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>> Hi, welcome to Fundamentals Friday.

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Today, we're going to take a look at

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the operational amplifier or better known as the op-amp,

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really important building block.

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Absolutely essential that you understand how they work.

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Now, there are two ways to learn about op-amps.

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One is this way, the hard way.

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We don't want to do it that way, that sucks.

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So, let's get rid of this and let's do it the easy way.

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So, what is an op-amp or an operational amplifier?

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Well, the name operational amplifier

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comes from the fact that when they were first developed,

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they were developed to do mathematical operations. Hence,

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the name operational amplifier and back then, we didn't have digital computers.

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They used these for analog computers,

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so analogue mathematical operations; addition, subtraction, integration,

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differentiation, stuff like that, even that real hard calculus stuff,

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op-amps could actually do these operations in hardware.

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Not all this digital software rubbish.

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So, that's where they came from.

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So although, we don't have analog computers today,

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we still use them for those mathematical operations.

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You can turn an op-amp into an integrator, for example.

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You can turn it into a summer which is just an adder and things like that.

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So, they are really useful circuit building blocks but the main thing we've got to look

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at is the operational amplifier as an actual amplifier,

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because that's what they're most commonly used for

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and probably what you'll mostly use them for as well.

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So, an op-amp is essentially just an amplifier.

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Yes, it can be used for those mathematical operations

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but essentially, what it comes down to is

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this is a differential amplifier and what that means is that,

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it's got two inputs over here which we'll talk about and

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an output and it's got some gain in there,

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because amplifies have a gain.

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What it does is it takes the difference between these two input signals,

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amplifies it by its internal gain or what's called open loop gain,

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and gives you an output voltage.

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But op-amps really can't be used as differential amplifiers on their own,

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even though that's what they are.

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Rather confusing, but an important aspect you should understand.

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So, why can't this be used as just a differential amplifier,

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input signal here, output signal with some gain in there?

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Well, the answer is they are not designed to be used as differential amplifiers as

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strange as that may seem because they are essentially differential amplifiers.

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That was that hard circuit you saw over here before was actually

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the internal circuitry of an op-amp showing it as a differential amplifier.

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But hey, let's forget about differential amplifiers.

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I shouldn't even mentioned it, but it is important to understand

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the operation of how an op-amp actually works.

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Now, the reason they don't work as differential amplifiers is

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because the op-amp, the natural gain,

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the internal natural gain of the op-amp is enormous and that's

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the first thing you need to know about op-amps is it's not quite infinite,

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but you can think of it as infinitely large.

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It's like millions of times and well,

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the datasheet won't even tell you.

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So, if we just try to use an op-amp like this with

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no external circuitry and just feed like one millivolt on the input here,

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the gain is so large that the output voltage is going to be so

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huge that it's just not a practical device at all.

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So, that's why you never see an op-amp without

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any external circuitry or what's called negative feedback.

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So, that brings us to

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our first practical application for the op-amp which is a comparator.

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Before we look at that, we will look at the symbol here.

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Now, an op-amp is typically drawn as a triangle like this.

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It's got two inputs over here and one input here.

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Sometimes, it might be flipped depending on the ease of

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drawing your circuit and the way the signal flows but it's exactly the same thing.

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Now, these two inputs here,

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the positive input is called the non-inverting input.

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Easy to remember because it's positive.

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The inverting input is likewise easy to remember because it's negative.

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Negative inverts something.

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So, that's the terminology you should be using when referring to op-amp's.

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Very important to get the terminology right otherwise,

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you'll sound like a bit of a deal.

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Now, there's an output pin here,

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easy and there's two power supply pins,

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a positive and a negative one, which we'll talk about as well.

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So, I mentioned that the gain of an op-amp

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naturally inside is designed to be enormous, almost infinite.

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So, what happens if you just feed voltage on the input here?

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Well, let's assume that we have one volt on our non-inverting input here and we have

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1.01 volts or slightly above 10 millivolts or even one millivolt above this one here.

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Well, the amplifier will actually amplify

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the difference or attempt to amplify the difference between these two inputs.

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So, the output here will be this huge gain like a million times that one millivolt.

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So, it'll try and output hundreds and hundreds of thousands of volts and well,

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it can't do it because well your circuit is only 5,10,15 volts something like that.

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So, your output is going to saturate.

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So, if you've got one volt here and let's say,

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1.001 volts here, then your output is going to go boom right up to V plus.

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It's just going to saturate right up at the positive voltage.

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So, we've got ourselves a comparator and likewise,

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if you switch those voltages around so that

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the non-inverting input is bigger than the inverting input even by a tiny amount.

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Bingo. Your output is then going to go from positive and it's going

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to slam right down to the negative right down here.

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So, you can see that it's just used as a comparator.

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It's going to be a very crude comparator,

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and you can use an op-amp as a comparator in a pinch,

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but they are quite as good as a proper comparator that you can actually buy.

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They're designed to be comparators,

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but hey, we can actually use op-amps as comparators.

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But that's what happens if you connect an op-amp with

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no feedback at all and what that's called is the open loop configuration.

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Because there is no loop. There's no loop.

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The loop is open and we'll close the loop in a minute.

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But with an open-loop configuration like that,

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an op-amp is just a comparator.

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So, now, that we've got that little non-circuiter out of the way,

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the odd bowl configuration of the comparator for the op-amp,

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let's have a look at what way op-amps come really useful,

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and that's as proper amplifiers.

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Now, to do that, as I said,

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we need to go from the open-loop configuration with

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no feedback to adding what's called negative feedback,

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and hence, the t-shirt, negative feedback.

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Once you do that, op-amps become incredibly useful and powerful devices.

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Now, there are two rules with op-amps.

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That's all you have to remember.

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It's fantastic. This is how easy op-amps are.

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If you know these two rules, if you remember these two rules,

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you can analyze practically any op-amp circuit.

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You can't get into the real nitty-gritty details of the performance of it perhaps,

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but you can look at a schematic and you can understand how it works,

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and the two rules are very simple.

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Rule number one, no current flows in or out of these inputs.

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So, there's nothing flowing in or out of these two input pins, ever. That's it.

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Nothing. Nothing flows in or out regardless of how you connect the circuit out,

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whether it was the open-loop comparator configuration we saw before,

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or whether or not, it's a closed loop configuration and

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inverting or non-inverting amplifiers we're going to look at,

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nothing flows in or out.

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Rule number two.

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Now, this rule only applies when you have a closed loop like this.

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It doesn't apply at all to the open loop.

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One we just saw with the comparator.

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That's why I did the comparative first even though

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it might have been a little bit confusing to stop that way.

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Most people stop op-amp explanations with these two rules.

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But I wanted to show you that comparative first because to highlight,

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that rule number two it does not apply or only applies

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to closed loop configurations with negative feedback.

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Now, rule number two is the op-amp does whatever it can internally.

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Internal circuitry, which we won't go into, but it does whatever

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it can to keep these two input voltages the same.

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Now, the op-amp can't actually change its input voltage.

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These are inputs, it has no way to actually drive a voltage out and keep them the same,

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but it can do it with feedback,

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and that's why this rule only applies to closed loop configuration.

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So, the op-amp only has control over its output.

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But if you have feedback, it will change this output voltage to make

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sure this input equals this input here,

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and that's a very powerful rule of op-amps.

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If you see a closed loop configuration like this,

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you can be pretty sure, that rule, is going to apply.

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So, using these two rules,

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let's look at the simplest op-amp configuration possible,

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and it's not this.

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It actually has no external components.

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So, what it has is the output tied back to the inverting input like

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this and your phages signal or your voltage

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into the non-inverting positive input like that,

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and this is called an op-amp buffer.

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So, using our two rules,

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very easy to analyze this op-amp buffer circuit.

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Let's just do DC, because op-amps.

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The other thing is op-amps are DC coupled amplifiers like

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an amplified DC as well as AC signals. It's very important property.

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So, but let's do the DC case.

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We're fading one volt into a non-inverting input here.

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What do we get on the output of our op-amp?

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Well, look, rule number 2, always applies. When you've got feedback in an op-amp circuit.

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The op-amp tries to keep these two input voltages identical.

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So, because of the rule, this inverting input here,

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is going to be equal to this pin up here.

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The op-amp will ensure that by driving this output to get this input to match this one.

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So, if you got one volt here,

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then we've got one volt here,

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and because it's just connected by a bit of wire,

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we got to get one volt out here.

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That's why it's called a buffer.

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It's not an amplifier because there is no gain.

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One volt in, one volt out,

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minus one volt in, minus one volt out.

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Whatever the voltage is within

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the limits of the power supply voltages you see. What you see is that?

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Well, rule number 1. No current flows in or out of the inputs.

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So, nothing, no current flows in.

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So, if you've got a load over here, I don't know,

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it could be some sort of sensor or whatever.

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It could be a low pass filter. For example, like you're fading a pulse with

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modulated signal from your micro-controller or something like that,

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and then you want to buffer that voltage off there.

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Because no current flows into the input.

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This op-amp does not disturb your sensor or your circuit

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that you're actually trying to do.

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It's what's called a very high impedance input, essentially open circuits.

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So, it doesn't disturb anything you hook up to it.

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But the op-amp has what's called a low impedance output,

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so it can drive a reasonable amount of current,

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milli-amps, tens of milli-amps.

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That sought of things some can go as high as a couple of 100 milli-amps via power op-amps,

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but it can drive a reasonable amount of current.

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So, that's why it's buffering the signal,

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a high impedance signal and giving you a low impedance output.

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Just allows you to drive things with a sensitive input like that.

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Pretty easy. Very useful configuration, the op-amp buffer.

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Now the next configuration we're going to take a look at

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is what's called the non-inverting amplifier,

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and this is where we tie him L op-amp based that huge,

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unwieldy gain that changes everywhere with temperature and it's horrible.

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Anyway, it's got this massive unusable gain in there as

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a differential amplifier but as a single ended amplifier,

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that's what single end domains you fade input here,

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and it's always referenced to ground.

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We can use these as a single ended amplifier,

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and we can time that gain by adding negative feedback on it,

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and I want to explain negative and positive feedback in the mechanisms and how it works.

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Because, well, that's for a more advanced topic.

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But anyway, we fade in a feedback resistor here.

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Just like we did before,

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we showed it up but we put a resistor in there and we put a resistor back down to ground.

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So, what it's doing now is this input, the inverting input,

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is taking a small portion. This feedback resistor we'll call R_f,

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is always bigger than R_1 here.

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So, we've just got a voltage divider here that feeds back a smallest part of the input,

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and that's essentially what negative feedback it.

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You're taking a part of the output and you're feeding it back to the input,

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and there's a very simple formula you need to remember for

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this non-inverting amplifier configuration.

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I won't try and derive it, but the gain of this amplifier or what's called A_v,

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that's the actual terminology used.

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A_v is just gain. You can use gain.

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Gain equals R_f. The feedback resistor divided by R_1,

239
00:14:03,335 --> 00:14:05,910
which goes down to ground here, plus one.

240
00:14:05,910 --> 00:14:08,860
You've got to add that plus one on there. So, easy.

241
00:14:08,860 --> 00:14:11,790
If we've got annoying k feedback resistor and a 1K,

242
00:14:11,790 --> 00:14:13,635
resistor down to ground here.

243
00:14:13,635 --> 00:14:19,660
Now, gain is 9_k or 1K or nine plus one, a gain is equal to 10.

244
00:14:19,660 --> 00:14:25,890
So, if we fade one volt into the input here, will get 10 volts on the output, easy.

245
00:14:25,890 --> 00:14:29,420
Because we have got positive and negative rials which we'll get into,

246
00:14:29,420 --> 00:14:33,945
we can feed Ac or DC signals into here about ground

247
00:14:33,945 --> 00:14:39,175
and so we can feed negative one volt into here and we'll get negative 10 volts out.

248
00:14:39,175 --> 00:14:40,470
So, there you go.

249
00:14:40,470 --> 00:14:45,415
That is the basic configuration of a non-inverting amplifier.

250
00:14:45,415 --> 00:14:47,390
You might see weird configurations.

251
00:14:47,390 --> 00:14:50,625
They might be a capacitor across here or something like that,

252
00:14:50,625 --> 00:14:52,410
which we won't get into in this one.

253
00:14:52,410 --> 00:14:55,015
But the configuration is the same,

254
00:14:55,015 --> 00:14:57,380
if you see your input being fed into

255
00:14:57,380 --> 00:15:01,595
the non-inverting input and the feedback going back to the inverting input,

256
00:15:01,595 --> 00:15:04,760
you know that's a non-inverting amplifier,

257
00:15:04,760 --> 00:15:07,810
and this formula here applies.

258
00:15:07,810 --> 00:15:13,305
From this formula, you can also see why our buffer amplifier had a gain of one before,

259
00:15:13,305 --> 00:15:16,750
because their feedback resistor is zero, was zero.

260
00:15:16,750 --> 00:15:20,270
So, zero on one here which was infinite.

261
00:15:20,270 --> 00:15:26,720
So zero on over infinity or very large value is zero plus one.

262
00:15:26,720 --> 00:15:28,570
So, our gain is one.

263
00:15:28,570 --> 00:15:31,825
That's why our buffer had a gain of one, easy.

264
00:15:31,825 --> 00:15:36,940
The math doesn't lie. So, now we get onto the second of our two major configurations.

265
00:15:36,940 --> 00:15:40,465
We've already looked at the first one, which was the non-inverting amplifier.

266
00:15:40,465 --> 00:15:42,820
The buffer, was just a variation of that.

267
00:15:42,820 --> 00:15:45,790
Now, we have, instead of the non-inverting amplifier,

268
00:15:45,790 --> 00:15:48,515
we have the inverting amplifier.

269
00:15:48,515 --> 00:15:50,935
How can you tell it's an inverting amplifier?

270
00:15:50,935 --> 00:15:54,000
Well, just like before, we could tell it was a non-inverting

271
00:15:54,000 --> 00:15:57,275
one by the signal going into the positive input, here.

272
00:15:57,275 --> 00:16:00,495
The non-inverting input, hence, the name non inverting amplifier,

273
00:16:00,495 --> 00:16:07,465
our signaled nail goes into our inverting amplifier pin.

274
00:16:07,465 --> 00:16:10,340
So, hence, it's called an inverting amplifier.

275
00:16:10,340 --> 00:16:13,200
You'll notice that I've switched the two symbols around here.

276
00:16:13,200 --> 00:16:14,915
The positive is now on the bottom.

277
00:16:14,915 --> 00:16:20,680
Now, op-amp hasn't changed, I've just done that visually to make it a bit easier here,

278
00:16:20,680 --> 00:16:23,715
and that's what you'll commonly find in schematics

279
00:16:23,715 --> 00:16:27,085
and CAD packages and all stuff you might find them flipped around,

280
00:16:27,085 --> 00:16:28,765
upside down back to front.

281
00:16:28,765 --> 00:16:31,050
Whoop-de-doo, all going all around the place.

282
00:16:31,050 --> 00:16:33,780
Some pointing down for various feedback possible.

283
00:16:33,780 --> 00:16:36,665
So, that's exactly the same op-amp.

284
00:16:36,665 --> 00:16:38,520
It's just visually different.

285
00:16:38,520 --> 00:16:40,250
You can draw it anyway you all want.

286
00:16:40,250 --> 00:16:44,430
Now, our inverting amplifier, that this one is,

287
00:16:44,430 --> 00:16:47,040
we have the same as before. We have our feedback resistor,

288
00:16:47,040 --> 00:16:53,975
we have our negative feedback going to, in this case, our inverting amplifier pin,

289
00:16:53,975 --> 00:16:55,580
instead of our non-inverting one.

290
00:16:55,580 --> 00:17:01,560
So, now we are feeding out input through the resistor here.

291
00:17:01,560 --> 00:17:04,210
So, it's a different configuration, our signal is not going

292
00:17:04,210 --> 00:17:07,650
directly into the non-inverting pin.

293
00:17:07,650 --> 00:17:11,980
This brings up our next really important concept with op-amp that you

294
00:17:11,980 --> 00:17:13,954
really need to understand.

295
00:17:13,954 --> 00:17:19,984
Here's where rule number 1, really comes into play in trying to analyze this thing.

296
00:17:19,984 --> 00:17:23,464
It's called virtual ground. Stick with me.

297
00:17:23,464 --> 00:17:25,785
So, once again, how do we analyze this?

298
00:17:25,785 --> 00:17:28,835
Always go back to your two rules.

299
00:17:28,835 --> 00:17:30,600
What's our second rule here?

300
00:17:30,600 --> 00:17:33,460
The op-amp tries to keep the input voltages the same.

301
00:17:33,460 --> 00:17:37,270
In fact, it will, if you've got this non-inverting configuration

302
00:17:37,270 --> 00:17:38,850
and you haven't hit the rails yet.

303
00:17:38,850 --> 00:17:41,115
So, if the amplifier is working normally,

304
00:17:41,115 --> 00:17:44,010
within normal bounds of your past [inaudible] rail,

305
00:17:44,010 --> 00:17:47,865
these two inputs will always be the same.

306
00:17:47,865 --> 00:17:54,240
So, we're actually connected our non-inverting input down to ground here.

307
00:17:54,240 --> 00:17:56,580
It's connected to ground. We forced it to ground.

308
00:17:56,580 --> 00:17:58,055
It's never going to change.

309
00:17:58,055 --> 00:18:01,560
So, what is the inverting input here going to do?

310
00:18:01,560 --> 00:18:05,690
Well, of course, rule number 2, it's going to be identical, it's going to be the same.

311
00:18:05,690 --> 00:18:09,450
So, this point is also going to be ground or zero volts.

312
00:18:09,450 --> 00:18:13,800
So, this seems like almost like a pointless circuit,

313
00:18:13,800 --> 00:18:16,450
because look at rule number 1, no current flows in or out.

314
00:18:16,450 --> 00:18:22,255
So, there's no current flowing in or out of that pin and its ground.

315
00:18:22,255 --> 00:18:28,065
We've got both pins grounded and no current flows in or out.

316
00:18:28,065 --> 00:18:30,880
So, what's the point of having an op-amp?

317
00:18:30,880 --> 00:18:33,215
It's very confusing concept.

318
00:18:33,215 --> 00:18:37,565
But once you grasp it, you go, ugh, it's easy and it's quite brilliant.

319
00:18:37,565 --> 00:18:41,390
So, the op-amp you, remember, does whatever it needs to

320
00:18:41,390 --> 00:18:43,630
on the output drives it to whatever voltage

321
00:18:43,630 --> 00:18:46,360
positive and negative in order to make sure that

322
00:18:46,360 --> 00:18:50,495
this inverting pin here is equal to the non-inverting pin down here.

323
00:18:50,495 --> 00:18:52,620
Makes them the same. We've force this pin,

324
00:18:52,620 --> 00:18:54,150
so it can't change this pin.

325
00:18:54,150 --> 00:18:56,820
All it can do is change the voltage

326
00:18:56,820 --> 00:19:00,690
via the nature of the feedback resistor here to make this zero.

327
00:19:00,690 --> 00:19:04,635
Trust me, we'll do a practical measurement of this in a minute.

328
00:19:04,635 --> 00:19:07,885
This node here will actually be zero volts.

329
00:19:07,885 --> 00:19:10,730
This confuses the heck out of a lot of beginners.

330
00:19:10,730 --> 00:19:12,890
They build up their op-amps circuit, they start probing

331
00:19:12,890 --> 00:19:15,755
around and they've got their input signal here.

332
00:19:15,755 --> 00:19:17,490
It's a one kilohertz, one volt, side way, for example.

333
00:19:17,490 --> 00:19:22,545
And here's how they measure. This side of the resistor and the signals there.

334
00:19:22,545 --> 00:19:24,585
They measure this side of the resistor.

335
00:19:24,585 --> 00:19:27,300
It's ground, the signals is vanished.

336
00:19:27,300 --> 00:19:31,920
where's it gone? Strange, but true.

337
00:19:31,920 --> 00:19:36,905
So, let's follow this through and use our rules and see if we can analyze this circuit.

338
00:19:36,905 --> 00:19:40,249
Once again, the DC case to make it easy.

339
00:19:40,249 --> 00:19:43,590
We have got one volt on the input here.

340
00:19:43,590 --> 00:19:46,595
Positive one volt with respect to ground of course.

341
00:19:46,595 --> 00:19:49,090
Now, we've said before, that trust me,

342
00:19:49,090 --> 00:19:52,380
we'll measure it later but this pin is going to be ground.

343
00:19:52,380 --> 00:19:55,215
It is going to be zero volts there always.

344
00:19:55,215 --> 00:20:01,130
So, all we have got is one volt across our R_1 here, which is 1K. So,

345
00:20:01,130 --> 00:20:05,455
we're going to have, one milli-amp flowing through there.

346
00:20:05,455 --> 00:20:06,770
Where does it flow?

347
00:20:06,770 --> 00:20:10,655
Well, it doesn't flow down here to ground.

348
00:20:10,655 --> 00:20:14,415
How can it? Because no current. Rule number 1.

349
00:20:14,415 --> 00:20:17,910
No current flows into or out of the input pins.

350
00:20:17,910 --> 00:20:20,270
So, it can't flow through the ground here.

351
00:20:20,270 --> 00:20:23,870
It has to flow. It's going through here, it's going somewhere.

352
00:20:23,870 --> 00:20:26,085
There's one volt across that 1K resistor,

353
00:20:26,085 --> 00:20:28,720
Ohm's law, always that must be obeyed.

354
00:20:28,720 --> 00:20:30,930
So, that current is flowing, trust me.

355
00:20:30,930 --> 00:20:32,885
It can't flow into the input pin.

356
00:20:32,885 --> 00:20:34,335
When we know it's high impedance,

357
00:20:34,335 --> 00:20:37,985
so it must be flowing up here like this through

358
00:20:37,985 --> 00:20:42,150
this 10K resistor and it's being sourced from the output.

359
00:20:42,150 --> 00:20:45,335
Remember, this op-amp has internal circuitry.

360
00:20:45,335 --> 00:20:51,660
It's got an output buffer, so it can actually drive currents into

361
00:20:51,660 --> 00:20:56,010
and out of the various supplies back into there.

362
00:20:56,010 --> 00:20:59,330
That is where it's sinking the current too.

363
00:20:59,330 --> 00:21:01,550
That's the sneaky part about this.

364
00:21:01,550 --> 00:21:06,005
Our current is now being forced up this node, here,

365
00:21:06,005 --> 00:21:10,795
and is flowing through, in this case, feedback resistor R_f, which is 10K,

366
00:21:10,795 --> 00:21:13,450
I made it 10 times larger you will see why in a minute,

367
00:21:13,450 --> 00:21:15,965
then it must be flowing through this.

368
00:21:15,965 --> 00:21:18,630
So, we must have a voltage drop across that resistor.

369
00:21:18,630 --> 00:21:21,960
Once again, Ohm's law, always must be obeyed.

370
00:21:21,960 --> 00:21:26,500
So, if we have got that one milli-amp flowing through our 10K there,

371
00:21:26,500 --> 00:21:31,320
we're going to have 10 volt drop across this resistor with

372
00:21:31,320 --> 00:21:35,370
positive here and negative here.

373
00:21:35,370 --> 00:21:40,760
Aha, negative. These are voltages are with respect to the ground here.

374
00:21:40,760 --> 00:21:42,950
Now, here's where it gets a little bit tricky.

375
00:21:42,950 --> 00:21:45,815
This positive voltage here, it's we are going to get

376
00:21:45,815 --> 00:21:49,265
the plus 10 volts across that resistor there.

377
00:21:49,265 --> 00:21:55,050
But because this pin is positive, but were forced, we know these pin is zero, okay.

378
00:21:55,050 --> 00:21:59,045
We know it's zero because we've forced it by Y of the op-amp action

379
00:21:59,045 --> 00:22:03,150
and rule number 2 here, in what's called a virtual ground ,

380
00:22:03,150 --> 00:22:04,335
which I'll talk about in a minute.

381
00:22:04,335 --> 00:22:07,790
Then we have, that means, if this is ground,

382
00:22:07,790 --> 00:22:14,825
this is positive then we've got minus 10 volts coming out of here.

383
00:22:14,825 --> 00:22:21,360
Bingo. There's our inverting amplifier one vote in minus 10 volts out.

384
00:22:21,360 --> 00:22:30,260
So, our gain, our formula A_v gain equals R_f on R_1.

385
00:22:30,260 --> 00:22:34,130
There is no plus one with the inverting amplifier.

386
00:22:34,130 --> 00:22:38,175
The plus one only applies to the other non-inverting configuration.

387
00:22:38,175 --> 00:22:40,590
So, by Y of op-amp action,

388
00:22:40,590 --> 00:22:43,575
we'll call it a negative feedback here.

389
00:22:43,575 --> 00:22:46,140
This point, this node here,

390
00:22:46,140 --> 00:22:51,210
at the inverting pin is what's called a virtual ground.

391
00:22:51,210 --> 00:22:54,365
Because typically, in this configuration,

392
00:22:54,365 --> 00:22:58,100
it is actually grounded because we've grounded this pin, it doesn't have to be,

393
00:22:58,100 --> 00:23:00,760
we can fade other voltages into this pin and

394
00:23:00,760 --> 00:23:04,325
offset and do all sorts of other stuff but it's still called,

395
00:23:04,325 --> 00:23:06,615
even if you do fade another opinion here,

396
00:23:06,615 --> 00:23:08,720
it's still called virtual ground.

397
00:23:08,720 --> 00:23:10,890
Because it's virtual, it's not real,

398
00:23:10,890 --> 00:23:14,335
it's not hard tied, if it was hard tied to ground,

399
00:23:14,335 --> 00:23:17,045
if we actually tied that pin to ground,

400
00:23:17,045 --> 00:23:18,410
this thing wouldn't work.

401
00:23:18,410 --> 00:23:21,910
Because all of our current would flow through here.

402
00:23:21,910 --> 00:23:26,125
Through this resistor down to ground and around like that.

403
00:23:26,125 --> 00:23:28,610
Then this output here, well,

404
00:23:28,610 --> 00:23:30,760
it wouldn't know what to do the output would be zero

405
00:23:30,760 --> 00:23:33,180
because they'd be zero volts are difference in here.

406
00:23:33,180 --> 00:23:37,640
Remember it's still a differential amplifier as such.

407
00:23:37,640 --> 00:23:39,420
So, we've got zero votes difference here.

408
00:23:39,420 --> 00:23:40,585
We're going to get zero out.

409
00:23:40,585 --> 00:23:43,610
We'd have no current flowing through here and would have zero volts out.

410
00:23:43,610 --> 00:23:50,010
So, you can see that it doesn't work unless if you tied that hard brand.

411
00:23:50,010 --> 00:23:53,965
But when it becomes a virtual ground by nature of the op-amp action,

412
00:23:53,965 --> 00:23:55,670
it will magically works.

413
00:23:55,670 --> 00:23:57,105
I hope that makes sense.

414
00:23:57,105 --> 00:23:59,375
Because once you get it, it's really easy.

415
00:23:59,375 --> 00:24:02,395
So, if functionality wise it's pretty much exactly like

416
00:24:02,395 --> 00:24:04,650
the non-inverting amplifier except it

417
00:24:04,650 --> 00:24:08,435
inverts and that's it and the gain formula is slightly different.

418
00:24:08,435 --> 00:24:11,400
But apart from that pretty much works exactly the same,

419
00:24:11,400 --> 00:24:16,395
but that magic virtual ground is at play in this configuration.

420
00:24:16,395 --> 00:24:21,050
Of course, as with op-amps there DC couples or works with DC signals.

421
00:24:21,050 --> 00:24:23,230
You can just fade in a fixed DC voltage.

422
00:24:23,230 --> 00:24:26,880
As I said one volt DC and would give minus 10 volts out.

423
00:24:26,880 --> 00:24:31,830
In this case with these value resistance or we can fade in a one volt peak

424
00:24:31,830 --> 00:24:36,780
to peak or RMS sine wave for example, about the ground.

425
00:24:36,780 --> 00:24:38,375
So, it's centered on ground like this.

426
00:24:38,375 --> 00:24:40,550
This is the blue waveform here.

427
00:24:40,550 --> 00:24:43,200
Let's just say that's one volt, it's not quite the scale.

428
00:24:43,200 --> 00:24:47,730
But you'll get the idea and then our output will be the inverse of that.

429
00:24:47,730 --> 00:24:49,670
So, when the input rises,

430
00:24:49,670 --> 00:24:53,655
the output goes negative because it's an inverting amplifier.

431
00:24:53,655 --> 00:24:56,000
Now, of course one of the disadvantages of

432
00:24:56,000 --> 00:24:58,860
the inverting amplifier compared to the non-inverting we saw

433
00:24:58,860 --> 00:25:04,015
before is that as you can see there is input current coming from your load here.

434
00:25:04,015 --> 00:25:08,180
So, you don't want to use this when you have a high impedance load.

435
00:25:08,180 --> 00:25:12,275
Because then it can change the gain equation and marks everything up.

436
00:25:12,275 --> 00:25:16,970
That's where you want a non-inverting amplifier or at least a buffer.

437
00:25:16,970 --> 00:25:18,720
Some people will actually follow,

438
00:25:18,720 --> 00:25:24,440
will put a buffer on the input here and then drive the inverting amplifier.

439
00:25:24,440 --> 00:25:26,000
But usually in that sort of case,

440
00:25:26,000 --> 00:25:28,490
you'd probably use a non-inverting amplifier.

441
00:25:28,490 --> 00:25:34,390
Now, we have to go deeper into this and talk about the power supplies and split rials

442
00:25:34,390 --> 00:25:36,710
and all these sort of stuff and that

443
00:25:36,710 --> 00:25:40,810
single supply op-amps or try and keep it as brief as possible.

444
00:25:40,810 --> 00:25:42,450
Because assorting this configuration,

445
00:25:42,450 --> 00:25:45,240
the op-amp only has two power pins.

446
00:25:45,240 --> 00:25:48,700
It's usually called V plus and V minus.

447
00:25:48,700 --> 00:25:51,410
Now, v minus you can actually

448
00:25:51,410 --> 00:25:54,800
connect that to ground there is nothing regardless of what the daughter

449
00:25:54,800 --> 00:25:58,060
she's telling you there's nothing inherent in op-amps that

450
00:25:58,060 --> 00:26:01,325
make them really a single supply op-amps.

451
00:26:01,325 --> 00:26:04,760
So, you can take an op-amp that is V plus and V minus and

452
00:26:04,760 --> 00:26:09,425
connect these down to ground like that.

453
00:26:09,425 --> 00:26:11,210
There's nothing to stop you as long as you meet

454
00:26:11,210 --> 00:26:15,660
the minimum voltage specification and don't exceed the maximum etc.

455
00:26:15,660 --> 00:26:17,980
So, what happens if we did that in this case?

456
00:26:17,980 --> 00:26:21,850
Our input is a non-inverting input is also grounded here.

457
00:26:21,850 --> 00:26:24,625
Well, now it becomes a problem.

458
00:26:24,625 --> 00:26:27,680
You get into the practical limitations of op-amps.

459
00:26:27,680 --> 00:26:31,985
We've been talking about what's called an ideal op-amp up until this point.

460
00:26:31,985 --> 00:26:34,950
These rules here aren't strictly true,

461
00:26:34,950 --> 00:26:38,550
I lied but they still a fantastic way,

462
00:26:38,550 --> 00:26:43,835
even professionals use to analyze these circuits as a first order, as a first pass.

463
00:26:43,835 --> 00:26:45,485
No current flows in or out.

464
00:26:45,485 --> 00:26:48,335
Well, if you've been watching my videos you know I've done

465
00:26:48,335 --> 00:26:51,500
a previous video on this talking about input bias currents.

466
00:26:51,500 --> 00:26:55,020
A little itty bitty teeny-weeny currents can flow

467
00:26:55,020 --> 00:27:00,015
into and out of these pins depending on what type of op-amp you're actually got.

468
00:27:00,015 --> 00:27:04,110
That's a real practical limitation of these things.

469
00:27:04,110 --> 00:27:06,365
The other one is that,

470
00:27:06,365 --> 00:27:09,800
I talked about in previous video which I'll link in down below if you haven't seen it.

471
00:27:09,800 --> 00:27:16,045
The inputs cannot necessarily go right to the rials bit,

472
00:27:16,045 --> 00:27:17,750
whether it's positive, negative,

473
00:27:17,750 --> 00:27:19,580
reference to ground or whatever.

474
00:27:19,580 --> 00:27:25,200
So, you can get what's called a rial to rial op-amps or rial to rial input op-amps.

475
00:27:25,200 --> 00:27:30,055
In this case, if you had a rial to rial input op-amp then, yeah,

476
00:27:30,055 --> 00:27:33,325
you might be able to get away with this and have

477
00:27:33,325 --> 00:27:38,635
the non-inverting input tied down to ground like this.

478
00:27:38,635 --> 00:27:42,880
But hang on, what's the point of that?

479
00:27:42,880 --> 00:27:44,605
If you've only got ground,

480
00:27:44,605 --> 00:27:47,150
this is an inverting amplifier.

481
00:27:47,150 --> 00:27:48,595
It inverts your signal.

482
00:27:48,595 --> 00:27:50,315
So, if you fade one volt in,

483
00:27:50,315 --> 00:27:55,790
you are going to try the op-amp is going to try and give you minus 10 volts out.

484
00:27:55,790 --> 00:28:00,765
But how does it do that when your supply is negative of that?

485
00:28:00,765 --> 00:28:03,715
It doesn't work. So, you have to,

486
00:28:03,715 --> 00:28:05,530
it's got no room to do it.

487
00:28:05,530 --> 00:28:08,300
So, your op-amp has to always be payload in

488
00:28:08,300 --> 00:28:12,950
the configuration that you expect your input signals to be referenced to.

489
00:28:12,950 --> 00:28:18,770
So if we were to use the inverting op-amp configuration like this

490
00:28:18,770 --> 00:28:24,865
with a single supply rail like this and we wanted to amplify AC signals,

491
00:28:24,865 --> 00:28:29,300
well, the signals can't go negative like this.

492
00:28:29,300 --> 00:28:30,870
I get a negative on the input but you never

493
00:28:30,870 --> 00:28:32,690
go to get that negative voltage on the output.

494
00:28:32,690 --> 00:28:35,850
But you still want to amplify a signal cleanly like this.

495
00:28:35,850 --> 00:28:39,070
But what we need to do is the zero-point,

496
00:28:39,070 --> 00:28:43,800
needs to go right down the bottom here like this.

497
00:28:43,800 --> 00:28:45,320
So, we need to offset.

498
00:28:45,320 --> 00:28:46,650
So, if that's zero volts,

499
00:28:46,650 --> 00:28:49,515
we need to offset our input ref,

500
00:28:49,515 --> 00:28:54,365
our input and output reference by a certain amount of voltage. How much?

501
00:28:54,365 --> 00:28:58,270
Well, typically, half of your supply rial to maximize your headroom.

502
00:28:58,270 --> 00:29:00,170
How do we do that? I hinted at it.

503
00:29:00,170 --> 00:29:03,855
Before you feed in if this is V plus,

504
00:29:03,855 --> 00:29:06,365
you'd go a V plus on two,

505
00:29:06,365 --> 00:29:08,290
you would feed that volt is half rial.

506
00:29:08,290 --> 00:29:12,580
They usually do that simply by putting a resistor like

507
00:29:12,580 --> 00:29:17,680
that going to V plus and a resistor down there,

508
00:29:17,680 --> 00:29:19,225
going down to ground,

509
00:29:19,225 --> 00:29:20,995
and bingo voltage divider.

510
00:29:20,995 --> 00:29:22,320
They show half rial.

511
00:29:22,320 --> 00:29:26,990
So, we're offsetting a voltage here, a virtual ground.

512
00:29:26,990 --> 00:29:30,400
Remember this is still called a virtual ground even though it's not going to be.

513
00:29:30,400 --> 00:29:32,225
So, the voltage here,

514
00:29:32,225 --> 00:29:36,805
is going to be equal to the voltage here due to our second op-amp rule.

515
00:29:36,805 --> 00:29:40,055
So, if our power supply is 20 volts for example,

516
00:29:40,055 --> 00:29:45,730
this point here would be half that if we make these exactly the same value.

517
00:29:45,730 --> 00:29:47,895
Of course, mark them the same value of half rial.

518
00:29:47,895 --> 00:29:54,565
So, we have an offset voltage here at this point and that shifts away fro up.

519
00:29:54,565 --> 00:29:57,480
We'll see that in the practical experiments to follow.

520
00:29:57,480 --> 00:30:01,300
Now, as I said some time back you might see some other components

521
00:30:01,300 --> 00:30:05,120
around here like few capacitors and things like that around the circuit,

522
00:30:05,120 --> 00:30:10,370
that is to change the bandwidth of the circuit effectively.

523
00:30:10,370 --> 00:30:13,430
Because we're not going to go into it I'll have to do

524
00:30:13,430 --> 00:30:16,700
a second part of this video that goes into op-amp bandwidth and things like that.

525
00:30:16,700 --> 00:30:22,160
I have done one on cascading op-amp bandwidths which I'll linking down below.

526
00:30:22,160 --> 00:30:24,770
But suffice it to say that

527
00:30:24,770 --> 00:30:29,260
an ideal op-amp that we've been looking at has an infinite bandwidth.

528
00:30:29,260 --> 00:30:32,150
It's infinite frequencies and signals but in practice,

529
00:30:32,150 --> 00:30:35,030
no of course now you practical op-amp might have

530
00:30:35,030 --> 00:30:39,475
a one megahertz bandwidth or a 100 kilohertz bandwidth or something like that.

531
00:30:39,475 --> 00:30:41,970
It could be a nice fast 100 megahertz,

532
00:30:41,970 --> 00:30:45,600
but it's always going to have a bandwidth which changes with

533
00:30:45,600 --> 00:30:50,075
your gain or gain bandwidth product and I've done a separate video, I'll link it in.

534
00:30:50,075 --> 00:30:53,045
But sometimes you might see a little bypass capping,

535
00:30:53,045 --> 00:30:56,490
there might be 10 buff or a 100 buff, something like that.

536
00:30:56,490 --> 00:31:00,100
That's just a rolling off the frequency response of that.

537
00:31:00,100 --> 00:31:05,010
Likewise, you might see a little cap across something like this, for example,

538
00:31:05,010 --> 00:31:11,130
if you are offsetting this thing using a single supply like this.

539
00:31:11,130 --> 00:31:15,230
I won't go into the details but basically any noise

540
00:31:15,230 --> 00:31:19,305
on this point here will be amplified and picked up on the virtual ground,

541
00:31:19,305 --> 00:31:21,055
so you'll get noise on your output signal.

542
00:31:21,055 --> 00:31:24,945
So, you might stick a big OS in one or 10 micro-farad cap

543
00:31:24,945 --> 00:31:29,735
across here for example and really make that virtual ground really noise free.

544
00:31:29,735 --> 00:31:32,630
But that's beyond the basics.

545
00:31:32,630 --> 00:31:34,800
One little mistake that I noticed, oops!

546
00:31:34,800 --> 00:31:37,585
My formula here for the inverting amplifier,

547
00:31:37,585 --> 00:31:42,295
it needs a negative in front of it because the gain is actually native.

548
00:31:42,295 --> 00:31:44,400
So, the gain needs,

549
00:31:44,400 --> 00:31:49,125
in this case is not 10, it's minus 10.

550
00:31:49,125 --> 00:31:52,910
So, just back to this voltage rial thing briefly,

551
00:31:52,910 --> 00:31:55,520
because it is something that is rather

552
00:31:55,520 --> 00:31:59,440
confusing because there is no ground pin on an op-amp.

553
00:31:59,440 --> 00:32:01,585
There is only the positive and negative.

554
00:32:01,585 --> 00:32:03,170
So, we'll, where does your reference go?

555
00:32:03,170 --> 00:32:05,900
Well the reference is part of the external circuit.

556
00:32:05,900 --> 00:32:09,890
In this case, back to our non-inverting amplifier configuration.

557
00:32:09,890 --> 00:32:12,275
He's our ground reference here and then

558
00:32:12,275 --> 00:32:15,920
our positive and negative supply is here like this.

559
00:32:15,920 --> 00:32:19,035
I plus 15 volts and minus 15 volts.

560
00:32:19,035 --> 00:32:23,660
If we want to fade in a signal that goes both positive and negative.

561
00:32:23,660 --> 00:32:27,230
If we're only fading in a signal that's positive above ground

562
00:32:27,230 --> 00:32:32,220
then this here could be tied down to here like this.

563
00:32:32,220 --> 00:32:35,410
Then it has to be above that,

564
00:32:35,410 --> 00:32:38,120
the output cannot magically go negative.

565
00:32:38,120 --> 00:32:41,625
It can only go negative to a ground reference if you have

566
00:32:41,625 --> 00:32:45,905
that minus 15 volt rialling there. Clear as mud.

567
00:32:45,905 --> 00:32:48,650
Just like the inverting configuration,

568
00:32:48,650 --> 00:32:51,820
if we wanted to pair on this from a split supply,

569
00:32:51,820 --> 00:32:55,325
we can have this grounded like this and then we can add

570
00:32:55,325 --> 00:33:00,895
a bias voltage in here like this to actually offset the voltage.

571
00:33:00,895 --> 00:33:03,835
Then it can get into all sorts of we doing

572
00:33:03,835 --> 00:33:07,020
wonderful things with AC coupling these amplifies.

573
00:33:07,020 --> 00:33:10,790
All of the opening of configurations we looked at have been DC coupled,

574
00:33:10,790 --> 00:33:12,850
but you can actually AC couple them so much.

575
00:33:12,850 --> 00:33:18,160
Why is stopped might seem capacitors on the inputs and outputs to the op-amps.

576
00:33:18,160 --> 00:33:22,070
Now, he's a tricky configuration which I'll briefly touch on that

577
00:33:22,070 --> 00:33:24,740
combines the two different configurations

578
00:33:24,740 --> 00:33:27,585
we've seen before and a couple of the things we've looked at.

579
00:33:27,585 --> 00:33:29,440
It's the differential amplifier.

580
00:33:29,440 --> 00:33:31,425
You know how I said op-amps are,

581
00:33:31,425 --> 00:33:34,445
essentially a differential amplifier that's how they work,

582
00:33:34,445 --> 00:33:38,530
but they do that in the open-loop configuration.

583
00:33:38,530 --> 00:33:40,445
So, they hopeless, they're useless for that.

584
00:33:40,445 --> 00:33:47,320
But if you combine the inverting amplifier configuration that we just saw.

585
00:33:47,320 --> 00:33:49,850
So, we've got the feedback going here our signal going in,

586
00:33:49,850 --> 00:33:53,605
that's a standard inverting configuration.

587
00:33:53,605 --> 00:33:59,955
We have exactly those two resistors that we saw before to buyers that voltage up.

588
00:33:59,955 --> 00:34:02,275
But instead of going to the supplier rial,

589
00:34:02,275 --> 00:34:08,719
we make that other differential input and bingo it becomes a differential amplifier.

590
00:34:08,719 --> 00:34:12,545
I'll let you go through the actual calculation yourself to find out.

591
00:34:12,545 --> 00:34:15,260
But basically, the difference that we fading in,

592
00:34:15,260 --> 00:34:18,830
if we fade it in any one volt into here and 1.1 volts into here,

593
00:34:18,830 --> 00:34:21,344
we have a difference of 0.1 volts and

594
00:34:21,344 --> 00:34:25,270
the gain of this amplifier exactly like the inverting configuration,

595
00:34:25,270 --> 00:34:29,810
negative R_2, on R_1 we used R F before I'll call it R_2 here.

596
00:34:29,810 --> 00:34:33,440
So, R_2 on R_1 10K on 1K.

597
00:34:33,440 --> 00:34:35,590
We have a gain and you're going to add negative in there.

598
00:34:35,590 --> 00:34:37,804
So, it's a gain of minus 10.

599
00:34:37,804 --> 00:34:41,495
But because L bias voltages is not fixed it's

600
00:34:41,495 --> 00:34:46,760
actually the differential input signal. Look what happens.

601
00:34:46,760 --> 00:34:48,290
We got one volt here.

602
00:34:48,290 --> 00:34:49,969
We've got a divider it here.

603
00:34:49,969 --> 00:34:52,040
R_1 these two values are the same,

604
00:34:52,040 --> 00:34:53,469
R_1 is equal to R_1 here,

605
00:34:53,469 --> 00:34:54,925
R_2 is equal to R_2 here.

606
00:34:54,925 --> 00:35:00,515
They must match precisely to get good common mode rejection ratio which we won't go into.

607
00:35:00,515 --> 00:35:04,480
But suffice it to say if I got one volt on this point here relative to ground,

608
00:35:04,480 --> 00:35:09,205
we'll have 0.99999 repaid out at that point there,

609
00:35:09,205 --> 00:35:10,935
and that becomes our virtual ground.

610
00:35:10,935 --> 00:35:13,095
Bingo, I will have that same voltage there,

611
00:35:13,095 --> 00:35:19,610
then we'll have a 1.1 volts here that has X and then you subtract that from that,

612
00:35:19,610 --> 00:35:22,315
that and you get X amount of current flowing through here,

613
00:35:22,315 --> 00:35:25,235
which then must flow through the 10 K which has 1.

614
00:35:25,235 --> 00:35:30,030
999 voltage across it subtract the difference there.

615
00:35:30,030 --> 00:35:33,975
It's exactly the same configuration as before with the bias voltage.

616
00:35:33,975 --> 00:35:37,690
But they will lift with an output voltage of minus one.

617
00:35:37,690 --> 00:35:43,855
So, if amplified, the difference in our input signal by the gain here 10.

618
00:35:43,855 --> 00:35:48,530
It's not a terrific differential amplifier, but it works.

619
00:35:48,530 --> 00:35:53,545
So, we've timed out op-amp that is a differential amplifier anyway, but pretty unusable.

620
00:35:53,545 --> 00:35:57,555
We've actually made it into a pretty usable differential amplifier.

621
00:35:57,555 --> 00:36:00,500
Beauty. Just combines both of

622
00:36:00,500 --> 00:36:04,650
those techniques and there's lots of tricky stuff like this you can do with op-amps,

623
00:36:04,650 --> 00:36:08,860
and just briefly another one of these tricky configurations goes back to the name

624
00:36:08,860 --> 00:36:13,060
the operational amplifier and one of those mathematical operations the integrator.

625
00:36:13,060 --> 00:36:15,175
We won't go into integrals and all that sort of stuff.

626
00:36:15,175 --> 00:36:21,930
But what we can do basic inverting configuration here instead of a feedback resistor,

627
00:36:21,930 --> 00:36:25,130
we have a feedback capacitor. What does that do?

628
00:36:25,130 --> 00:36:28,590
Well, L standard input voltage here following the rule

629
00:36:28,590 --> 00:36:33,685
no current flows in but we have a virtual ground of course rule number two.

630
00:36:33,685 --> 00:36:35,955
So, if that's one K,

631
00:36:35,955 --> 00:36:40,420
and that's one volt there where we have one milli-amp flowing through that resistor.

632
00:36:40,420 --> 00:36:41,960
Where does it flow?

633
00:36:41,960 --> 00:36:43,475
Can't flow into the op-amp,

634
00:36:43,475 --> 00:36:47,100
it's got to flow up here and through the capacitor.

635
00:36:47,100 --> 00:36:53,215
So, you've got effectively a constant current of one milli-amp.

636
00:36:53,215 --> 00:36:57,275
This is now a constant current flowing through this resistor.

637
00:36:57,275 --> 00:37:01,095
When you have a constant current flowing through a capacitor,

638
00:37:01,095 --> 00:37:03,770
you end up with.

639
00:37:03,770 --> 00:37:08,255
>> Well, in this case, it's going to ramp negative, down like that.

640
00:37:08,255 --> 00:37:14,450
If our input is a step and it goes up like that,

641
00:37:14,450 --> 00:37:18,605
the constant current, because it takes time to charge a capacitor,

642
00:37:18,605 --> 00:37:22,545
the voltage on the capacitor will increase like that.

643
00:37:22,545 --> 00:37:24,945
I say increase because it's an inverting amplifier.

644
00:37:24,945 --> 00:37:26,195
So, it's going to go negative.

645
00:37:26,195 --> 00:37:28,025
But that's what it does,

646
00:37:28,025 --> 00:37:29,820
and that's an integrator,

647
00:37:29,820 --> 00:37:35,100
and that is actually a mathematical integral of your input signal.

648
00:37:35,100 --> 00:37:37,535
Anyway, that's way too much theory,

649
00:37:37,535 --> 00:37:41,055
more than I wanted to do and longer than I wanted to take actually.

650
00:37:41,055 --> 00:37:44,540
But suffice it to remember that these two rules

651
00:37:44,540 --> 00:37:48,270
of op-amps allow you to analyze practically any configuration,

652
00:37:48,270 --> 00:37:49,650
and as a bit of homework,

653
00:37:49,650 --> 00:37:54,260
I got to recommend you look at the summing op-amp configuration,

654
00:37:54,260 --> 00:37:56,840
the summing amplifier, and figure out how it works because

655
00:37:56,840 --> 00:37:59,690
you're going to be using those two rules to figure it out.

656
00:37:59,690 --> 00:38:01,220
So, I'll leave that one up to you.

657
00:38:01,220 --> 00:38:02,960
But enough of that, let's head on over to

658
00:38:02,960 --> 00:38:05,240
the benchy and see if we can measure some stuff.

659
00:38:05,240 --> 00:38:09,185
Make sure I wasn't bullshitting you about this virtual ground stuff.

660
00:38:09,185 --> 00:38:11,420
Let's check it out. Sounds a bit sas.

661
00:38:11,420 --> 00:38:13,500
See if it really works.

662
00:38:13,500 --> 00:38:15,405
All right, we're at the breadboard.

663
00:38:15,405 --> 00:38:19,910
Let's take a look at an inverting amplifier here because I wanted to show you

664
00:38:19,910 --> 00:38:25,700
that virtual ground point there just to show you that there really is no signal there.

665
00:38:25,700 --> 00:38:30,920
It actually vanishes in quote marks when you go from the input here to

666
00:38:30,920 --> 00:38:33,320
here and then it magically reappears at

667
00:38:33,320 --> 00:38:36,455
the output because that's how an op-amp works, as I've explained.

668
00:38:36,455 --> 00:38:39,230
Anyway, it got a jellybean LM358 here.

669
00:38:39,230 --> 00:38:40,550
It's actually a jewel op-amp.

670
00:38:40,550 --> 00:38:44,570
So, we've just tie it off the terminated the top op-amp here.

671
00:38:44,570 --> 00:38:50,295
We can probably do a separate video on that on how to properly terminate op-amps,

672
00:38:50,295 --> 00:38:52,190
that might make an interesting video.

673
00:38:52,190 --> 00:38:54,260
Thumbs up if you want to see that one.

674
00:38:54,260 --> 00:38:56,165
Anyway, here we go, I've got a configured,

675
00:38:56,165 --> 00:38:59,990
I've got a 10k input resistor here, 100k feedback.

676
00:38:59,990 --> 00:39:01,340
So, we got a gain of 10.

677
00:39:01,340 --> 00:39:04,340
The formula, of course, is the feedback resistor on that one,

678
00:39:04,340 --> 00:39:06,320
bingo, easy, times 10.

679
00:39:06,320 --> 00:39:09,555
So, I'm going to fade out two volts peak-to-peak input here.

680
00:39:09,555 --> 00:39:13,580
We should get 20 volts peak-to-peak on the output.

681
00:39:13,580 --> 00:39:18,335
So, we're using pretty much near the maximum supply rail of the LM358.

682
00:39:18,335 --> 00:39:21,335
In this case, I'm pairing it from plus/minus 15 volts.

683
00:39:21,335 --> 00:39:23,680
So, we have a split supply.

684
00:39:23,680 --> 00:39:24,980
So, our ground reference,

685
00:39:24,980 --> 00:39:27,110
our input signal is reference to a ground.

686
00:39:27,110 --> 00:39:28,545
I should actually draw that on there.

687
00:39:28,545 --> 00:39:30,195
There we go, that's clearer.

688
00:39:30,195 --> 00:39:33,725
So, our input is referenced to ground

689
00:39:33,725 --> 00:39:37,680
and our non-inverting input here is referenced to ground,

690
00:39:37,680 --> 00:39:39,845
and our output is referenced to ground also.

691
00:39:39,845 --> 00:39:44,730
But for signals to go negative or for output signals to go negative,

692
00:39:44,730 --> 00:39:47,720
we need a negative rail on here.

693
00:39:47,720 --> 00:39:49,785
So, we're using minus 15 volts.

694
00:39:49,785 --> 00:39:51,125
So, plus 15 to pair it,

695
00:39:51,125 --> 00:39:52,400
minus 15 as well.

696
00:39:52,400 --> 00:39:54,875
So, 30-volt total supply on there,

697
00:39:54,875 --> 00:39:59,015
allows us to go positive and negative signals, input and output.

698
00:39:59,015 --> 00:40:00,900
So, let's go over to our power supply.

699
00:40:00,900 --> 00:40:02,900
Here it is, plus/minus 15 volts.

700
00:40:02,900 --> 00:40:06,390
I got dual tracking on there and you notice that I've joined

701
00:40:06,390 --> 00:40:10,305
the supplies here generating the split supply.

702
00:40:10,305 --> 00:40:12,160
So, this one actually becomes the negative.

703
00:40:12,160 --> 00:40:14,895
So, this is our positive 15 from here to here.

704
00:40:14,895 --> 00:40:19,475
This is our negative 15 relative to here because we've strapped the positive one.

705
00:40:19,475 --> 00:40:24,660
However, and tada, there we go, we're feeding in.

706
00:40:24,660 --> 00:40:28,110
We've just got a one-kilohertz low-frequency signal,

707
00:40:28,110 --> 00:40:31,475
two volts peak-to-peak here on the input.

708
00:40:31,475 --> 00:40:36,160
You can see our input and output wave forms and these inputs are, of course,

709
00:40:36,160 --> 00:40:40,190
all AC coupled and their bandwidth limited as well to

710
00:40:40,190 --> 00:40:44,630
20 megahertz to reduce the noise and we're using our high resolution mode as well.

711
00:40:44,630 --> 00:40:47,315
So, we get some boxcar averaging in there.

712
00:40:47,315 --> 00:40:52,070
That's why we got a nice crisp waveform like that, beautiful.

713
00:40:52,070 --> 00:40:55,040
So, what happens if we turn our bandwidth spec to four?

714
00:40:55,040 --> 00:41:00,785
In this case, it's my one-gigahertz Tektonics 3000 series and we turn off "Hi Res" mode,

715
00:41:00,785 --> 00:41:02,720
going back to sample mode, there we go.

716
00:41:02,720 --> 00:41:06,975
We get our nice fuzzy wave forms because we've got that massively high bandwidth.

717
00:41:06,975 --> 00:41:09,435
That's the advantage. You can't go into averaging, of course,

718
00:41:09,435 --> 00:41:12,585
but "Hi Res" mode does boxcar averaging, just cleans it up.

719
00:41:12,585 --> 00:41:16,490
Of course, you can do envelope mode look at that, pretty horrible waveform.

720
00:41:16,490 --> 00:41:17,900
So, in looking at this sort of stuff,

721
00:41:17,900 --> 00:41:21,110
you definitely don't want to use your regular mode.

722
00:41:21,110 --> 00:41:23,240
You want "Hi Res" mode if you've got it.

723
00:41:23,240 --> 00:41:25,520
There you go, we're getting exactly what we expect.

724
00:41:25,520 --> 00:41:29,420
Look at that, the two volts peak-to-peak in roughly 20 volts out.

725
00:41:29,420 --> 00:41:33,095
There's probably going to be some error due to the resistors in here.

726
00:41:33,095 --> 00:41:35,270
Anyway, we get in our times 10.

727
00:41:35,270 --> 00:41:38,210
Of course, the blue waveform there is the input,

728
00:41:38,210 --> 00:41:40,065
that's 500 millivolts per division.

729
00:41:40,065 --> 00:41:44,695
So, we're getting our two volts peak-to-peak and our output is five volts per division.

730
00:41:44,695 --> 00:41:48,455
So, which is the yellow waveform there and look at that.

731
00:41:48,455 --> 00:41:51,170
Of course, because it's an inverting amplifier,

732
00:41:51,170 --> 00:41:54,625
the output is exactly 180 degrees out of phase.

733
00:41:54,625 --> 00:41:56,660
It's inverted. So, at the moment,

734
00:41:56,660 --> 00:41:58,920
I'm probing the input and the output.

735
00:41:58,920 --> 00:42:01,475
Now, you wanted to see the virtual ground, didn't you?

736
00:42:01,475 --> 00:42:03,470
What happens if I move my input probe,

737
00:42:03,470 --> 00:42:07,805
the blue waveform here from the input over to this?

738
00:42:07,805 --> 00:42:09,890
You'd expect to see the signal.

739
00:42:09,890 --> 00:42:13,595
But as I've told you and as you should trust me,

740
00:42:13,595 --> 00:42:15,985
let's move the probe over.

741
00:42:15,985 --> 00:42:19,100
>> That is our virtual ground point.

742
00:42:19,100 --> 00:42:22,025
Look, flat has attack.

743
00:42:22,025 --> 00:42:24,105
The signal has vanished.

744
00:42:24,105 --> 00:42:27,495
Magic. But of course you know it's not magic,

745
00:42:27,495 --> 00:42:32,975
it's just standard op-amp behavior with virtual ground on the input.

746
00:42:32,975 --> 00:42:34,850
That's how an op-amp works,

747
00:42:34,850 --> 00:42:37,300
and none of the current hasn't magically vanished.

748
00:42:37,300 --> 00:42:38,970
The current is going through the resistor.

749
00:42:38,970 --> 00:42:40,740
Ohm's Law still holds.

750
00:42:40,740 --> 00:42:44,450
Current is changing because we've got an AC resistor here.

751
00:42:44,450 --> 00:42:49,110
There's AC current flowing through this resistor and it's all flowing up here.

752
00:42:49,110 --> 00:42:53,910
But this point, by the nature of the op-amp action and the negative feedback,

753
00:42:53,910 --> 00:42:55,860
that is a virtual ground.

754
00:42:55,860 --> 00:42:57,885
An op-amp rule number two there.

755
00:42:57,885 --> 00:42:59,350
Inputs are the sign.

756
00:42:59,350 --> 00:43:02,990
The op-amp changes the output here in

757
00:43:02,990 --> 00:43:07,910
order to ensure that point is equal to that input there.

758
00:43:07,910 --> 00:43:11,390
Easy. That's why we don't see any signal on there.

759
00:43:11,390 --> 00:43:16,100
So trap for young players when you're probably being around circuits like this,

760
00:43:16,100 --> 00:43:18,245
don't think your signal is vanished.

761
00:43:18,245 --> 00:43:21,890
Virtual ground. Remember your op-amps rules, always.

762
00:43:21,890 --> 00:43:26,855
Now, I actually chose the LM358 for a reason because it

763
00:43:26,855 --> 00:43:32,130
is not like a regular op-amp and not quite like a rail to rail op-amp.

764
00:43:32,130 --> 00:43:34,280
It's halfway in-between.

765
00:43:34,280 --> 00:43:35,600
Check it out. Here we go.

766
00:43:35,600 --> 00:43:37,920
It eliminates the need for dual supplies.

767
00:43:37,920 --> 00:43:42,060
Okay. You can use it as a single supply op-amp.

768
00:43:42,060 --> 00:43:45,880
But as I said you can use any op-amp as a single supply op-amp.

769
00:43:45,880 --> 00:43:49,470
But this one is extra special in that it allows direct

770
00:43:49,470 --> 00:43:54,065
sensing near ground and V-out also goes to ground.

771
00:43:54,065 --> 00:43:57,335
So effectively, it's not rail to rail.

772
00:43:57,335 --> 00:44:01,295
It won't go up to the all the way to the positive rail on the input and output,

773
00:44:01,295 --> 00:44:04,175
but it will go down to ground or the

774
00:44:04,175 --> 00:44:07,630
negative because an op-amp doesn't have a ground pin.

775
00:44:07,630 --> 00:44:09,070
It's the negative rail.

776
00:44:09,070 --> 00:44:11,795
So, even if we pair it from splits supplies,

777
00:44:11,795 --> 00:44:13,745
plus minus 15 luck we are now,

778
00:44:13,745 --> 00:44:18,995
it will still go down to that minus 15-volt pin or that pin four.

779
00:44:18,995 --> 00:44:21,485
It'll go down the input.

780
00:44:21,485 --> 00:44:26,195
This input here will allow to sense all the way down to the negative rail and also

781
00:44:26,195 --> 00:44:31,380
the output will go all the way down to the negative rail and I'll demonstrate.

782
00:44:31,380 --> 00:44:34,515
What we've got to look at here is a couple of things on the data sheet.

783
00:44:34,515 --> 00:44:38,085
Now, input common-mode range and our voltage range here.

784
00:44:38,085 --> 00:44:41,010
As we said, it goes all the way down to

785
00:44:41,010 --> 00:44:44,205
that negative P and all zero volts as they call it here.

786
00:44:44,205 --> 00:44:45,675
But on the positive side,

787
00:44:45,675 --> 00:44:51,970
this op-amp will not go since all go to the airport less than

788
00:44:51,970 --> 00:44:59,370
1.5 volts below or above 1.5 volts below the positive rail V plus there.

789
00:44:59,370 --> 00:45:03,030
So, if we've got an output signal of 10 volts for example,

790
00:45:03,030 --> 00:45:09,245
the voltage range says if we want to get an output voltage of 10 volts peak,

791
00:45:09,245 --> 00:45:13,640
what we need a V plus rail of at least one and a half volts above that.

792
00:45:13,640 --> 00:45:15,620
So, 11.5 volts.

793
00:45:15,620 --> 00:45:20,450
So, what we're going to do is lower the voltages here on these rails.

794
00:45:20,450 --> 00:45:24,140
We're going to lower V plus from 15 volts down to

795
00:45:24,140 --> 00:45:30,000
11.5 and around about that 11.5 volts because we're getting 10 volts peak.

796
00:45:30,000 --> 00:45:32,955
On the output, 20 volts peak-to-peak, 10 volts peak.

797
00:45:32,955 --> 00:45:35,795
We should start seeing distortion or clipping of

798
00:45:35,795 --> 00:45:38,715
that waveform at around about 11 and a half volts.

799
00:45:38,715 --> 00:45:39,935
Let's see if we do.

800
00:45:39,935 --> 00:45:41,145
Okay. So, here we go.

801
00:45:41,145 --> 00:45:42,445
We have 15 volts.

802
00:45:42,445 --> 00:45:47,340
I'm going to drop it down by 0.1 volts at a time and notice I have a split supply.

803
00:45:47,340 --> 00:45:48,560
It's dual tracking.

804
00:45:48,560 --> 00:45:51,275
So, a wave form is still looking good

805
00:45:51,275 --> 00:45:55,090
but we expect it to start clipping around about 11 and a half.

806
00:45:55,090 --> 00:45:56,265
It might not be precise.

807
00:45:56,265 --> 00:45:58,935
This is not an exact value on the data shape but then we go,

808
00:45:58,935 --> 00:46:01,330
11 and half it's still there.

809
00:46:01,330 --> 00:46:05,270
There we go. It's starting to clip.

810
00:46:05,270 --> 00:46:10,090
You can say it. It's actually about 11.2 volts there.

811
00:46:10,090 --> 00:46:13,780
You can start to say wave form flattened out.

812
00:46:13,780 --> 00:46:20,560
Now, I'll wind down even more because this is not a symmetrical supply op-amp.

813
00:46:20,560 --> 00:46:21,855
It actually goes down to zero.

814
00:46:21,855 --> 00:46:25,590
We don't start seeing clipping on the bottom here,

815
00:46:25,590 --> 00:46:29,435
on the bottom rail, until a significant time.

816
00:46:29,435 --> 00:46:31,530
After that now, we're getting both.

817
00:46:31,530 --> 00:46:36,070
But I want it back up there and that's about 11.1 volts.

818
00:46:36,070 --> 00:46:38,910
But we're seeing that clipping on the top and we won't

819
00:46:38,910 --> 00:46:42,190
see it on the bottom for time after.

820
00:46:42,190 --> 00:46:45,740
So there you go, just be aware of that and if we had

821
00:46:45,740 --> 00:46:51,760
even a worse op-amp in this respect like LM741 or something like that,

822
00:46:51,760 --> 00:46:53,820
that can't even go down to the negative rail,

823
00:46:53,820 --> 00:46:59,280
we would start to see these rails clip right roughly at the same time.

824
00:46:59,280 --> 00:47:03,260
You remember that open-loop gain I was telling you about? How large is it?

825
00:47:03,260 --> 00:47:05,970
Well, it tells you a couple of ways in the datasheet.

826
00:47:05,970 --> 00:47:08,290
Not all data sheets will have it, but this one does.

827
00:47:08,290 --> 00:47:10,310
Large DC voltage gain.

828
00:47:10,310 --> 00:47:16,025
So, it doesn't say it's open-loop gain but that is effectively the DC voltage gain,

829
00:47:16,025 --> 00:47:21,220
is the gain of the inherent differential amplifier in there and they put it in dB.

830
00:47:21,220 --> 00:47:24,080
So, you use your 20 log formula.

831
00:47:24,080 --> 00:47:28,545
You reverse that and you get about a 100,000.

832
00:47:28,545 --> 00:47:32,910
Likewise, here on the datasheet they've got another way to tell you it's called now,

833
00:47:32,910 --> 00:47:34,085
it's called something different.

834
00:47:34,085 --> 00:47:37,440
It's called the large signal voltage gain there,

835
00:47:37,440 --> 00:47:39,815
it specify for a certain rail. But there we go.

836
00:47:39,815 --> 00:47:44,500
Typically, a hundred and they specify in volts per millivolt.

837
00:47:44,500 --> 00:47:48,950
So, if you divide 100 volts by 1 millivolt what do you get?

838
00:47:48,950 --> 00:47:50,970
Same figure, 100,000.

839
00:47:50,970 --> 00:47:52,280
There is your open-loop gain.

840
00:47:52,280 --> 00:47:56,500
So, there's just a quick out practical demonstration showing the virtual ground effect

841
00:47:56,500 --> 00:48:00,765
there and also the voltage rail limitations for positive and negative.

842
00:48:00,765 --> 00:48:04,985
I should do another part of this video on op-amp limitations,

843
00:48:04,985 --> 00:48:06,870
practical limitations, things like that.

844
00:48:06,870 --> 00:48:07,950
That would be interesting.

845
00:48:07,950 --> 00:48:10,785
Thumbs up if you want to see that one.

846
00:48:10,785 --> 00:48:14,685
I'll leave you with one last thing. I want to explain it.

847
00:48:14,685 --> 00:48:16,510
I'll leave it to you to try and figure out.

848
00:48:16,510 --> 00:48:20,825
I chose these values higher than what I had on the white board there.

849
00:48:20,825 --> 00:48:22,330
I chose them for a reason.

850
00:48:22,330 --> 00:48:26,665
Let's lower them down to 10K and 1K here and

851
00:48:26,665 --> 00:48:31,785
see what happens with this specific op-amp LM358.

852
00:48:31,785 --> 00:48:33,450
Let's drop these down,

853
00:48:33,450 --> 00:48:34,650
still quite high values,

854
00:48:34,650 --> 00:48:38,440
1K and 10K, 10 ohms or something like that.

855
00:48:38,440 --> 00:48:40,350
But let's give it a go.

856
00:48:40,350 --> 00:48:44,685
There it is, a 1K input resistor, 10K feedback resistor.

857
00:48:44,685 --> 00:48:46,085
Exactly the same gain,

858
00:48:46,085 --> 00:48:49,600
exactly the same inputs signal but what's

859
00:48:49,600 --> 00:48:57,700
that little funny business there and over there?

860
00:48:58,380 --> 00:49:02,240
If we measure our virtual ground point,

861
00:49:02,240 --> 00:49:05,045
look at these little sparks there and there

862
00:49:05,045 --> 00:49:10,045
corresponding to that little bumping that wave form.

863
00:49:10,045 --> 00:49:11,410
Interesting.

864
00:49:11,410 --> 00:49:14,360
So, as professor Julius Sumner Miller said,

865
00:49:14,360 --> 00:49:16,160
why is it so?

866
00:49:16,160 --> 00:49:20,380
I'll leave that to you to figure out. Catch you next time.