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Square Law Modulator and AM generation using Analog Multiplier | Generation of AM signal - YouTube
Channel: ALL ABOUT ELECTRONICS
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Hey friends, welcome to the YouTube channel
ALL ABOUT ELECTRONICS.
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So, if you have followed the previous video
then we have discussed various aspects of
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the Amplitude Modulation.
So, in this video, we will see the different
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techniques for generating this AM wave.
Now, there are three different ways by which,
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we can generate this AM wave.
The one is using the analog multiplier, while
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the second technique is using the non-linear
device.
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And this modulation technique is known as
the square law modulator.
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Then the third method of generation is known
as the Switching Modulator.
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So, in this video, we will talk about the
first two methods.
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And we will learn about the switching modulator
in the next video.
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So, let's say, this m(t) is the message signal.
And this Ac cos (2*pi*fc*t) or Ac cos (wct)
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is the carrier signal.
So, as we have discussed in the previous video,
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if we add some offset Ac to this message signal
and multiply that signal with the carrier
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signal, that is cos (wct) then we can generate
this AM wave.
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And here, this multiplication can be achieved
using the analog multiplier.
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Then the second way is, using this analog
multiplier we can multiply the message signal
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and the carrier signal.
And then this carrier signal can be added
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with this multiplied signal.
Now, usually during this AM generation, this
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message signal also gets multiplied by some
constant factor.
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So, typically, the modulated output would
be of this form.
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And if we take this Ac cos (wct) outside,
then we can write this same expression in
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this way.
So, this is another way to express this AM
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signal.
And in fact, in many textbooks, this amplitude
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modulated wave is expressed in this format.
And practically also, when we generate this
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AM wave, using any of this method, then the
message signal usually gets multiplied by
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some constant.
So, in such case, this expression is more
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meaningful.
And here this Ka is known as the amplitude
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sensitivity.
So, if we compare this expression with the
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earlier expression, then in the earlier expression,
this Ka is equal to 1/Ac right !!
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So, these are the two different ways by which
the AM signal can be represented.
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Alright, so now let's see, how we can generate
this AM signal using the multiplier IC AD
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633.
So, this is the functional block diagram of
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the analog multiplier IC.
And here, one input is applied between the
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X1 and X2. While the second input is applied
between Y1 and Y2.
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And for the addition, we can apply the third
input over here.
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So, if we see the output w, then it can be
expressed as (X1 - X2) (Y1- Y2)/ 10 + Z.
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Now, here let's say, this X is the message
signal, while the Y is carrier signal.
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That is equal to Ac cos (wct)
And if we apply the same carrier signal as
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Z, then we can generate the AM wave.
So, in that case, the modulated output, s(t)
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can be given as m(t) Ac cos (wct)/ 10 + Ac
cos (wct)
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And if we take this Ac cos (wct) outside,
then we can write this expression as Ac [ 1
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+ m(t)/ 10] cos (wct)
So, here we can say that amplitude sensitivity,
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that is Ka is equal to 1/10
So, in this way, we can generate this linear
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amplitude modulated signal using this multiplier
IC.
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Alright, so now let's talk about the second
method.
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That is a square law modulator.
So, in this square law modulator, a non-linear
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device or circuit is used to generate this
modulated output.
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And any device, which has non-linear V-I characteristics,
can be used as a non-linear device.
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So, as you are aware, a diode or a transistor
can be used as a non-linear V-I characteristic.
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And because of that, they can be used as a
non-linear device.
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For example, if we apply this input voltage
to the diode and passes the diode current
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through the load resistor R, then the output
voltage across the load would be of this form.
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So, as you can see, it contains the second
order, third order, or even higher-order terms.
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But when this input Vin is very small then
the higher-order terms can be neglected.
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And in that case, we can consider this equation
up to second-order terms.
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So, here because of the square-law characteristic
of the non-linear device, it is possible to
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generate the modulated output.
And hence this type of modulator is known
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as the square-law modulator.
So, in this type of modulator, the input signal
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is the summation of the message signal and
the carrier signal.
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And that signal is applied to the non-linear
device.
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And the output of the non-linear device is
then applied to the bandpass filter.
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So, this filter passes only the required frequency
components and at the output of the bandpass
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filter, we will get the desired modulated
output.
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So, this is the general overview of the square
law modulator.
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But now, let's understand, how this modulated
output is generated.
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So, as I mentioned, even a diode or transistor
can act as a non-linear device.
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Because if you are aware, the diode has non-linear
V-I characteristics.
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And the non-linear relationship between the
current and the voltage can be given by this
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Shocklyes equation.
So, although, the diode has this exponential
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characteristics but during the certain region
of operation, it behaves like a square-law
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device.
For example, when the diode is biased over
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here, and on top of it, when we apply the
small input signal, then it can be used as
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a square-law device.
That means in that case, the input to the
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diode that is Vd is equal to Vdo + Vin (t).
Where this Vdo is the DC biasing voltage,
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and this Vin(t) is the input signal.
Now, when we expand this diode current using
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Taylor's series around this Vdo, then we can
write this diode current Id as, a1*vin + a2*vin^2
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+ a3*vin^3 +---- so on.
Now, when this applied input signal is very
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small, then we can neglect the higher-order
terms.
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And when this diode current is passed through
the load resistor, then the voltage across
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the load or the output voltage will follow
this relationship.
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That means the output of the non-linear device
will be given by this expression.
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Now, as I said, this Vin (t) is equal to m(t)
+ Ac cos (wct) right !!
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So, here, the output of this non-linear device
can be given as a* Vin (t), that is a * [ m(t)
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+ Ac cos (wct)] + b* [ m(t) + Ac cos (wct)]^2
That
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is equal to a * [ m(t) + Ac cos (wct)] + b*
m^2(t) + 2b*Ac*m(t) cos (wct)+ b*Ac^2 cos^2(wct).
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So, if we expand all these terms, then we will get this expression.
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Now, here if you
see these two terms, then they are of our
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interest.
Because these two terms will give us the AM
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signal.
So, let's write these two terms separately.
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That is equal to a*Ac cos (wct) + 2b*Ac*m(t)
cos (wct)
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Or further if we simplify it, then we can
write it as, a*Ac*[ 1 + (2b/a)*m(t)] cos (wct)
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so, if we compare this expression, with the
standard amplitude modulated signal, then
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we can say that here this amplitude sensitivity
or Ka is equal to 2b/a.
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Now, here to get this signal, first of all,
we need to remove all other components.
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And that can be done using the bandpass filter.
And to understand that, first of all, let's
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see the frequency spectrum of all these terms.
So, here, let's say the frequency spectrum
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of the message signal is equal to M(f).
And this message signal contains the maximum
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frequency up to B.
Now, if we see the spectrum of all these components,
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then it can be shown like this.
So, here this term is the frequency spectrum
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of m(t).
While the frequency spectrum of this m^2(t)
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will vary from 2B to -2B.
Now, when this message signal gets multiplied
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with the carrier signal, then the entire spectrum
of the message signal will get shifted to
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the frequency plus-minus fc.
And along with that, we will also get the
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discrete frequency component at the frequency
plus-minus fc.
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And because of this term, we will get the
frequency component at plus-minus 2fc.
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So, here we are interested in this portion
of the spectrum.
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And this portion can be recovered using the
bandpass filter.
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And here for the simplicity, let me just show
you only a positive spectrum.
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So, here the band-pass filter should be designed
in such a way that, its center frequency is
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around fc.
And the passband of this bandpass filter should
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be at least equal to 2B, so that, we can filter
out the desired spectrum.
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Apart from that, we also need to make sure
that, the passband of the filter does not
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overlap with any other frequencies.
Or in this case, if you see, this fc - B should
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be much greater than 2B.
Or from this, we can say that this carrier
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frequency fc should be much greater than 3B,
right !!
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So, while designing this bandpass filter,
we also need to keep this thing in mind.
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So, in this way, using the square law modulator,
it is possible to generate the AM wave.
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Now, here, since the amplitude of the AM signal
is very small, so we need to amplify it using
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the pre-amplifier and the amplifier.
So, this is all about the square law modulator.
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And in the next video, we will learn about
the switching modulator.
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So, if you have any questions or suggestions,
do let me know here in the comments section
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below.
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