Power in frequency modulation (FM) In an FM signal with a given carrier amplitude, how does the total transmitted power change as the modulation index is varied?

Introduction / Context:
FM is a constant-envelope modulation. Unlike AM, where carrier plus sidebands alter the total power with modulation depth, FM redistributes power among the carrier and multiple sidebands while keeping the overall power nearly constant for a constant carrier amplitude.

Given Data / Assumptions:

• Carrier amplitude is fixed by the transmitter PA and limiter stages.
• Modulation index β = frequency deviation / modulating frequency.
• Linear, ideal FM without overdrive or limiter compression changes in amplitude.

Concept / Approach:

In FM, instantaneous frequency varies while amplitude stays constant. Bessel distributions determine how power shifts from the carrier to sidebands as β changes, but the sum of carrier and all sideband powers remains equal to the original carrier power (ignoring practical losses). Thus total radiated power is essentially independent of β.

Step-by-Step Solution:

Verification / Alternative check:

Spectrum analyzer measurements show carrier amplitude may decrease at certain β zeros while sidebands grow, but integrated power stays constant.

Why Other Options Are Wrong:

(a), (b), (c), and (e) contradict constant-envelope FM theory; total power does not trend up or down with β under ideal conditions.

Common Pitfalls:

Confusing bandwidth expansion (Carson rule) with power change; equating FM with AM power behavior.

Final Answer:

Power remains essentially constant as the modulation index changes