Question

An FM signal having a modulation Index of $M$ is passed through a frequency tripler. The FM signal at the output of tripler will have a modulation index of _______.

• A. unaltered
• B. 3M
• C. 6M
• D. M/3

Hint:

FM modulation index increases in direct proportion to frequency multiplication — remember: tripler $\Rightarrow$ $3M$, doubler $\Rightarrow$ $2M$.

Answer 1

The Correct Option is B

Step 1: Understanding Modulation Index
The modulation index ($\beta$) in frequency modulation (FM) is defined as the ratio of frequency deviation $\Delta f$ to modulating frequency $f_m$: \[ \beta = \frac{\Delta f}{f_m} \] Step 2: What does a frequency tripler do?
A frequency tripler multiplies the carrier frequency and frequency deviation by 3. However, the modulating frequency remains unchanged, since it's determined by the original signal. \[ \Delta f' = 3 \Delta f \text{and} f_m' = f_m \] Step 3: Effect on modulation index
Using the formula: \[ \beta' = \frac{\Delta f'}{f_m'} = \frac{3 \Delta f}{f_m} = 3 \times \frac{\Delta f}{f_m} = 3M \] Step 4: Common misconception
Students may think frequency multipliers only affect carrier frequency, but they also scale frequency deviation proportionally — hence the modulation index increases. Conclusion: The new modulation index is $3M$ at the output of the tripler.