WEBVTT 00:00:00.290 --> 00:00:04.890 >> Now, let's go back to our original problem and suppose that we want to design 00:00:04.890 --> 00:00:10.570 our output voltage to a be a linear combination of our input voltage and a constant. 00:00:10.580 --> 00:00:13.800 Refer to table four dash three in your book, 00:00:13.800 --> 00:00:17.865 and this will show you various Op-amp circuits that you already know how to design. 00:00:17.865 --> 00:00:20.130 Inverting summers, non-inverting summers, 00:00:20.130 --> 00:00:22.755 inverting and non-inverting amplifiers, 00:00:22.755 --> 00:00:26.040 subtracting amplifiers and voltage followers, or buffers. 00:00:26.040 --> 00:00:30.480 Let's figure out how to use these to design the systems that we want to build. 00:00:30.480 --> 00:00:34.545 To do this, I've developed a set of system and circuit design cards. 00:00:34.545 --> 00:00:37.530 One side of the card is the system side, 00:00:37.530 --> 00:00:39.525 that tells us what operation is needed. 00:00:39.525 --> 00:00:42.060 In this case, we would have a multiplier. 00:00:42.060 --> 00:00:44.360 That's a non-inverting amplifier where 00:00:44.360 --> 00:00:48.350 our input voltage is multiplied by some number greater than one, 00:00:48.350 --> 00:00:51.410 to give us the output voltage, right here. 00:00:51.410 --> 00:00:54.290 On the other side of the card is the circuit side. 00:00:54.290 --> 00:00:56.390 This is the part that you would actually build. 00:00:56.390 --> 00:00:59.660 The part that is shown on the front is the area that's within 00:00:59.660 --> 00:01:05.670 this blue dashed line here and that shows you the design for a non-inverting amplifier. 00:01:07.670 --> 00:01:11.465 So, here are two other system and circuit design cards. 00:01:11.465 --> 00:01:12.570 Here's the system side, 00:01:12.570 --> 00:01:14.075 here's the circuit side. 00:01:14.075 --> 00:01:16.490 There's the non-inverting amplifier that you're used to, 00:01:16.490 --> 00:01:20.660 here's an inverting amplifier where we multiply by a negative number. 00:01:20.660 --> 00:01:25.130 While we're at it, let's also take a look at the very important input, 00:01:25.130 --> 00:01:27.620 resistances for these circuits. 00:01:27.620 --> 00:01:29.705 When I look into this circuit, 00:01:29.705 --> 00:01:31.640 I'm going to run up against 00:01:31.640 --> 00:01:35.130 the input resistance of the Op-amp which we know is very high. 00:01:35.130 --> 00:01:40.685 So, Rin for a non-inverting amplifier is approximately equal to infinity. 00:01:40.685 --> 00:01:43.190 But when I look into the inverting amplifier, 00:01:43.190 --> 00:01:45.155 I know it looks infinite in this direction, 00:01:45.155 --> 00:01:49.310 but my current is able to follow this path right here, 00:01:49.310 --> 00:01:55.255 which means that it is not going to have an infinite input resistance. 00:01:55.255 --> 00:01:56.715 So, in this case, 00:01:56.715 --> 00:01:58.820 it's not equal to infinity. 00:01:58.820 --> 00:02:03.785 That means I probably don't need a buffer if I'm doing a non-inverting amplifier, 00:02:03.785 --> 00:02:10.050 but I do need a buffer right here if I am doing an inverting amplifier. 00:02:10.340 --> 00:02:15.110 Here are two summers, the system design card and the circuit design card. 00:02:15.110 --> 00:02:18.065 Again, let's take a look at the input resistance. 00:02:18.065 --> 00:02:20.180 When I look into the inverting summer, 00:02:20.180 --> 00:02:23.340 is that input resistance infinity? No, it isn't. 00:02:23.340 --> 00:02:25.860 Rin is not equal to infinity, 00:02:25.860 --> 00:02:30.035 so plan to use a buffer if you're using an inverting summer. 00:02:30.035 --> 00:02:33.080 When I look into the non-inverting summer however, 00:02:33.080 --> 00:02:35.270 that input resistance is close to 00:02:35.270 --> 00:02:39.610 infinity and so I won't be needing a buffer for that device. 00:02:39.610 --> 00:02:42.725 Here's another system and circuit design card. 00:02:42.725 --> 00:02:44.960 This is a differencing amplifier, 00:02:44.960 --> 00:02:48.140 where I will multiply both of my voltages by a constant, 00:02:48.140 --> 00:02:49.640 but then I will subtract them. 00:02:49.640 --> 00:02:52.530 Here's how I designed that system. 00:02:53.060 --> 00:02:57.365 Switches are other important things that Op-amps are able to do. 00:02:57.365 --> 00:03:01.460 Remember we talked about a single-pole double-throw switch in an example 00:03:01.460 --> 00:03:07.425 previously where my Op-amp railed out between Vcc and minus Vcc. 00:03:07.425 --> 00:03:11.150 That's the equivalent of doing a single-pole double-throw switch. 00:03:11.150 --> 00:03:16.610 Here's a single-pole single-throw switch where it goes between Vcc and ground. 00:03:16.610 --> 00:03:21.120 Here's the system design card and here's how you build the circuit. 00:03:21.590 --> 00:03:25.100 Now, a buffer of course is a very important part of many of 00:03:25.100 --> 00:03:27.890 our circuits and that's because I'm able to buffer 00:03:27.890 --> 00:03:33.320 the input and output resistances of various devices so that I can design them separately. 00:03:33.320 --> 00:03:34.685 That's the key idea. 00:03:34.685 --> 00:03:37.030 Here is the symbol we often use for a buffer. 00:03:37.030 --> 00:03:40.520 A buffer is a unity gain amplifier where we simply multiply 00:03:40.520 --> 00:03:44.885 our input value by one in order to get our output voltage. 00:03:44.885 --> 00:03:46.630 This is the system design card, 00:03:46.630 --> 00:03:49.745 here's the circuit design card that shows us how to build it. 00:03:49.745 --> 00:03:52.730 We simply connect the negative terminal, 00:03:52.730 --> 00:03:57.740 the negative input to the output terminal and that gives us a gain of one. 00:03:57.740 --> 00:04:00.260 When I look into the input of a buffer, 00:04:00.260 --> 00:04:04.925 I can see that I'm going up against the input resistance of the Op-amp, 00:04:04.925 --> 00:04:07.895 so, Rin for a buffer is always 00:04:07.895 --> 00:04:12.240 approximately equal to infinity and that's why we like them so well. 00:04:12.560 --> 00:04:15.740 So, let's talk about an example where we might want 00:04:15.740 --> 00:04:18.454 to do a linear combination of voltages. 00:04:18.454 --> 00:04:21.050 Perhaps these four voltages came from a series 00:04:21.050 --> 00:04:23.480 of sensors and some of them we really trust, 00:04:23.480 --> 00:04:25.970 we want to multiply them by a large number, 00:04:25.970 --> 00:04:27.530 and some we don't trust quite as much, 00:04:27.530 --> 00:04:29.870 we want to multiply them by a small number. 00:04:29.870 --> 00:04:35.240 So, here's the equation that we might like to have in order to get our output voltage. 00:04:35.240 --> 00:04:37.445 There are many ways we could build this circuit. 00:04:37.445 --> 00:04:38.960 We could add things up first, 00:04:38.960 --> 00:04:40.070 we could subtract them first, 00:04:40.070 --> 00:04:41.510 we could multiply them. 00:04:41.510 --> 00:04:45.050 Many different combinations could give us the same output voltage. 00:04:45.050 --> 00:04:48.155 Then here's an example of the way that I chose to do it. 00:04:48.155 --> 00:04:50.810 Here is an input resistance, sorry. 00:04:50.810 --> 00:04:58.040 Here is an input voltage V1 another input voltage V2, V3, and V4. 00:04:58.040 --> 00:05:02.900 I'm going to use a non-inverting amplifier to multiply the first voltage by three, 00:05:02.900 --> 00:05:04.905 the second voltage by four, 00:05:04.905 --> 00:05:06.885 the third voltage by five, 00:05:06.885 --> 00:05:09.115 and the fourth voltage by eight. 00:05:09.115 --> 00:05:13.000 I can design a non-inverting amplifier that will do this and I know 00:05:13.000 --> 00:05:17.350 that I will be able to do that when I get to the circuit design side of the card. 00:05:17.350 --> 00:05:21.950 Well, now that I have multiplied each of my voltages by their appropriate value, 00:05:21.950 --> 00:05:25.165 I'm going to take the ones that are positive, right here, 00:05:25.165 --> 00:05:28.955 and I'm going to put them into a non-inverting summer and add them up. 00:05:28.955 --> 00:05:32.060 So, basically, I'm doing this operation and 00:05:32.060 --> 00:05:35.555 here's the output of this non-inverting summer. 00:05:35.555 --> 00:05:37.010 On the other side, 00:05:37.010 --> 00:05:39.110 I'm going to take the minus five and the minus 00:05:39.110 --> 00:05:41.690 eight and put them into an inverting summer. 00:05:41.690 --> 00:05:47.590 So, I'm basically doing this part of the math and it's going to show up here. 00:05:47.590 --> 00:05:50.660 Finally, I'm simply going to add them up and that gives me 00:05:50.660 --> 00:05:53.760 V out on the other side using a non-inverting summer. 00:05:53.760 --> 00:05:57.875 So, this is how I use the system design side of my card, 00:05:57.875 --> 00:06:00.485 in order to design the operations, 00:06:00.485 --> 00:06:03.455 the math, that I want my circuit to do. 00:06:03.455 --> 00:06:08.690 Then I flip the cards over to the circuit side and it shows me how to build them. 00:06:08.690 --> 00:06:11.030 The non-inverting amplifier of course, 00:06:11.030 --> 00:06:13.820 has simply use two resistors and I design them so 00:06:13.820 --> 00:06:16.760 that the gain is three, four, five, eight. 00:06:16.760 --> 00:06:19.010 Whatever are my gains need to be. 00:06:19.010 --> 00:06:23.795 Sorry. Then, I put them into a non-inverting summer, 00:06:23.795 --> 00:06:28.325 an inverting summer, and finally a non-inverting summer as shown here. 00:06:28.325 --> 00:06:31.310 Now that we know what circuits we're going to do, 00:06:31.310 --> 00:06:33.950 let's take a look at the input resistances in 00:06:33.950 --> 00:06:37.615 order to decide if we need to put buffers in the circuit. 00:06:37.615 --> 00:06:41.600 So, remember that I can design each of these elements independently 00:06:41.600 --> 00:06:45.140 as long as the input resistance is near infinity. 00:06:45.140 --> 00:06:48.845 Here's my non-inverting summer and sure when I look in here, 00:06:48.845 --> 00:06:51.830 Rin is approximately equal to infinity. 00:06:51.830 --> 00:06:55.865 So, I do not need buffers on the lines going into this circuit. 00:06:55.865 --> 00:06:59.000 When I look at the inverting summer however, 00:06:59.000 --> 00:07:01.250 my input resistance is not close to 00:07:01.250 --> 00:07:05.095 infinity and so I'm going to need a couple of buffers here. 00:07:05.095 --> 00:07:07.805 So, right there I'm going to put a buffer on 00:07:07.805 --> 00:07:11.660 either end of the inputs going into my inverting summer. 00:07:11.660 --> 00:07:13.490 So, what does that mean? 00:07:13.490 --> 00:07:18.530 It means that I can design this card completely separately from this one. 00:07:18.530 --> 00:07:21.590 I can design that separately from the non-inverting summer, 00:07:21.590 --> 00:07:24.080 separately from the inverting summer and so on, 00:07:24.080 --> 00:07:26.240 until I have designed my complete circuit 00:07:26.240 --> 00:07:29.910 and then I can hook it up in the fashion shown here. 00:07:30.920 --> 00:07:36.790 Sometimes we draw those buffers as black triangles and included that new here as well. 00:07:37.090 --> 00:07:39.980 Now, I'd like you to take a chance to read 00:07:39.980 --> 00:07:41.990 through example four dash five in your book which is 00:07:41.990 --> 00:07:46.205 a practical application of this to the design of an elevation sensor. 00:07:46.205 --> 00:07:49.370 I'll let you take the time to work through that example and see if you 00:07:49.370 --> 00:07:53.105 understand how the various elements of the system can be put together. 00:07:53.105 --> 00:07:56.975 Here's the linear response that your sensor has, 00:07:56.975 --> 00:08:00.795 and here's the output that you would like to receive. 00:08:00.795 --> 00:08:03.450 See if you can design that circuit. 00:08:03.450 --> 00:08:06.650 So, thank you very much for joining me today. 00:08:06.650 --> 00:08:09.890 I'm sure you're dying with curiosity about what the front picture was. 00:08:09.890 --> 00:08:11.110 This is White Canyon, 00:08:11.110 --> 00:08:14.030 a nice ride in American Fork.