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All questions of Transmission Lines for UPSC CSE Exam

The reflection coefficient of a transmission line with a short-circuited load is 
  • a)
    infinite
  • b)
    1∠1800
  • c)
    zero
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?

Rhea Reddy answered
For a short-circuited load,
reflection coefficient of voltage

and reflection coefficient of current,

Here, only option (b) matches the answer

A transmission line whose characteristic impedance is purely resistive
  • a)
    must be lossless line
  • b)
    must be a distortionless line
  • c)
    may not be a lossless line
  • d)
    may not be a distortionless line
Correct answer is option 'A'. Can you explain this answer?

Starcoders answered
If the transmission line is to have neither frequency nor delay distortion, then α (attenuation constant) and velocity of propagation cannot be functions of frequency.
V = ω/β β 
must be a direct function of frequency to achieve this condition
LG = CR
L/C = R/G
z0 = √((R + jωL)/(G + jωC))
For a lossless line,
z0 = √(L/C)
α = √(RG) = 0 for R = 0, G = 0
β = ω√(LC)
A loss less line is always a distortion less line.

In a transmission line terminated by characteristic impedance, Z0
  • a)
    the incident current is zero for only applied voltage.
  • b)
    there are large number of maximum and minimum on the line.
  • c)
    the reflection is maximum due to termination.
  • d)
    there is no reflection of the incident wave.
Correct answer is option 'D'. Can you explain this answer?

Sanjana Chopra answered
When a transmission line is terminated by an impedance Z, then reflection coefficient are:

Here, Z0 = Characteristic impedance of transmission line.
Since Z = Z0 therefore reflection co-efficient of voltage (pv) and current (pI) both will be zero, i.e there will be no reflection of incident wave.

Which of the following statements related to a transmission line is/are correct?
1. Transmission line elements are integral parts of the antenna, in some antenna system.
2. A feeder is a particular case of a transmission Sine.
3. A lossless transmission line doesn’t has resistance but, has a non-zero value of leakage conductance.
4. At radio frequency (RF), R and G both are neglected.
  • a)
    1 and 2 only
  • b)
    1, 2 and 4 only
  • c)
    2 and 4 only
  • d)
    1, 2, 3 and 4
Correct answer is option 'B'. Can you explain this answer?

Debanshi Basak answered
Transmission Line Statements

1. Transmission line elements are integral parts of the antenna, in some antenna system.
- This statement is correct as transmission lines are often used in antenna systems to efficiently transfer RF energy from the transmitter to the antenna.

2. A feeder is a particular case of a transmission line.
- This statement is correct as a feeder is a type of transmission line that is used to connect the transmitter to the antenna.

4. At radio frequency (RF), R and G both are neglected.
- This statement is correct as at high frequencies like RF, the resistance (R) and conductance (G) of the transmission line are often neglected due to the skin effect and other factors.
Therefore, the correct statements related to a transmission line are 1, 2, and 4.

If a transmission line of length less than λ/4  is short circuited, it behaves as
  • a)
    series resonant circuit
  • b)
    pure capacitive reactance
  • c)
    pure inductive reactance
  • d)
    parallel resonant circuit
Correct answer is option 'C'. Can you explain this answer?

Mira Sharma answered
One-tenth of the wavelength is used to transmit a signal, then the line can be considered as a lumped element. This means that the transmission line can be modeled as a series of discrete components, such as resistors, capacitors, and inductors, that are connected in a particular configuration to achieve the desired signal transmission characteristics.

In this lumped element model, the transmission line is assumed to have uniform characteristics along its entire length, and the signal propagates through the line instantaneously. This approximation is valid for low-frequency signals and short transmission lines, but it becomes less accurate as the frequency and length of the transmission line increase.

For higher frequency signals or longer transmission lines, a distributed element model must be used to accurately describe the signal propagation. In this model, the transmission line is considered as a continuous medium with varying characteristics along its length, and the signal is modeled as a wave that travels through this medium. The distributed element model is more complex than the lumped element model, but it provides a more accurate description of signal transmission in high-frequency and long-distance applications.

The input impedance of a short circuited quarter wave long transmission line is
  • a)
    purely reactive
  • b)
    purely resistive
  • c)
    dependent on the characteristic impedance of the line
  • d)
    none of the above
Correct answer is option 'D'. Can you explain this answer?

Pranjal Datta answered
Explanation:

Input impedance is the impedance seen by the input of a transmission line. The input impedance of a short circuited quarter wave long transmission line can be explained as follows:

- A quarter wave long transmission line is a transmission line whose length is equal to one-fourth of the wavelength of the signal being transmitted.
- When this transmission line is short circuited at the input end, the voltage at the input end becomes zero and the current becomes maximum.
- The signal then travels along the transmission line towards the load. After traveling a quarter wavelength, the signal gets reflected at the load end.
- The reflected signal travels back towards the input end and when it reaches the input end, it gets reflected again due to the short circuit.
- The two reflected signals add up at the input end and create a standing wave pattern.
- The input impedance of the short circuited quarter wave long transmission line is the impedance seen by the input end of the line due to the standing wave pattern.

Answer:

The input impedance of a short circuited quarter wave long transmission line is neither purely reactive nor purely resistive. It is a complex impedance that depends on the characteristic impedance of the line, the frequency of the signal being transmitted, and the length of the line. Therefore, option D is the correct answer.

The characteristic impedance of a distortionless line is
  • a)
    inductive
  • b)
    capacitive
  • c)
    complex
  • d)
    real
Correct answer is option 'D'. Can you explain this answer?

Nayanika Kaur answered
Characteristic impedance,

or, 

(Since L/R = C/G for a distortionless line)


Hence, characteristic impedance of a distortionless line is purely real.

Consider a lossless line with characteristic impedance R0 and VSWR = S. Then, the impedance at the point of voltage maxima and voltage minima are respectively given by
  • a)
    SRand R0/S
  • b)
    R0/S and SR0
  • c)
    R0/S and R0/S
  • d)
    SRand SR0
Correct answer is option 'A'. Can you explain this answer?

Ritika Sarkar answered
Impedance at Points of Voltage Maxima and Minima on a Lossless Line

Introduction:
In the study of transmission lines, the voltage standing wave ratio (VSWR) is an important parameter that characterizes the behavior of the line. The VSWR is the ratio of the maximum voltage to the minimum voltage along the line. In the case of a lossless line with a characteristic impedance R0, we can determine the impedance at the points of voltage maxima and minima.

Explanation:
To understand why the impedance at the points of voltage maxima and minima is given by option 'A' (SR0 and R0/S), let's consider the behavior of the voltage and current along the transmission line.

1. Voltage and Current Distribution:
- When a signal travels along a lossless transmission line, it experiences reflections at the line's ends due to impedance mismatch.
- These reflections result in the formation of standing waves along the line, with voltage and current nodes and antinodes.
- At voltage maxima, the voltage reaches its highest positive peak, while at voltage minima, the voltage reaches its lowest negative peak.
- The voltage and current distribution along the line can be described by the voltage and current standing wave patterns.

2. Relationship between VSWR and Impedance:
- The VSWR is defined as the ratio of the maximum voltage (Vmax) to the minimum voltage (Vmin) along the transmission line.
- VSWR = (Vmax / Vmin)
- The VSWR can also be expressed in terms of impedance as VSWR = (Zmax / Zmin), where Zmax and Zmin are the maximum and minimum impedances along the line, respectively.

3. Impedance at Voltage Maxima and Minima:
- At the points of voltage maxima, the voltage is maximum, and the current is minimum. This implies that the impedance at voltage maxima (Zmax) is equal to the characteristic impedance of the line (R0) multiplied by the VSWR (S).
Zmax = SR0
- Similarly, at the points of voltage minima, the voltage is minimum, and the current is maximum. This implies that the impedance at voltage minima (Zmin) is equal to the characteristic impedance of the line (R0) divided by the VSWR (S).
Zmin = R0/S

Conclusion:
In a lossless transmission line with a characteristic impedance R0 and VSWR = S, the impedance at the points of voltage maxima and minima are given by SR0 and R0/S, respectively (option 'A'). This relationship is derived from the behavior of voltage and current standing waves along the line. Understanding these relationships is crucial in the design and analysis of transmission lines in various electrical and electronic systems.

Assertion (A): A transmission line act as resonant circuit and is used in many applications at high frequencies in antenna design and other ratio circuitory
Reason (R): An open and short-circuited lines behaves like resonant circuit when length of line is an integral multiple of λ/3.
  • a)
    Both A and R are true and R is a correct explanation of A.
  • b)
    Both A and R are true but R is not a correct explanation of A.
  • c)
    A is true but R is false. .
  • d)
    A is false but R is true.
Correct answer is option 'C'. Can you explain this answer?

Samridhi Bose answered
Assertion is correct because when a transmission line is open or short-circuited it behaves as resonant circuit. However, reason is false because this happens when length of the line is an integral multiple of λ/4.
We knnw that
Zoc = -j cot βl
and Zsc = jZ0 tan βl
Thus, when βl = length of line = nλ/4 , then
cot βl = 0
and tan βl = ∞
∴ Zoc = 0
and Zsc = ∞
This means a quarter wave short-circuit line represents an infinite impedance at inpul terminals, just like a parallel resonant (LC) circuil and a λ/4 open circuit line present zero impedance at input terminals just like a series resonant LC circuit.

Consider the following statements:
1. Propagation constant is a dimensionless quantity.
2. When the line is lossless, propagation constant is directly proportional to the frequency.
3. Propagation constant when multiplied with the frequency gives the electrical length of the line.
Which of the above statements is/are true?
  • a)
    3 only
  • b)
    2 only
  • c)
    1, 2 and 3
  • d)
    2 and 3 only
Correct answer is option 'C'. Can you explain this answer?

Poulomi Ahuja answered
  • Propagation constant is dimensionless quantity because it is the ratio of voltages or currents.

    or,

    (where, P = Propagation constant) Hence, statement-1 is correct.
  • For a lossless transmission line,

    ∴ VP α f
    Thus, statement - 2 is also correct.
  • Statement-3 is also true.
    Thus, all statements are true.

A transmission line works as a
  • a)
    LPF
  • b)
    HPF
  • c)
    attenuator
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?

Sakshi Chauhan answered
Introduction:
A transmission line is a specialized structure used to transfer electric power or signals from one point to another. It consists of two or more conductors separated by a dielectric material. Transmission lines are commonly used in various electronic systems and communication networks.

Explanation:
A transmission line works as a Low Pass Filter (LPF). Let's understand why:

1. Frequency Response:
A transmission line exhibits a frequency-dependent behavior. It can transmit signals with a wide range of frequencies, but the transmission characteristics vary with frequency. The frequency response of a transmission line depends on its physical length, impedance, and termination.

2. Attenuation:
Attenuation refers to the decrease in signal strength as it propagates through a transmission line. In a transmission line, attenuation is caused by resistive losses, dielectric losses, and radiation losses. These losses increase with frequency, resulting in a reduction in signal amplitude.

3. Phase Shift:
Phase shift refers to the change in the phase angle of a signal as it propagates through a transmission line. A transmission line introduces a phase shift that is frequency-dependent. Higher frequencies experience greater phase shifts compared to lower frequencies.

4. Cutoff Frequency:
The cutoff frequency of a transmission line is the frequency at which the transmission characteristics change significantly. Above the cutoff frequency, the transmission line starts behaving as a low pass filter. It attenuates higher frequency components of the signal and allows lower frequency components to pass through with minimal distortion.

5. Filtering Effect:
Due to the frequency-dependent attenuation and phase shift, a transmission line effectively filters out high-frequency components and allows low-frequency components to pass through. This filtering effect is similar to that of a low pass filter. Hence, a transmission line can be considered as a low pass filter.

Conclusion:
In conclusion, a transmission line works as a Low Pass Filter (LPF) due to its frequency-dependent characteristics, attenuation, phase shift, and filtering effect. It attenuates higher frequency components and allows lower frequency components to pass through with minimal distortion.

A line becomes distortionless 
  • a)
    it is terminated into Z0
  • b)
    LR = GC
  • c)
    LG = CR
  • d)
    it is properly matched
Correct answer is option 'C'. Can you explain this answer?

Jaya Rane answered
A distortionless transmission line is one in which the attenuation constant α is independent of frequency while the phase.constant β is linearly dependent on frequency.

The real part of the propagation constant shows:
  • a)
    reduction in voltage, current values of signal amplitude
  • b)
    reduction of only voltage amplitude
  • c)
    reduction of only current amplitude
  • d)
    variation of phase shift/position of-voltage
Correct answer is option 'A'. Can you explain this answer?

Explanation:

Real part of the propagation constant:
The real part of the propagation constant in a transmission line represents the attenuation or reduction in the voltage and current values of the signal amplitude as it propagates along the transmission line. This means that as the signal travels through the line, its amplitude decreases due to factors such as resistance and conductor losses.

Effect on signal amplitude:
- The reduction in amplitude affects both the voltage and current components of the signal.
- This attenuation is a result of energy dissipation in the form of heat as the signal propagates through the transmission line.

Consequence:
- The reduction in signal amplitude can lead to signal degradation over long transmission lines.
- To compensate for this attenuation, amplifiers or repeaters may be used along the transmission line to boost the signal strength.

Significance:
Understanding the real part of the propagation constant is crucial in designing and analyzing communication systems. It helps in predicting signal strength variations and ensuring reliable signal transmission over long distances.
In conclusion, the real part of the propagation constant indicates the reduction in voltage and current values of the signal amplitude as it travels through a transmission line. This understanding is essential for maintaining signal integrity and quality in communication systems.

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