A message signal is used to modulate a carrier frequency. If the peak voltages of message signal and carrier signals are increased by 0.1% and 0.3% respectively, then

Options

A. 0.4
B. `0.0`
C. `-0.4`
D. `-0.2`

Answer

D

Explanation

We know that, the modulation index is given by
`mu=A_(m)/A_(c)` ...(i)
where, `A_(m)=` maximum amplitude of massage signal and `A_(C)=` maximum amplitude of Carrier-signal.
Given, `A_(m)=` and `A_(C)` are increased by 0.1 % and 0.3 % then the modulation index becomes,
`mu_(1)=(A_(m)+0.001 A_(m))/(A_(C)+0.003 A_(C))`
`=(1001 A_(m))/(1003 A_(C))=1001/1003 mu" "`[From Eq. (i)]
`implies mu_(1)/m=1001/1003`
The percentage change in modulation index,
`=(mu_(1)-mu)/muxx100`
`=(1001-1003)/1003xx100`
`=-2/1003xx100=-0.2 %`