Distortionless Line MCQ Quiz - Objective Question with Answer for Distortionless Line - Download Free PDF
Last updated on Mar 12, 2025
Latest Distortionless Line MCQ Objective Questions
Distortionless Line Question 1:
A system is said to be distortion less if its group delay is ______.
Answer (Detailed Solution Below)
Distortionless Line Question 1 Detailed Solution
A system is said to be distortion less if its group delay is constant.
Explanation:
- Group Delay: Group delay is the time delay experienced by the envelope of a signal as it passes through a system. It represents how much the different frequency components of a signal are delayed relative to each other.
- Distortionless Transmission: For a system to be distortionless, all frequency components of the input signal must be delayed by the same amount. This ensures that the shape of the signal's envelope remains unchanged as it passes through the system.
Key Points:
- Constant Group Delay: If the group delay is constant across all frequencies, it means that the same amount delays all frequency components. This results in a distortion less output signal.
- Variable Group Delay: If the group delay varies with frequency, different frequency components will experience different delays. This leads to distortion, such as changes in the shape of the signal's envelope.
In summary: A constant group delay is a crucial condition for distortion-less transmission, ensuring that the output signal retains the same shape as the input signal.
Distortionless Line Question 2:
A TEM mode transmission line is having distributed circuit parameters as R = 1 ohm/m, L = 200 nH/m, G = 300 μS/m, C = 60 pF, the line is
Answer (Detailed Solution Below)
Distortionless Line Question 2 Detailed Solution
Concept:
For a lossless line:
R = G = 0
A distortion less line satisfies the following condition:
\(\frac{{R}}{{L}} = \frac{{G}}{{C}}\)
Calculation:
Given:
R = 1 ohm/m, L = 200 nH/m, G = 300 μS/m, C = 60 pF,
R ≠ G ≠ 0
Hence, it is not Lossless line
\(\frac{R}{L}=\frac{1}{200\times10^{-9}}=5\times10^6\) ----(1)
\(\frac{G}{C}=\frac{300\times10^{-6}}{60\times10^{-12}}=5\times10^6\) -----(2)
From equation 1 and equation 2, we can say that the line is distortionless.
Distortionless Line Question 3:
A lossy transmission line has resistance per unit length R = 0.05 Ω/m. The line is distortionless and has a characteristic impedance of 50 Ω. The attenuation constant (in Np/m, correct to three decimal places) of the line is _________.
Answer (Detailed Solution Below) 0.001
Distortionless Line Question 3 Detailed Solution
Concept:
For a distortionless transmission line:
\(\frac{R}{G}=\frac{L}{C}\)
The characteristic impedance is given by:
\(Z_0 =\sqrt\frac{L}{C}=\sqrt\frac{R}{G}\)
Also, the attenuation constant is given by:
\(α=\sqrt{RG}\) ---(1)
Calculation:
Given R = 0.05 Ω/m, Z0 = 50 Ω
\(50=\sqrt\frac{R}{G}\) ---(2)
Multiplying Equation (1) and (2), we get:
50α = R
\(\alpha=\frac{0.05}{50}=0.001~Np/m\)
Distortionless Line Question 4:
In a distortion less co-axial cable the value of series resistance per meter and parallel capacitance values are doubled then the value of attenuation constant α and phase constant β respectively
Answer (Detailed Solution Below)
Distortionless Line Question 4 Detailed Solution
In a distortion less transmission line R/L = G/C
Propagation constant \(\gamma = \sqrt {RG} + j\omega \sqrt {LC} \;\left( {is\;of\;form\;\alpha + j\beta } \right)\)
Hence when R and C are doubled L and G must also be doubled to keep line distortion less hence α and β and doubled.
Distortionless Line Question 5:
A transmission line is distortionless if
Answer (Detailed Solution Below)
Distortionless Line Question 5 Detailed Solution
A transmission line is distortionless if:
\(\frac{{\rm{R}}}{{\rm{L}}} = \frac{{\rm{G}}}{{\rm{C}}}\)
Rewriting this we have:
LG = RC
Note:
If \(\frac{{\rm{R}}}{{\rm{L}}} = \frac{{\rm{G}}}{{\rm{C}}}\) then phase velocity is given by
\({v_p} = \frac{\omega }{\beta } = \frac{1}{{\sqrt {LC} }}\)
the phase velocity is independent of frequency hence the transmission line is distortionless.
Top Distortionless Line MCQ Objective Questions
A lossy transmission line has resistance per unit length R = 0.05 Ω/m. The line is distortionless and has a characteristic impedance of 50 Ω. The attenuation constant (in Np/m, correct to three decimal places) of the line is _________.
Answer (Detailed Solution Below) 0.001
Distortionless Line Question 6 Detailed Solution
Download Solution PDFConcept:
For a distortionless transmission line:
\(\frac{R}{G}=\frac{L}{C}\)
The characteristic impedance is given by:
\(Z_0 =\sqrt\frac{L}{C}=\sqrt\frac{R}{G}\)
Also, the attenuation constant is given by:
\(α=\sqrt{RG}\) ---(1)
Calculation:
Given R = 0.05 Ω/m, Z0 = 50 Ω
\(50=\sqrt\frac{R}{G}\) ---(2)
Multiplying Equation (1) and (2), we get:
50α = R
\(\alpha=\frac{0.05}{50}=0.001~Np/m\)
A transmission line has a characteristic impedance of 50 Ω and a resistance of 0.1 Ω/m. If the line is distortionless, the attenuation constant (in Np/m) is
Answer (Detailed Solution Below)
Distortionless Line Question 7 Detailed Solution
Download Solution PDFConcept:
For distortionless transmission line, we have
\(LG = RC\)
Characteristic impedance:
\({Z_o} = \sqrt {\frac{L}{C}} = \sqrt {\frac{R}{G}} \) ---(1)
Attenuation constant:
\(\alpha = \sqrt {RG} \) --- (2)
Calculation:
From equation (1) and (2), we get
\(\alpha = \sqrt R \frac{{\sqrt R }}{{{Z_o}}} = \frac{R}{{{Z_o}}}\;\)
Putting the values of R and Z0, we get
\( \Rightarrow \alpha = \frac{{0.1}}{{50}} = 0.002\;Np/m\)
A TEM mode transmission line is having distributed circuit parameters as R = 1 ohm/m, L = 200 nH/m, G = 300 μS/m, C = 60 pF, the line is
Answer (Detailed Solution Below)
Distortionless Line Question 8 Detailed Solution
Download Solution PDFConcept:
For a lossless line:
R = G = 0
A distortion less line satisfies the following condition:
\(\frac{{R}}{{L}} = \frac{{G}}{{C}}\)
Calculation:
Given:
R = 1 ohm/m, L = 200 nH/m, G = 300 μS/m, C = 60 pF,
R ≠ G ≠ 0
Hence, it is not Lossless line
\(\frac{R}{L}=\frac{1}{200\times10^{-9}}=5\times10^6\) ----(1)
\(\frac{G}{C}=\frac{300\times10^{-6}}{60\times10^{-12}}=5\times10^6\) -----(2)
From equation 1 and equation 2, we can say that the line is distortionless.
Distortionless Line Question 9:
A transmission line is distortionless if
Answer (Detailed Solution Below)
Distortionless Line Question 9 Detailed Solution
A transmission line is distortionless if:
\(\frac{{\rm{R}}}{{\rm{L}}} = \frac{{\rm{G}}}{{\rm{C}}}\)
Rewriting this we have:
LG = RC
Note:
If \(\frac{{\rm{R}}}{{\rm{L}}} = \frac{{\rm{G}}}{{\rm{C}}}\) then phase velocity is given by
\({v_p} = \frac{\omega }{\beta } = \frac{1}{{\sqrt {LC} }}\)
the phase velocity is independent of frequency hence the transmission line is distortionless.
Distortionless Line Question 10:
A lossy transmission line has resistance per unit length R = 0.05 Ω/m. The line is distortionless and has a characteristic impedance of 50 Ω. The attenuation constant (in Np/m, correct to three decimal places) of the line is _________.
Answer (Detailed Solution Below) 0.001
Distortionless Line Question 10 Detailed Solution
Concept:
For a distortionless transmission line:
\(\frac{R}{G}=\frac{L}{C}\)
The characteristic impedance is given by:
\(Z_0 =\sqrt\frac{L}{C}=\sqrt\frac{R}{G}\)
Also, the attenuation constant is given by:
\(α=\sqrt{RG}\) ---(1)
Calculation:
Given R = 0.05 Ω/m, Z0 = 50 Ω
\(50=\sqrt\frac{R}{G}\) ---(2)
Multiplying Equation (1) and (2), we get:
50α = R
\(\alpha=\frac{0.05}{50}=0.001~Np/m\)
Distortionless Line Question 11:
A transmission line has a characteristic impedance of 50 Ω and a resistance of 0.1 Ω/m. If the line is distortionless, the attenuation constant (in Np/m) is
Answer (Detailed Solution Below)
Distortionless Line Question 11 Detailed Solution
Concept:
For distortionless transmission line, we have
\(LG = RC\)
Characteristic impedance:
\({Z_o} = \sqrt {\frac{L}{C}} = \sqrt {\frac{R}{G}} \) ---(1)
Attenuation constant:
\(\alpha = \sqrt {RG} \) --- (2)
Calculation:
From equation (1) and (2), we get
\(\alpha = \sqrt R \frac{{\sqrt R }}{{{Z_o}}} = \frac{R}{{{Z_o}}}\;\)
Putting the values of R and Z0, we get
\( \Rightarrow \alpha = \frac{{0.1}}{{50}} = 0.002\;Np/m\)
Distortionless Line Question 12:
A distortionless transmission line is characterized by:
R = 0.25 Ω/m, L = 0.5 μH/m, C = 200 pF/m, and G = 100 μS/m. The characteristic impedance of the line is _________\({\rm{Ω }}\).
Answer (Detailed Solution Below) 49.9 - 50.1
Distortionless Line Question 12 Detailed Solution
Concept:
For distortionless transmission line, we have
\(LG = RC\)
Characteristic impedance:
\({Z_o} = \sqrt {\frac{L}{C}} = \sqrt {\frac{R}{G}} \)
Calculation:
With R = 0.25 Ω/m, L = 0.5 μH/m, C = 200 pF/m, and G = 100 μS/m, the characteristic impedance will be:
\({{\rm{Z}}_0} = \sqrt {\frac{{\rm{L}}}{{\rm{C}}}} = \sqrt {\frac{{0.5 \times {{10}^6}}}{{200 \times {{10}^{ - 12}}}}} \)
Z0 = 50 Ω
Distortionless Line Question 13:
The voltage standing wave ratio, VSWR is 2 for a lossless transmission line with characteristic impedance Z0 = 50Ω. The first minima is at a distance of λ/4 from the load. The load impedance is:
Answer (Detailed Solution Below)
Distortionless Line Question 13 Detailed Solution
Concept:
1. If voltage maxima or minima occur at the load then the load impedance is purely resistive.
2. Voltage standing wave ratio: It is the ratio of maximum voltage to minimum voltage.
If the voltage minima occur at load ZL < Z0 then
\(VSWR = \frac{{{Z_0}}}{{{Z_L}}}\)
If the voltage maxima occur at load ZL > Z0 then
\(VSWR = \frac{{{Z_L}}}{{{Z_0}}}\)
Analysis:
In a transmission line, Maxima and Minima are separated by λ/4. As minima occur at a distance of λ/4 from the load.
Hence there is a maxima formed at the load.
Now, VSWR = 2
\( \Rightarrow \left| \Gamma \right| = {{VSWR - 1} \over {VSWR + 1}} = {1 \over 3}\)
For lossless line when maxima or minima is formed at the load, then the phase of Γ is zero.
Thus \(\Gamma = + {1 \over 3}\ or - {1 \over 3}\)
For maxima at the load \({Z_L} > {Z_o}\) and Γ is +ve and
For minima formed at the load \(Z_L
Thus, \(\Gamma = {1 \over 3} = {{{Z_L} - {Z_o}} \over {{Z_L} + {Z_o}}}\)
ZL = 2Z0 = 100 Ω
Distortionless Line Question 14:
A TEM mode transmission line is having distributed circuit parameters as R = 1 ohm/m, L = 200 nH/m, G = 300 μS/m, C = 60 pF, the line is
Answer (Detailed Solution Below)
Distortionless Line Question 14 Detailed Solution
Concept:
For a lossless line:
R = G = 0
A distortion less line satisfies the following condition:
\(\frac{{R}}{{L}} = \frac{{G}}{{C}}\)
Calculation:
Given:
R = 1 ohm/m, L = 200 nH/m, G = 300 μS/m, C = 60 pF,
R ≠ G ≠ 0
Hence, it is not Lossless line
\(\frac{R}{L}=\frac{1}{200\times10^{-9}}=5\times10^6\) ----(1)
\(\frac{G}{C}=\frac{300\times10^{-6}}{60\times10^{-12}}=5\times10^6\) -----(2)
From equation 1 and equation 2, we can say that the line is distortionless.
Distortionless Line Question 15:
In a distortion less co-axial cable the value of series resistance per meter and parallel capacitance values are doubled then the value of attenuation constant α and phase constant β respectively
Answer (Detailed Solution Below)
Distortionless Line Question 15 Detailed Solution
In a distortion less transmission line R/L = G/C
Propagation constant \(\gamma = \sqrt {RG} + j\omega \sqrt {LC} \;\left( {is\;of\;form\;\alpha + j\beta } \right)\)
Hence when R and C are doubled L and G must also be doubled to keep line distortion less hence α and β and doubled.