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## Q. 1.1.18

Consider the amplitude modulated (AM) signal $A_{c} \cos \omega_{c} t+2 \cos \omega_{m} t \cos \omega_{c} t$ . For demodulating the signal using envelope detector, the minimum value of $A_{ c }$ should be

(a) 2                                           (b) 1

(c) 0.5                                        (d) 0

## Verified Solution

Modulated signal

\begin{aligned}\phi_{A M}(t) &=A_{C} \cos \omega_{c} t+2 \cos \omega_{m} t+\cos \omega_{c} t \\&=\left( AC +2 \cos \omega_{ m } t\right) \cos w_{ c } t\end{aligned}

Condition for envelope detection of an Aμ signal is

\begin{aligned}&= A +2 \cos \omega_{ m } t \geq 0 \\&A_{ C }-2 \geq 0 \\&A_{ C } \geq 2\end{aligned}

Therefore, minimum value of $A_{C}$ should be 2.
Hence, the correct option is (a).