Communication System

Maximum voltage of an AM wave: $V_{\max}$Minimum voltage of an AM wave: $V_{\;\text{min}\;}$Amplitude of the modulating signal is calculated as:$A_m = \frac{V_{\max} - V_{\min}}{2}$Amplitude of the carrier signal is calculated as:$A_C = \frac{V_{\max} + V_{\min}}{2}$The modulation index or modulation factor $m$ is defined as the ratio of the amplitude of the modulating signal to the amplitude of the carrier signal:$m = \frac{A_m}{A_C}$Substituting the expressions for $A_m$ and $A_C$, the modulation index becomes:$m = \frac{\frac{V_{\max} - V_{\min}}{2}}{\frac{V_{\max} + V_{\min}}{2}} \Rightarrow m = \frac{V_{\max} - V_{\min}}{V_{\max} + V_{\min}}$