Amplitude Demodulation - Free MCQ Practice Test with solutions, GATE ECE

Modulation:
The process in which the characteristics of carrier signal is varied in accordance with baseband message signal to make bandpass signal.
Sampling :
The process of conversion of continuous time signals into discrete time signal.
Encoding :
The process of putting the message in the form in which it is to be communicated.
ex: Analog signal into digital form.
Demodulation :
The process of recovery of message signal from modulated signal.
Hence correct option is "3".

• Signals from various radio stations reaching the receiver input are not of the same strength. Signals from the strong stations are strong and those from weak stations are weak.
•  If the receiver gain is constant, then the receiver output will fluctuate proportionally to the strength of the input signal.
• This is not desirable. ∴ The automatic gain control (AGC) is used to adjust the receiver gain. automatically so as to keep the receiver output constant irrespective of the strength of the input signal.

Automatic Gain Control (AGC):

• Automatic gain control (AGC) works in FM radio transmitter/receiver that maintains Automatic controlling of weak and strong signals which is received by the radio receiver.
• The automatic frequency control voltage of the FM transmitter VCO is DC voltage.
• AGC maintains a constant level of the output signal based on the received signal nature, i.e. it maintains the same volume of the output when stations of different strengths are received.
• AGC adjusts the gain of RF and IF amplifiers according to need.
• AGC can handle problems like overloading and fading in the receiver.

For envelope detector, the time constant must satisfy the following relation:

For the good performance of the envelope detector:
Application:
Given:
f_m = 10 kHz
modulation index (μ) = 0.6
From (1), we get

= 0.02 msec
Derivation of RC time constant formula for the envelope detector: )
For the output of the envelope detector to closely follow the modulating signal, the slope of v_o is always greater than that of the envelope of AM signal input.
The output v_o is the voltage across the capacitor which is exponentially decaying

Neglecting higher power terms as RC>>t

For successful detection, the rate of discharge of the capacitor i.e. magnitude of the slope of v₀(t) must be more than that of the envelope
The envelope of the AM signal is 
The slope of the message signal

The slope of output voltage

For DETECTION slope of capacitor voltage should be always more than the envelope of AM signal

RC must be less than the minimum of R.H.S.

Conventional AM signals are easily demodulated by an envelope detector.
It consists of a diode and an RC circuit, which is a simple low-pass filter as shown:

• During the positive half-cycle of the input signal, the diode conducts and the capacitor charges up to the peak value of the input signal.
• When the input falls below the voltage on the capacitor, the diode becomes reverse-biased and the input disconnects form the output.
• During this period, the capacitor discharges slowly through resistor R.
• On the next cycle of the carrier, the diode again conducts when the input signal exceeds the voltage across the capacitor.

The time constant given by RC must be selected to follow the variations in the envelope of the modulated signal.

• If RC is too large, then the discharge of the capacitor is too slow and the output will not be able to follow the envelope.
• If RC is too small, then the output of the filter falls very rapidly after each peak and will not follow the envelope closely.

This is explained by the given figure:

So, for the good performance of the envelope detector:
\(\frac{1}{\omega_c}<

For demodulation of Am using envelope detector the time constant of circuit is given by

ω  → Bandwidth of the message signal
Application
The message signal can be rewritten as:
10 (1 + 0.6 cos (2π × 10³t)) cos (2π × 10⁵ t)
here
f_c = 10⁵ Hz
f_m = 10³ Hz

10⁵ < R < 10⁷
10 kΩ < R < 10 MΩ 

• AM detector employs envelope detector which is the low pass filter
• The output of the envelope detector follows the envelope of the message signal

• The envelope detector is used when the modulation index is ≤ 1
• When modulation index is greater than 1, then synchronous detection is used

Envelop detector is used to track the peak amplitude of the message signal.
A cos 2π fct + B sin 2π fct



Peak amplitude =  
= output of envelope detector

The impulse response of a Hilbert transformer is given as:

The Fourier transform representation is:
H(f) = -j sgn(f)
|H(f)| = 1
Application:
Fourier transform of a standard rectangular pulse is given as:

For the given input signal, the Fourier representation will be:

Using Parseval's theorem, the energy is calculated as: