Question

The plot of modulation index versus carrier amplitude yields a

• A. Horizontal line
• B. Circle
• C. Hyperbola
• D. Parabola

Hint:

Modulation index \(m = V_m / V_c\).
If \(V_m\) is held constant, then \(m\) is inversely proportional to \(V_c\).
The graph of \(y = k/x\) (where k is a constant) is a rectangular hyperbola.

Answer 1

The Correct Option is C

To understand how the plot of modulation index versus carrier amplitude results in a hyperbola, we need to examine the relationship between these two parameters in amplitude modulation (AM). The modulation index, denoted as \( m \), is defined by the ratio of the peak amplitude of the modulating signal \( A_m \) to the peak amplitude of the carrier signal \( A_c \). It can be expressed as:

Equation:
\( m = \frac{A_m}{A_c} \)

In this equation, if we try to plot \( m \) against \( A_c \), the relationship becomes evident. As the carrier amplitude \( A_c \) increases, for a constant \( A_m \), the modulation index \( m \) decreases. This inverse relationship, where one variable is inversely proportional to another, graphically represents a hyperbola. Thus, the plot of modulation index \( m \) versus carrier amplitude \( A_c \) yields a hyperbola.

Conclusion: The correct answer to the question "The plot of modulation index versus carrier amplitude yields a" is a Hyperbola.