If the channel bandwidth available to a frequency-modulated (FM) system is doubled while keeping other conditions comparable to amplitude modulation (AM), by what factor does the improvement ratio γFM/γAM (output SNR ratio of FM to AM) typically increase?
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AFactor of 2
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BFactor of 3
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CFactor of 4
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DFactor of 6
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ENo change
Answer
Correct Answer: Factor of 4
Explanation
Introduction / Context:One advantage of wideband FM is improved output signal-to-noise ratio (SNR) compared with AM, for a given received carrier power. This improvement grows with FM system deviation and effectively with the occupied bandwidth. Understanding how γFM/γAM scales with bandwidth guides design trade-offs between spectral efficiency and noise performance.
Given Data / Assumptions:
- γ denotes the ratio of output SNR to input SNR.
- We compare FM and AM under comparable received power and noise conditions.
- Bandwidth is increased by a factor of 2.
Concept / Approach:
For wideband FM, the output SNR improvement over AM is approximately proportional to the square of the peak frequency deviation (or modulation index for single-tone), which in turn scales with the occupied bandwidth (per Carson’s rule intuition). If bandwidth is doubled, the improvement factor scales roughly as the square, yielding approximately four times greater γFM/γAM, ignoring pre-emphasis and receiver details.
Step-by-Step Solution:
Assume wideband FM regime where SNR_o(FM) ∝ (deviation)^2 for a given noise floor.If bandwidth B → 2B, effective deviation (and thus improvement) scales → improvement factor ≈ (2)^2 = 4.Therefore, γFM/γAM increases by a factor of approximately 4.Verification / Alternative check:
Classic FM noise theory shows that, absent threshold effects, FM demodulator output noise decreases as deviation increases; empirical lab setups confirm about quadratic scaling before practical limits (receiver IF bandwidth, pre-emphasis) intervene.
Why Other Options Are Wrong:
- Factors 2 or 3: underestimate the quadratic dependence in the wideband regime.
- Factor 6: not supported by the square-law trend.
- No change: contradicts FM noise advantage principles.
Common Pitfalls:
Applying this scaling in the narrowband FM regime or near the FM threshold where different behaviors occur; ignoring pre-emphasis/de-emphasis which alters high-frequency noise shaping but not the basic wideband scaling trend.
Final Answer:
Factor of 4