physics-class-12-unit-08-chapter-01-detection-of-amplitude-modulated-waves-l-1-4-wxnd-wbovly

### <Success style="font-size:25px"> Detection Of Amplitude Modulated Waves L-1 </Success>
### <primary style="font-size:24px"> Amplitude Waves </primary>
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* $E_{am}=A_c(1+\mu \sin \omega_m t) \sin(\omega_c t)$

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

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

* $\omega_c \rightarrow$ Angular frequency of carrier wave

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<footer style = "font-size: 18px"> $\rightarrow$ Detection of Amplitude Modulated Waves $\rightarrow$ <span style = "color:blue"> Amplitude Waves </span> $\rightarrow$ Amplitude Modulated Index $\rightarrow$ Amplitude Modulated Wave </footer>

### <Success style="font-size:25px"> Detection Of Amplitude Modulated Waves L-1 </Success>
### <primary style="font-size:24px"> Amplitude Modulated Index </primary>
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- <span style="color:green">In forward bias</span> $\rightarrow$ PN junction behaves as a short circuit

- <span style="color:green"> In reverse bias</span> $\rightarrow$ 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 $V(t)=V_0(1-e^{-t/Rc})$

- <span style="color:blue">Rc $\rightarrow$ time constant</span>

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

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<footer style = "font-size: 18px">Amplitude Modulated Index $\rightarrow$ Amplitude Modulated Wave $\rightarrow$ <span style = "color:blue"> Amplitude Modulated Index </span> $\rightarrow$ Amplitude Modulated Index $\rightarrow$ Amplitude Modulated Index </footer>

### <Success style="font-size:25px"> Detection Of Amplitude Modulated Waves L-1 </Success>
### <primary style="font-size:24px"> Amplitude Modulated Index </primary>
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- 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 $(>> \frac{1}{f})$

- <span style="color:green">Amplitude modulated wave</span>

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

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<footer style = "font-size: 18px">Amplitude Modulated Wave $\rightarrow$ Amplitude Modulated Index $\rightarrow$ <span style = "color:blue"> Amplitude Modulated Index </span> $\rightarrow$ Amplitude Modulated Index $\rightarrow$ Amplitude Modulated Index </footer>

### <Success style="font-size:25px"> Detection Of Amplitude Modulated Waves L-1 </Success>
### <primary style="font-size:24px"> Amplitude Modulated Index </primary>
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* 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 $\mu = \frac{A_m}{A_c}$

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<footer style = "font-size: 18px">Amplitude Modulated Index $\rightarrow$ Amplitude Modulated Index $\rightarrow$ <span style = "color:blue"> Amplitude Modulated Index </span> $\rightarrow$ Amplitude Modulated Index $\rightarrow$ Thank You </footer>

### <Success style="font-size:25px"> Detection Of Amplitude Modulated Waves L-1 </Success>
### <primary style="font-size:24px"> Amplitude Modulated Index </primary>
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* 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

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