1 00:00:00,000 --> 00:00:03,975 >> Hello, this is Dr. Cynthia Furse at the University of Utah, 2 00:00:03,975 --> 00:00:08,080 and today we're going to talk about designing op-amp systems. 3 00:00:08,180 --> 00:00:12,105 Electrical engineering is about what can you do to a voltage. 4 00:00:12,105 --> 00:00:14,550 A lot of times we like to add voltages together, 5 00:00:14,550 --> 00:00:16,079 we like to add constants to them, 6 00:00:16,079 --> 00:00:18,405 we like to multiply them by various values, 7 00:00:18,405 --> 00:00:20,580 in order to make the circuit do what we want. 8 00:00:20,580 --> 00:00:22,770 Let's suppose that we want our output to be 9 00:00:22,770 --> 00:00:26,895 a linear combination of a constant and our input voltage like this. 10 00:00:26,895 --> 00:00:30,764 This math might look like 2 times v_2 11 00:00:30,764 --> 00:00:36,435 plus minus 2 times some voltage, something like this. 12 00:00:36,435 --> 00:00:39,415 So, how do we design that system? 13 00:00:39,415 --> 00:00:41,280 Whenever we are designing systems, 14 00:00:41,280 --> 00:00:44,105 we like to break them down into individual components. 15 00:00:44,105 --> 00:00:46,190 For example, we wouldn't really want to have to 16 00:00:46,190 --> 00:00:48,230 consider the power plant, the breaker box, 17 00:00:48,230 --> 00:00:50,450 and all the outlets in your house individually 18 00:00:50,450 --> 00:00:52,955 every time we wanted to design a lamp or a fan. 19 00:00:52,955 --> 00:00:56,510 We'll take that entire distribution system and we'll model that as 20 00:00:56,510 --> 00:01:00,345 a single source voltage with its source resistance, 21 00:01:00,345 --> 00:01:03,440 and then we might consider the lamp and the fan in 22 00:01:03,440 --> 00:01:07,415 parallel like so and we design each of them independently. 23 00:01:07,415 --> 00:01:11,894 In order to design individual blocks like this independently, 24 00:01:11,894 --> 00:01:13,725 there's a very important concept, 25 00:01:13,725 --> 00:01:17,225 that concept is input and output resistances. 26 00:01:17,225 --> 00:01:19,030 Let's suppose that we have a circuit, 27 00:01:19,030 --> 00:01:20,965 any circuit, that's this black box. 28 00:01:20,965 --> 00:01:22,840 If we look in, 29 00:01:22,840 --> 00:01:26,825 that's going to give us the input resistance and if we look into the output side, 30 00:01:26,825 --> 00:01:29,045 that's going to give us the output resistance. 31 00:01:29,045 --> 00:01:32,540 A lot of times in the book and elsewhere, you will see Z. 32 00:01:32,540 --> 00:01:35,505 That is impedance as opposed to resistance, 33 00:01:35,505 --> 00:01:36,960 it's a complex resistance, 34 00:01:36,960 --> 00:01:41,015 so just consider that to be the same as resistance for this case. 35 00:01:41,015 --> 00:01:43,190 If we are looking in to either side, 36 00:01:43,190 --> 00:01:44,660 that's the same thing as using 37 00:01:44,660 --> 00:01:49,045 the Thevenin resistances and you calculate it in the same way. 38 00:01:49,045 --> 00:01:54,305 Now, let's consider the basics of input and output resistance. 39 00:01:54,305 --> 00:01:58,895 Here is an example of an equivalent circuit that we would be very likely to build, 40 00:01:58,895 --> 00:02:01,940 we would have a source right here with its input equivalent, 41 00:02:01,940 --> 00:02:06,095 connected onto some amplifier circuit driving some load. 42 00:02:06,095 --> 00:02:08,660 If we wanted to figure out how these we're working, 43 00:02:08,660 --> 00:02:12,545 we would consider the input and output impedances of each of our blocks. 44 00:02:12,545 --> 00:02:15,140 Here for example is our input circuit. 45 00:02:15,140 --> 00:02:16,760 Now even though it's called an input circuit, 46 00:02:16,760 --> 00:02:19,300 you notice it doesn't really have an input resistance, 47 00:02:19,300 --> 00:02:21,110 it only has an output resistance. 48 00:02:21,110 --> 00:02:23,105 The output resistance looking in, 49 00:02:23,105 --> 00:02:24,530 resistance would be here. 50 00:02:24,530 --> 00:02:29,650 We would short out our voltage source and the only resistance there would be Zs. 51 00:02:29,650 --> 00:02:32,220 Now, let's consider the amplifier circuit. 52 00:02:32,220 --> 00:02:33,929 Looking into the amplifier, 53 00:02:33,929 --> 00:02:39,880 remember the fact that when we have a op-amp, 54 00:02:39,880 --> 00:02:44,235 the input resistance is approximately infinity, it's very high. 55 00:02:44,235 --> 00:02:46,215 So, when we look into an op-amp, 56 00:02:46,215 --> 00:02:49,500 Zin is equal to infinity. 57 00:02:49,500 --> 00:02:51,300 Let's consider the Zout, 58 00:02:51,300 --> 00:02:53,185 remember that when we have an op-amp, 59 00:02:53,185 --> 00:02:55,670 we have an output resistance Rout, 60 00:02:55,670 --> 00:02:58,895 so our Zout is approximately zero. 61 00:02:58,895 --> 00:03:00,980 Then let's look into our load, 62 00:03:00,980 --> 00:03:04,600 Zin, is ZL like this. 63 00:03:04,600 --> 00:03:08,870 So, we now have looked at our input and output resistances or 64 00:03:08,870 --> 00:03:12,530 impedances for each one of the elements in our circuit, 65 00:03:12,530 --> 00:03:14,780 and input impedance is looking into the input 66 00:03:14,780 --> 00:03:18,300 and an output impedance is looking in to the output. 67 00:03:18,320 --> 00:03:20,700 Now, let's go back to our circuit, 68 00:03:20,700 --> 00:03:22,850 let's take a look again at the circuit and 69 00:03:22,850 --> 00:03:25,655 decide what our input and output resistances are. 70 00:03:25,655 --> 00:03:27,755 Just like in my previous case, 71 00:03:27,755 --> 00:03:31,990 the output resistance of the source block is simply Zs. 72 00:03:31,990 --> 00:03:35,110 Now, let's look at this fan block right here. 73 00:03:35,110 --> 00:03:38,630 The input resistance right there would be 74 00:03:38,630 --> 00:03:42,520 Rfan and the output resistance would also be Rfan. 75 00:03:42,520 --> 00:03:45,420 Now, here's our last load right here, that's the lamp, 76 00:03:45,420 --> 00:03:50,070 and looking into the lamp that gives me an input resistance of Rlamp. 77 00:03:50,600 --> 00:03:53,660 Okay. Now, let's consider how we connect 78 00:03:53,660 --> 00:03:56,405 circuits that have different input and output resistances. 79 00:03:56,405 --> 00:03:58,670 If we wanted to connect circuit number one, 80 00:03:58,670 --> 00:04:02,090 which has its input and output resistances right here 81 00:04:02,090 --> 00:04:06,700 and we wanted to consider circuit two with its input and output resistances, 82 00:04:06,700 --> 00:04:09,320 let's see what would happen if we hook them together. 83 00:04:09,320 --> 00:04:13,215 Here's an example where I'll just be connecting a source impedance to a load. 84 00:04:13,215 --> 00:04:14,605 So, if I look in here, 85 00:04:14,605 --> 00:04:16,950 the output resistance is Zs, 86 00:04:16,950 --> 00:04:18,285 and if I look in here, 87 00:04:18,285 --> 00:04:20,760 the input resistance is ZL. 88 00:04:20,760 --> 00:04:24,055 Now, imagine what would happen if I hook them together. 89 00:04:24,055 --> 00:04:28,345 The output voltage that I might want like here would be Vout1, 90 00:04:28,345 --> 00:04:33,025 and let's suppose that I wanted to drive this circuit with the source Vs, 91 00:04:33,025 --> 00:04:34,920 and I'm going to drive this, 92 00:04:34,920 --> 00:04:37,100 maybe a mixer input impedance or something, 93 00:04:37,100 --> 00:04:39,630 and I connect them up like this. 94 00:04:39,820 --> 00:04:43,820 What does that give me? That is a voltage divider, 95 00:04:43,820 --> 00:04:45,905 we know something about voltage dividers. 96 00:04:45,905 --> 00:04:51,840 We know that Vout1 is equal to 97 00:04:51,840 --> 00:04:58,860 V_s times ZL over ZL plus Zs because that's the voltage divider. 98 00:04:58,860 --> 00:05:04,765 Now, if ZL is small compared to Zs, 99 00:05:04,765 --> 00:05:07,790 we're not going to get the voltage that we wanted at all. 100 00:05:07,790 --> 00:05:09,290 The only time that we are going to get 101 00:05:09,290 --> 00:05:11,615 the voltage that we want it to be deriving it with, 102 00:05:11,615 --> 00:05:15,220 is if ZL is very large compared to the Zs. 103 00:05:15,220 --> 00:05:24,430 So, ZL much greater than Zs will give us the result that Vout1 is equal to Vs. 104 00:05:25,400 --> 00:05:29,070 So, this is a really important feature. 105 00:05:29,070 --> 00:05:34,395 When we are designing circuits and I showed it graphically here, 106 00:05:34,395 --> 00:05:39,680 if the input resistance of the second circuit is very large, 107 00:05:39,680 --> 00:05:42,440 Zin2 is much greater than Zin1, 108 00:05:42,440 --> 00:05:46,290 then we can consider these two circuits to be independent. 109 00:05:46,290 --> 00:05:47,930 We can design them separately. 110 00:05:47,930 --> 00:05:51,950 Any other case we can't do that and we'd have to analyze the entire circuit together. 111 00:05:51,950 --> 00:05:57,660 So, we like it very much if the input impedance of a circuit is very high. 112 00:05:58,510 --> 00:06:01,485 Now, in the event that doesn't happen, 113 00:06:01,485 --> 00:06:04,505 what we're going to do is put something called a buffer in the circuit. 114 00:06:04,505 --> 00:06:07,340 A buffer multiplies the incoming voltage by one, 115 00:06:07,340 --> 00:06:11,870 but it has this magic thing that the input impedance of the buffer is always large, 116 00:06:11,870 --> 00:06:14,885 and the output impedance of the buffer is always small. 117 00:06:14,885 --> 00:06:17,310 That makes us so that we can always put a buffer in here, 118 00:06:17,310 --> 00:06:19,670 we can always design our block separately. 119 00:06:19,670 --> 00:06:21,890 So, the buffer allows us to design 120 00:06:21,890 --> 00:06:26,500 our input equivalent circuit separate from our load equivalent circuit. 121 00:06:26,500 --> 00:06:31,380 Now, another word that we often use for this is loading. 122 00:06:32,260 --> 00:06:40,605 So, loading occurs when ZL is approximately equal to or less than Zs. 123 00:06:40,605 --> 00:06:44,490 In this case, loading happens to make it so that 124 00:06:44,490 --> 00:06:51,395 the output voltage that we want isn't the same as the output voltage that we input, 125 00:06:51,395 --> 00:06:54,480 so loading is a bad thing. 126 00:06:54,890 --> 00:06:59,620 Now, let's review again connecting input and output resistances. 127 00:06:59,620 --> 00:07:04,930 If I have a large input resistance and I connect it to a small output resistance, 128 00:07:04,930 --> 00:07:07,210 I can design my circuit without a buffer, 129 00:07:07,210 --> 00:07:13,065 I can individually designed circuit one and circuit two as if they were not interrelated, 130 00:07:13,065 --> 00:07:16,390 any other time I have to analyze the entire circuit. 131 00:07:16,390 --> 00:07:21,205 In the event that I didn't have Zin2 much greater than Zout2, 132 00:07:21,205 --> 00:07:24,270 what I would do is put a buffer in that case, 133 00:07:24,270 --> 00:07:26,560 and that is going to make it so that I always have 134 00:07:26,560 --> 00:07:30,010 a large input impedance and a small output impedance. 135 00:07:30,010 --> 00:07:33,400 So, these are our two design criteria that allow us 136 00:07:33,400 --> 00:07:37,820 to design individual elements of a more complex circuit.