Write short notes on:
The second method of the non-coherent AM detection is Envelope Detector. In this circuit modulated signal Vin(t) is used as an input signal. The source resistance RS is connected in series with the active non-linear p-n junction diode. Two passive elements of capacitor C and load resistance RL at the output end are connected in parallel configuration as like LPF. The circuit diagram of the ‘Envelope Detector’ is given bellow.
Figure 1 Envelop detector circuit
Let us consider an AM waveform Vc(t) = Ac [1 + max(t)]cos2πfct. The carrier signal frequency fc is very much larger than the modulating signal frequency fm and it is also assumed that the value of modulation index ma ≤ 1. Figure 2(a) shows the modulated signal with under modulation configuration which is applied at the input of the ‘Envelope Detector’ circuit.
 Under modulation.png)
Figure 2(a)
 Across capacitor.png)
Figure 2(b)
 After filtering Of Envelope.png)
Figure 2(c)
Figure 2(a) Modulated signal with m1 < 1 (b) Output of the envelope detector for the variation of RLC and (c) Recovered message signal after filtering.
Working Principle of the circuit:
The junction diode is forward biased when +ve half cycle of the modulated signal is transmitted and for –ve half cycle diode goes to reverse bias and no signal is transmitted through it. The diode offers zero resistance at forward biased configuration and infinite resistance at reverse biased configuration. At forward biased condition capacitor C charges up rapidly up to the peak value of the input signal. After the +ve half cycle, –ve half cycle come up and diode goes to reverse biased. At that time input signal voltage is less than the output signal voltage of the diode and capacitor C discharges through the load resistance RL. The voltage across the capacitor becomes less for the discharging mechanism. The discharge process is continuing until the next peak is come up. At the condition, when the voltage across the capacitor is less compare to the input signal of the diode, the capacitor again charges up and the process is repeated in circular motion.
We assumed that the charging time constant RSC is very small compared to the time period of the carrier signal and discharging time constant RLC is too large to ensure that capacitor discharge slowly through the load resistance RL between the two +ve peak of the carrier signal. On the other hand it is also remember that the discharging time constant not equal to the maximum rate of change the peak value of the modulating signal.
Hence we can write RSC ≪ 1/fc and RSC ≪ 1/fc ≪ RLC ≪ 1/fm.
Here fc and fm are the carrier frequency and maximum frequency component of the modulating signal.
The waveform at the output of the envelope detector and desired signal after filtered out at the receiving end of the circuit are given in Figure 2(b) and (c).
What is the function of delay time?
State and prove the Parseval’s theorem for power.
What is strip line?
State Channel capacity theorem
