Q.In an FM system, when the modulating frequency is 400 Hz and modulating voltage is 2.4 V, the deviation is 4.8 kHz. Calculate the modulation index. What is the modulation index if the modulating voltage is raised to 3.2 V and modulating frequency is dropped to 250 Hz?

The frequency deviation of an FM system is proportional to the modulating voltage through a deviation constant $K_f$; once $K_f$ is known, a new voltage gives a new deviation and hence a new mod …

[!TLDR]

The initial modulation index is 12; using the deviation constant $K_f = 2\ \text{kHz/V}$, raising the voltage to 3.2 V (deviation 6.4 kHz) at 250 Hz gives a new index of 25.6.

The modulation index is $m_f = \Delta f/f_m$. For the first condition,

The frequency deviation produced per volt of modulating signal is the deviation constant (frequency sensitivity):

When the modulating voltage is raised to $V_m = 3.2\ \text{V}$, the new deviation is

$\Delta f = K_f\,V_m = (2\times10^{3})(3.2) = 6.4\times10^{3}\ \text{Hz}$ …