Question

A message signal of frequency $100\, MHz$ and peak voltage $100\, V$ is used to execute amplitude modulation on a carrier wave of frequency $300\, GHz$ and peak voltage $400\, V$. The modulation index and difference between the two side band frequencies are :

• A. $4 ; 1 \times 10^8 \; Hz$
• B. $0.25 ; 1 \times 10^8 \; Hz$
• C. $4 ; 2 \times 10^8 \; Hz$
• D. $0.25 ; 2 \times 10^8 \; Hz$

Answer 1

Answer: (D)

$0.25 ; 2 \times 10^8 \; Hz$

Answer 2

$f_{m} =100 MHz = 10^{8} Hz ,\left(V_{m}\right)_{0} =100 V$
$f_{c} = 300 GHz ,\left(V_{c}\right)_{0} =400 V$
Modulaton Index $= \frac{\left(V_{m}\right)_{0}}{\left(V_{c}\right)_{0}} = \frac{100}{400} =\frac{1}{4} =0.25$
Upper band frequency (UBF) = $f_c + f_m$
Lower band frequency (LBF) = $f_c - f_m$
$\therefore$ UBF - LBF = $2f_m = 2 \times 10^8 \, Hz$