 N
Zo = 60√ 1
cosh−1(13.98)
Zo= 35.36 MΩ
Where,
N = 12
[ ( 4 D2
d 1d 2 ) – (
d 1d 2
) – (( d 2d 1
) ]
N = 12
[ ( 4 (30)2
(12 )(10) ) – (
1210
) – ( 1012
) ]N= 13.98
79. For a parallel-wire line, determine the conductance if the conductivity is 200 x10-6
S/m and the conductor diameter is 12 mm. The conductor spacing is 10mm.
a. 1.56 mS/m
b. 1.23 mS/m c. 1.76 mS/md. 1.89mS/m
Solution:
G = πσ
ln2 Dd
G = π ¿¿G= 1.23 mS/m
80. What is the characteristic impedance of an open-line with conductors 4mm in diameter separated by 15 mm?
a. 241.52 Ω b. 242.66Ωc. 243.62Ωd. 244Ω
Solution:
Zo = 276√∈ t
log 2 Dd
Zo = 276√ 1
log 2(15)
4
Zo= 241.52Ω
81. The Forward power in a transmission line is 150 W and reverse power is 20 W. Calculate the SWR on the line.
a. 2.15 b. .2.14c. 2.13d. .2.12
Solution:
SWR =1+√
PrefPinc
1−√PrefPinc
SWR =1+√
20150
1−√20150
SWR = 2.15
82. What is the characteristic impedance of a coaxial cable using a solid polyethylene dielectric having a relative permeability of 2.3 ,an inner conductor of 1 mm diameter and an outer conductor of diameter 5 mm?a. 64Ωb.65.9Ωc. 63.6Ωd.67.9Ω
Solution:
Zo= 138√∈ t
log Dd
Zo= 138√ 2.3
log 51
Zo= 63.6Ω
83. Calculate the velocity factor of a coaxial cable used as a transmission line, with the characteristic impedance of 50 Ω, capacitance is 40 pF/m and inductance equal to 50μH/m.
a. 22.36 x10 6 m/s
b. 23.36 x106 m/s
c. 24.36 x106 m/s
d. 25.36 x106 m/s
Solution:
Vp = c Vf
Vf= VpC
=22.36 x106 m /s
3 x 108 m /s
Vf= 0.0745
Where :
Vp= 1
√ LC =
1
√ (50 x10−6)(40 x 10−12)
Vp=22.36x 106 m/sa
84. What is the characteristic impedance of a coaxial cable using solid polyethylene dielectric having a relative permeability of 2.3, an inner conductor of 1mm diameter and an outer conductor of diameter 5mm?
a. 4.25ft.
b. 4.26ft.
c. 4.24ft.
d. 4.23ft.
Solution:
Λ = Vpf
= cVff
Λ = (3 x108 )(0.69)
40 x 106
Λ = 5.175m = 16.974 ft
Length = λ4
= 16.974 ft
4
Length = 4.24 ft.
85. What is the actual length in feet of one-half wavelength of a coax with velocity factor of 0.63 at 28 MHz?
a.11.10ft
b. 11.08ft
c. 11.07ft
d. 11.05ft
Solution:
Λ = Vpf
= cVff
Λ = (3 x108 )(0.63)
28 x 106
Λ= 6.75 m
Length = λ2
= 3.375 m
= 11.07 ft.
86. What is the actual length in feet of one-quarter wavelength of a coax with a velocity factor of 0.68 at 30 MHz?
a. 5.576 ft
b. 5.577 ft
c. 5.578 ft
d. 5.579 ft
Solution:
Λ = Vpf
= cVff
Λ = (3 x108 )(0.63)
28 x 106 = 6.8m
Length = λ4
= 1.7 m = 5.576 ft
87. What is the actual length in feet of a one half wavelength of a coax with a velocity factor of 0.61 at 27 MHz?
a. 11.12ft. b. 11.13ft.c. 11.14ft.d. 11.15ft.
Solution:
Λ = Vpf
=C Vff
Λ = (3 x108 )(0.61)
27 x 106
Λ= 6.78 m= 22.23 ft
Length = λ2
= 11.12 ft.
88. What is the actual length in feet of a one half wavelength of a coax with a velocity factor of 0.59 at 26Mhz?
a. 11.20ftb. 11.19ftc. 11.17ftd. 11.16ft
Solution:
Λ = Vpf
=C Vff
Λ = (3 x108 )(0.59)
26 x 106
Λ= 6.8 m = 22.33 ft.
Length = λ2
= 11.16ft
89. What is the actual length in feet of a one quarter wavelength of a coax with a velocity factor of 0.695 at 42 MHz?
a. 4.05ftb. 4.06ft
c. 4.07ft d. 4.08
Solution:
Λ = Vpf
=C Vff
Λ = (3 x108 )(0.695)
42 x 106
Λ= 4.96 m= 16.28 ft
Length = λ2
= 4.07ft
90. An amplifier with 20 dB gain is connected to another with 10dB gain by means of a transmission line with a loss of 4dB if a signal with a power level of -14 dB were applied to the system, calculate the power output.
a.13 dBmb.12 dBmc.11 dBmd. 10 dBm
Solution:Po(dBm)= Pi(dBm) + GT(dBm) – LT(dBm)
Po(dBm)= -14(dBm) + (20+10)(dBm) – (4)(dBm)
Po= 12 dBm
91. An attenuator has a loss of 26 dB. If a power of 3W is applied to the attenuator, find the output power.
a. 7. 50 mWb. 7. 51mWc. 7.53 mWd. 7.54 mW
Solution:
L(dB)= 10 log Pin
Pout
Pout = Pin
log−1[
L (dB )10
]
Pout = 3W
log−1[26 dB
10]
Pout= 7. 54 mW
92. What would be the approximate series impedance of a quarter- wave matching line used to match a 600 ohms feed to 70 ohms antenna?
a. 204.94Ω b. 204.95Ωc. 204.96Ωd. 204.97Ω
Solution:Zo’ = √ ZoZl
Zo’ = √ (600)(70) = 204.94Ω
93. What is impedance of a balance 4-wire with a diameter of 0.25 cm and spaced 2.5 cm apart using an insulator with a dielectric constant of 2.56?
D
D
a. 100Ω
b. 101Ωc. 102Ωd. 103Ω
Solution:For d<< D1 D2
Zo= 138√∈ t
log( 2 D 2d ) [1+(D 2
D 1 )2]
1/2
D1=D2 = 2.5 cm
Zo= 138
√ 2.56log( 2(2.5)
0.25 ) [1+(2.52.5 )
2]1/2
Zo= 99.23 ΩZo= 100Ω
94. What is the characteristic impedance of a single wire with diameter d =0.25 mm placed at the center between grounded parallel planes separated by 1mm apart? The wire is held by a material with a velocity factor of 0.75.
a. 76 ohmsb. 77 ohmsc. 74 ohmsd. 75 ohms
Solution:
For dh<0.75
Zo= 138√∈ t
log ( 4 hπd
)
Zo= 138(0.75) log(4 (1)
π (0.25))
Zo= 75 ohms
Where d = 0.25 mm
h= 1 mm
1√∈ t
= Vf = 0.75
95. What is the phase coefficient of a transmission line at the frequency of 10MHz if the velocity of propagation is 2.5 x 108
m/s?
a.0.23 rad/mb.0.25 rad/mc.0.24 rad/md. 0.26 rad/m
Solution:
β= ωVp
=2 πfVp
β=2 π (10 x 106)
2.5 x108
Β = 0.25 rad/m
96. Determine the conductance of a two wire open line with the following parameters: D = 4inches ; d= 1in and ρ= 2.6 x10 8 Ω-m.
a. 2.76 x 10 -9 S/m b. 2.77 x 10 -9 S/mc. 2.78 x 10 -9 S/md. 2.79 x 10 -9 S/m
Solution:
G = πσ
ln2 Dd
G = π (3.85x 10−9)
ln2(4)0.1
G= 2.76 x 10-9 S/m
Where
σ=1ρ= 1
2.6 x 108=3.85 x10−9 S /m
97. What is the input impedance of a transmission line if its characteristic impedance is 300ohms and the load is 600 ohms? Assume a quarter wavelength section only
a. 180 ohmsb. 170 ohmsc. 160 ohmsd. 150 ohms Solution:
Zin= Zo (Zl+Zo tanh γlZo+Zl t anh γl
)
For l= λ4
line,
Zin= ( Z o2
Zl) =
(300 )2
(600)=150 ohms
98. Determine the standing wave ratio of a 300 ohms line whose load is 400 +j 150 ohms.
a. 1.68b. 1.67 c. 1.66d. 1.65
Solution:
SWR = 1+τ1−τ
τ=Zl−ZoZl+Zo
¿(400+ j150 )−300(400+ j150 )+300
= 0.25 < 44.22
SWR = 1+0.251−0.25
= 1.67
99. What proportion of the incident is reflected back from the loadfor a 75ohms line terminated with Zl = 50-j25 ohms?
a. 7.82 %b. 7.83%c. 7.84% d. 7.85%
Solution:
τ=Zl−ZoZl+Zo
¿(50− j25 )−75(50− j25 )+75
¿35.35←135
127.48←11.31
τ=0.28←123.69=¿/τ /<0
%PrefPinc
=(τ )2 x100%
%PrefPinc
=(0.28 )2 x100 %
%PrefPinc
= 7.84%
100. Find the inductance of a meter length transmission line if the characteristic impedance is 52 ohms and the capacitance is 75 pf/m.A. 1.015 µhB. 2.250 µhC. 1.025µhD. 2.450 µhSolution:
Zo = √ LC
L = Zo2CL = (52)2 (75x10-12)L = 203 nH/mL = 203 nH/m (5 meter)L = 1.015µH
101. An open wire line with a 2mm diameter each separated by 12mm. Calculate the char impedance.A. 298 ΩB. 250 ΩC. 300 ΩD. 450 ΩSolution:
Zo = 276
√Є r log (
2 Dd
)
Zo = 276
√1 log [
2(12)2
]
Zo = 298 Ω
102. A coaxial cable with inner diameter of 3mm and an outer diameter of 9mm. Determine the characteristic impedance if the dielectric is polyethylene having єr = 2.3A. 43.4ΩB. 50.2 ΩC. 32.6 ΩD. 47.7 Ω
Solution:
Zo = 138
√Є r log (
Dd
)
Zo = 138
√2.3 log (
93
)
Zo = 43.4Ω
103. A coaxial transmission line uses Teflon as a dielectric (єr = 2.1). What is the propagation velocity of the signal?A. 207x10 6 m/s B. 301x106 m/sC. 245x106 m/sD. 195x106 m/sSolution:
Vf = 1
√Є r
Vf = 1
√2.1Vf = 0.69Vp = VfCVp = 0.69 ( 3x108 )Vp = 207x106 m/s
104. A 530 Mhz signal is propagating along a RG 8/u coaxial cable with a velocity factor 0.66. If a 75 degrees phase shift is needed, what is the length of the transmission line?A. 7.8 cmB. 8.5 cmC. 5.3 cmD. 6.7 cmSolution:
Vp = VfCVp = 0.66 ( 300x106 )
Vp = 198x106 m/s
λ = Vpf
λ = 198 x 106
530 x 106
λ = 0.374m
L = 0.374 ( 75
360 ) = 0.078cm
L = 7.8 cm
105. Calculate the SWR of the line is the 75Ω and is terminated by 50ΩA. 1.5B. 1.6C. 1.7D. 1.8Solution:
SWR = ZoZL
= 7550
= 1.5
106. A transmitter sends a 5W of power to a 75Ω line. Suppose the transmitter and the line is matched but the load is not. Determine the power absorbed by the load if the coefficient of reflection is 0.75.A. 2.1875 WB. 3.1875 WC. 4.1875 WD. 5.1875 WSolution:
Pref = 2.8125 WPL = Pinc – PrefPL = 5W – 2.8125WPL = 2.1875W
107. A generator sends a 250 W of power down a line. If the SWR of the line is 2.5, determine the power absorbed by the load.A. 204.1 W
B. 304.1 WC. 404.1 WD.504.1 WSolution:
PL = 4 SW R
(1+SWR)2 Pinc
PL = 4 (2.5)
(1+2.5)2 250W
PL = 204.1W
108. A 75Ω characteristic impedance transmission line is terminated in by the load impedance of 120Ω. Determine the input impedance looking into the line 1m long, if the line has a velocity factor of 0.9 and operates at a frequency of 50Mhz.A. 34.4-j12.2B. 34.4+j12.2C. 44.4-j12.2D. 44.4+j12.2Solution:
λ = Vpf
= 0.9(300 x106)
50 x106 = 5.4m
θ = 1m
5.4 m (360°) = 66.67 °
Zin = Zo ZL+ jZo tan θZo+ jZLtanθ
Zin = (50)120+ j (75 ) ¿¿Zin = 34.4 – j12.2
109. A parallel tuned circuit is to be constructed from a shorted section of parallel wire line. If the operating frequency is 2.4 Ghz and the dielectric used is polyethylene, what is the length of the shorted section?A. 2.06 cm
B. 3.06 cmC. 4.06 cmD. 5.06 cmSolution:
Vf = 1
√Є r
Vf = 1
√2.3 = 0.66
Vp = VfCVp = 0.66 (300x106) = 198x106 m/s
λ = Vpf
= 198
2400 = 0.0825m
L = λ4
= 0.0825
4
L = 2.0625 cm
110.The transmitter has an output power of 150W. Suppose the line is 50m long and perfectly matched with a loss of 3 db/100m, how much power is received in the antenna?A. 106.2 WB. 206.2 WC. 306.2 WD. 406.2 WSolution:
άL = 50m ¿ )
άL = 1.5 dB ¿ )άL = 0.173Pout = Pin e-2 άL
Pout = 150 e-2 (0.173)
Pout = 106.2 W
111.TDR equipment receives a signal 250 ns after the test signal had been transmitted. If the discontinuity of the line is found 35m from the test point, what is the velocity factor of the line?A. 0.933B. 1.933
C. 2.933D. 3.933Solution:
d = Vpt2
= Vfct
2
Vf = 2 dct
Vf = (2 )(35 m)
(300 x106 )(250 x 10−9)
Vf = 0.933
112.The line has 97% velocity factor. If two minima are located 30cm apart, determine the frequency.A. 485 MhzB. 585 MhzC. 685 MhzD. 785 MhzSolution:
λ = 2 (30cm) = 60cm
f = Vpλ
f = 0.97(300 x 106)
0.60f = 485 MHz
113.The power incident in the line is 200W. Assuming the reflected power is 15W, what is the SWR of the line?A. 1.75B. 2.75C. 3.75D.4.75Solution:
SWR = 1+√ Pref
Pinc
1−√ PrefPinc
SWR = 1+√ 15
200
1−√ 15200
SWR = 1.75
114.A transmission line 90m long has a characteristic impedance of 75Ω. The line is connected through a 15V dc source and 75Ω source resistance at time t=0. What is the voltage across the input immediately after t=0?A. 7.5VB. 8.5VC. 9.5 VD. 10.5 V
Solution:
Vin = Vs2
= 152
= 7.5 V
115.A transmission line 90m long has a characteristic impedance of 75. The line is connected through a 15V dc source and 75Ω source resistance at time t=0. The voltage across the input end changes to 10V, with the same polarity as before, at time t=1.5µs. What is the resistance that terminates the lines?A. 150ΩB. 250ΩC. 350ΩD. 450ΩSolution:
V10 = ¿ )Vs
VsV 10
= R+75
R = 1 +
75R
R = 75
(Vs
V 10−1)
R = 75
(1510
−1) = 150Ω
116.A parallel wire transmission line has an inductance of 120 nH/m and a characteristic impedance of 320Ω. Calculate the capacitance of the line.A. 1.17 pF/mB. 2.17 pF/mC. 3.17 pF/mD. 4.17 pF/mSolution:
Zo = √ LC
C = L
Z o2 = 120 x 10−9
(320 )2
C = 1.17 pF/m117.A radio frequency 50Ω transmission
line is connected to a coil with internal resistance of 20Ω and inductive resistance of 5Ω at a frequency of 10Mhz. The line is to be matched to the load by means of a quarter-wave line and a stub that are connected across the load. Calculate the characteristic impedance of the quarter-wave transformer.A. 32.6 ΩB. 42.6 ΩC. 52.6 ΩD. 63.6 ΩSolution:
YL = 1
ZL =
120+5 j
= (47 –j12) mS
YL = GL = 47 mS
ZL = 1
GL
ZL = 1
47mS = 21.3Ω
Zo = √ZoZLZo = √ (50 )(21.3) = 32.6Ω
118.An open-wire line has a 3mm diameter separated 6mm from each other by an dielectric. Calculate the characteristic impedance of the line.A. 166 ΩB. 266 ΩC. 366 ΩD. 466 ΩSolution:
Zo = 276
√Є r log (
2 Dd
)
Zo = 276
√1 log [
2(6)3
]
Zo = 166 Ω
119.A radio frequency coaxial transmission line has a characteristic impedance of 50Ω and is connected across the terminals of a signal generator, line and the load are matched, determine the current which flows into the line.A. 100 mAB. 200 mAC. 300 mAD. 400 mASolution:
Is = Vs
ZL+Zo
Is = 10
50+50
Is = 100mA
120. A certain instrument measures the input impedance of a line and gave a reading of 1200 ohms when its far-end terminals open circuited and 300 ohms when it is short circuited. Calculate the characteristic impedance of the line.
a.500Ω
b.600 Ω
c.700 Ω
d.800 Ω
Solution:
Zo=√Zoc Z sc
Zo=√ (1200 )(300)
Zo=600 ohms
121. A transmission line has an inductance of 253 nH/m and a capacitance of 56 pF/m. If the physical length of the line is 1.5 m, calculate its electrical length at a frequency of 265 MHz.
a.3/2 λ
b. 1/2 λ
c. 4/2 λ
d. 5/2 λ
Solution:
V p=1
√ LC
V p=1
√ (253 x10−9 ) (56 x10−12)
V p=2.65 x 108 ms
λ=V p
f
λ=2.65 x 108
265 x 106
λ=1 m
Electrical length = 1.5 m (λ
1m)
Electrical length = 1.5 λ
Electrical length = 3/2 λ
122. A radio-frequency transmission line has a capacitance of 46.8 pF/m and a phase constant of 30°/m. Determine the inductance of the line at a frequency of 30 MHz.
a. 164
b.165
c.166
d.167
Solution:
β=30 °( 2 π360 ° )
β=π6
rad /m
β=ω √LC=2 πf √ LC
π6=2 πf √LC
L=( 112 f )
2
( 1C )
L=( 1
12 (30 x106 ) )2
( 146.8 x10−12 )
L=165nHm
123. The reflected current at the load of a mismatched line is 3 mA. If the reflection coefficient of the load is 0.7, what is the incident current?
a. 4.5
b.4.4
c.4.3
d.4.2
Solution:
τ=I ref
I inc
I inc=Iref
τ
I inc=3 mA0.7
I inc=4.3 mA
124. A radio frequency transmission lines has a characteristic impedance of 75 ohms. If the line is terminated by an aerial with an
input impedance of 72 ohms, calculate the SWR of the line.
a. 1.01
b.1.02
c.1.03
d.1.04
Solution:
τ=ZL−Zo
Z L+Zo
τ=72−7572+75
τ=−0.02
SWR=1+|(−0.02 )|1−|(−0.02 )|
SWR=1.04
125. A lossless transmission line is connected to a 10 ohms load. If the SWR=5, calculate the percentage of the incident power that is dissipated in the load.
a.55%
b.56%
c.57%
d.58%
Solution:
τ=SWR−1SWR+1
τ=5−15+1
τ=0.67
Pr ef =τ2 Pinc
PD=Pinc−Pref
PD=(1−τ2 ) Pinc
PD=(1−0.672 ) Pinc
PD=0.56 Pinc
PD=56 % Pinc
126. The reflection coefficient on a loss-free line of 72 ohms characteristic impedance is 60%. Calculate the load impedance (purely resistive) and which is smaller than 72 ohms.
a.17
b.18
c.19
d.20
Solution:
τ=ZL−Zo
Z L+Zo
−0.6=Z L−72
Z L+72
−0.6 ( ZL+72 )=ZL−72
−0.6 ZL−43.2=Z L−72
1.6ZL=28.8
ZL=18 ohms
127. A radio frequency 50 ohms transmission line is connected to a coil with internal resistance of 20 ohms and inductive reactance of 5 ohms at a frequency of 10 MHz. The line is to be matched to the load by means of a quarter-wave line and a stub that are connected across the load. Calculate the reactance of the stub.
a.83.2
b.83.3
c.83.4
d.83.5
Solution:
Y L=1Z1
Y L=1
20+5 j
Y L= (47− j 12 )mS
Bstub= j 12 mS
X stub=1
Bstub
X stub=83.3 ohms
128. A lossless line has a 75 ohms characteristic impedance and is connected to 50 ohms load. If the sending current of 1 mA flows into the line. Calculate the power reflected from the load.
a.1
b.1
c.3
d.4
Solution:
Pinc=I inc2 Zo
Pinc= (1x 10−3 )2 75
Pinc=75 µW
τ=ZL−Zo
Z L+Zo
τ=50−7550+75
τ=−0.2
Pref=τ2 Pinc
Pref= (0.2 )2 (75 µW )
Pref=3 µW
129. A loss-free line transmission line has an inductance of 263.2 nH/m and a capacitance of 46.8 pF/m. If the generator produces a sinusoidal voltage at 3 MHz of 2 V peak, determine the phase change if the line is 3 m long.
a. 11.34
b.11.35
c.11.36
d.11.37
Solution:
β=ω √LC
β=2 π (3 MHz )(√(263.2nHm )(46.8
pFm ))
β=0.021 π rad /m
Phase change at 3 meters long:
βL=(0.021 πradm )(3m( 180 °
π ))βL=11.34
