Question
How much does increasing a receiver’s bandwidth from 50 Hz to 1,000 Hz increase the receiver’s noise floor?
Answer Options
- A) 3 dB
- B) 5 dB
- C) 10 dB
- D) 13 dB
Correct Answer: D
Explanation
Noise power entering a receiver is uniformly distributed across the frequency spectrum (often called ‘white noise’). The total amount of noise energy captured by the receiver is therefore directly proportional to its bandwidth. The relationship between bandwidth change and noise power change is logarithmic (in dB).
To calculate the increase in noise floor, we use the formula 10 \log_{10}(B_2 / B_1). Here, the increase is 10 \log_{10}(1000 Hz / 50 Hz) = 10 \log_{10}(20). Since 10 \log_{10}(20) \approx 13 dB, increasing the bandwidth from 50 Hz to 1000 Hz increases the noise floor by approximately 13 dB. This principle underscores why using the minimum necessary bandwidth is critical for detecting weak signals.
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