Question

An audio signal $v_m = 20 \sin 2\pi(1500t)$ amplitude modulates a carrier $v_c = 80 \sin 2\pi(100,000t)$. The value of percent modulation is ________

Hint:

The modulation index must be $\leq 1$ ($100%$) to avoid "overmodulation," which causes distortion in the received signal.

Answer 1

Correct Answer: 25

Step 1: Modulation index $m = \frac{A_m}{A_c}$.
Step 2: Here, amplitude of message signal $A_m = 20$ and amplitude of carrier $A_c = 80$.
Step 3: $m = \frac{20}{80} = 0.25$.
Step 4: Percent modulation $= m \times 100 = 0.25 \times 100 = 25%$.