Question

Sinusoidal carrier of 20V, 2 MHz is frequency modulated by sinusoidal message signal of 10V, 50 kHz and Kf=55 kHz/V. Find ∆f, Modulation Index, band width and power.​

Answer 1

refer to the attachment

Answer 2

Given:

$\text { For message signal }$

$\text { Frequency, } \mathrm{f}_{\mathrm{m}}=\mathbf{2 0} \mathrm{kHz}$

$\text { Peak voltage, } \mathbf{A}_{\mathrm{m}}=\mathbf{2 0} \mathbf{V}$

$\text { For carrier frequency }$

$\text { Frequency, } \mathrm{f}_{\mathrm{c}}=2 \mathrm{MHz}=\mathbf{2 0 0 0} \mathrm{kHz}$

$\text { Peak voltaqe, } \mathbf{A}_{c}=\mathbf{4 0} \mathbf{V}$

$\text { (i) Modulation frequency is given by }$

$\mu=\frac{\mathbf{A}_{\mathbf{m}}}{\mathbf{A}_{\mathrm{c}}}=\frac{\mathbf{2 0}}{\mathbf{4 0}}=\mathbf{0 . 5}$

$\text { (ii) The side band will be at }\left(f_{c} \pm f_{m}\right)=$

$\begin{array}{l}(\mathbf{2 0 0 0} \pm \mathbf{2 0}) \mathrm{kHz}= \\\mathbf{2 0 2 0} \mathrm{kHz} \text { and } \mathbf{1 9 8 0} \mathbf{k H} \mathbf{z}\end{array}$

The answer is :

(1) Modulation Index=2020kHz

(2) Band width and power=1980kHz