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Chapter 20: Problem 2752

For \(100 \%\) modulation, What is the value of minimum amplitude $\left(E_{\min }\right)$ of the modulated wave? (A) Zero (B) 1 (C) 2 (D) 3

Short Answer

Expert verified
(B) 1

Step by step solution

01

Write down the given information

We are given that the modulation index, m, is 100% or 1. Our goal is to find the minimum amplitude, \(E_{min}\), of the modulated wave. #Step 2: Solve for E_min using the modulation index formula#
02

Solve for E_min using the modulation index formula

Since we know that \(m = 1\), we can rearrange the modulation index formula to solve for \(E_{min}\): \( 1 = \frac{A_c - E_{min}}{A_c + E_{min}} \) Now we need to isolate \(E_{min}\) on one side of the equation. To do so, first multiply both sides by \(A_c + E_{min}\): \( A_c + E_{min} = A_c - E_{min} \) Next, add \(E_{min}\) to both sides: \( 2E_{min} = A_c \) Now, divide both sides by 2 to get: \( E_{min} = \frac{A_c}{2} \) Since the minimum amplitude, \(E_{min}\), is half of the amplitude of the carrier wave, \(A_c\), this means that it must be some nonzero value. Comparing this result with the given options, we find that the correct answer is: (B) 1

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