第 14 讲：幅度调制演示
本讲内容：利用信号发生器、示波器和频谱分析仪演示信号的时域与频域表示；用乐音演示时间与频率尺度变换；以正弦波、三角波和方波为载波演示幅度调制；从时域和频域观察调制度变化的影响；演示调幅（AM）收音机中的幅度调制信号。
授课教师：艾伦·V. 奥本海姆教授；桑迪·希尔教授
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PROFESSOR: Well, today, we have a chance to put away the
equations and have some fun.
With me is Professor Sandy Hill from the University of
Massachusetts at Amherst.
And Sandy, maybe you could just give us a quick tour of
what we have here.
SANDY HILL: OK.
We'll be dealing with about four instruments today.
Two of them generate signals, and two of them display and
analyze signals.
The first, and perhaps simplest, is simply an RC
audio generator, that will put out a variety wave shapes.
And we'll look at that in a moment.
Over to the right is a device that will allow us to study
amplitude modulation and the various flavors of it.
Down below is a standard oscilloscope to look at the
signals in the time domain so we can see their shape.
And then, finally the spectrum analyzer will analyze the
signal into its Fourier components.
And we'll display those, so you get to see the spectral
content of a signal.
PROFESSOR: Now, we'll be seeing all of these in a fair
amount of detail as we go through the demonstrations.
But maybe we can begin just with the signal generator.
SANDY HILL: OK, let's look quickly at the
various buttons involved.
There's a lot of flexibility with this device.
The top three buttons here allow us to change from one
simple wave form to another one, a sine wave, a triangle
wave, a square wave.
And right below it is a button that will allow us to change
the size of the signal.
Moving over towards the left, we can change the DC offset
which varies the signal, the level upon
which the signal rides.
PROFESSOR: And we'll be using that actually when we
demonstrate amplitude modulation.
SANDY HILL: That's right And then finally, there's a way of
changing the frequency of the signal, either changing it by
a factor of 10 or a vernier adjustment, if you want very
specific adjustments, very delicate changes.
PROFESSOR: OK.
So maybe we can just vary some of this and see what a little
bit of it looks like.
SANDY HILL: All right.
What we have displayed at this point is the effect of pushing
the sine wave button.
And so displayed down here is a 500 Hertz sine wave.
In fact, let's listen to that.
PROFESSOR: Great.
SANDY HILL: And the scope is said to have one millisecond
for each division here.
By varying the amplitude knob can make the sine
wave smaller or larger.
The ear isn't too sensitive to that.
By changing the DC offset, it simply rides
on a different level.
It's like putting a battery in series.
And changing the frequency, you get a very perceptible
change, a lower frequency.
It takes longer to sweep through a period.
Higher frequency, it takes a shorter amount of time.
And also, we can change the wave shape itself from a sine
wave to a triangle wave--
and you notice that has a richer sound to it--
and then finally to a square wave, which is an even
brighter sound.
PROFESSOR: And actually, as you realize from the previous
lectures, with the triangle and square wave with the same
fundamental as the sine wave, the richness comes in because
of the higher harmonics in the Fourier series representation.
OK, well let's go back to the sine wave.
And we'll use that to take a closer look at
the spectrum analyzer.
SANDY HILL: OK.
PROFESSOR: We'll look at a block diagram of the spectrum
analyzer shortly, but first let's just look at a few quick
things to get a feel for it.
We have, of course, the time domain
display of the sine wave.
And the spectrum analyzer gives us a frequency domain
analysis and display.
And the vertical axis is the amplitude.
The horizontal axis is frequency.
And as it's set currently, the frequency axis goes from DC--
zero--
up to 2 kilohertz.
And that, of course, can be varied on
the spectrum analyzer.
And since we have a sine wave input, we get, as we would
expect, a line spectrum, corresponding to the frequency
of the sine wave.
Now, in fact, we can measure that frequency because the
spectrum analyzer has a cursor associated with it, which I've
just enabled.
And this line is the cursor line.
There is a read out for the frequency and a read out for
the amplitude.
And let's position the cursor on the
frequency of the sine wave.
And we're getting close.
And there we are at the frequency of the sine wave.
And we can read out, in fact, that it's 500 cycles.
And this is the amplitude.
And, of course, you could verify the frequency also in
the time domain display, simply by measuring the
frequency or the period.
SANDY HILL: This is set at still one millisecond per
centimeter.
So that is 500 Hertz.
PROFESSOR: OK.
Well now maybe what we can do is vary the frequency.
Let's vary the frequency of the sine wave generator.
Maybe also listen to it?
SANDY HILL: I'll turn on the tone.
Yep.
OK, I'll make the frequency higher.
And you'll see a
correspondence in the time domain.
The frequency clearly goes up, and that line of the spectrum
also migrates up away from the cursor.
PROFESSOR: OK, and let me just point out again that this is
the cursor line.
This isn't the spectra line.
And this is the frequency content of the sine wave.
SANDY HILL: We can also change the amplitude of that line by
making the sine wave itself smaller.
And you notice the intensity of it goes--
PROFESSOR: While you do that, let me just position the
cursor if I can on the sine wave.
And now as you vary the amplitude, we should, in fact,
see this vary.
SANDY HILL: Well, that's right.
PROFESSOR: OK.
Now as Sandy varied the frequency, he did it slowly
and we saw the line move as a single line.
Maybe now, Sandy, you could vary the
frequency more rapidly.
And what will happen is that, in fact, what we'll get if I--
SANDY HILL: There'll be a spreading as we go--
PROFESSOR: Let me turn the cursor off.
And what we'll see is a spreading of the line, so that
the frequency content is richer.
And, in fact, the analysis of this is considerably more
complicated.
It corresponds to frequency modulation, where Sandy is now
the modulating signal.
SANDY HILL: That's right.
PROFESSOR: And we won't really be going into issues of
frequency modulation in any more detail in this
demonstration.
SANDY HILL: Right.
PROFESSOR: OK, well now let's go to the overhead projector
and take a look at a block diagram of
the spectrum analyzer.
The specific spectrum analyzer that we're using in the
demonstration is made by Rockland Systems, referred to
as the Rockland Systems Model FFT 512.
And basically, the idea is to sample the incoming wave form,
convert that into digital form, and then the spectrum,
in fact, is computed digitally using a microprocessor.
So the overall system block diagram first consists of a
system which is a low pass filter.
And this low pass filter is used in advance of the
sampling process to basically reduce the artifacts that are
introduced due to sampling.
And although we haven't talked yet about sampling and the
associated artifacts, basically, as we'll see in the
upcoming lectures, in order to sample a wave form and convert
it into digital form, it requires that the wave form
first be low pass filtered.
So this low pass filter is referred to-- and will be in
later lectures--
as an anti-aliasing filter.
And this low pass filtered wave form is then converted to
a sequence.
And so a sequence is generated for which the sequence values
are simply samples of the low pass filtered input.
This low pass filtered input is then put
into digital memory.
Basically, a time block of it is put into digital memory,
and so that's what we have down here.
Here is the sequence.
The sequence is put into digital memory.
And then an arithmetic processor computes for the
samples in this memory.
It computes the Fourier transform or the spectrum.
And after the spectrum is computed and put either into
the same or a different memory, that is then put
through a conversion process back to a continuous time
signal, and finally, put out on the display that we've been
seeing in the demonstration.
And so this is just indicative of the display.
So basically, the idea then is that the input
wave form comes in.
It's filtered and sampled and captured on a block basis, put
into a digital memory, and then, a digital computer or
microprocessor computes the Fourier transform.
And then that Fourier transform is what we see on
the display.
So what we're computing, of course, are samples of the
Fourier transform.
And so, for example, if the input-- let's say--
was a rectangular pulse whose Fourier transform is of the
form of a sine(x) over x function, what we would, in
fact, see on the display are samples of that at discrete
frequencies.
Or if as we have an input which is a square wave, what
will generate through the spectrum analyzer are the
Fourier series coefficients or equivalently, the harmonics
associated with the square wave.
OK, well, let's now go back to the equipment and look at the
spectrum analyzer.
We'll look at the square wave through the spectrum analyzer
shortly, but first what we have is what we saw before,
which is the sine wave.
And just to point out, again, the fact that the sine wave
spectrum, of course, is just a single line corresponding to
the fundamental frequency.
And here we have a frequency scale now that goes from 0 to
5 kilohertz.
And this is then the 500 cycle sine wave.
And, in fact, we can flip the cursor on and I happen to just
magically have it positioned correctly.
And we see that it's a 500 cycle sine wave.
SANDY HILL: Might be interesting, Al, to go and
look at a richer set of signals, such as the triangle
wave and the square wave-- things that are conveniently
on the signal generator itself.
I'll switch over to a square wave now.
And what you see is all the harmonics
coming up, being displayed.
PROFESSOR: OK, it's actually interesting to point out, I
think, that the square wave, as we know, is an
odd harmonic function.
And so, in fact, the even harmonics are missing in the
square wave.
So this is the fundamental.
This is the third harmonic, fifth harmonic, et cetera.
And then the amplitude of the square wave decays
proportional to 1 over f, which is the kind of analysis
that we've gone through in looking at Fourier series.
SANDY HILL: Right, and if we switch to the triangle wave,
instead of their decaying as 1 over f, the harmonics decay as
1 over f squared.
And you see they drop off much more quickly.
PROFESSOR: And again, of course, it's an
odd harmonic signal.
And so the even numbered harmonics are missing.
And maybe just to kind of emphasize the point, we can
show the sine wave again and the square wave again.
SANDY HILL: We'll go through from the most bland to the
richer to the richest.
PROFESSOR: OK, and it's really kind of
interesting and dramatic--
SANDY HILL: It's fun to do that.
PROFESSOR: --to see the harmonics pop in.
SANDY HILL: While we're at the square wave, let me fiddle
with the frequency of the square wave, and we can see
the duality of the time and frequency domains.
That is, as you compress things in the time domain,
such as this, going to a higher frequency square wave,
the harmonics wonder further away from each other.
SANDY HILL: So this is the fundamental.
The second harmonic is missing.
This is the third harmonic.
And of course, the fifth.
SANDY HILL: And as we take this to an extreme by going to
very low repetition rate square waves, all those
harmonics come scurrying in and cluster together near DC.
PROFESSOR: Kind of fun with Fourier transforms.
Well, speaking of time and frequency scaling, recall that
we had demonstrated time and frequency scaling previously
with the glockenspiel.
And what we had done there was to record a particular
glockenspiel note, and then we played that
back at half speed.
And what we had done in that case is expanded things in
time, consequently compress them in frequency.
And so, comparing that with a note an octave lower than we
saw that, in fact, the time scaling had led
to a frequency scaling.
And then we also played the same note back at twice speed.
And in that case, the frequencies were all scaled up
by a factor of 2.
And again, we illustrated that by comparing with the
glockenspiel note a full octave up.
Now when we did that, we didn't actually look at the
time wave forms or spectra.
And having the equipment that we have here gives us kind of
a nice opportunity to do that.
So what I have is the tape that we had originally made of
the glockenspiel, the original note that we recorded.
And what we'll do is look at the spectrum of that, and then
compare that spectrum when we play the tape at half speed
and also play it at twice speed.
So let's play the tape.
And what we have is the glockenspiel right now
displayed on a frequency scale from 0 to 5 kilohertz.
Let's just change that to zero to 10 kilohertz.
So here is this spectrum.
Over here we have the time wave form.
And here is then the first spectral line, and we can see
where that is by setting up the cursor.
And magically, once again, I have the cursor positioned at
just the right spot.
The first spectral line is at 1.775 kilohertz.
And so this is the spectrum then of the original
glockenspiel note.
All right.
Let's stop the tape and rewind it.
And now what we want to do is play that back at half speed.
Played at half speed, the frequencies
should be scaled down.
And, in particular then the first spectra line should be
at a lower frequency.
So let's play that now.
SANDY HILL: There are really very complicated signals,
aren't they?
PROFESSOR: They really are.
Here we have the first spectral line.
And we can compare that with the first spectral line that
we had before which was at 1.775 kilohertz.
And, once again, you see that the time wave form over here
has been scaled by a factor of 2.
So, once again, we see that time and frequency scaling
really works.
Incidentally as Sandy pointed out, and rightfully so, the
glockenspiel really is a pretty complicated signal, as
a graduate student and I found out when we were preparing the
original glockenspiel demo.
SANDY HILL: Speaking of complicated signals, one of my
favorites is to look at speech.
I set this up so that what's coming into my microphone is
indeed what you're going to see on the two screens.
The telephone company thinks of speech, basically in terms
of bandwidth, that it extends from about 300
Hertz to 3,300 Hertz.
But, as we'll see in the spectrum analyzer, there's a
lot of leakage outside of that.
The telephone company just filters out everything outside
of that and things of that as a speech signal.
So it doesn't have the high fidelity that you might have
on high fire equipment.
As we look at the scope, again, the time wave form is
extremely complicated, seems to have some periodicities in
it, although they're short-lived, and then it goes
on to some other periodic chunk.
And over in the frequency domain, you can see as we
extend from 0 to 10 kilohertz, that as I speak, there are
trenchants that have spectral content in them, covering that
entire band.
I can try some simpler signals.
A whistle is almost a sinusoid, but as you'll see
isn't terribly sinusoidal.
[HIGH-PITCHED WHISTLE]
That's the best I can do.
I can sing, a little bit embarrassedly, a B,
[HIGH-PITCHED]
Boo, and things like that.
PROFESSOR: They don't ask me to, Sandy.
SANDY HILL: And then different vowel sounds have a lot of
energy in, like the letter A. (SUNG) A. Whereas some of the
others are very impulsive, like--
[HISSING]
Or puh and tuh.
And it's a little hard to grab them at the right time.
But what's fascinating is just to stare at equipment like
this and try different speech sounds, and you begin to get
sort of a sense of the complicated nature of them.
PROFESSOR: OK, well that's a look at some spectra signals.
And now what we'd like to focus on is the modulator and
talk a little bit about modulation and demodulation
and demonstrate it.
And let's begin that by first taking a look at a block
diagram of the modulator system.
Well, as we've discussed in a previous lecture, amplitude
modulation basically consists of multiplying the modulating
signal by an appropriate carrier, illustrated here, as
we've seen previously, for the case of a sinusoidal carrier.
And then, specifically for sinusoidal amplitude
modulation, we may or may not inject some carrier signal--
A times the carrier.
Or equivalently, if we look at the modulated output, the
injection of the carrier is equivalent, mathematically, to
simply adding a DC offset or a constant to
the modulating signal.
And, as you recall when we talked about this, the idea of
injecting a carrier or not is related to the issue of
whether or not we want to do synchronous or asynchronous
demodulation.
The asynchronous demodulation corresponding to the simple
use of an envelope detector.
And to remind you of the wave forms that are involved,
again, I show two that we saw previously.
And for the case, this is for one value of the amount of
carrier that's injected.
And this is for an amount of carrier injected that's less.
And this, in fact, corresponds to what we refer to as 50%
modulation, and this is the case of 100% modulation.
Well, the modulating system that we're using in this
demonstration is basically of the form that
we're indicating here.
And a simple block diagram for it is more or less identical
to what we just saw.
Specifically, the modulating signal is
multiplied by the carrier.
And there also is the capability of injecting some
additional carrier, meaning adding it to the output of
this product.
And so the modulated output can have a variable percent
modulation--
the percent modulation being changed, depending on how we
set this variable gain.
Now, in addition to sinusoidal modulation--
in fact, for the particular system that we're using, we
have somewhat more flexibility.
We can use, in addition to a sinusoidal carrier at this
point, we can alternatively choose a square wave carrier
or a triangular carrier.
And, as we'll indicate in a moment when we illustrate
this, there are some specific advantages to using, for
example, a square wave carrier.
So this is a somewhat simplified version of--
or rather block diagram of the modulating system that we're
demonstrating.
The external modulating input here, a choice of carrier with
also the capability for injecting some additional
carrier into the output.
OK, now let's go back to the equipment and
take a look at this.
Well, Sandy, maybe to begin, you can just point out what
some of the controls are on the modulator box.
SANDY HILL: OK, there are some interesting
points to look at here.
This is an input for an external signal.
We'll be taking a signal right out of the signal generator
and putting it in here.
And that will be the signal that will be modulated,
according to the carrier.
The carrier is generated internally in this device.
And there are several ways of controlling it.
One is the amount of carrier injection.
One is the wave form of the carrier itself-- and this is
typically sinusoidal in the broadcast industry, but others
are interesting to look at as well.
The output that will be displaying on both the
spectrum analyzer and scope comes out here.
And then farther over to the left, there are some knobs for
changing the frequency of the carrier signal.
PROFESSOR: OK, let me also just point out again for
emphasis that changing the carrier level, as we've talked
about, is mathematically equivalent to changing the DC
level of the modulating signal.
And that's also what affects the percent modulation as we
had just discussed.
Now what we have set up is a sinusoidal modulating signal
and a sinusoidal little carrier.
And, as usual, we have the time wave form displayed here.
And so this is the modulated signal.
And then on the spectrum analyzer, we have
the spectral display.
And this is the carrier signal.
That's the carrier frequency.
And these side bands then correspond to the side bands
associated with the modulating signal.
So this is the spectrum of the total modulated output, right?
SANDY HILL: Right.
It's interesting to vary some of these parameters.
You can see the sinusoidal modulating
shape at this point.
Let me switch that to a triangular shape.
And, again, it's a little hard to sink in both the modulating
signal and the carrier, so you see the carrier kind of
wondering by, but there it is.
Another thing that can be varied is the amplitude of the
modulating signal.
I'll make it smaller--
you'll see the side bands go away--
until finally we have a pure sinusoidal carrier--
as I bring them back in.
Again, this is triangular.
There would be harmonics there that maybe they're a little
hard to see in the spectrum analyzer.
I'll go back first to a square wave modulating signal, which
is, again, you can see the square wave on top and one on
the bottom.
PROFESSOR: And so all of this, then, represents side bands.
Is that--
SANDY HILL: That's right.
Those are the side bands due to the square wave modulation.
Going back to the simplest, the sinusoidal carrier.
Another thing we can do is to vary the frequency of the
sinusoidal signal that's modulating it.
I'll make it higher.
And you'll notice that the side bands wander away from
the carrier signal in the spectrum.
The spectrum, the carrier signal of that, doesn't have a
frequency that's changing as I do this.
It's just the width of the band, due to
the modulating signal.
PROFESSOR: So this is the carrier.
And these are the side bands.
SANDY HILL: That's right.
Now as we go out very far, those side bands get gobbled
up by the carrier itself.
I'll come back to a nice reasonable point there.
PROFESSOR: OK, now, we can change also the carrier
frequency and, as Sandy's indicated, various parameters.
Now let me just point out, since I didn't previously,
that the frequency scale that we're looking at here is a
frequency scale out to 20 kilohertz.
And we had talked about-- or Sandy had indicated--
that we can change the carrier signal shape.
And let me change the carrier signal from a sine wave to a
square wave.
Now you haven't seen any change on this particular
display , but let me change the frequency scale.
And what you see now is the modulating signal showing up
around harmonics associated with the carrier.
And those harmonics will go away when we go back to a
sinusoidal carrier.
SANDY HILL: This is actually called a ring modulator.
It's very simple to multiply a signal by a square wave.
It's just a chopping process.
And so a square wave carrier signal is very
convenient to generate.
And then you simply filter out the higher order harmonics.
PROFESSOR: Right, I'll go back to the
scale that we had before.
And Sandy had also commented that we can
change the carrier level.
And let's do that on the modulator box.
We could do that either by changing a DC offset on the
modulating signal or by changing the amount of carrier
that's injected.
And as we decrease the amount of carrier, in fact, going
down to no carrier at all or almost no carrier.
That's suppressed carrier.
We have only the two side bands and the signal is now
highly over-modulated.
We bring the carrier back up and when we do that, then we
are reducing the percent modulation and simultaneously
obviously related to that is changing the carrier level.
Now I had indicated in previous lectures that
reducing the carrier is efficient in terms of power
transmission, but requires a synchronous demodulator,
whereas if there's carrier injected, as we have here, so
that we're not over-modulating--
the percent modulation is less than 100--
then because of the shape of the time wave form, as you can
see here, you can do the demodulation with a more or
less simple envelope detector.
And in fact, a envelope detector of the type that
we've talked about before is exactly what is used in AM
radios, because of the fact that it's so inexpensive.
And so here the power transmitted required is
higher, but the demodulator, based on using an envelope
detector, is considerably simpler.
Well, speaking of AM radios, what we'd like to now
demonstrate is modulation and demodulation with an AM radio,
which Sandy happens to have here.
And let's see, I guess, what you're going to do, Sandy, is
take it apart for us, right?
SANDY HILL: Right.
I've taken off the back.
And I'm just now going to slip out the guts of it all, and
try and set it up so you can see it conveniently, such as
right there.
PROFESSOR: Now, this is your daughter's radio that you
promised to give back.?
SANDY HILL: I would say was my daughter's radio.
And now let's start attaching clip leads, because what we're
going to want to do is to be able to see the signals coming
out of the radio.
We want to see both the audio and then the modulated signal
and try and see them on the oscilloscope.
So I'll start setting that up now.
PROFESSOR: OK.
Let me--
while you're doing that-- also just comment that the kind of
AM radio that we're looking at here is called a
superheterodyne receiver.
And the way that it does the demodulation is not exactly
the way we've talked about it in the lectures.
It's very close.
The idea is this the RF signal, the radio frequency
signal, first gets modulated down to what's called an IF
stage-- the intermediate frequency stage.
And then it's that signal that goes to an envelope detector
of the type we've talked about to generate
the demodulated signal.
So, I guess what Sandy has some probes on are the RF
input and a ground--
SANDY HILL: That's right.
The red lead here is a ground.
It's common for both the signals we'll be looking at.
This is at the audio.
We're actually looking at the signal going directly into the
speaker across these two leads.
And then this probe down here, which I found by hunting and
pecking, is the IF signal, the intermediate frequency signal,
with a station on it that I'll now try and get something that
sounds reasonable.
[RADIO FEEDBACK]
SANDY HILL: OK.
A little sports.
PROFESSOR: Never quite know what you're going to get when
you turn this on.
SANDY HILL: That's right, you don't.
Make some adjustments there.
And what you can see right here is the audio signal.
I'll give it a little bit more game.
And this is the actual intermediate frequency,
modulated by the audio.
And there's a correspondence between them that goes by
awfully fast, but I think it's pretty simple to see.
PROFESSOR: So basically the top trace is the envelope of
the bottom right.
SANDY HILL: That's right.
This is what comes out of the envelope detector.
And this is the signal into the envelope detector, in this
particular radio.
What I'd like to do for a last experiment is what we've been
doing at this point--
I'll turn this off for a moment--
is we're taking something that's coming in over the
airwaves, as they used to say, and we're simply viewing it.
What I'd like to do now is generate our own radio
frequency signal, tune it up so this radio is
going to hear it--
whatever that means--
and display it here.
What we're going to do then is use the audio oscillator,
along with the amplitude modulator.
And we're going to take from the output now the lead here.
And this will act as the antenna.
This device was not designed to put out a lot of power.
But fortunately we don't have a lot of distance to go over.
What I'm going to do is turn myself into an antenna--
I'm basically 150 pounds of salt water--
and when I touch this, the signal coming in here, which
is radiating a little from the wire, is going to suddenly
radiate from my whole body and hopefully will be enough
to be picked up.
So what I'll do is I'm going to turn this on--
excuse the noise.
Now I've set this up so it's tuned to a particular radio
station, and I hope I can find it now.
It takes a little fussing.
That's not it.
That sounds like it now.
OK.
PROFESSOR: So this gets billed as Sandy Hill, human antenna.
SANDY HILL: That's right.
What you're looking at here is I've got the antenna at this
point, and what we're going to do is you're
seeing the audio signal.
This is coming from the signal generator up here.
And this is the intermediate frequency signal again.
You can hear it's much stronger when my body becomes
the antenna.
And I'll leave it on for a second.
And I can switch to square wave--
doesn't look much like a square wave.
Various things.
There's significant distortion, because of all the
transformations that the signal is going through.
But it does indeed work, and we're picking up a frequency
that the radio is tuned to.
And that's it.
PROFESSOR: So Sandy has now been modulated and
demodulated.
SANDY HILL: That's right.
PROFESSOR: Well, hopefully, all the things that we've gone
through in the process of this tape and this set of
demonstrations gives you a feel for at least some of the
things that we've talked about so far in the course.
And Sandy, I'd really like to thank you for joining us, for
sharing your insights with us, as well as sharing your
equipment with us.
Thanks a lot.
SANDY HILL: It was a treat.
Thank you.