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Welcome back to Linear Circuits.

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This lesson is going to be a lab demo on a
guitar string.

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So, we're following up on the topic of
frequency spectrum with this experiment.

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So, in the previous class, we introduced
the frequency spectrum

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as a way of plotting the frequency content
of signals.

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This lesson objective is to demonstrate
the use of a spectrum analyzer.

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Well, this is a common measurement
instrument

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for computing and displaying the frequency
spectrum.

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And the guitar string is really a nice

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experiment, because it produces a lot of
harmonics.

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And you're able to see the different
harmonic

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and the frequency content of, of a
particular signal.

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So, our lab demo is guitar string
frequency spectrum.

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This platform is a guitar string.

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We have a pick up standard commercial
guitar

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pick up, which is very similar to the

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homemade guitar pick up that we saw before

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when we looked at inductance and
applications of inductance.

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The homemade one was just a coil of wire
around a permanent magnet.

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So this one uses the same principle,

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but it's has a better resolution to it.

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And the guitar, our string is a steel
guitar string.

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So, as you pluck the guitar string, it
vibrates inside the magnetic field

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induced by this in, this guitar pickup,
and it causes a current.

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So the current flows in through these
lines right here.

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And then we're using this, this

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dead acquisition board to just record

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those signals, and we'll display the
signals.

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So again, as I pluck this string

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[SOUND],

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I'm inducing electrical current.
Now, I want to look at this string, this

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electrical current on a on a oscilloscope.
So if I look back at my oscilloscope here.

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I've got this set to record from this
channel.

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Now, let me go ahead and hit the guitar
string and we'll see what it looks like.

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[SOUND]

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And you can see a signal

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that looks fairly

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periodic, and it decays over time.
Let's go ahead and zoom in on this.

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We definitely see something that looks
periodic, and that's what gives you the

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tone that you hear from the guitar string,
but it's not a pure tone.

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And this, this particular screen shot has
a lot of jaggedness

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in there, and that's because the
resolution under which I recorded it.

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[INAUDIBLE]

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I changed the resolution,

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and we'll record this again.

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And we'll see it in a little bit better
resolution

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There we go.
Alright.

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So, rerunning this with a better
resolution.

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Let me go ahead and zoom in on it a little
bit more.

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And we can see, this is what a

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guitar string vibration looks like when I
pluck it.

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If I look at this, I see definitely a a
fundamental frequency.

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From here to here is the fundamental
period, that's the basic tone that

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you've got.
That's the basic note in other words.

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But I also see some things happening in
the middle.

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In fact, I see a dip right here, about
half way.

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So a dip, I see a dip here, a dip about
half way and a dip here.

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And that dip halfway corresponds to a
second harmonic.

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So, it's another frequency in there.

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And then if I look at this, I see a peak
right here.

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That's about a third of the way, that's
really

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a third harmonic.

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And then we actually see a fourth harmonic
here as well.

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So I see multiple harmonics in this
signal.

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Now, to analyze this a little better, it's
easier to look at a

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[UNKNOWN]

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dynamic spectrum analyzer.

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Going back to the platform here.

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A dynamic system, a dynamic spectrum
analyzer

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is accomplished by taking your recorded
signal,

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feeding it into a data, data acquisition
board and then you record that signal.

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Now I'm going to put the, that instrument
up here.

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And let's go ahead and run this.

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The dynamic spectrum analyzer takes the
recorded signal and performs a

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fast voyage transfer on it in order to get
the frequency spectrum.

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And what you see plotted here is the
magnitude in decibels versus frequency.

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And the frequency is on a linear scale.

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But once we put something into decibels,
it is actually a log scale.

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Because to compute the decibels,

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magnitude in decibels, we take 20 times
the log of the magnitude.

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Now, what we see here is that there's a, a
little bit

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of a peak right there and I have not yet
played a note.

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So, it's curious to see where that peak
occurs.

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May I turn my cursor on and go ahead

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and slide it across to see where the peak
occurs.

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It occurs right there.

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And if I look at that frequency, that is
at 60 hertz.

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Now, it's very, very common to get noise
at 60 hertz.

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This is electromagnetic noise.

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And it's induced by power lines in the
room.

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it could be induced by vibrations from
equipment,

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which is powered by 60 hertz power lines.

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So, in this country the line current

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is at 60 hertz.

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So, we see 60 hertz signals in noise and
signals.

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In other countries, you might have 50
hertz and

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then therefore your noise would be at 50
hertz.

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But that peak there has nothing to do

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with our experiment, so we're going to
ignore that.

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That 60 hertz peak in our experiment.

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We're just going, looking at the peaks due
to plucking this string.

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So, if I pluck this string again,

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[SOUND]

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what I see are all these peaks.
This is the

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fundamental frequency that we saw in our
time trace.

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This is the second harmonic, the third
harmonic.

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And in this case, the second harmonic is
almost

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as strong as the first harmonic, a little
bit lower.

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And let's go ahead and measure what that
frequency is.

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I turn my cursor on,

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slide this across.
It's,

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that's as

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close as I can, it's around 440 and that's
an A note.

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Now, what we're seeing is that we've got
our A note.

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And then we've got our higher harmonics,
and that's

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what gives the richness of sound in a, in
music.

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In most

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musical instruments, they rely on the
harmonics

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to give it the richness of the sound.

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So in this case, we've looked at the,
we've looked

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at the application of the frequency
spectra in order to analyze the signal.

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We will be using this experiment later
when we go on to filtering.

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You might say, what if we don't want to
hear that second harmonic?

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What if we wanted to get rid of the, the
60 hertz signal?

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And so, we want to use this experiment
later for filtering.

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The basic concepts that we've covered
though, were

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to look at the dynamic spectrum analyzer
and

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to look at the frequency res, frequency
spectrum that we get out of a real signal.

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Thank you.

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So in summary, the Dynamic Sys, Spectrum
Analyzer

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is an instrument to measure and compute
the frequency

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spectrum of measured signals.
The guitar string is a great platform.

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Because it produces all kinds of frequency
content and harmonics in there.

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And we can look at the fundamental
frequency and

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we can look at those harmonics, and
measure them.

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We will see the, this experiment later on,
when we get to the topic of filtering.

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So,

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in the next lesson, we will combine the
transfer function concepts with the

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frequency conc spectrum concepts in order
to

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determine the frequency response of a
circuit.

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I will see you online, and I hope that

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you go to the form and ask and answer
questions.

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Thank you.