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If transmitter bandwidth is doubled in FM, then SNR is 
1. also doubled
2. improved four fold
3. decreased by one fourth
4. unaffected

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Correct Answer - Option 3 : decreased by one fourth

We have output \(\rm SNR\) of an FM system is:

\(\rm {\left( {\frac{S}{N}} \right)_o} = 3{\left( {\frac{{\Delta f}}{f}} \right)^2}.{S_X}.\gamma\)

where \(\rm \gamma = \frac{{{S_i}}}{{\eta B}}\) is \(\rm SNR\) of baseband system or channel signal to noise ration.

As for baseband \(\rm {S_o} = {S_i}\left( {\therefore \frac{{{S_o}}}{{\eta B}} = \frac{{{S_i}}}{{\eta B}}} \right)\).

Carson's rule: Bandwidth of FM BWFM = 2 [ Δf + fm ].

fm is doubled then, the bandwidth is also doubled and hence according to the relation, we can see that the 

SNR is decreased by one fourth. 

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