If an FM signal with modulation index mf is passed through a frequency tripler circuit, what will be the new modulation index of the output signal?

Introduction / Context:
Frequency multipliers are commonly used in FM transmitter chains to shift carrier frequency while maintaining modulation. Understanding how frequency deviation and modulation index scale through multipliers is fundamental for FM system design.

Given Data / Assumptions:

• Input modulation index = mf.
• Frequency multiplier factor = 3 (tripler).

Concept / Approach:

Modulation index mf = frequency deviation / modulating frequency. Through a frequency multiplier of factor N, both carrier frequency and frequency deviation are multiplied by N, while modulating frequency remains the same. Hence, the modulation index is also multiplied by N.

Step-by-Step Solution:

Verification / Alternative check:

Transmission chain design examples: a baseband FM oscillator with mf, followed by doublers/triplers, scales mf accordingly.

Why Other Options Are Wrong:

• mf: ignores multiplication effect.
• mf/3 or mf/9: contradict actual scaling (inverse relation would only occur if modulating frequency also changed, which it does not).
• sqrt(3) * mf: not the relation for frequency multipliers.

Common Pitfalls:

Forgetting that both carrier and deviation scale equally, preserving deviation ratio multiplication.

Final Answer:

3mf