Question

When a sinusoidal carrier signal is frequency modulated by two message signals

$m_1\left(t\right)=\cos \left(2\pi f_{1}t\right)Vand{m}_2\left(t\right)=2\cos \left(2\pi f_{2}t\right)V$ individually, the modulation index of the resultant FM signals are 10 rad and 20 rad respectively. If the same modulator is used in both the cases, then select the correct one of the following relations.

• A. $f_2=\left(0.5\right)f_1$
• B. $f_2={2f}_1$
• C. $f_2=f_1$
• D. $f_2={4f}_1$

Answer 1

The correct option is C

$f_2=f_1$

${\beta }_1=\frac{\Delta f_1}{f_{m1}}=\frac{A_{m1}{k}_f}{f_1}=10rad...\left(i\right)$

${\beta }_2=\frac{\Delta f_2}{f_{m2}}=\frac{A_{m2}{k}_f}{f_2}=20rad...\left(ii\right)$

From equation (i) and (ii), it is clear that,


$\frac{A_{m2}{k}_f}{f_2}=2\times \frac{A_{m1}{k}_f}{f_1}$

$\frac{f_2}{f_1}=\frac{A_{m2}}{2A_{m1}}=\frac{2}{2\times 1}=1Giventhat,A_{m1}=1Vand{A}_{m2}=2V$

So, $f_2=f_1$