WEBVTT 00:00:00.000 --> 00:00:04.410 >> The next of the common op-amp configurations 00:00:04.410 --> 00:00:07.455 that we're going to consider is known as the inverting amplifier. 00:00:07.455 --> 00:00:11.100 It takes its name from the fact that the source voltage that's going to be 00:00:11.100 --> 00:00:16.665 amplified is connected to the inverting terminal. 00:00:16.665 --> 00:00:19.020 So, with that then, 00:00:19.020 --> 00:00:24.240 we might have rightfully assume that because of the name inverting amplifier, 00:00:24.240 --> 00:00:31.545 that the output voltage is going to be the opposite in sign of the source voltage. 00:00:31.545 --> 00:00:35.490 So, let's go ahead and analyze this as in the same manner that we have 00:00:35.490 --> 00:00:42.480 the other op-amp circuits by writing a node equation at the inverting op-amp terminal. 00:00:42.480 --> 00:00:46.580 Before we do that we're going to remember that due to the virtual short, 00:00:46.580 --> 00:00:49.595 the voltage at the inverting terminal V sub n is 00:00:49.595 --> 00:00:52.760 equal to the voltage at the non-inverting terminal, 00:00:52.760 --> 00:00:54.650 and in this case, V sub p 00:00:54.650 --> 00:00:58.535 the voltage at the non-inverting terminal has been tied to ground. 00:00:58.535 --> 00:01:01.625 So, V sub n is going to equal zero also. 00:01:01.625 --> 00:01:05.480 Lets go ahead and write the equation leaving V sub n in place so that we can see what's 00:01:05.480 --> 00:01:09.565 happening and we'll go back and replace V sub n with zero. 00:01:09.565 --> 00:01:13.610 So, starting here, adding the currents leaving 00:01:13.610 --> 00:01:17.840 this node starting with the current going in that direction we have, 00:01:17.840 --> 00:01:24.780 V sub n minus V sub s divided by R sub s, 00:01:24.780 --> 00:01:29.795 plus the current leaving the node going in that direction is going to be 00:01:29.795 --> 00:01:35.885 V sub n minus V out divided by R sub f, 00:01:35.885 --> 00:01:41.270 plus the current entering the inverting terminal of the op-amp which of course is zero. 00:01:41.270 --> 00:01:42.485 So, there's nothing right there, 00:01:42.485 --> 00:01:46.855 thus the sum of those two terms must equals zero. 00:01:46.855 --> 00:01:50.760 Now, let's replace V sub n with zero in both places. 00:01:50.760 --> 00:01:54.920 That's zero. That then is zero and we're left with 00:01:54.920 --> 00:02:00.870 negative V sub s over R sub s minus V out over R sub f equals 0. 00:02:00.870 --> 00:02:04.190 So, let's just take this negative V out over R sub f to the other side of 00:02:04.190 --> 00:02:10.745 the equation as a positive V out over R sub f. 00:02:10.745 --> 00:02:14.630 It's a simple task now to solve for V out as 00:02:14.630 --> 00:02:19.835 R sub f. Multiplying both sides of the equation by R sub f we get then that 00:02:19.835 --> 00:02:24.875 V out is equal to negative V sub s 00:02:24.875 --> 00:02:31.239 times R sub f over R sub s. As we anticipated, 00:02:31.239 --> 00:02:35.495 the sign on the output is going to be opposite sign of the source voltage, 00:02:35.495 --> 00:02:39.050 and we then can note that the gain for 00:02:39.050 --> 00:02:45.335 the inverting op-amp is equal to negative R sub f over R sub 00:02:45.335 --> 00:02:51.230 s. It's good to compare this gain term with 00:02:51.230 --> 00:02:54.560 a gain term that we derived in 00:02:54.560 --> 00:02:58.010 the non-inverting amplifier and go back and look at your notes. 00:02:58.010 --> 00:03:04.470 But, you may recall that the gain for the non-inverting amplifier was equal to 00:03:04.470 --> 00:03:12.425 one plus R sub f over r sub s. This is supposed to be R sub s there. 00:03:12.425 --> 00:03:15.004 When you compare these two terms, 00:03:15.004 --> 00:03:16.430 you'll notice they're very similar. 00:03:16.430 --> 00:03:22.160 They both have the ratio R sub f over R sub s. But in the non-inverting case, 00:03:22.160 --> 00:03:24.455 there's also one added to it. 00:03:24.455 --> 00:03:28.340 So, for the same circuit, the gain, 00:03:28.340 --> 00:03:31.655 if the source was on the non-inverting terminal, 00:03:31.655 --> 00:03:34.460 would be one larger than the gain 00:03:34.460 --> 00:03:38.615 experienced when the source is on the inverting terminal. 00:03:38.615 --> 00:03:40.925 Now, what does that inversion mean? 00:03:40.925 --> 00:03:44.645 Well, let's just take a couple of examples here real fast. 00:03:44.645 --> 00:03:52.355 Let's let R sub f equal 2 kilo-ohms, 00:03:52.355 --> 00:03:56.875 and we'll let R sub s equal 1 kilo ohm. 00:03:56.875 --> 00:04:02.190 So, that the ratio R sub f over R sub s is equal to 2, 00:04:02.190 --> 00:04:04.440 and for this first instance, 00:04:04.440 --> 00:04:05.550 for the first example, 00:04:05.550 --> 00:04:10.720 let's just assume that V sub s equals say 5 volts. 00:04:10.720 --> 00:04:14.120 Then our output voltage would be V out 00:04:14.120 --> 00:04:19.295 would equal negative V sub s 00:04:19.295 --> 00:04:26.295 times 2 or negative 10 volts. 00:04:26.295 --> 00:04:30.755 So, DC values are just inverted or just have an opposite sign. 00:04:30.755 --> 00:04:33.170 What about time-varying voltages? 00:04:33.170 --> 00:04:39.690 What if our V source was equal to 00:04:39.690 --> 00:04:49.100 say 5 cosine of omega t. What would the output voltage be? 00:04:49.100 --> 00:04:58.895 Well, V out would be negative 2 times 5 times the cosine of omega t, 00:04:58.895 --> 00:05:05.190 or that's equal to negative 10 cosine of omega t. Well, 00:05:05.190 --> 00:05:08.130 what does that sine, what's the amplitude of the output? 00:05:08.130 --> 00:05:11.480 Where the amplitude is going to be twice as large as the amplitude of the input, 00:05:11.480 --> 00:05:15.725 but it's also going to have a sign reversal. What does that mean? 00:05:15.725 --> 00:05:20.350 Well, if this was our original, 00:05:22.670 --> 00:05:26.200 where this was five, 00:05:26.720 --> 00:05:30.680 the output is going to have twice the amplitude. 00:05:30.680 --> 00:05:35.165 Let's just say that that's twice the amplitude. 00:05:35.165 --> 00:05:37.880 But it's also going to have a sign reversal. 00:05:37.880 --> 00:05:40.625 That means wherever the input was positive, 00:05:40.625 --> 00:05:48.045 the output is going to be negative and wherever the input with negative, 00:05:48.045 --> 00:05:54.240 the output will be positive and so on. 00:05:54.240 --> 00:05:56.810 In other words, we say also, 00:05:56.810 --> 00:05:59.510 or another way of putting it is that the output is 00:05:59.510 --> 00:06:03.740 180 degrees out of phase with the input and 00:06:03.740 --> 00:06:11.875 that's what the minus sign in the inverting op-amp gain term does to us. 00:06:11.875 --> 00:06:15.890 Putting it that way makes it sound a little ominous. 00:06:15.890 --> 00:06:19.490 What it does to us, now it's not doing anything to us, 00:06:19.490 --> 00:06:21.710 it's not hurting us and generally speaking, 00:06:21.710 --> 00:06:25.680 that sign inversion doesn't really impact anything. 00:06:25.680 --> 00:06:26.865 It just sits there, 00:06:26.865 --> 00:06:29.870 and when you build these kinds of circuits up in 00:06:29.870 --> 00:06:32.810 the laboratory and look at them on the oscilloscope, 00:06:32.810 --> 00:06:36.300 you'll note that there's a 180 degree phase shift.