Generation of AM Signal
The circuit that generates the AM waves is called as
amplitude modulator. Basically there are two such
modulator circuits namely :
1. Square Law Modulator
2. Switching Modulator
Both of these circuits use a non-linear elements such
as a diode for their implementation . Both these
modulators are low power modulator circuits .
Square Law Modulator
Generation of AM Waves using the square law
modulator could be understood in a better way by
observing the square law modulator circuit shown in
the following figure .
Nonlinear
m(t) device
Ac cos ωct
~ V0
It consists of the following :
1. A non-linear device
2. A bandpass filter
3. A carrier source and modulating signal
The modulating signal and carrier are connected in
series with each other and their sum V1(t) is applied at
the input of the non-linear device, such as diode,
transistor etc.
When a nonlinear element such as a diode is suitably
biased and operated in a restricted portion of its
characteristic curve i.e. signal applied to the diode is
relatively weak, we find that the transfer characteristic
of the diode load resistor combination can be
represented closely by a square law. Thus,
…………(1)
The input output relation for non-linear device is as
under :
……………….(2)
where a and b are constants.
Now, substituting the expression (1) in (2), we get
Or,
Or,
The five terms in the expression for V2(t) are as under :
Term 1: ax(t) : Modulating Signal
Term 2 : a Ec cos (2π fct ) : Carrier Signal
Term 3 : b x2 (t) : Squared modulating Signal
Term 4 : 2 b x(t) cos ( 2π fct ) : AM wave with only
sidebands
Term 5 : b Ec2 cos2 (2π fct ) : Squared Carrier
Out of these five terms, terms 2 and 4 are useful
whereas the remaining terms are not useful .
Let us club terms 2, 4 and 1, 3, 5 as follows to get ,
The LC tuned circuit acts as a bandpass filter . This
bandpass filter eliminates the unuseful terms from the
equation of v2(t) .
Hence the output voltage vo(t) contains only the useful
terms .
Or,
Therefore ,
……….(3)
Comparing this with the expression for standard AM
wave i.e.
,
We find that the expression for Vo(t) of equation (3)
represents an AM wave with m = (2b/a) .
Switching Modulator
The switching modulator using a diode has been shown
in the following figure.
This diode is assumed to be operating as a switch . The
modulating signal x(t) and the sinusoidal carrier signal
c(t) are connected in series with each other. Therefore,
the input voltage to the diode is given by:
The amplitude of carrier is much larger than that of x(t)
and c(t) decides the status of the diode (ON or OFF ) .
Let us assume that the diode acts as an ideal switch .
Hence, it acts as a closed switch when it is forward
biased in the positive half cycle of the carrier and offers
zero impedance . Whereas it acts as an open
switch when it is reverse biased in the negative half
cycle of the carrier and offers an infinite impedance.
Therefore, the output voltage v2(t) = v1(t) in the
positive half cycle of c(t) and v2(t) = 0 in the negative
half cycle of c(t) .
Hence , v2(t) = v1(t) for c(t) > 0
v2(t) = 0 for c(t) < 0
In other words , the load voltage v2(t) varies
periodically between the values v1(t) and zero at the
rate equal to carrier frequency fc .
We can express v2(t) mathematically as under :
….(4)
where, gp(t) is a periodic pulse train of duty cycle equal
to one half cycle period i.e. T0 /2 (where T0 = 1/fc) .
Let us express gp(t) with the help of Fourier series as
under :
….(5)
…(6)
Substituting gp(t) into equation (4), we get
Therefore,
..(7)
The odd harmonics in this expression are unwanted. So
they can be eliminated.
The second and third terms together represents the
AM wave . Clubing the second and third terms together
, we obtain
This is the required expression for the AM wave with
m=[4/πEc] . With the help of a Band Pass filter (BPF)
only the 2nd and the 3rd components of the above
expression are allowed to pass attenuating all other
components.
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Detection or Demodulation of AM Wave
The process of recovering the message signal from the
received modulated signal is known as demodulation .
This process of detection is exactly opposite to that of
modulation .
Types of Demodulation
There are two types of AM detectors or demodulators
such as :
1. Square Law Demodulation
2. Envelope Demodulation
Square Law Demodulation
The block diagram of square law demodulator is shown
in the following figure.
Square Law Demodulator
Working Operation and Analysis
The input output characteristics i.e., the transfer
characteristics of a square law demodulator is non-
linear and it is expressed mathematically as :
……(1)
where, v1(t) = input voltage to the detector = AM wave
As we know,
Now, substituting for v1(t) in equation (1) , we get
……….(2)
But,
Therefore,
Substituting this, we get
Out of these terms, the only desired term is bEc2 mx(t).
This desired term is extracted by using a low pass filter
(LPF).
Hence, we get
vo (t) = ( bEc2m ) x(t) ……………………….(3)
This means that we have recovered the message signal
x(t) at the output of the detector .
Envelope Demodulation
The envelope demodulator is a simple and very
efficient device which is suitable for the detection of a
narrowband AM signal.
An envelope demodulator produces an output signal
that follows the envelope of the input AM signal
exactly .
Circuit Diagram
The envelope demodulator consists of a diode and RC
filter .
Working Principle
The standard AM wave is applied at the input of the
demodulator . In every positive half cycle of the input,
the demodulator diode is forward biased and charge
the filter capacitor C connected across the load
resistance R to almost the peak value of the input
voltage. As soon as the capacitor charges to the peak
value, the diode stop conducting.
The capacitor will now discharge through R between
the positive peaks as shown in the figure. The
discharging process continues until the next positive
half cycle. When the input signal becomes greater than
the capacitor voltage, the diode conducts again and
the process repeats itself .
Waveforms
The input-output waveforms for the envelope
demodulator is shown in the above figure. It shows the
charging discharging of the filter capacitor and the
approximate output voltage .
Here we have assumed that the diode is ideal and the
AM wave applied to the input of the demodulator is
supplied by a source having internal resistance Rs .
The capacitor charges through D and Rs when the diode
is on and it discharges through R when the diode is off.
The charging time constant RsC should be short
compared to the carrier period 1/fc .
Thus, RsC << 1/fc
On the other hand, the discharging time constant RC
should be long enough so that the capacitor discharges
slowly through the load resistance R .
Therefore, 1/fc << RC.
