Correct Answer - Option 4 : (a) and (d)
Concept:
General equation of FM modulated signal is expressed as:
(S)FM = AC cos [ωct + kf ∫m(t) dt]
m(t) = Modulating signal
kf = Frequency sensitivity (Hz/volt)
ωc = Carrier frequency (rad/sec)
Ac = Carrier Amplitude
Total peak to peak voltage = 2Ac
Also, the frequency deviation in FM is defined as:
Δf = |kf.m(t)|max
Calculation:
Given 2AC = 1.2
So the peak voltage is:
Ac = 0.6 volts
Option (a) is therefore correct.
Given frequency deviation Δf = 10 kHz
Since m(t) is a sin wave with 0.6 V as peak amplitude, frequency deviation can be written as:
⇒ (kf)(0.6) = 10 kHz
\( \Rightarrow {k_f} = \frac{{10}}{{0.6}}\;\frac{{kHz}}{{Volts}}\)
The detector, however, senses voltage or ampere per Hz or rad/sec. It is therefore expressed as Volts/Hz
Taking the reciprocal of frequency sensitivity we get the detector sensitivity (D) as:
\(D = \frac{{0.6}}{{10}}\frac{{Volts}}{{kHz}}\)
D = 60 μV/Hz
Hence both Option (a) and (d) are therefore correct.