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Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and the receiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless link
- a)increases by a factor of 2
- b)decrease by a factor 2
- c)remains unchanged
- d)decreases by a factor of √2
Correct answer is option 'C'. Can you explain this answer?
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Understanding Wireless Link Capacity
In wireless communication, the capacity of a link can be influenced by various factors such as antenna characteristics and the distance between the transmitter and receiver. Let's analyze the scenario provided.
Effect of Doubling Parameters
When the effective areas of the transmitter and receiver antennas are both doubled, and the distance between them is also doubled, we need to consider how these changes affect the capacity.
Key Considerations:
- Antenna Effective Area (A): Doubling the effective area of the antennas increases the gain, which can enhance the received signal strength.
- Distance (d): When you double the distance, the signal strength diminishes due to the inverse square law, which states that the power received decreases with the square of the distance.
Impact on Capacity
The capacity \(C\) of a wireless link can be approximated using the Shannon-Hartley theorem:
\[ C = B \cdot \log_2(1 + \frac{P}{N}) \]
Where:
- \(B\) is the bandwidth,
- \(P\) is the received power,
- \(N\) is the noise power.
When both the antenna areas and distance are modified:
- Received Power (\(P\)): It increases due to the larger antenna areas, but decreases because of increased distance. The net effect can lead to a situation where the increase in \(P\) due to larger areas may not fully compensate for the decrease caused by distance.
- Overall Effect: The modifications ultimately balance out, resulting in no net change in capacity.
Conclusion
Thus, the maximum capacity of the wireless link remains unchanged, leading us to the correct answer:
Option C: Remains unchanged.
In wireless communication, the capacity of a link can be influenced by various factors such as antenna characteristics and the distance between the transmitter and receiver. Let's analyze the scenario provided.
Effect of Doubling Parameters
When the effective areas of the transmitter and receiver antennas are both doubled, and the distance between them is also doubled, we need to consider how these changes affect the capacity.
Key Considerations:
- Antenna Effective Area (A): Doubling the effective area of the antennas increases the gain, which can enhance the received signal strength.
- Distance (d): When you double the distance, the signal strength diminishes due to the inverse square law, which states that the power received decreases with the square of the distance.
Impact on Capacity
The capacity \(C\) of a wireless link can be approximated using the Shannon-Hartley theorem:
\[ C = B \cdot \log_2(1 + \frac{P}{N}) \]
Where:
- \(B\) is the bandwidth,
- \(P\) is the received power,
- \(N\) is the noise power.
When both the antenna areas and distance are modified:
- Received Power (\(P\)): It increases due to the larger antenna areas, but decreases because of increased distance. The net effect can lead to a situation where the increase in \(P\) due to larger areas may not fully compensate for the decrease caused by distance.
- Overall Effect: The modifications ultimately balance out, resulting in no net change in capacity.
Conclusion
Thus, the maximum capacity of the wireless link remains unchanged, leading us to the correct answer:
Option C: Remains unchanged.
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Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and thereceiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless linka)increases by a factor of 2b)decrease by a factor 2c)remains unchangedd)decreases by a factor of√2Correct answer is option 'C'. Can you explain this answer?
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Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and thereceiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless linka)increases by a factor of 2b)decrease by a factor 2c)remains unchangedd)decreases by a factor of√2Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and thereceiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless linka)increases by a factor of 2b)decrease by a factor 2c)remains unchangedd)decreases by a factor of√2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and thereceiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless linka)increases by a factor of 2b)decrease by a factor 2c)remains unchangedd)decreases by a factor of√2Correct answer is option 'C'. Can you explain this answer?.
Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and thereceiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless linka)increases by a factor of 2b)decrease by a factor 2c)remains unchangedd)decreases by a factor of√2Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and thereceiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless linka)increases by a factor of 2b)decrease by a factor 2c)remains unchangedd)decreases by a factor of√2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and thereceiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless linka)increases by a factor of 2b)decrease by a factor 2c)remains unchangedd)decreases by a factor of√2Correct answer is option 'C'. Can you explain this answer?.
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ample number of questions to practice Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and thereceiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless linka)increases by a factor of 2b)decrease by a factor 2c)remains unchangedd)decreases by a factor of√2Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GATE tests.
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