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?

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:

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