A phase modulated wave can be generated from frequency modulator by connecting a _ before the modulator and a frequency modulated wave can be generated from phase modulator by connecting a before the modulator.

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HPCL Engineer Instrumentation 11 Aug 2021 Official Paper

Answer 1

The output of FM modulator is of form

$s (t) = A_{c} \cos (ω_{c} t + k_{f} \int_{- m}^{t} m (τ) d τ)$

After passing the modulating signal through the differentiator we give $\frac{d}{d t} m (t)$ as the input to the frequency modulator, i.e.

sdfs

The expression of the output signal will be:

$s (t) = A_{c} \cos (ω_{c} t + \frac{d}{d t} (k_{f} \int_{- m}^{t} m (τ) d τ))$

The differentiation of the integral will simply give the original signal.

We get a phase modulated signal which is of the form:

$s (t) = A_{c} \cos (ω_{c} t + k_{p} m (t))$