In this course students learn the basic concepts of acoustics and electronics and how they can applied to understand musical sound and make music with electronic instruments. Topics include: sound waves, musical sound, basic electronics, and applications of these basic principles in amplifiers and speaker design.
Wah Pedal Circuit Analysis, Continued
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来自 University of Rochester 的课程
音频和音乐工程基础：第 1 部分，音乐声电子
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从本节课中
Week 6 - Guitar Pickup and Effects Analysis MB & Design and Construction of a Guitar Amplifier MB
Building the guitar amplifier, how to solder, getting the amp to work - systematic testing and troubleshooting. Visualizing sound waves, frequency content and tone, signal modification in electro-acoustic systems, tube amplifiers and distortion, wah pedal, talk box.
与讲师见面
Robert ClarkProvost and Senior Vice President for Research and Professor
Mechanical Engineering
Mark BockoDistinguished Professor and Chair
Electrical and Computer Engineering
Okay, so now we're going to talk about exactly how that's done.
But for now, let's just assume that the capacitor is able to be varied from 0.01
microfarads to 1 microfarad. And so I just generated a set of response
curves here. For this circuit basically, it's this
voltage divider for these typical values, and different values of the capacitor.
Here's the lowest value 0.01 microfarads. And so the center frequency of the
response is out here above 2 kHz. If I increase the capacitance to 1
microfarad, then it moves down to about, the response to about 200 Hertz.
And the you can see how the width increases as I change the value of the
capacitance, as well. And so, by, if I had some way to vary the
value of this capacitor, I could make this filter sweep its center frequency
over this range. Now, the other thing about this and
that's really the, the presence of this R1 It makes this a so called shelving of
band-pass filters. So the response does not go to zero at
zero frequency like it would if that resistor were not there.
Putting that resistor there makes that response go to something finite.
So no matter where this filter is, I'm still not killing off the low
frequencies. But I'm accentuating some band of
frequencies that I can move from maybe 100 Hertz in a typical Wah Pedal.
Up to a couple of kilohertz, and so that's functionally what the Wah Pedal
does. The trick now is to figure out how in the
world do you build this variable capacitor.
Okay, now, here is a Op Amp version of the Wah Pedal.
That, that, you, there's a, a few ideas for how to do this on, on the internet.
But, we, we, put this, this, schematic together, and prototyped it, and, and it
works. now, this is kind of a culmination of
everything you've learned about in this course.
It has a lot of A/C circuit, design and A/C circuit analysis, plus we're using Op
Amps. Now, we're introducing this one
interesting idea of feedback to the capacitor.
Which is, a new idea here and really the essence of what makes this thing work.
So I've redrawn the schematic here is the, the two resistors in series,
followed by the RLC. And the RNL are grounded.
The C is not grounded. It's attached to the output of an
amplifier. Now what you do is you take the output,
it essentially comes from this point here.
And you can put that into a simple inverting Op Amp, and you can set the
gain wherever you like. the prototypes that we've built, the
gains may be 50 to 100, so that's the ratio of this resistor to that resistor.
If you wanted a gain of 50, this resistor is 50 times that resistor.
And then, there's the output, and so then what we do is take the output and we go
through a potentiometer. And the wiper on the potentiometer then
goes to a simple buffer stage, and so this a unity game buffer built with an
ambient. And the output of that is connected to
the end of the capacitor. So, the capacitor is not grounded, it's
attached to this output. Now, what happens when you do that is,
you're, instead of grounding the capacitor.
You're using feedback on the far side of the capacitor in a way that makes the
capacitor look larger or smaller than it really is.
Now, this is a little hard to understand but give this a, a little bit of thought.
Here's a capacitor, it has a capacitance C and there's a voltage V across that
capacitor. And, here's the relationship between the
current and the voltage. So, the current is just j omega C times
the voltage, or, if you like the voltage. Is I times the impedance and the
impedance is 1 over j omega C. Now, to make this thing look like, so if
I apply a certain voltage to it, and then I ask, how much current is going to flow
through it. That's a reflection of what the
capacitance is. If I apply, say 1 volt at, say 1 kHz.
I'm going to have a current flowing through this in magnitude, that is
proportional to the size of the capacitor.
If I could somehow increase that current. Then that's like making the capacitor
look like it's bigger, for that given voltage, okay.
So that's the key thing, if I have a fixed voltage, but I can find some way to
make the current bigger than it would be. With just a grounded capacitor then I can
make that capacitor look bigger. And so what you do Is you apply feedback
to the other terminal of the capacitor. And then, what happens is, when the
voltage on this end is pulled up a little bit, the voltage on the other end of the
capacitor is pulled down. And so, notice that this is inverting and
this is non-inverting. So if this voltage here goes up a little
bit, then this voltage here goes down a little bit.
And so I'm pulling the capacitor in two different direction.
So, I'm, when I, every time I add a little voltage to it, the current should
go up a little bit. but what happens is I'm taking, and I'm
taking that voltage, amplifying it, applying it to the other terminal,
pulling the other terminal even farther away.
So I'm increasing the voltage across this capacitor.
And that looks just like I've increased the capacitance.
So there, there are two ways to get more current through this capacitor.
One of them is to increase the capacitance for a given voltage.
The other one is to use this feedback applied to the other terminal of the
capacitor. To, every time I, so that every time I
increase this voltage a little bit, I pull this one away.
And that makes this thing, makes this capacitor, look like it has a larger
capacitance. Now, you can kind of think of a
mechanical analog of this Imagine you have a spring.
And say one end of the spring is attached to a rigid base, and I grab the other
end, and I try to pull it up. I'm going to experience the spring
constant when I try to pull that. So if I apply a certain force, the spring
moves by a certain amount with a certain velocity.
Now, if I were to take, and let's say I had some kind of a recover system that
monitored how I'm pulling on this spring. So that when I try to pull up, the spring
is going to take and move the base and go with me.
So it's going to make it easier to pull up.
And it's going to make it look like the spring if weaker than it really is and a
weaker spring is like having a larger capacitor.
If you go back to the, the lecture where I was talking about mechanical analogs to
electrical components, a spring and a capacitor are analogous to each other.
but you have to be careful, a stiff spring is like a very small capacitor.
A large capacitor is like a very weak spring.
So, if I want to make the capacitor look larger, what I need to do is pull this
voltage the other way and that's going to make C, the effect of C larger.
That's the same as with the spring, when I pull on the spring.
Moving the other end of the spring along with my, my pole.
That makes the spring look weaker, if I turned it around, and, and, every time I
try to pull the spring up, I pulled down. Then that would make the spring seem
stiffer, and I wouldn't get as much displacement for the same force.
So, I hope that this intuitive explanation helps a little bit.
But this is a, a nice illustration of how you can use feedback in electronic
circuits, to, do some interesting things. So, the bottom line here, and don't worry
if you don't understand all of the details of this.
But I just wanted to kind of pull everything together.
And so you can see how you can use everything you've learned so far to
really understand something that looks mighty confusing at first glance, the Wah
Pedal schematic. But what you're doing is using feedback
to change the apparent size of C. And every time I change the apparent size
of this capacitor, I'm shifting the resonant frequency of this guy, and so
just by moving the foot switch. So for the foot switch it's all the way
down, so it's zero. Then there's no voltage being applied to
the capacitor. And this actually looks like a ground
because look at this. You know enough about Op Amps to figure
this out. If the wiper is down here at ground then
this terminal of the Op Amp is grounded. Now, you the know that the ideal Op Amp
model always wants to keep these two, inputs, the non-inverting and the
inverting input at the same voltage. So, if this one's grounded, then this one
looks like a ground. And, so, in that case, when the wah pedal
is all the way down here, the potentiometer and the wah pedal is all
the way down to ground. Then, this looks like ground.
And, the capacitor just has it's nominal value, whatever.
If it was a 0.01 microfarad apacitor, it will behave like a 0.01 microfarad
capacitor. But if I move the Wah Pedal potentiometer
up here. Now, I'm going to be applying a, every
time this tries to go positive, I'm going to be applying a negative voltage
to this end of the capacitor. And I'm thereby making the capacitor look
larger. So the further up this potentiometer the
wiper is the larger this capacitor looks and the lower the frequency is going to
be. So, that, in a nutshell, is how a wah
pedal works. And the last thing is that, assuming that
you build the guitar amplifier and you found that to be an enjoyable and
rewarding experience. This would be a wonderful project for you
to attempt on your own afterward. So and so I hope that this helped you
understand this a little bit better. And appreciate how with the simple tools
that we've been able to, the analytical tools that we've been able to assemble in
just a few weeks. How you can really start to look at some
of this electronics that was probably quite mystifying before, and really start
to understand how it works.
