The signal $\backslash ($ y$($t$)\backslash )$ at the PLL output therefore presents a variation proportional to the variation $\backslash (\backslash$Delta $\backslash$mathrm$\{$m$\}\backslash )$ of the modulating signal. So if the modulating signal varies slowly enough for the PLL to reach its permanent speed at any time, we have indeed a demodulation of the FM signal.

In practice, we insert a low$-$pass filter into the action chain of the PLL which allows its performance to be adjusted $($response time, gain, overshoot, etc.$)$

Exercise $1$:

Determine :

$1.$ the expression of its instantaneous frequency $\backslash ($ f$($t$)\backslash )$

$2.$ the frequency f $,$ of the carrier

$3.$ the frequency $\backslash ($ F $\backslash )$ of the modulating signal

$4.$ The $\backslash (\backslash$Delta f $\backslash )$ frequency deviation

$5.$ the modulation index $\backslash ($ m $\backslash )$

$6.$ the appearance of the spectrum of the modulated signal

$7.$ its spectral size B

$8.$ its power for antenna with resistance $\backslash ($ R$=50\backslash$Omega $\backslash )$