Question

A message signal of frequency $10\, kHz$ and peak value of $10\,volts$ is used to moderate a carrier of frequency $1 \,MHz$ and peak voltage $20 \, volts$. The modulation index and side bands produced are

• A. $0.4$ and $1200\, kHz$, $990\, kHz$
• B. $0.5$ and $1010\, kHz$, $990\, kHz$
• C. $0.2$ and $1010\, kHz$, $1000\, kHz$
• D. $0.5$ and $1500\, kHz$, $1000\, Hz$

Answer 1

Answer: (B)

$0.5$ and $1010\, kHz$, $990\, kHz$

Answer 2

Modulation index, $\mu = \frac{A_m}{A_c}$
Side band frequencies are
USB = $\upsilon_c + \upsilon_m,$ LSB = $\upsilon_c - \upsilon_m$
Here, $A_m = 10 \, V , A_c = 20 \, V$
$\upsilon_c = { 1 \, NHz = 1000 \, kHz ,} \upsilon_m = { 10 \, kHz}$
$\therefore \:\:\:\: \mu = \frac{10}{20} = 0.5$
${USB = 1000 + 10 = 1010 kHz }$
${LSB = 1000 - 10 = 990 kHz}$