0:01

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.

1:58

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.

6:39

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.

8:22

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.