$E_{am}=A_c(1+\mu \sin \omega_m t) \sin(\omega_c t)$

$A_c(1+\mu \sin \omega_m t) \rightarrow$ Amplitude of amplitude modulated wave

$\omega_m t \rightarrow$ Angular frequency of modulated wave (messege signal)

$\omega_c \rightarrow$ Angular frequency of carrier wave

$\mu_ = \frac{A_m}{A_c}$ $=\frac{\text{Amplitude of modulated wave}}{\text{Amplitude of carrier wave}}$

for $\mu \leq 1$

Wave is nicely modulated, message signal is not distorted while modulation process

Over modulation

For $A>1$

Messege (information) signal is distorted

In reverse bias $\rightarrow$ PN junction behaves as open circuit

We select $R_s$ such that the time constant $R_s C$ is very small $(<<\frac{1}{f})$ for charging of capacitor $V(t)=V_0(1-e^{-t/Rc})$

Rc $\rightarrow$ time constant

We need the capacitor to discharge slowly. R.C should be large

What happens when the amplitude modulated wave is passed through this circuit?

(1) $R_s C$ is very small $(<< \frac{1}{f})$

(2) $R_L C$ is very large $(>> \frac{1}{f})$

Amplitude modulated wave

$C_m(t)=A_c(1+ \mu \sin \omega_m t) \sin \omega_c t$

After rectifier circuit + smoothening filter

we get

$V(t)=A_c (1+ \mu \sin \omega_m t)$

$V(t)=A_c + A_c \mu \sin \omega_m t)$

$A_c \rightarrow$ DC part due to amplitude of carrier wave

$A_c \mu \sin \omega_m t) \rightarrow$ Original message signal

We get d.c. + original message $\mu = \frac{A_m}{A_c}$

We pass this through a capacitor to black the dc

At output we get the message signal

$(A_c + A_m \sin \omega_m t) \xRightarrow{Capacitor} A_m \sin(\omega_m t)$ Original Signal

After If stage + Reciever $\rightarrow$ Amplifier $\rightarrow$ Reciever of information