WEBVTT 00:00:00.000 --> 00:00:03.344 >> Hi, welcome to Fundamentals Friday. 00:00:03.344 --> 00:00:04.590 Today, we're going to take a look at 00:00:04.590 --> 00:00:08.759 the operational amplifier or better known as the op-amp, 00:00:08.759 --> 00:00:10.620 really important building block. 00:00:10.620 --> 00:00:14.325 Absolutely essential that you understand how they work. 00:00:14.325 --> 00:00:17.280 Now, there are two ways to learn about op-amps. 00:00:17.280 --> 00:00:21.390 One is this way, the hard way. 00:00:21.390 --> 00:00:23.700 We don't want to do it that way, that sucks. 00:00:23.700 --> 00:00:28.530 So, let's get rid of this and let's do it the easy way. 00:00:28.530 --> 00:00:31.725 So, what is an op-amp or an operational amplifier? 00:00:31.725 --> 00:00:34.124 Well, the name operational amplifier 00:00:34.124 --> 00:00:36.260 comes from the fact that when they were first developed, 00:00:36.260 --> 00:00:39.810 they were developed to do mathematical operations. Hence, 00:00:39.810 --> 00:00:44.720 the name operational amplifier and back then, we didn't have digital computers. 00:00:44.720 --> 00:00:47.735 They used these for analog computers, 00:00:47.735 --> 00:00:52.510 so analogue mathematical operations; addition, subtraction, integration, 00:00:52.510 --> 00:00:55.995 differentiation, stuff like that, even that real hard calculus stuff, 00:00:55.995 --> 00:01:00.000 op-amps could actually do these operations in hardware. 00:01:00.000 --> 00:01:02.130 Not all this digital software rubbish. 00:01:02.130 --> 00:01:03.435 So, that's where they came from. 00:01:03.435 --> 00:01:05.600 So although, we don't have analog computers today, 00:01:05.600 --> 00:01:09.875 we still use them for those mathematical operations. 00:01:09.875 --> 00:01:13.965 You can turn an op-amp into an integrator, for example. 00:01:13.965 --> 00:01:17.850 You can turn it into a summer which is just an adder and things like that. 00:01:17.850 --> 00:01:21.800 So, they are really useful circuit building blocks but the main thing we've got to look 00:01:21.800 --> 00:01:25.950 at is the operational amplifier as an actual amplifier, 00:01:25.950 --> 00:01:28.400 because that's what they're most commonly used for 00:01:28.400 --> 00:01:31.265 and probably what you'll mostly use them for as well. 00:01:31.265 --> 00:01:34.230 So, an op-amp is essentially just an amplifier. 00:01:34.230 --> 00:01:36.470 Yes, it can be used for those mathematical operations 00:01:36.470 --> 00:01:38.750 but essentially, what it comes down to is 00:01:38.750 --> 00:01:43.790 this is a differential amplifier and what that means is that, 00:01:43.790 --> 00:01:46.250 it's got two inputs over here which we'll talk about and 00:01:46.250 --> 00:01:48.890 an output and it's got some gain in there, 00:01:48.890 --> 00:01:51.590 because amplifies have a gain. 00:01:51.590 --> 00:01:56.060 What it does is it takes the difference between these two input signals, 00:01:56.060 --> 00:02:00.005 amplifies it by its internal gain or what's called open loop gain, 00:02:00.005 --> 00:02:02.720 and gives you an output voltage. 00:02:02.720 --> 00:02:09.414 But op-amps really can't be used as differential amplifiers on their own, 00:02:09.414 --> 00:02:11.245 even though that's what they are. 00:02:11.245 --> 00:02:14.885 Rather confusing, but an important aspect you should understand. 00:02:14.885 --> 00:02:19.125 So, why can't this be used as just a differential amplifier, 00:02:19.125 --> 00:02:22.240 input signal here, output signal with some gain in there? 00:02:22.240 --> 00:02:26.020 Well, the answer is they are not designed to be used as differential amplifiers as 00:02:26.020 --> 00:02:30.070 strange as that may seem because they are essentially differential amplifiers. 00:02:30.070 --> 00:02:33.640 That was that hard circuit you saw over here before was actually 00:02:33.640 --> 00:02:38.225 the internal circuitry of an op-amp showing it as a differential amplifier. 00:02:38.225 --> 00:02:40.990 But hey, let's forget about differential amplifiers. 00:02:40.990 --> 00:02:44.560 I shouldn't even mentioned it, but it is important to understand 00:02:44.560 --> 00:02:48.680 the operation of how an op-amp actually works. 00:02:48.680 --> 00:02:51.190 Now, the reason they don't work as differential amplifiers is 00:02:51.190 --> 00:02:54.440 because the op-amp, the natural gain, 00:02:54.440 --> 00:02:58.760 the internal natural gain of the op-amp is enormous and that's 00:02:58.760 --> 00:03:03.860 the first thing you need to know about op-amps is it's not quite infinite, 00:03:03.860 --> 00:03:06.560 but you can think of it as infinitely large. 00:03:06.560 --> 00:03:09.290 It's like millions of times and well, 00:03:09.290 --> 00:03:10.865 the datasheet won't even tell you. 00:03:10.865 --> 00:03:14.210 So, if we just try to use an op-amp like this with 00:03:14.210 --> 00:03:19.400 no external circuitry and just feed like one millivolt on the input here, 00:03:19.400 --> 00:03:22.580 the gain is so large that the output voltage is going to be so 00:03:22.580 --> 00:03:27.140 huge that it's just not a practical device at all. 00:03:27.140 --> 00:03:30.230 So, that's why you never see an op-amp without 00:03:30.230 --> 00:03:34.285 any external circuitry or what's called negative feedback. 00:03:34.285 --> 00:03:35.420 So, that brings us to 00:03:35.420 --> 00:03:39.650 our first practical application for the op-amp which is a comparator. 00:03:39.650 --> 00:03:42.770 Before we look at that, we will look at the symbol here. 00:03:42.770 --> 00:03:46.295 Now, an op-amp is typically drawn as a triangle like this. 00:03:46.295 --> 00:03:49.010 It's got two inputs over here and one input here. 00:03:49.010 --> 00:03:52.595 Sometimes, it might be flipped depending on the ease of 00:03:52.595 --> 00:03:57.225 drawing your circuit and the way the signal flows but it's exactly the same thing. 00:03:57.225 --> 00:03:59.225 Now, these two inputs here, 00:03:59.225 --> 00:04:03.515 the positive input is called the non-inverting input. 00:04:03.515 --> 00:04:06.050 Easy to remember because it's positive. 00:04:06.050 --> 00:04:10.460 The inverting input is likewise easy to remember because it's negative. 00:04:10.460 --> 00:04:12.315 Negative inverts something. 00:04:12.315 --> 00:04:16.680 So, that's the terminology you should be using when referring to op-amp's. 00:04:16.680 --> 00:04:18.980 Very important to get the terminology right otherwise, 00:04:18.980 --> 00:04:20.570 you'll sound like a bit of a deal. 00:04:20.570 --> 00:04:22.540 Now, there's an output pin here, 00:04:22.540 --> 00:04:24.960 easy and there's two power supply pins, 00:04:24.960 --> 00:04:28.460 a positive and a negative one, which we'll talk about as well. 00:04:28.460 --> 00:04:31.490 So, I mentioned that the gain of an op-amp 00:04:31.490 --> 00:04:35.720 naturally inside is designed to be enormous, almost infinite. 00:04:35.720 --> 00:04:39.785 So, what happens if you just feed voltage on the input here? 00:04:39.785 --> 00:04:45.395 Well, let's assume that we have one volt on our non-inverting input here and we have 00:04:45.395 --> 00:04:52.640 1.01 volts or slightly above 10 millivolts or even one millivolt above this one here. 00:04:52.640 --> 00:04:55.310 Well, the amplifier will actually amplify 00:04:55.310 --> 00:04:59.090 the difference or attempt to amplify the difference between these two inputs. 00:04:59.090 --> 00:05:06.590 So, the output here will be this huge gain like a million times that one millivolt. 00:05:06.590 --> 00:05:11.685 So, it'll try and output hundreds and hundreds of thousands of volts and well, 00:05:11.685 --> 00:05:16.485 it can't do it because well your circuit is only 5,10,15 volts something like that. 00:05:16.485 --> 00:05:18.770 So, your output is going to saturate. 00:05:18.770 --> 00:05:22.640 So, if you've got one volt here and let's say, 00:05:22.640 --> 00:05:31.215 1.001 volts here, then your output is going to go boom right up to V plus. 00:05:31.215 --> 00:05:34.820 It's just going to saturate right up at the positive voltage. 00:05:34.820 --> 00:05:37.955 So, we've got ourselves a comparator and likewise, 00:05:37.955 --> 00:05:41.030 if you switch those voltages around so that 00:05:41.030 --> 00:05:46.310 the non-inverting input is bigger than the inverting input even by a tiny amount. 00:05:46.310 --> 00:05:51.935 Bingo. Your output is then going to go from positive and it's going 00:05:51.935 --> 00:05:56.505 to slam right down to the negative right down here. 00:05:56.505 --> 00:06:01.170 So, you can see that it's just used as a comparator. 00:06:01.170 --> 00:06:03.305 It's going to be a very crude comparator, 00:06:03.305 --> 00:06:06.480 and you can use an op-amp as a comparator in a pinch, 00:06:06.480 --> 00:06:12.000 but they are quite as good as a proper comparator that you can actually buy. 00:06:12.000 --> 00:06:13.420 They're designed to be comparators, 00:06:13.420 --> 00:06:16.830 but hey, we can actually use op-amps as comparators. 00:06:16.830 --> 00:06:20.760 But that's what happens if you connect an op-amp with 00:06:20.760 --> 00:06:25.875 no feedback at all and what that's called is the open loop configuration. 00:06:25.875 --> 00:06:28.210 Because there is no loop. There's no loop. 00:06:28.210 --> 00:06:31.485 The loop is open and we'll close the loop in a minute. 00:06:31.485 --> 00:06:33.990 But with an open-loop configuration like that, 00:06:33.990 --> 00:06:36.960 an op-amp is just a comparator. 00:06:36.960 --> 00:06:40.625 So, now, that we've got that little non-circuiter out of the way, 00:06:40.625 --> 00:06:44.180 the odd bowl configuration of the comparator for the op-amp, 00:06:44.180 --> 00:06:47.930 let's have a look at what way op-amps come really useful, 00:06:47.930 --> 00:06:50.475 and that's as proper amplifiers. 00:06:50.475 --> 00:06:52.290 Now, to do that, as I said, 00:06:52.290 --> 00:06:55.500 we need to go from the open-loop configuration with 00:06:55.500 --> 00:06:59.350 no feedback to adding what's called negative feedback, 00:06:59.350 --> 00:07:02.255 and hence, the t-shirt, negative feedback. 00:07:02.255 --> 00:07:07.925 Once you do that, op-amps become incredibly useful and powerful devices. 00:07:07.925 --> 00:07:11.235 Now, there are two rules with op-amps. 00:07:11.235 --> 00:07:13.095 That's all you have to remember. 00:07:13.095 --> 00:07:16.145 It's fantastic. This is how easy op-amps are. 00:07:16.145 --> 00:07:18.720 If you know these two rules, if you remember these two rules, 00:07:18.720 --> 00:07:22.830 you can analyze practically any op-amp circuit. 00:07:22.830 --> 00:07:27.090 You can't get into the real nitty-gritty details of the performance of it perhaps, 00:07:27.090 --> 00:07:30.875 but you can look at a schematic and you can understand how it works, 00:07:30.875 --> 00:07:33.510 and the two rules are very simple. 00:07:33.510 --> 00:07:39.660 Rule number one, no current flows in or out of these inputs. 00:07:39.660 --> 00:07:48.000 So, there's nothing flowing in or out of these two input pins, ever. That's it. 00:07:48.000 --> 00:07:53.100 Nothing. Nothing flows in or out regardless of how you connect the circuit out, 00:07:53.100 --> 00:07:56.550 whether it was the open-loop comparator configuration we saw before, 00:07:56.550 --> 00:08:00.995 or whether or not, it's a closed loop configuration and 00:08:00.995 --> 00:08:04.025 inverting or non-inverting amplifiers we're going to look at, 00:08:04.025 --> 00:08:06.015 nothing flows in or out. 00:08:06.015 --> 00:08:07.760 Rule number two. 00:08:07.760 --> 00:08:13.355 Now, this rule only applies when you have a closed loop like this. 00:08:13.355 --> 00:08:16.080 It doesn't apply at all to the open loop. 00:08:16.080 --> 00:08:17.625 One we just saw with the comparator. 00:08:17.625 --> 00:08:20.040 That's why I did the comparative first even though 00:08:20.040 --> 00:08:22.755 it might have been a little bit confusing to stop that way. 00:08:22.755 --> 00:08:25.680 Most people stop op-amp explanations with these two rules. 00:08:25.680 --> 00:08:29.555 But I wanted to show you that comparative first because to highlight, 00:08:29.555 --> 00:08:33.615 that rule number two it does not apply or only applies 00:08:33.615 --> 00:08:38.284 to closed loop configurations with negative feedback. 00:08:38.284 --> 00:08:44.685 Now, rule number two is the op-amp does whatever it can internally. 00:08:44.685 --> 00:08:48.270 Internal circuitry, which we won't go into, but it does whatever 00:08:48.270 --> 00:08:53.190 it can to keep these two input voltages the same. 00:08:53.190 --> 00:08:57.710 Now, the op-amp can't actually change its input voltage. 00:08:57.710 --> 00:09:03.235 These are inputs, it has no way to actually drive a voltage out and keep them the same, 00:09:03.235 --> 00:09:06.290 but it can do it with feedback, 00:09:06.290 --> 00:09:10.240 and that's why this rule only applies to closed loop configuration. 00:09:10.240 --> 00:09:13.020 So, the op-amp only has control over its output. 00:09:13.020 --> 00:09:17.080 But if you have feedback, it will change this output voltage to make 00:09:17.080 --> 00:09:21.245 sure this input equals this input here, 00:09:21.245 --> 00:09:25.445 and that's a very powerful rule of op-amps. 00:09:25.445 --> 00:09:27.885 If you see a closed loop configuration like this, 00:09:27.885 --> 00:09:31.475 you can be pretty sure, that rule, is going to apply. 00:09:31.475 --> 00:09:33.135 So, using these two rules, 00:09:33.135 --> 00:09:37.270 let's look at the simplest op-amp configuration possible, 00:09:37.270 --> 00:09:38.425 and it's not this. 00:09:38.425 --> 00:09:40.845 It actually has no external components. 00:09:40.845 --> 00:09:45.725 So, what it has is the output tied back to the inverting input like 00:09:45.725 --> 00:09:48.005 this and your phages signal or your voltage 00:09:48.005 --> 00:09:51.290 into the non-inverting positive input like that, 00:09:51.290 --> 00:09:54.315 and this is called an op-amp buffer. 00:09:54.315 --> 00:09:56.285 So, using our two rules, 00:09:56.285 --> 00:09:59.895 very easy to analyze this op-amp buffer circuit. 00:09:59.895 --> 00:10:03.425 Let's just do DC, because op-amps. 00:10:03.425 --> 00:10:08.250 The other thing is op-amps are DC coupled amplifiers like 00:10:08.250 --> 00:10:13.610 an amplified DC as well as AC signals. It's very important property. 00:10:13.610 --> 00:10:16.980 So, but let's do the DC case. 00:10:16.980 --> 00:10:20.805 We're fading one volt into a non-inverting input here. 00:10:20.805 --> 00:10:23.145 What do we get on the output of our op-amp? 00:10:23.145 --> 00:10:31.480 Well, look, rule number 2, always applies. When you've got feedback in an op-amp circuit. 00:10:31.480 --> 00:10:36.380 The op-amp tries to keep these two input voltages identical. 00:10:36.380 --> 00:10:39.480 So, because of the rule, this inverting input here, 00:10:39.480 --> 00:10:42.360 is going to be equal to this pin up here. 00:10:42.360 --> 00:10:47.800 The op-amp will ensure that by driving this output to get this input to match this one. 00:10:47.800 --> 00:10:49.085 So, if you got one volt here, 00:10:49.085 --> 00:10:50.825 then we've got one volt here, 00:10:50.825 --> 00:10:53.100 and because it's just connected by a bit of wire, 00:10:53.100 --> 00:10:55.485 we got to get one volt out here. 00:10:55.485 --> 00:10:57.020 That's why it's called a buffer. 00:10:57.020 --> 00:11:00.525 It's not an amplifier because there is no gain. 00:11:00.525 --> 00:11:02.310 One volt in, one volt out, 00:11:02.310 --> 00:11:05.000 minus one volt in, minus one volt out. 00:11:05.000 --> 00:11:07.400 Whatever the voltage is within 00:11:07.400 --> 00:11:12.030 the limits of the power supply voltages you see. What you see is that? 00:11:12.030 --> 00:11:17.285 Well, rule number 1. No current flows in or out of the inputs. 00:11:17.285 --> 00:11:19.900 So, nothing, no current flows in. 00:11:19.900 --> 00:11:21.905 So, if you've got a load over here, I don't know, 00:11:21.905 --> 00:11:25.200 it could be some sort of sensor or whatever. 00:11:25.200 --> 00:11:31.830 It could be a low pass filter. For example, like you're fading a pulse with 00:11:31.830 --> 00:11:35.415 modulated signal from your micro-controller or something like that, 00:11:35.415 --> 00:11:37.515 and then you want to buffer that voltage off there. 00:11:37.515 --> 00:11:40.115 Because no current flows into the input. 00:11:40.115 --> 00:11:45.250 This op-amp does not disturb your sensor or your circuit 00:11:45.250 --> 00:11:46.570 that you're actually trying to do. 00:11:46.570 --> 00:11:51.820 It's what's called a very high impedance input, essentially open circuits. 00:11:51.820 --> 00:11:53.990 So, it doesn't disturb anything you hook up to it. 00:11:53.990 --> 00:11:58.710 But the op-amp has what's called a low impedance output, 00:11:58.710 --> 00:12:02.080 so it can drive a reasonable amount of current, 00:12:02.080 --> 00:12:04.080 milli-amps, tens of milli-amps. 00:12:04.080 --> 00:12:08.090 That sought of things some can go as high as a couple of 100 milli-amps via power op-amps, 00:12:08.090 --> 00:12:10.425 but it can drive a reasonable amount of current. 00:12:10.425 --> 00:12:13.230 So, that's why it's buffering the signal, 00:12:13.230 --> 00:12:16.995 a high impedance signal and giving you a low impedance output. 00:12:16.995 --> 00:12:22.385 Just allows you to drive things with a sensitive input like that. 00:12:22.385 --> 00:12:26.105 Pretty easy. Very useful configuration, the op-amp buffer. 00:12:26.105 --> 00:12:28.585 Now the next configuration we're going to take a look at 00:12:28.585 --> 00:12:31.725 is what's called the non-inverting amplifier, 00:12:31.725 --> 00:12:35.950 and this is where we tie him L op-amp based that huge, 00:12:35.950 --> 00:12:40.890 unwieldy gain that changes everywhere with temperature and it's horrible. 00:12:40.890 --> 00:12:43.800 Anyway, it's got this massive unusable gain in there as 00:12:43.800 --> 00:12:47.750 a differential amplifier but as a single ended amplifier, 00:12:47.750 --> 00:12:50.000 that's what single end domains you fade input here, 00:12:50.000 --> 00:12:52.080 and it's always referenced to ground. 00:12:52.080 --> 00:12:56.065 We can use these as a single ended amplifier, 00:12:56.065 --> 00:13:01.260 and we can time that gain by adding negative feedback on it, 00:13:01.260 --> 00:13:05.100 and I want to explain negative and positive feedback in the mechanisms and how it works. 00:13:05.100 --> 00:13:07.855 Because, well, that's for a more advanced topic. 00:13:07.855 --> 00:13:10.885 But anyway, we fade in a feedback resistor here. 00:13:10.885 --> 00:13:11.970 Just like we did before, 00:13:11.970 --> 00:13:16.330 we showed it up but we put a resistor in there and we put a resistor back down to ground. 00:13:16.330 --> 00:13:20.125 So, what it's doing now is this input, the inverting input, 00:13:20.125 --> 00:13:25.213 is taking a small portion. This feedback resistor we'll call R_f, 00:13:25.213 --> 00:13:28.580 is always bigger than R_1 here. 00:13:28.580 --> 00:13:34.595 So, we've just got a voltage divider here that feeds back a smallest part of the input, 00:13:34.595 --> 00:13:36.660 and that's essentially what negative feedback it. 00:13:36.660 --> 00:13:42.255 You're taking a part of the output and you're feeding it back to the input, 00:13:42.255 --> 00:13:45.325 and there's a very simple formula you need to remember for 00:13:45.325 --> 00:13:48.510 this non-inverting amplifier configuration. 00:13:48.510 --> 00:13:53.639 I won't try and derive it, but the gain of this amplifier or what's called A_v, 00:13:53.639 --> 00:13:55.455 that's the actual terminology used. 00:13:55.455 --> 00:13:58.020 A_v is just gain. You can use gain. 00:13:58.020 --> 00:14:03.335 Gain equals R_f. The feedback resistor divided by R_1, 00:14:03.335 --> 00:14:05.910 which goes down to ground here, plus one. 00:14:05.910 --> 00:14:08.860 You've got to add that plus one on there. So, easy. 00:14:08.860 --> 00:14:11.790 If we've got annoying k feedback resistor and a 1K, 00:14:11.790 --> 00:14:13.635 resistor down to ground here. 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. 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. 00:14:25.890 --> 00:14:29.420 Because we have got positive and negative rials which we'll get into, 00:14:29.420 --> 00:14:33.945 we can feed Ac or DC signals into here about ground 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. 00:14:39.175 --> 00:14:40.470 So, there you go. 00:14:40.470 --> 00:14:45.415 That is the basic configuration of a non-inverting amplifier. 00:14:45.415 --> 00:14:47.390 You might see weird configurations. 00:14:47.390 --> 00:14:50.625 They might be a capacitor across here or something like that, 00:14:50.625 --> 00:14:52.410 which we won't get into in this one. 00:14:52.410 --> 00:14:55.015 But the configuration is the same, 00:14:55.015 --> 00:14:57.380 if you see your input being fed into 00:14:57.380 --> 00:15:01.595 the non-inverting input and the feedback going back to the inverting input, 00:15:01.595 --> 00:15:04.760 you know that's a non-inverting amplifier, 00:15:04.760 --> 00:15:07.810 and this formula here applies. 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, 00:15:13.305 --> 00:15:16.750 because their feedback resistor is zero, was zero. 00:15:16.750 --> 00:15:20.270 So, zero on one here which was infinite. 00:15:20.270 --> 00:15:26.720 So zero on over infinity or very large value is zero plus one. 00:15:26.720 --> 00:15:28.570 So, our gain is one. 00:15:28.570 --> 00:15:31.825 That's why our buffer had a gain of one, easy. 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. 00:15:36.940 --> 00:15:40.465 We've already looked at the first one, which was the non-inverting amplifier. 00:15:40.465 --> 00:15:42.820 The buffer, was just a variation of that. 00:15:42.820 --> 00:15:45.790 Now, we have, instead of the non-inverting amplifier, 00:15:45.790 --> 00:15:48.515 we have the inverting amplifier. 00:15:48.515 --> 00:15:50.935 How can you tell it's an inverting amplifier? 00:15:50.935 --> 00:15:54.000 Well, just like before, we could tell it was a non-inverting 00:15:54.000 --> 00:15:57.275 one by the signal going into the positive input, here. 00:15:57.275 --> 00:16:00.495 The non-inverting input, hence, the name non inverting amplifier, 00:16:00.495 --> 00:16:07.465 our signaled nail goes into our inverting amplifier pin. 00:16:07.465 --> 00:16:10.340 So, hence, it's called an inverting amplifier. 00:16:10.340 --> 00:16:13.200 You'll notice that I've switched the two symbols around here. 00:16:13.200 --> 00:16:14.915 The positive is now on the bottom. 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, 00:16:20.680 --> 00:16:23.715 and that's what you'll commonly find in schematics 00:16:23.715 --> 00:16:27.085 and CAD packages and all stuff you might find them flipped around, 00:16:27.085 --> 00:16:28.765 upside down back to front. 00:16:28.765 --> 00:16:31.050 Whoop-de-doo, all going all around the place. 00:16:31.050 --> 00:16:33.780 Some pointing down for various feedback possible. 00:16:33.780 --> 00:16:36.665 So, that's exactly the same op-amp. 00:16:36.665 --> 00:16:38.520 It's just visually different. 00:16:38.520 --> 00:16:40.250 You can draw it anyway you all want. 00:16:40.250 --> 00:16:44.430 Now, our inverting amplifier, that this one is, 00:16:44.430 --> 00:16:47.040 we have the same as before. We have our feedback resistor, 00:16:47.040 --> 00:16:53.975 we have our negative feedback going to, in this case, our inverting amplifier pin, 00:16:53.975 --> 00:16:55.580 instead of our non-inverting one. 00:16:55.580 --> 00:17:01.560 So, now we are feeding out input through the resistor here. 00:17:01.560 --> 00:17:04.210 So, it's a different configuration, our signal is not going 00:17:04.210 --> 00:17:07.650 directly into the non-inverting pin. 00:17:07.650 --> 00:17:11.980 This brings up our next really important concept with op-amp that you 00:17:11.980 --> 00:17:13.954 really need to understand. 00:17:13.954 --> 00:17:19.984 Here's where rule number 1, really comes into play in trying to analyze this thing. 00:17:19.984 --> 00:17:23.464 It's called virtual ground. Stick with me. 00:17:23.464 --> 00:17:25.785 So, once again, how do we analyze this? 00:17:25.785 --> 00:17:28.835 Always go back to your two rules. 00:17:28.835 --> 00:17:30.600 What's our second rule here? 00:17:30.600 --> 00:17:33.460 The op-amp tries to keep the input voltages the same. 00:17:33.460 --> 00:17:37.270 In fact, it will, if you've got this non-inverting configuration 00:17:37.270 --> 00:17:38.850 and you haven't hit the rails yet. 00:17:38.850 --> 00:17:41.115 So, if the amplifier is working normally, 00:17:41.115 --> 00:17:44.010 within normal bounds of your past [inaudible] rail, 00:17:44.010 --> 00:17:47.865 these two inputs will always be the same. 00:17:47.865 --> 00:17:54.240 So, we're actually connected our non-inverting input down to ground here. 00:17:54.240 --> 00:17:56.580 It's connected to ground. We forced it to ground. 00:17:56.580 --> 00:17:58.055 It's never going to change. 00:17:58.055 --> 00:18:01.560 So, what is the inverting input here going to do? 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. 00:18:05.690 --> 00:18:09.450 So, this point is also going to be ground or zero volts. 00:18:09.450 --> 00:18:13.800 So, this seems like almost like a pointless circuit, 00:18:13.800 --> 00:18:16.450 because look at rule number 1, no current flows in or out. 00:18:16.450 --> 00:18:22.255 So, there's no current flowing in or out of that pin and its ground. 00:18:22.255 --> 00:18:28.065 We've got both pins grounded and no current flows in or out. 00:18:28.065 --> 00:18:30.880 So, what's the point of having an op-amp? 00:18:30.880 --> 00:18:33.215 It's very confusing concept. 00:18:33.215 --> 00:18:37.565 But once you grasp it, you go, ugh, it's easy and it's quite brilliant. 00:18:37.565 --> 00:18:41.390 So, the op-amp you, remember, does whatever it needs to 00:18:41.390 --> 00:18:43.630 on the output drives it to whatever voltage 00:18:43.630 --> 00:18:46.360 positive and negative in order to make sure that 00:18:46.360 --> 00:18:50.495 this inverting pin here is equal to the non-inverting pin down here. 00:18:50.495 --> 00:18:52.620 Makes them the same. We've force this pin, 00:18:52.620 --> 00:18:54.150 so it can't change this pin. 00:18:54.150 --> 00:18:56.820 All it can do is change the voltage 00:18:56.820 --> 00:19:00.690 via the nature of the feedback resistor here to make this zero. 00:19:00.690 --> 00:19:04.635 Trust me, we'll do a practical measurement of this in a minute. 00:19:04.635 --> 00:19:07.885 This node here will actually be zero volts. 00:19:07.885 --> 00:19:10.730 This confuses the heck out of a lot of beginners. 00:19:10.730 --> 00:19:12.890 They build up their op-amps circuit, they start probing 00:19:12.890 --> 00:19:15.755 around and they've got their input signal here. 00:19:15.755 --> 00:19:17.490 It's a one kilohertz, one volt, side way, for example. 00:19:17.490 --> 00:19:22.545 And here's how they measure. This side of the resistor and the signals there. 00:19:22.545 --> 00:19:24.585 They measure this side of the resistor. 00:19:24.585 --> 00:19:27.300 It's ground, the signals is vanished. 00:19:27.300 --> 00:19:31.920 where's it gone? Strange, but true. 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. 00:19:36.905 --> 00:19:40.249 Once again, the DC case to make it easy. 00:19:40.249 --> 00:19:43.590 We have got one volt on the input here. 00:19:43.590 --> 00:19:46.595 Positive one volt with respect to ground of course. 00:19:46.595 --> 00:19:49.090 Now, we've said before, that trust me, 00:19:49.090 --> 00:19:52.380 we'll measure it later but this pin is going to be ground. 00:19:52.380 --> 00:19:55.215 It is going to be zero volts there always. 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, 00:20:01.130 --> 00:20:05.455 we're going to have, one milli-amp flowing through there. 00:20:05.455 --> 00:20:06.770 Where does it flow? 00:20:06.770 --> 00:20:10.655 Well, it doesn't flow down here to ground. 00:20:10.655 --> 00:20:14.415 How can it? Because no current. Rule number 1. 00:20:14.415 --> 00:20:17.910 No current flows into or out of the input pins. 00:20:17.910 --> 00:20:20.270 So, it can't flow through the ground here. 00:20:20.270 --> 00:20:23.870 It has to flow. It's going through here, it's going somewhere. 00:20:23.870 --> 00:20:26.085 There's one volt across that 1K resistor, 00:20:26.085 --> 00:20:28.720 Ohm's law, always that must be obeyed. 00:20:28.720 --> 00:20:30.930 So, that current is flowing, trust me. 00:20:30.930 --> 00:20:32.885 It can't flow into the input pin. 00:20:32.885 --> 00:20:34.335 When we know it's high impedance, 00:20:34.335 --> 00:20:37.985 so it must be flowing up here like this through 00:20:37.985 --> 00:20:42.150 this 10K resistor and it's being sourced from the output. 00:20:42.150 --> 00:20:45.335 Remember, this op-amp has internal circuitry. 00:20:45.335 --> 00:20:51.660 It's got an output buffer, so it can actually drive currents into 00:20:51.660 --> 00:20:56.010 and out of the various supplies back into there. 00:20:56.010 --> 00:20:59.330 That is where it's sinking the current too. 00:20:59.330 --> 00:21:01.550 That's the sneaky part about this. 00:21:01.550 --> 00:21:06.005 Our current is now being forced up this node, here, 00:21:06.005 --> 00:21:10.795 and is flowing through, in this case, feedback resistor R_f, which is 10K, 00:21:10.795 --> 00:21:13.450 I made it 10 times larger you will see why in a minute, 00:21:13.450 --> 00:21:15.965 then it must be flowing through this. 00:21:15.965 --> 00:21:18.630 So, we must have a voltage drop across that resistor. 00:21:18.630 --> 00:21:21.960 Once again, Ohm's law, always must be obeyed. 00:21:21.960 --> 00:21:26.500 So, if we have got that one milli-amp flowing through our 10K there, 00:21:26.500 --> 00:21:31.320 we're going to have 10 volt drop across this resistor with 00:21:31.320 --> 00:21:35.370 positive here and negative here. 00:21:35.370 --> 00:21:40.760 Aha, negative. These are voltages are with respect to the ground here. 00:21:40.760 --> 00:21:42.950 Now, here's where it gets a little bit tricky. 00:21:42.950 --> 00:21:45.815 This positive voltage here, it's we are going to get 00:21:45.815 --> 00:21:49.265 the plus 10 volts across that resistor there. 00:21:49.265 --> 00:21:55.050 But because this pin is positive, but were forced, we know these pin is zero, okay. 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 00:21:59.045 --> 00:22:03.150 and rule number 2 here, in what's called a virtual ground , 00:22:03.150 --> 00:22:04.335 which I'll talk about in a minute. 00:22:04.335 --> 00:22:07.790 Then we have, that means, if this is ground, 00:22:07.790 --> 00:22:14.825 this is positive then we've got minus 10 volts coming out of here. 00:22:14.825 --> 00:22:21.360 Bingo. There's our inverting amplifier one vote in minus 10 volts out. 00:22:21.360 --> 00:22:30.260 So, our gain, our formula A_v gain equals R_f on R_1. 00:22:30.260 --> 00:22:34.130 There is no plus one with the inverting amplifier. 00:22:34.130 --> 00:22:38.175 The plus one only applies to the other non-inverting configuration. 00:22:38.175 --> 00:22:40.590 So, by Y of op-amp action, 00:22:40.590 --> 00:22:43.575 we'll call it a negative feedback here. 00:22:43.575 --> 00:22:46.140 This point, this node here, 00:22:46.140 --> 00:22:51.210 at the inverting pin is what's called a virtual ground. 00:22:51.210 --> 00:22:54.365 Because typically, in this configuration, 00:22:54.365 --> 00:22:58.100 it is actually grounded because we've grounded this pin, it doesn't have to be, 00:22:58.100 --> 00:23:00.760 we can fade other voltages into this pin and 00:23:00.760 --> 00:23:04.325 offset and do all sorts of other stuff but it's still called, 00:23:04.325 --> 00:23:06.615 even if you do fade another opinion here, 00:23:06.615 --> 00:23:08.720 it's still called virtual ground. 00:23:08.720 --> 00:23:10.890 Because it's virtual, it's not real, 00:23:10.890 --> 00:23:14.335 it's not hard tied, if it was hard tied to ground, 00:23:14.335 --> 00:23:17.045 if we actually tied that pin to ground, 00:23:17.045 --> 00:23:18.410 this thing wouldn't work. 00:23:18.410 --> 00:23:21.910 Because all of our current would flow through here. 00:23:21.910 --> 00:23:26.125 Through this resistor down to ground and around like that. 00:23:26.125 --> 00:23:28.610 Then this output here, well, 00:23:28.610 --> 00:23:30.760 it wouldn't know what to do the output would be zero 00:23:30.760 --> 00:23:33.180 because they'd be zero volts are difference in here. 00:23:33.180 --> 00:23:37.640 Remember it's still a differential amplifier as such. 00:23:37.640 --> 00:23:39.420 So, we've got zero votes difference here. 00:23:39.420 --> 00:23:40.585 We're going to get zero out. 00:23:40.585 --> 00:23:43.610 We'd have no current flowing through here and would have zero volts out. 00:23:43.610 --> 00:23:50.010 So, you can see that it doesn't work unless if you tied that hard brand. 00:23:50.010 --> 00:23:53.965 But when it becomes a virtual ground by nature of the op-amp action, 00:23:53.965 --> 00:23:55.670 it will magically works. 00:23:55.670 --> 00:23:57.105 I hope that makes sense. 00:23:57.105 --> 00:23:59.375 Because once you get it, it's really easy. 00:23:59.375 --> 00:24:02.395 So, if functionality wise it's pretty much exactly like 00:24:02.395 --> 00:24:04.650 the non-inverting amplifier except it 00:24:04.650 --> 00:24:08.435 inverts and that's it and the gain formula is slightly different. 00:24:08.435 --> 00:24:11.400 But apart from that pretty much works exactly the same, 00:24:11.400 --> 00:24:16.395 but that magic virtual ground is at play in this configuration. 00:24:16.395 --> 00:24:21.050 Of course, as with op-amps there DC couples or works with DC signals. 00:24:21.050 --> 00:24:23.230 You can just fade in a fixed DC voltage. 00:24:23.230 --> 00:24:26.880 As I said one volt DC and would give minus 10 volts out. 00:24:26.880 --> 00:24:31.830 In this case with these value resistance or we can fade in a one volt peak 00:24:31.830 --> 00:24:36.780 to peak or RMS sine wave for example, about the ground. 00:24:36.780 --> 00:24:38.375 So, it's centered on ground like this. 00:24:38.375 --> 00:24:40.550 This is the blue waveform here. 00:24:40.550 --> 00:24:43.200 Let's just say that's one volt, it's not quite the scale. 00:24:43.200 --> 00:24:47.730 But you'll get the idea and then our output will be the inverse of that. 00:24:47.730 --> 00:24:49.670 So, when the input rises, 00:24:49.670 --> 00:24:53.655 the output goes negative because it's an inverting amplifier. 00:24:53.655 --> 00:24:56.000 Now, of course one of the disadvantages of 00:24:56.000 --> 00:24:58.860 the inverting amplifier compared to the non-inverting we saw 00:24:58.860 --> 00:25:04.015 before is that as you can see there is input current coming from your load here. 00:25:04.015 --> 00:25:08.180 So, you don't want to use this when you have a high impedance load. 00:25:08.180 --> 00:25:12.275 Because then it can change the gain equation and marks everything up. 00:25:12.275 --> 00:25:16.970 That's where you want a non-inverting amplifier or at least a buffer. 00:25:16.970 --> 00:25:18.720 Some people will actually follow, 00:25:18.720 --> 00:25:24.440 will put a buffer on the input here and then drive the inverting amplifier. 00:25:24.440 --> 00:25:26.000 But usually in that sort of case, 00:25:26.000 --> 00:25:28.490 you'd probably use a non-inverting amplifier. 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 00:25:34.390 --> 00:25:36.710 and all these sort of stuff and that 00:25:36.710 --> 00:25:40.810 single supply op-amps or try and keep it as brief as possible. 00:25:40.810 --> 00:25:42.450 Because assorting this configuration, 00:25:42.450 --> 00:25:45.240 the op-amp only has two power pins. 00:25:45.240 --> 00:25:48.700 It's usually called V plus and V minus. 00:25:48.700 --> 00:25:51.410 Now, v minus you can actually 00:25:51.410 --> 00:25:54.800 connect that to ground there is nothing regardless of what the daughter 00:25:54.800 --> 00:25:58.060 she's telling you there's nothing inherent in op-amps that 00:25:58.060 --> 00:26:01.325 make them really a single supply op-amps. 00:26:01.325 --> 00:26:04.760 So, you can take an op-amp that is V plus and V minus and 00:26:04.760 --> 00:26:09.425 connect these down to ground like that. 00:26:09.425 --> 00:26:11.210 There's nothing to stop you as long as you meet 00:26:11.210 --> 00:26:15.660 the minimum voltage specification and don't exceed the maximum etc. 00:26:15.660 --> 00:26:17.980 So, what happens if we did that in this case? 00:26:17.980 --> 00:26:21.850 Our input is a non-inverting input is also grounded here. 00:26:21.850 --> 00:26:24.625 Well, now it becomes a problem. 00:26:24.625 --> 00:26:27.680 You get into the practical limitations of op-amps. 00:26:27.680 --> 00:26:31.985 We've been talking about what's called an ideal op-amp up until this point. 00:26:31.985 --> 00:26:34.950 These rules here aren't strictly true, 00:26:34.950 --> 00:26:38.550 I lied but they still a fantastic way, 00:26:38.550 --> 00:26:43.835 even professionals use to analyze these circuits as a first order, as a first pass. 00:26:43.835 --> 00:26:45.485 No current flows in or out. 00:26:45.485 --> 00:26:48.335 Well, if you've been watching my videos you know I've done 00:26:48.335 --> 00:26:51.500 a previous video on this talking about input bias currents. 00:26:51.500 --> 00:26:55.020 A little itty bitty teeny-weeny currents can flow 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. 00:27:00.015 --> 00:27:04.110 That's a real practical limitation of these things. 00:27:04.110 --> 00:27:06.365 The other one is that, 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. 00:27:09.800 --> 00:27:16.045 The inputs cannot necessarily go right to the rials bit, 00:27:16.045 --> 00:27:17.750 whether it's positive, negative, 00:27:17.750 --> 00:27:19.580 reference to ground or whatever. 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. 00:27:25.200 --> 00:27:30.055 In this case, if you had a rial to rial input op-amp then, yeah, 00:27:30.055 --> 00:27:33.325 you might be able to get away with this and have 00:27:33.325 --> 00:27:38.635 the non-inverting input tied down to ground like this. 00:27:38.635 --> 00:27:42.880 But hang on, what's the point of that? 00:27:42.880 --> 00:27:44.605 If you've only got ground, 00:27:44.605 --> 00:27:47.150 this is an inverting amplifier. 00:27:47.150 --> 00:27:48.595 It inverts your signal. 00:27:48.595 --> 00:27:50.315 So, if you fade one volt in, 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. 00:27:55.790 --> 00:28:00.765 But how does it do that when your supply is negative of that? 00:28:00.765 --> 00:28:03.715 It doesn't work. So, you have to, 00:28:03.715 --> 00:28:05.530 it's got no room to do it. 00:28:05.530 --> 00:28:08.300 So, your op-amp has to always be payload in 00:28:08.300 --> 00:28:12.950 the configuration that you expect your input signals to be referenced to. 00:28:12.950 --> 00:28:18.770 So if we were to use the inverting op-amp configuration like this 00:28:18.770 --> 00:28:24.865 with a single supply rail like this and we wanted to amplify AC signals, 00:28:24.865 --> 00:28:29.300 well, the signals can't go negative like this. 00:28:29.300 --> 00:28:30.870 I get a negative on the input but you never 00:28:30.870 --> 00:28:32.690 go to get that negative voltage on the output. 00:28:32.690 --> 00:28:35.850 But you still want to amplify a signal cleanly like this. 00:28:35.850 --> 00:28:39.070 But what we need to do is the zero-point, 00:28:39.070 --> 00:28:43.800 needs to go right down the bottom here like this. 00:28:43.800 --> 00:28:45.320 So, we need to offset. 00:28:45.320 --> 00:28:46.650 So, if that's zero volts, 00:28:46.650 --> 00:28:49.515 we need to offset our input ref, 00:28:49.515 --> 00:28:54.365 our input and output reference by a certain amount of voltage. How much? 00:28:54.365 --> 00:28:58.270 Well, typically, half of your supply rial to maximize your headroom. 00:28:58.270 --> 00:29:00.170 How do we do that? I hinted at it. 00:29:00.170 --> 00:29:03.855 Before you feed in if this is V plus, 00:29:03.855 --> 00:29:06.365 you'd go a V plus on two, 00:29:06.365 --> 00:29:08.290 you would feed that volt is half rial. 00:29:08.290 --> 00:29:12.580 They usually do that simply by putting a resistor like 00:29:12.580 --> 00:29:17.680 that going to V plus and a resistor down there, 00:29:17.680 --> 00:29:19.225 going down to ground, 00:29:19.225 --> 00:29:20.995 and bingo voltage divider. 00:29:20.995 --> 00:29:22.320 They show half rial. 00:29:22.320 --> 00:29:26.990 So, we're offsetting a voltage here, a virtual ground. 00:29:26.990 --> 00:29:30.400 Remember this is still called a virtual ground even though it's not going to be. 00:29:30.400 --> 00:29:32.225 So, the voltage here, 00:29:32.225 --> 00:29:36.805 is going to be equal to the voltage here due to our second op-amp rule. 00:29:36.805 --> 00:29:40.055 So, if our power supply is 20 volts for example, 00:29:40.055 --> 00:29:45.730 this point here would be half that if we make these exactly the same value. 00:29:45.730 --> 00:29:47.895 Of course, mark them the same value of half rial. 00:29:47.895 --> 00:29:54.565 So, we have an offset voltage here at this point and that shifts away fro up. 00:29:54.565 --> 00:29:57.480 We'll see that in the practical experiments to follow. 00:29:57.480 --> 00:30:01.300 Now, as I said some time back you might see some other components 00:30:01.300 --> 00:30:05.120 around here like few capacitors and things like that around the circuit, 00:30:05.120 --> 00:30:10.370 that is to change the bandwidth of the circuit effectively. 00:30:10.370 --> 00:30:13.430 Because we're not going to go into it I'll have to do 00:30:13.430 --> 00:30:16.700 a second part of this video that goes into op-amp bandwidth and things like that. 00:30:16.700 --> 00:30:22.160 I have done one on cascading op-amp bandwidths which I'll linking down below. 00:30:22.160 --> 00:30:24.770 But suffice it to say that 00:30:24.770 --> 00:30:29.260 an ideal op-amp that we've been looking at has an infinite bandwidth. 00:30:29.260 --> 00:30:32.150 It's infinite frequencies and signals but in practice, 00:30:32.150 --> 00:30:35.030 no of course now you practical op-amp might have 00:30:35.030 --> 00:30:39.475 a one megahertz bandwidth or a 100 kilohertz bandwidth or something like that. 00:30:39.475 --> 00:30:41.970 It could be a nice fast 100 megahertz, 00:30:41.970 --> 00:30:45.600 but it's always going to have a bandwidth which changes with 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. 00:30:50.075 --> 00:30:53.045 But sometimes you might see a little bypass capping, 00:30:53.045 --> 00:30:56.490 there might be 10 buff or a 100 buff, something like that. 00:30:56.490 --> 00:31:00.100 That's just a rolling off the frequency response of that. 00:31:00.100 --> 00:31:05.010 Likewise, you might see a little cap across something like this, for example, 00:31:05.010 --> 00:31:11.130 if you are offsetting this thing using a single supply like this. 00:31:11.130 --> 00:31:15.230 I won't go into the details but basically any noise 00:31:15.230 --> 00:31:19.305 on this point here will be amplified and picked up on the virtual ground, 00:31:19.305 --> 00:31:21.055 so you'll get noise on your output signal. 00:31:21.055 --> 00:31:24.945 So, you might stick a big OS in one or 10 micro-farad cap 00:31:24.945 --> 00:31:29.735 across here for example and really make that virtual ground really noise free. 00:31:29.735 --> 00:31:32.630 But that's beyond the basics. 00:31:32.630 --> 00:31:34.800 One little mistake that I noticed, oops! 00:31:34.800 --> 00:31:37.585 My formula here for the inverting amplifier, 00:31:37.585 --> 00:31:42.295 it needs a negative in front of it because the gain is actually native. 00:31:42.295 --> 00:31:44.400 So, the gain needs, 00:31:44.400 --> 00:31:49.125 in this case is not 10, it's minus 10. 00:31:49.125 --> 00:31:52.910 So, just back to this voltage rial thing briefly, 00:31:52.910 --> 00:31:55.520 because it is something that is rather 00:31:55.520 --> 00:31:59.440 confusing because there is no ground pin on an op-amp. 00:31:59.440 --> 00:32:01.585 There is only the positive and negative. 00:32:01.585 --> 00:32:03.170 So, we'll, where does your reference go? 00:32:03.170 --> 00:32:05.900 Well the reference is part of the external circuit. 00:32:05.900 --> 00:32:09.890 In this case, back to our non-inverting amplifier configuration. 00:32:09.890 --> 00:32:12.275 He's our ground reference here and then 00:32:12.275 --> 00:32:15.920 our positive and negative supply is here like this. 00:32:15.920 --> 00:32:19.035 I plus 15 volts and minus 15 volts. 00:32:19.035 --> 00:32:23.660 If we want to fade in a signal that goes both positive and negative. 00:32:23.660 --> 00:32:27.230 If we're only fading in a signal that's positive above ground 00:32:27.230 --> 00:32:32.220 then this here could be tied down to here like this. 00:32:32.220 --> 00:32:35.410 Then it has to be above that, 00:32:35.410 --> 00:32:38.120 the output cannot magically go negative. 00:32:38.120 --> 00:32:41.625 It can only go negative to a ground reference if you have 00:32:41.625 --> 00:32:45.905 that minus 15 volt rialling there. Clear as mud. 00:32:45.905 --> 00:32:48.650 Just like the inverting configuration, 00:32:48.650 --> 00:32:51.820 if we wanted to pair on this from a split supply, 00:32:51.820 --> 00:32:55.325 we can have this grounded like this and then we can add 00:32:55.325 --> 00:33:00.895 a bias voltage in here like this to actually offset the voltage. 00:33:00.895 --> 00:33:03.835 Then it can get into all sorts of we doing 00:33:03.835 --> 00:33:07.020 wonderful things with AC coupling these amplifies. 00:33:07.020 --> 00:33:10.790 All of the opening of configurations we looked at have been DC coupled, 00:33:10.790 --> 00:33:12.850 but you can actually AC couple them so much. 00:33:12.850 --> 00:33:18.160 Why is stopped might seem capacitors on the inputs and outputs to the op-amps. 00:33:18.160 --> 00:33:22.070 Now, he's a tricky configuration which I'll briefly touch on that 00:33:22.070 --> 00:33:24.740 combines the two different configurations 00:33:24.740 --> 00:33:27.585 we've seen before and a couple of the things we've looked at. 00:33:27.585 --> 00:33:29.440 It's the differential amplifier. 00:33:29.440 --> 00:33:31.425 You know how I said op-amps are, 00:33:31.425 --> 00:33:34.445 essentially a differential amplifier that's how they work, 00:33:34.445 --> 00:33:38.530 but they do that in the open-loop configuration. 00:33:38.530 --> 00:33:40.445 So, they hopeless, they're useless for that. 00:33:40.445 --> 00:33:47.320 But if you combine the inverting amplifier configuration that we just saw. 00:33:47.320 --> 00:33:49.850 So, we've got the feedback going here our signal going in, 00:33:49.850 --> 00:33:53.605 that's a standard inverting configuration. 00:33:53.605 --> 00:33:59.955 We have exactly those two resistors that we saw before to buyers that voltage up. 00:33:59.955 --> 00:34:02.275 But instead of going to the supplier rial, 00:34:02.275 --> 00:34:08.719 we make that other differential input and bingo it becomes a differential amplifier. 00:34:08.719 --> 00:34:12.545 I'll let you go through the actual calculation yourself to find out. 00:34:12.545 --> 00:34:15.260 But basically, the difference that we fading in, 00:34:15.260 --> 00:34:18.830 if we fade it in any one volt into here and 1.1 volts into here, 00:34:18.830 --> 00:34:21.344 we have a difference of 0.1 volts and 00:34:21.344 --> 00:34:25.270 the gain of this amplifier exactly like the inverting configuration, 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. 00:34:29.810 --> 00:34:33.440 So, R_2 on R_1 10K on 1K. 00:34:33.440 --> 00:34:35.590 We have a gain and you're going to add negative in there. 00:34:35.590 --> 00:34:37.804 So, it's a gain of minus 10. 00:34:37.804 --> 00:34:41.495 But because L bias voltages is not fixed it's 00:34:41.495 --> 00:34:46.760 actually the differential input signal. Look what happens. 00:34:46.760 --> 00:34:48.290 We got one volt here. 00:34:48.290 --> 00:34:49.969 We've got a divider it here. 00:34:49.969 --> 00:34:52.040 R_1 these two values are the same, 00:34:52.040 --> 00:34:53.469 R_1 is equal to R_1 here, 00:34:53.469 --> 00:34:54.925 R_2 is equal to R_2 here. 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. 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, 00:35:04.480 --> 00:35:09.205 we'll have 0.99999 repaid out at that point there, 00:35:09.205 --> 00:35:10.935 and that becomes our virtual ground. 00:35:10.935 --> 00:35:13.095 Bingo, I will have that same voltage there, 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, 00:35:19.610 --> 00:35:22.315 that and you get X amount of current flowing through here, 00:35:22.315 --> 00:35:25.235 which then must flow through the 10 K which has 1. 00:35:25.235 --> 00:35:30.030 999 voltage across it subtract the difference there. 00:35:30.030 --> 00:35:33.975 It's exactly the same configuration as before with the bias voltage. 00:35:33.975 --> 00:35:37.690 But they will lift with an output voltage of minus one. 00:35:37.690 --> 00:35:43.855 So, if amplified, the difference in our input signal by the gain here 10. 00:35:43.855 --> 00:35:48.530 It's not a terrific differential amplifier, but it works. 00:35:48.530 --> 00:35:53.545 So, we've timed out op-amp that is a differential amplifier anyway, but pretty unusable. 00:35:53.545 --> 00:35:57.555 We've actually made it into a pretty usable differential amplifier. 00:35:57.555 --> 00:36:00.500 Beauty. Just combines both of 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, 00:36:04.650 --> 00:36:08.860 and just briefly another one of these tricky configurations goes back to the name 00:36:08.860 --> 00:36:13.060 the operational amplifier and one of those mathematical operations the integrator. 00:36:13.060 --> 00:36:15.175 We won't go into integrals and all that sort of stuff. 00:36:15.175 --> 00:36:21.930 But what we can do basic inverting configuration here instead of a feedback resistor, 00:36:21.930 --> 00:36:25.130 we have a feedback capacitor. What does that do? 00:36:25.130 --> 00:36:28.590 Well, L standard input voltage here following the rule 00:36:28.590 --> 00:36:33.685 no current flows in but we have a virtual ground of course rule number two. 00:36:33.685 --> 00:36:35.955 So, if that's one K, 00:36:35.955 --> 00:36:40.420 and that's one volt there where we have one milli-amp flowing through that resistor. 00:36:40.420 --> 00:36:41.960 Where does it flow? 00:36:41.960 --> 00:36:43.475 Can't flow into the op-amp, 00:36:43.475 --> 00:36:47.100 it's got to flow up here and through the capacitor. 00:36:47.100 --> 00:36:53.215 So, you've got effectively a constant current of one milli-amp. 00:36:53.215 --> 00:36:57.275 This is now a constant current flowing through this resistor. 00:36:57.275 --> 00:37:01.095 When you have a constant current flowing through a capacitor, 00:37:01.095 --> 00:37:03.770 you end up with. 00:37:03.770 --> 00:37:08.255 >> Well, in this case, it's going to ramp negative, down like that. 00:37:08.255 --> 00:37:14.450 If our input is a step and it goes up like that, 00:37:14.450 --> 00:37:18.605 the constant current, because it takes time to charge a capacitor, 00:37:18.605 --> 00:37:22.545 the voltage on the capacitor will increase like that. 00:37:22.545 --> 00:37:24.945 I say increase because it's an inverting amplifier. 00:37:24.945 --> 00:37:26.195 So, it's going to go negative. 00:37:26.195 --> 00:37:28.025 But that's what it does, 00:37:28.025 --> 00:37:29.820 and that's an integrator, 00:37:29.820 --> 00:37:35.100 and that is actually a mathematical integral of your input signal. 00:37:35.100 --> 00:37:37.535 Anyway, that's way too much theory, 00:37:37.535 --> 00:37:41.055 more than I wanted to do and longer than I wanted to take actually. 00:37:41.055 --> 00:37:44.540 But suffice it to remember that these two rules 00:37:44.540 --> 00:37:48.270 of op-amps allow you to analyze practically any configuration, 00:37:48.270 --> 00:37:49.650 and as a bit of homework, 00:37:49.650 --> 00:37:54.260 I got to recommend you look at the summing op-amp configuration, 00:37:54.260 --> 00:37:56.840 the summing amplifier, and figure out how it works because 00:37:56.840 --> 00:37:59.690 you're going to be using those two rules to figure it out. 00:37:59.690 --> 00:38:01.220 So, I'll leave that one up to you. 00:38:01.220 --> 00:38:02.960 But enough of that, let's head on over to 00:38:02.960 --> 00:38:05.240 the benchy and see if we can measure some stuff. 00:38:05.240 --> 00:38:09.185 Make sure I wasn't bullshitting you about this virtual ground stuff. 00:38:09.185 --> 00:38:11.420 Let's check it out. Sounds a bit sas. 00:38:11.420 --> 00:38:13.500 See if it really works. 00:38:13.500 --> 00:38:15.405 All right, we're at the breadboard. 00:38:15.405 --> 00:38:19.910 Let's take a look at an inverting amplifier here because I wanted to show you 00:38:19.910 --> 00:38:25.700 that virtual ground point there just to show you that there really is no signal there. 00:38:25.700 --> 00:38:30.920 It actually vanishes in quote marks when you go from the input here to 00:38:30.920 --> 00:38:33.320 here and then it magically reappears at 00:38:33.320 --> 00:38:36.455 the output because that's how an op-amp works, as I've explained. 00:38:36.455 --> 00:38:39.230 Anyway, it got a jellybean LM358 here. 00:38:39.230 --> 00:38:40.550 It's actually a jewel op-amp. 00:38:40.550 --> 00:38:44.570 So, we've just tie it off the terminated the top op-amp here. 00:38:44.570 --> 00:38:50.295 We can probably do a separate video on that on how to properly terminate op-amps, 00:38:50.295 --> 00:38:52.190 that might make an interesting video. 00:38:52.190 --> 00:38:54.260 Thumbs up if you want to see that one. 00:38:54.260 --> 00:38:56.165 Anyway, here we go, I've got a configured, 00:38:56.165 --> 00:38:59.990 I've got a 10k input resistor here, 100k feedback. 00:38:59.990 --> 00:39:01.340 So, we got a gain of 10. 00:39:01.340 --> 00:39:04.340 The formula, of course, is the feedback resistor on that one, 00:39:04.340 --> 00:39:06.320 bingo, easy, times 10. 00:39:06.320 --> 00:39:09.555 So, I'm going to fade out two volts peak-to-peak input here. 00:39:09.555 --> 00:39:13.580 We should get 20 volts peak-to-peak on the output. 00:39:13.580 --> 00:39:18.335 So, we're using pretty much near the maximum supply rail of the LM358. 00:39:18.335 --> 00:39:21.335 In this case, I'm pairing it from plus/minus 15 volts. 00:39:21.335 --> 00:39:23.680 So, we have a split supply. 00:39:23.680 --> 00:39:24.980 So, our ground reference, 00:39:24.980 --> 00:39:27.110 our input signal is reference to a ground. 00:39:27.110 --> 00:39:28.545 I should actually draw that on there. 00:39:28.545 --> 00:39:30.195 There we go, that's clearer. 00:39:30.195 --> 00:39:33.725 So, our input is referenced to ground 00:39:33.725 --> 00:39:37.680 and our non-inverting input here is referenced to ground, 00:39:37.680 --> 00:39:39.845 and our output is referenced to ground also. 00:39:39.845 --> 00:39:44.730 But for signals to go negative or for output signals to go negative, 00:39:44.730 --> 00:39:47.720 we need a negative rail on here. 00:39:47.720 --> 00:39:49.785 So, we're using minus 15 volts. 00:39:49.785 --> 00:39:51.125 So, plus 15 to pair it, 00:39:51.125 --> 00:39:52.400 minus 15 as well. 00:39:52.400 --> 00:39:54.875 So, 30-volt total supply on there, 00:39:54.875 --> 00:39:59.015 allows us to go positive and negative signals, input and output. 00:39:59.015 --> 00:40:00.900 So, let's go over to our power supply. 00:40:00.900 --> 00:40:02.900 Here it is, plus/minus 15 volts. 00:40:02.900 --> 00:40:06.390 I got dual tracking on there and you notice that I've joined 00:40:06.390 --> 00:40:10.305 the supplies here generating the split supply. 00:40:10.305 --> 00:40:12.160 So, this one actually becomes the negative. 00:40:12.160 --> 00:40:14.895 So, this is our positive 15 from here to here. 00:40:14.895 --> 00:40:19.475 This is our negative 15 relative to here because we've strapped the positive one. 00:40:19.475 --> 00:40:24.660 However, and tada, there we go, we're feeding in. 00:40:24.660 --> 00:40:28.110 We've just got a one-kilohertz low-frequency signal, 00:40:28.110 --> 00:40:31.475 two volts peak-to-peak here on the input. 00:40:31.475 --> 00:40:36.160 You can see our input and output wave forms and these inputs are, of course, 00:40:36.160 --> 00:40:40.190 all AC coupled and their bandwidth limited as well to 00:40:40.190 --> 00:40:44.630 20 megahertz to reduce the noise and we're using our high resolution mode as well. 00:40:44.630 --> 00:40:47.315 So, we get some boxcar averaging in there. 00:40:47.315 --> 00:40:52.070 That's why we got a nice crisp waveform like that, beautiful. 00:40:52.070 --> 00:40:55.040 So, what happens if we turn our bandwidth spec to four? 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, 00:41:00.785 --> 00:41:02.720 going back to sample mode, there we go. 00:41:02.720 --> 00:41:06.975 We get our nice fuzzy wave forms because we've got that massively high bandwidth. 00:41:06.975 --> 00:41:09.435 That's the advantage. You can't go into averaging, of course, 00:41:09.435 --> 00:41:12.585 but "Hi Res" mode does boxcar averaging, just cleans it up. 00:41:12.585 --> 00:41:16.490 Of course, you can do envelope mode look at that, pretty horrible waveform. 00:41:16.490 --> 00:41:17.900 So, in looking at this sort of stuff, 00:41:17.900 --> 00:41:21.110 you definitely don't want to use your regular mode. 00:41:21.110 --> 00:41:23.240 You want "Hi Res" mode if you've got it. 00:41:23.240 --> 00:41:25.520 There you go, we're getting exactly what we expect. 00:41:25.520 --> 00:41:29.420 Look at that, the two volts peak-to-peak in roughly 20 volts out. 00:41:29.420 --> 00:41:33.095 There's probably going to be some error due to the resistors in here. 00:41:33.095 --> 00:41:35.270 Anyway, we get in our times 10. 00:41:35.270 --> 00:41:38.210 Of course, the blue waveform there is the input, 00:41:38.210 --> 00:41:40.065 that's 500 millivolts per division. 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. 00:41:44.695 --> 00:41:48.455 So, which is the yellow waveform there and look at that. 00:41:48.455 --> 00:41:51.170 Of course, because it's an inverting amplifier, 00:41:51.170 --> 00:41:54.625 the output is exactly 180 degrees out of phase. 00:41:54.625 --> 00:41:56.660 It's inverted. So, at the moment, 00:41:56.660 --> 00:41:58.920 I'm probing the input and the output. 00:41:58.920 --> 00:42:01.475 Now, you wanted to see the virtual ground, didn't you? 00:42:01.475 --> 00:42:03.470 What happens if I move my input probe, 00:42:03.470 --> 00:42:07.805 the blue waveform here from the input over to this? 00:42:07.805 --> 00:42:09.890 You'd expect to see the signal. 00:42:09.890 --> 00:42:13.595 But as I've told you and as you should trust me, 00:42:13.595 --> 00:42:15.985 let's move the probe over. 00:42:15.985 --> 00:42:19.100 >> That is our virtual ground point. 00:42:19.100 --> 00:42:22.025 Look, flat has attack. 00:42:22.025 --> 00:42:24.105 The signal has vanished. 00:42:24.105 --> 00:42:27.495 Magic. But of course you know it's not magic, 00:42:27.495 --> 00:42:32.975 it's just standard op-amp behavior with virtual ground on the input. 00:42:32.975 --> 00:42:34.850 That's how an op-amp works, 00:42:34.850 --> 00:42:37.300 and none of the current hasn't magically vanished. 00:42:37.300 --> 00:42:38.970 The current is going through the resistor. 00:42:38.970 --> 00:42:40.740 Ohm's Law still holds. 00:42:40.740 --> 00:42:44.450 Current is changing because we've got an AC resistor here. 00:42:44.450 --> 00:42:49.110 There's AC current flowing through this resistor and it's all flowing up here. 00:42:49.110 --> 00:42:53.910 But this point, by the nature of the op-amp action and the negative feedback, 00:42:53.910 --> 00:42:55.860 that is a virtual ground. 00:42:55.860 --> 00:42:57.885 An op-amp rule number two there. 00:42:57.885 --> 00:42:59.350 Inputs are the sign. 00:42:59.350 --> 00:43:02.990 The op-amp changes the output here in 00:43:02.990 --> 00:43:07.910 order to ensure that point is equal to that input there. 00:43:07.910 --> 00:43:11.390 Easy. That's why we don't see any signal on there. 00:43:11.390 --> 00:43:16.100 So trap for young players when you're probably being around circuits like this, 00:43:16.100 --> 00:43:18.245 don't think your signal is vanished. 00:43:18.245 --> 00:43:21.890 Virtual ground. Remember your op-amps rules, always. 00:43:21.890 --> 00:43:26.855 Now, I actually chose the LM358 for a reason because it 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. 00:43:32.130 --> 00:43:34.280 It's halfway in-between. 00:43:34.280 --> 00:43:35.600 Check it out. Here we go. 00:43:35.600 --> 00:43:37.920 It eliminates the need for dual supplies. 00:43:37.920 --> 00:43:42.060 Okay. You can use it as a single supply op-amp. 00:43:42.060 --> 00:43:45.880 But as I said you can use any op-amp as a single supply op-amp. 00:43:45.880 --> 00:43:49.470 But this one is extra special in that it allows direct 00:43:49.470 --> 00:43:54.065 sensing near ground and V-out also goes to ground. 00:43:54.065 --> 00:43:57.335 So effectively, it's not rail to rail. 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, 00:44:01.295 --> 00:44:04.175 but it will go down to ground or the 00:44:04.175 --> 00:44:07.630 negative because an op-amp doesn't have a ground pin. 00:44:07.630 --> 00:44:09.070 It's the negative rail. 00:44:09.070 --> 00:44:11.795 So, even if we pair it from splits supplies, 00:44:11.795 --> 00:44:13.745 plus minus 15 luck we are now, 00:44:13.745 --> 00:44:18.995 it will still go down to that minus 15-volt pin or that pin four. 00:44:18.995 --> 00:44:21.485 It'll go down the input. 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 00:44:26.195 --> 00:44:31.380 the output will go all the way down to the negative rail and I'll demonstrate. 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. 00:44:34.515 --> 00:44:38.085 Now, input common-mode range and our voltage range here. 00:44:38.085 --> 00:44:41.010 As we said, it goes all the way down to 00:44:41.010 --> 00:44:44.205 that negative P and all zero volts as they call it here. 00:44:44.205 --> 00:44:45.675 But on the positive side, 00:44:45.675 --> 00:44:51.970 this op-amp will not go since all go to the airport less than 00:44:51.970 --> 00:44:59.370 1.5 volts below or above 1.5 volts below the positive rail V plus there. 00:44:59.370 --> 00:45:03.030 So, if we've got an output signal of 10 volts for example, 00:45:03.030 --> 00:45:09.245 the voltage range says if we want to get an output voltage of 10 volts peak, 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. 00:45:13.640 --> 00:45:15.620 So, 11.5 volts. 00:45:15.620 --> 00:45:20.450 So, what we're going to do is lower the voltages here on these rails. 00:45:20.450 --> 00:45:24.140 We're going to lower V plus from 15 volts down to 00:45:24.140 --> 00:45:30.000 11.5 and around about that 11.5 volts because we're getting 10 volts peak. 00:45:30.000 --> 00:45:32.955 On the output, 20 volts peak-to-peak, 10 volts peak. 00:45:32.955 --> 00:45:35.795 We should start seeing distortion or clipping of 00:45:35.795 --> 00:45:38.715 that waveform at around about 11 and a half volts. 00:45:38.715 --> 00:45:39.935 Let's see if we do. 00:45:39.935 --> 00:45:41.145 Okay. So, here we go. 00:45:41.145 --> 00:45:42.445 We have 15 volts. 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. 00:45:47.340 --> 00:45:48.560 It's dual tracking. 00:45:48.560 --> 00:45:51.275 So, a wave form is still looking good 00:45:51.275 --> 00:45:55.090 but we expect it to start clipping around about 11 and a half. 00:45:55.090 --> 00:45:56.265 It might not be precise. 00:45:56.265 --> 00:45:58.935 This is not an exact value on the data shape but then we go, 00:45:58.935 --> 00:46:01.330 11 and half it's still there. 00:46:01.330 --> 00:46:05.270 There we go. It's starting to clip. 00:46:05.270 --> 00:46:10.090 You can say it. It's actually about 11.2 volts there. 00:46:10.090 --> 00:46:13.780 You can start to say wave form flattened out. 00:46:13.780 --> 00:46:20.560 Now, I'll wind down even more because this is not a symmetrical supply op-amp. 00:46:20.560 --> 00:46:21.855 It actually goes down to zero. 00:46:21.855 --> 00:46:25.590 We don't start seeing clipping on the bottom here, 00:46:25.590 --> 00:46:29.435 on the bottom rail, until a significant time. 00:46:29.435 --> 00:46:31.530 After that now, we're getting both. 00:46:31.530 --> 00:46:36.070 But I want it back up there and that's about 11.1 volts. 00:46:36.070 --> 00:46:38.910 But we're seeing that clipping on the top and we won't 00:46:38.910 --> 00:46:42.190 see it on the bottom for time after. 00:46:42.190 --> 00:46:45.740 So there you go, just be aware of that and if we had 00:46:45.740 --> 00:46:51.760 even a worse op-amp in this respect like LM741 or something like that, 00:46:51.760 --> 00:46:53.820 that can't even go down to the negative rail, 00:46:53.820 --> 00:46:59.280 we would start to see these rails clip right roughly at the same time. 00:46:59.280 --> 00:47:03.260 You remember that open-loop gain I was telling you about? How large is it? 00:47:03.260 --> 00:47:05.970 Well, it tells you a couple of ways in the datasheet. 00:47:05.970 --> 00:47:08.290 Not all data sheets will have it, but this one does. 00:47:08.290 --> 00:47:10.310 Large DC voltage gain. 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, 00:47:16.025 --> 00:47:21.220 is the gain of the inherent differential amplifier in there and they put it in dB. 00:47:21.220 --> 00:47:24.080 So, you use your 20 log formula. 00:47:24.080 --> 00:47:28.545 You reverse that and you get about a 100,000. 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, 00:47:32.910 --> 00:47:34.085 it's called something different. 00:47:34.085 --> 00:47:37.440 It's called the large signal voltage gain there, 00:47:37.440 --> 00:47:39.815 it specify for a certain rail. But there we go. 00:47:39.815 --> 00:47:44.500 Typically, a hundred and they specify in volts per millivolt. 00:47:44.500 --> 00:47:48.950 So, if you divide 100 volts by 1 millivolt what do you get? 00:47:48.950 --> 00:47:50.970 Same figure, 100,000. 00:47:50.970 --> 00:47:52.280 There is your open-loop gain. 00:47:52.280 --> 00:47:56.500 So, there's just a quick out practical demonstration showing the virtual ground effect 00:47:56.500 --> 00:48:00.765 there and also the voltage rail limitations for positive and negative. 00:48:00.765 --> 00:48:04.985 I should do another part of this video on op-amp limitations, 00:48:04.985 --> 00:48:06.870 practical limitations, things like that. 00:48:06.870 --> 00:48:07.950 That would be interesting. 00:48:07.950 --> 00:48:10.785 Thumbs up if you want to see that one. 00:48:10.785 --> 00:48:14.685 I'll leave you with one last thing. I want to explain it. 00:48:14.685 --> 00:48:16.510 I'll leave it to you to try and figure out. 00:48:16.510 --> 00:48:20.825 I chose these values higher than what I had on the white board there. 00:48:20.825 --> 00:48:22.330 I chose them for a reason. 00:48:22.330 --> 00:48:26.665 Let's lower them down to 10K and 1K here and 00:48:26.665 --> 00:48:31.785 see what happens with this specific op-amp LM358. 00:48:31.785 --> 00:48:33.450 Let's drop these down, 00:48:33.450 --> 00:48:34.650 still quite high values, 00:48:34.650 --> 00:48:38.440 1K and 10K, 10 ohms or something like that. 00:48:38.440 --> 00:48:40.350 But let's give it a go. 00:48:40.350 --> 00:48:44.685 There it is, a 1K input resistor, 10K feedback resistor. 00:48:44.685 --> 00:48:46.085 Exactly the same gain, 00:48:46.085 --> 00:48:49.600 exactly the same inputs signal but what's 00:48:49.600 --> 00:48:57.700 that little funny business there and over there? 00:48:58.380 --> 00:49:02.240 If we measure our virtual ground point, 00:49:02.240 --> 00:49:05.045 look at these little sparks there and there 00:49:05.045 --> 00:49:10.045 corresponding to that little bumping that wave form. 00:49:10.045 --> 00:49:11.410 Interesting. 00:49:11.410 --> 00:49:14.360 So, as professor Julius Sumner Miller said, 00:49:14.360 --> 00:49:16.160 why is it so? 00:49:16.160 --> 00:49:20.380 I'll leave that to you to figure out. Catch you next time.