Standing Wave Ratio MCQ Quiz in मल्याळम - Objective Question with Answer for Standing Wave Ratio - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക
Last updated on Mar 11, 2025
Latest Standing Wave Ratio MCQ Objective Questions
Top Standing Wave Ratio MCQ Objective Questions
Standing Wave Ratio Question 1:
A transmission line having a characteristic impedance of 50 Ω is terminated at one end by j50 Ω. The voltage standing wave ratio produced will be
Answer (Detailed Solution Below)
Standing Wave Ratio Question 1 Detailed Solution
Concept:
The voltage standing wave ratio is defined as the ratio of the maximum voltage (or current) to the minimum voltage (or current).
\(VSWR = \frac{{{{\rm{V}}_{{\rm{max}}}}}}{{{{\rm{V}}_{{\rm{min}}}}}} = \frac{{{{\rm{I}}_{{\rm{max}}.}}}}{{{{\rm{I}}_{{\rm{min}}.}}}}\)
This can also be written as:
\(VSWR = \frac{{1 + {\rm{|Γ| }}}}{{1 - {\rm{|Γ|}}}}\)
Γ = Reflection coefficient, defined as:
\({\rm{Γ }} = \frac{{{Z_L} - {Z_0}}}{{{Z_L} + {Z_0}}}\)
ZL = Load impedance
Z0 = Characteristic Impedance
Calculation:
Given:
Z0 = 50 Ω
ZL = j50 Ω
\({\rm{Γ }} = \frac{{{Z_L} - {Z_0}}}{{{Z_L} + {Z_0}}}\)
\({\rm{Γ }} = \frac{{50j - 50}}{{50j + 50}} = \frac{j-1}{1+j}\)
\({\rm{Γ }} = \frac{(j-1)(1-j)}{(1+j)(1-j)}\)
Γ = j
Now:
\(VSWR = \frac{{1 + |j|}}{{1 - |j|}} = \infty\)
Standing Wave Ratio Question 2:
Consider a transmission line having a characteristic impedance of 100 Ω and connected to a 50 Ω resistance load. The line is very long, and the voltage measured at the load has a magnitude of 50 V. The maximum voltage that appears on the line is:
Answer (Detailed Solution Below)
Standing Wave Ratio Question 2 Detailed Solution
Concept:
The voltage at load is superposition of 2 waves
1) Forward travelling wave
2) Reflected wave
If V+ is the amplitude of forward travelling wave
Then voltage at load
VL = V+ + VR
VL = V+ + Γ V+
VL = V+ (1 + Γ)
Where VR = Reflected wave voltage
Also:
Vmax = |V+| (1 + (Γ(z)))
\(=\left| {{V}^{+}} \right|\left( 1+\frac{SWR-1}{SWR+1} \right)\)
\(=\left| {{V}^{+}} \right|\left( \frac{2~S\omega R}{S\omega R+1} \right)\)
Similarly,
\({{V}_{min}}=\left| {{V}^{+}} \right|\left( 1-\text{ }\!\!\Gamma\!\!\text{ }\left( z \right) \right)\)
\(=\left| {{V}^{+}} \right|\left( \frac{2}{SWR+1} \right)\)
Calculations:
Reflection coefficient (ΓL)
\({{\text{ }\!\!\Gamma\!\!\text{ }}_{L}}=\frac{{{Z}_{L}}-{{Z}_{0}}}{{{Z}_{L}}+{{Z}_{0}}}\)
\(=\frac{50-100}{50+100}\)
\(=\frac{-1}{3}\)
\(=\frac{1}{3}{{e}^{j\pi }}\)
\(\left| {{\text{ }\!\!\Gamma\!\!\text{ }}_{L}} \right|=\frac{1}{3}~,~{{\theta }_{L}}=-\pi \)
\(SWR=\frac{1+\left| {{\text{ }\!\!\Gamma\!\!\text{ }}_{L}} \right|}{1-\left| {{\text{ }\!\!\Gamma\!\!\text{ }}_{L}} \right|}=\frac{3+1}{3-1}=2\)
To calculate minimum and maximum voltage first calculate forward voltage amplitude.
\({{V}_{L}}={{V}^{+}}\left( 1+{{\text{ }\!\!\Gamma\!\!\text{ }}_{L}} \right)\)
\({{V}^{+}}=\frac{{{V}_{L}}}{\left( 1+{{\text{ }\!\!\Gamma\!\!\text{ }}_{L}} \right)}=\frac{50}{\left( 1-\frac{1}{3} \right)}=\frac{50}{\frac{2}{3}}\)
= 75 V
\({{V}_{max}}=\left| {{V}^{+}} \right|\left( \frac{2~SWR}{SWR+1} \right)\)
\(=75\left( \frac{2\times 2}{2+1} \right)\)
\(=75\times \frac{4}{3}=100~V\)Standing Wave Ratio Question 3:
A lossless line having characteristic impedance Zo is terminated with a load impedance of jZo. VSWR of the line will be:
Answer (Detailed Solution Below)
Standing Wave Ratio Question 3 Detailed Solution
Concept:
\(VSWR = \frac{{\left( {1 + \left| {\rm{\Gamma }} \right|} \right)}}{{\left( {1 - \left| {\rm{\Gamma }} \right|} \right)}}\;,\)
\(where\;{\rm{\Gamma }} = \frac{{{Z_L} - {Z_0}}}{{{Z_L} + {Z_0}}}\)
Calculation:
Given ZL= jZ0
\(So,\;{\rm{\Gamma }} = \frac{{j{Z_0} - {Z_0}}}{{j{Z_0} + {Z_0}}} = \frac{{\left( {j - 1} \right)\left( {j - 1} \right)}}{{\left( {j + 1} \right)\left( {j - 1} \right)}} = \frac{{ - 1 + 1 - 2j}}{{ - 2}} = j\)
\(VSWR = \frac{{1 + \left| j \right|}}{{1 - \left| j \right|}} = \frac{{1 + 1}}{{1 - 1}} = \infty\)Standing Wave Ratio Question 4:
A lossless transmission line is terminated by a load which reflects a part of the incident power. If percentage of the power that is transmitted is 75%, what is value of VSWR is ______.
Answer (Detailed Solution Below)
Standing Wave Ratio Question 4 Detailed Solution
Transmitted power = 75%
⇒ Reflected power = 25% = 1/4
Magnitude of reflection coefficient,
\(\left| {\rm{\Gamma }} \right| = \sqrt {1/4} = 1/2\)
Also, \(\left| {\rm{\Gamma }} \right| = \frac{{VSWR - 1}}{{VSWR + 1}} = \frac{1}{2}\)
VSWR = 3
Standing Wave Ratio Question 5:
A lossless transmission line is terminated in a load which reflects a part of the incident power. If VSWR is 2, the reflection coefficient will be :
Answer (Detailed Solution Below)
Standing Wave Ratio Question 5 Detailed Solution
Explanation:
Lossless Transmission Line and VSWR:
Definition: A lossless transmission line is a theoretical transmission line in which there is no dissipation of electrical energy as heat. This means that the conductors and the dielectric material between them are perfect, resulting in no energy loss as the signal propagates along the line.
VSWR (Voltage Standing Wave Ratio) is a measure of how efficiently RF power is transmitted from the power source, through a transmission line, into the load. It is defined as the ratio of the maximum voltage to the minimum voltage in a standing wave pattern along the transmission line.
The VSWR is given by:
VSWR = (1 + |Γ|) / (1 - |Γ|)
Where |Γ| is the magnitude of the reflection coefficient.
The reflection coefficient (Γ) represents the fraction of the incident power that is reflected back from the load. It is a measure of the impedance mismatch between the transmission line and the load.
Calculation of Reflection Coefficient:
Given that the VSWR is 2, we can use the VSWR formula to find the reflection coefficient.
VSWR = (1 + |Γ|) / (1 - |Γ|)
Substitute VSWR = 2 into the formula:
2 = (1 + |Γ|) / (1 - |Γ|)
To find |Γ|, we solve the equation step-by-step:
Step 1: Cross-multiply to eliminate the fraction:
2 * (1 - |Γ|) = 1 + |Γ|
Step 2: Distribute the 2 on the left-hand side:
2 - 2|Γ| = 1 + |Γ|
Step 3: Combine like terms to isolate |Γ|:
2 - 1 = 2|Γ| + |Γ|
1 = 3|Γ|
Step 4: Solve for |Γ|:
|Γ| = 1 / 3
Therefore, the reflection coefficient (|Γ|) is 1/3.
Correct Option Analysis:
The correct option is:
Option 1: 1/3
This option correctly represents the calculated value of the reflection coefficient when the VSWR is 2.
Additional Information
To further understand the analysis, let’s evaluate the other options:
Option 2: 3/4
This option is incorrect. If we use 3/4 in the VSWR formula, we would get:
VSWR = (1 + 3/4) / (1 - 3/4) = 7 / 1 = 7
This does not match the given VSWR of 2.
Option 3: Thu Jan 02 2025 00:00:00 GMT+0530 (India Standard Time)
This option is clearly irrelevant to the calculation of the reflection coefficient.
Option 4: Mon Feb 03 2025 00:00:00 GMT+0530 (India Standard Time)
Similar to option 3, this option is irrelevant to the calculation of the reflection coefficient.
Conclusion:
Understanding the relationship between VSWR and the reflection coefficient is crucial for analyzing transmission line performance. The reflection coefficient (|Γ|) provides valuable insight into the impedance matching of the transmission line and the load. In this case, with a VSWR of 2, the reflection coefficient is accurately calculated to be 1/3, confirming that option 1 is correct.
```Standing Wave Ratio Question 6:
A transmission line having Z0 = 75 Ω is used to deliver power to 300 Ohm load. The VSWR of the circuit is
Answer (Detailed Solution Below)
Standing Wave Ratio Question 6 Detailed Solution
Concept:
The voltage standing wave ratio is defined as the ratio of the maximum voltage (or current) to the minimum voltage (or current).
\(VSWR = \frac{{{{\rm{V}}_{{\rm{max}}}}}}{{{{\rm{V}}_{{\rm{min}}}}}} = \frac{{{{\rm{I}}_{{\rm{max}}.}}}}{{{{\rm{I}}_{{\rm{min}}.}}}}\)
VSWR is also given by:
\(VSWR = \frac{{1 + {\rm{Γ }}}}{{1 - {\rm{Γ }}}}\)
Γ = Reflection coefficient, defined as:
\({\rm{Γ }} = \frac{{{Z_L} - {Z_0}}}{{{Z_L} + {Z_0}}}\)
ZL = Load impedance
Z0 = Characteristic Impedance
For ΓL varying from 0 to 1, VSWR varies from 1 to ∞.
Application:
Given ZL = 300 Ω
The reflection coefficient is calculated to be:
\({\rm{Γ }} = \frac{{{300} - {75}}}{{{300} + {75}}}=0.6\)
VSWR is now calculated as:
\(VSWR = \frac{{1 + {\rm{\Gamma }}}}{{1 - {\rm{\Gamma }}}} = \frac{{1 + 0.6}}{{1 - 0.6}} =4\)
Standing Wave Ratio Question 7:
VSWR of a purely resistive load of normalized value n+j0 for n < 1 is:
Answer (Detailed Solution Below)
Standing Wave Ratio Question 7 Detailed Solution
Concept:
If the load is purely resistive for lossless line i.e. characteristic impedance must be purely resistive then;
I) VSWR \( = \frac{{{Z_L}}}{{{Z_O}}}\) when ZL > ZO
II) VSWR \( = \frac{{{Z_O}}}{{{Z_L}}}\) when ZO > ZL
Normalized impedance ‘Z’ means \(\frac{Z}{{{Z_O}}}\)
Calculation:
Given, normalized resistive load
i.e. \({\left( {{Z_L}} \right)_n} = \frac{{{Z_L}}}{{{Z_O}}} = n\)
but n < 1 ⇒ ZO > ZL
\(\therefore VSWR = \frac{{{Z_O}}}{{{Z_L}}}\)
\( = \frac{1}{n}\)
Note:
1) Value of VSWR lie from 1 < VSWR < ∞
2) For open circuit or for short circuit
3) Range of reflection coefficient (|Γ|) is;
0 < |Γ| < 1
Standing Wave Ratio Question 8:
A lossless transmission line having characteristic impedance 120 Ω is operating at 5 × 108 rad / s. If the line is terminated by a load impedance, consists if an inductance of 0.6 μH in series with a 100 Ω resistance, then VSWR on the line is ________.
Answer (Detailed Solution Below)
Standing Wave Ratio Question 8 Detailed Solution
Concept:
Voltage standing wave ratio (VSWR) is mathematically defined as:
\(VSWR = \frac{{\left( {1 + \left|\Gamma \right|} \right)}}{{\left( {1 - \left| \Gamma \right|} \right)}}\) ---(1)
Γ = Reflection coefficient given by:
\(\Gamma_L= \frac{{{Z_L} - {Z_o}}}{{{Z_L} + {Z_o}}}\)
ZL = Load Impedance
Z0 = Characteristic impedance
Calculation:
ZL = R + jXL
= R + jωL
= 100 + j5 × 108 × 0.6 × 10-6
ZL = 100 + j300 Ω
\({\rm{\Gamma }} = \frac{{{Z_L} - {Z_0}}}{{{Z_L} + {Z_0}}} = \frac{{\left( {100 + j300} \right) - 120}}{{\left( {100 + j300} \right) + 120}}\)
= 0.62 + j0.52
= 0.808 ∠40°
\(VSWR = \frac{{1 + \left| {\rm{\Gamma }} \right|}}{{1 - \left| {\rm{\Gamma }} \right|}} = \frac{{1 + 0.808}}{{1 - 0.808}}\)
\(VSWR = 9.4\)
Standing Wave Ratio Question 9:
Indicate the false statement. The SWR on a transmission line is infinity, the line is terminated in _________
Answer (Detailed Solution Below)
Standing Wave Ratio Question 9 Detailed Solution
VSWR is given by:
\(VSWR = \frac{{1 + \left| {\rm{\Gamma }} \right|}}{{1 - \left| {\rm{\Gamma }} \right|}}\)
VSWR = infinite means reflection coefficient |Γ| = 1
Γ = 1 or -1
Reflection coefficient is given by
\({\rm{\Gamma }} = \frac{{\left( {{Z_L} - {Z_o}} \right)}}{{{Z_L} + {Z_0}}}\)
For short circuit, ZL = 0
Γ = -1 and S = ∞
For open circuit, ZL = ∞
Γ = +1 and S = ∞
Input impedance in both cases, short circuit and open circuit, is complex.Standing Wave Ratio Question 10:
A load of 3 + j4Ω is connected to a 1Ω lossless line. The magnitude of reflection coefficient at the load will be :
Answer (Detailed Solution Below)
Standing Wave Ratio Question 10 Detailed Solution
Explanation:
To find the magnitude of the reflection coefficient (Γ) at the load, we need to use the formula:
|Γ| = |(ZL - Z0) / (ZL + Z0)|
Where ZL is the load impedance and Z0 is the characteristic impedance of the lossless transmission line. Given:
- ZL = 3 + j4Ω
- Z0 = 1Ω
Step-by-Step Solution:
1. Calculate the numerator (ZL - Z0):
ZL - Z0 = (3 + j4) - 1 = 2 + j4
2. Calculate the denominator (ZL + Z0):
ZL + Z0 = (3 + j4) + 1 = 4 + j4
3. Find the magnitude of the numerator and the denominator:
|ZL - Z0| = |2 + j4| = √(22 + 42) = √(4 + 16) = √20 = 2√5
|ZL + Z0| = |4 + j4| = √(42 + 42) = √(16 + 16) = √32 = 4√2
4. Calculate the magnitude of the reflection coefficient:
|Γ| = |(ZL - Z0) / (ZL + Z0)| = |(2 + j4) / (4 + j4)| = (2√5) / (4√2) = (2√5) / (2√2 * 2) = √5 / (2√2) = (√5 / √2) / 2 = √(5/2) / 2
By simplifying √(5/2):
√(5/2) ≈ 1.58
Therefore:
|Γ| ≈ 1.58 / 2 ≈ 0.79
Hence, the magnitude of the reflection coefficient at the load is approximately 0.79. Therefore, the correct answer is Option 2.