Difficulty: Easy
Correct Answer: 2 M_f
Explanation:
Introduction / Context:
Frequency multipliers are common in FM transmitters and test setups. They multiply the carrier frequency by an integer n and also scale the peak frequency deviation. Knowing how modulation index transforms is crucial for meeting deviation and spectral mask limits after multiplication stages.
Given Data / Assumptions:
Concept / Approach:
For an n-times frequency multiplier, Δfout = n * Δfin, and fm,out = fm,in. Therefore, Mf,out = Δfout / fm,out = n * Δfin / fm,in = n * Mf,in. With n = 2, the output modulation index doubles.
Step-by-Step Solution:
Verification / Alternative check:
Spectral lines (Bessel components) shift and scale consistently with the multiplier, reflecting increased deviation (wider spectrum) proportional to n.
Why Other Options Are Wrong:
Common Pitfalls:
Assuming the modulating frequency doubles—only the carrier and deviation are multiplied by the frequency multiplier.
Final Answer:
2 M_f
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