1 00:00:00,380 --> 00:00:05,660 In this lesson, we will discuss the diode model. And the model I am referring to now 2 00:00:05,660 --> 00:00:10,710 is what is known as the large signal model. It simply refers to the fact that we are dealing 3 00:00:10,710 --> 00:00:14,830 with total quantities that is, the total voltage across the diode and the total current in 4 00:00:14,830 --> 00:00:42,650 the diode, and not incremental values over certain operating point. 5 00:00:42,650 --> 00:00:53,720 This is the diode symbol and we have the anode and cathode. By convention I will define the 6 00:00:53,720 --> 00:00:59,680 voltage across the diode to be positive at the anode terminal, the value of V D of course 7 00:00:59,680 --> 00:01:05,920 can be anything. And the current I D will be flowing into the anode as per passive sign 8 00:01:05,920 --> 00:01:18,560 convention. Now we already have seen a model for this. The diode current is I s times exponential 9 00:01:18,560 --> 00:01:31,969 diode voltage by thermal voltage minus one, where I s is the reverse saturation current. 10 00:01:31,969 --> 00:01:46,829 And V t which is K T by q is the thermal voltage, and if you substitute the value as for three 11 00:01:46,829 --> 00:01:56,990 hundred Kelvin or room temperature, this is approximately 25 milli volts. And we also 12 00:01:56,990 --> 00:02:11,150 know what the characteristic look likes graphically; the current can be substantial, when V D is 13 00:02:11,150 --> 00:02:23,980 positive; and it will saturate to minus I s, when V D is negative. And of course, the 14 00:02:23,980 --> 00:02:34,920 current is zero, when the diode voltage is zero. Now, even with this expression for the 15 00:02:34,920 --> 00:02:42,390 diode current and even for very simple circuits, evaluation becomes very difficult, because 16 00:02:42,390 --> 00:02:46,730 you have to solve equations numerically. So, we have a number of approximation to this, 17 00:02:46,730 --> 00:02:49,920 which I am going to discuss now. 18 00:02:49,920 --> 00:02:57,850 So, one of the first thing to do sometimes this is very convenient is to neglect this 19 00:02:57,850 --> 00:03:03,880 one, when compared to this. And of course, this works only when this term is very large, 20 00:03:03,880 --> 00:03:08,420 and when is it very large when V D is large and positive. When I say large and positive 21 00:03:08,420 --> 00:03:16,980 V D must be much more than the thermal voltage. In this case, clearly the exponential of this 22 00:03:16,980 --> 00:03:24,060 is much more than this. For a V D of a few thermal voltages, this turns out to be correct 23 00:03:24,060 --> 00:03:30,590 right; couple of 100 milli volts is all we need. And in this case, the diode current 24 00:03:30,590 --> 00:03:39,140 can be approximated to be I s exponential V D by V t. Of course, it must be remembered 25 00:03:39,140 --> 00:03:45,200 that this holds only when V D is much more than the thermal voltage. 26 00:03:45,200 --> 00:03:52,260 Now, if you do plot this, what happens is in this region where the current it substantial, 27 00:03:52,260 --> 00:03:56,650 you will get approximately the same value. One crucial difference between the exact expression 28 00:03:56,650 --> 00:04:03,660 and this is that a new expression does not go to zero when V D equals zero. So, this 29 00:04:03,660 --> 00:04:08,650 means that if you plot this characteristic, there will be a part in the second quadrant 30 00:04:08,650 --> 00:04:14,069 which means that the devices is not passive. Of course the reality is that near the origin, 31 00:04:14,069 --> 00:04:19,820 near V D equal to zero, this expression should not even be used; it is only an approximation. 32 00:04:19,820 --> 00:04:26,090 And another approximation frequently used is that because the reverse bias current is 33 00:04:26,090 --> 00:04:33,540 so small, this value of I s is quite small and again when I say small compared to currents 34 00:04:33,540 --> 00:04:45,030 you normally see in forward bias. Then you assume that there is no current flowing through 35 00:04:45,030 --> 00:04:50,071 the diode, that is in reverse bias there is no current in the diode. This is one of the 36 00:04:50,071 --> 00:04:56,660 approximation that is frequently used. Of course, we have still left with the nonlinear 37 00:04:56,660 --> 00:05:03,060 equation and this is useful for certain classes of circuits, but still even for simple arbitrary 38 00:05:03,060 --> 00:05:08,770 circuits, you have to solve nonlinear equations, and we would like to avoid that for hand calculations. 39 00:05:08,770 --> 00:05:16,490 So, the next approximation that you see is that if you look at this part of the curve, 40 00:05:16,490 --> 00:05:24,160 curve is quite steep. I am plotting I D versus V D and curve is very steep. So, what you 41 00:05:24,160 --> 00:05:29,711 can say is that in this part of the curve, the diode voltage does not changed much, it 42 00:05:29,711 --> 00:05:35,860 of course changes. In fact, I will use this approximate expression to find the expression 43 00:05:35,860 --> 00:05:40,780 for the diode voltage. So, V D will be the thermal voltage times the natural logarithm 44 00:05:40,780 --> 00:05:54,310 of the diode current by the saturation current. So, now let say I D is doubled, I D becomes 45 00:05:54,310 --> 00:06:06,460 2 I D then this changes to V t ln 2 I D by I s, which is basically the old value of V 46 00:06:06,460 --> 00:06:20,550 t ln I D by I s plus V t times the natural logarithm of two. And if you calculate this, 47 00:06:20,550 --> 00:06:27,590 it will come out to be approximately 17.5 milli volts. So, even doubling the current, 48 00:06:27,590 --> 00:06:34,540 changes the diode voltage only by something less than 20 milli volts. 49 00:06:34,540 --> 00:06:40,420 So, we can make a reasonable approximation that for a range of currents the diode voltage 50 00:06:40,420 --> 00:06:49,060 is constant that is we assumed the characteristic to be exactly vertical where the diode voltage 51 00:06:49,060 --> 00:06:53,260 is not changing at all. Of course, this gives you very bad errors when you come close to 52 00:06:53,260 --> 00:07:00,210 the origin but that is ok; we assume that the diode is operating somewhere here. So, 53 00:07:00,210 --> 00:07:07,210 we say essentially the next level of approximation is to say that the diode voltage is the constant 54 00:07:07,210 --> 00:07:43,199 when there is some current flowing in the forward direction. And also we know that the 55 00:07:43,199 --> 00:07:47,259 current is very small in the reverse bias region and we already approximated that to 56 00:07:47,259 --> 00:07:54,509 zero earlier, that is we assumed characteristic of this type and we can continue that all 57 00:07:54,509 --> 00:08:01,520 the way till here. So, we assume that there is zero current up to this point, and at this 58 00:08:01,520 --> 00:08:05,770 point, the voltage will be constant and it can carry any current. 59 00:08:05,770 --> 00:08:21,740 So, the next level of approximation is as follows. Forward bias which means that 60 00:08:21,740 --> 00:08:28,090 substantial I D flowing, of course in the forward direction. In the reverse direction, 61 00:08:28,090 --> 00:08:41,620 substantial current cannot flow in the diode at all. So, in this case, what happens, V 62 00:08:41,620 --> 00:08:50,470 D is some constant, which is denoted by V D ON. And what is the value of this constant, 63 00:08:50,470 --> 00:08:55,890 essentially the way you work out this constant value is you have certain types of diodes 64 00:08:55,890 --> 00:09:00,080 that you normally use, and you have certain range of currents that you normally operated, 65 00:09:00,080 --> 00:09:04,260 and for that you just look for a reasonable value. And it turns out that the reasonable 66 00:09:04,260 --> 00:09:15,800 value for this is point seven volt. Now, this does not have to be the case, if you operate 67 00:09:15,800 --> 00:09:19,820 diodes with very small currents, it could be smaller than this; and also in diodes, 68 00:09:19,820 --> 00:09:23,530 which carry very large currents, it could be more than this even as much as one volt. 69 00:09:23,530 --> 00:09:28,740 But we will assume that it is 0.7 volts. But the important thing is that it is assumed 70 00:09:28,740 --> 00:09:32,420 to be a constant regardless of the value of current. 71 00:09:32,420 --> 00:09:41,500 And then I will call it reverse bias, basically when the diode is OFF. By the way I refer 72 00:09:41,500 --> 00:09:46,880 to this as the diode being OFF, and I shouldnâ€™t really call this reverse bias, because V D 73 00:09:46,880 --> 00:09:52,649 is not necessarily negative, it also includes V D less than 0.7 volts. So, this means that 74 00:09:52,649 --> 00:10:00,450 if V D is less than 0.7 volts, this means the current will be zero. If V D is less than 75 00:10:00,450 --> 00:10:08,200 V D ON, the current will be zero. The forward bias is when the diode is ON, but it looks 76 00:10:08,200 --> 00:10:12,490 like some kind of switch where you can go from OFF state, where there is no current; 77 00:10:12,490 --> 00:10:28,490 to ON state, where the voltage is constant and it can support any current. Now this is 78 00:10:28,490 --> 00:10:33,280 fine, this is in fact what we will use for our large signal calculations. 79 00:10:33,280 --> 00:10:39,350 And there will be some cases where we can approximate this even further, let say we 80 00:10:39,350 --> 00:10:43,980 have circuits where the voltages are much larger than point seven volts, it turns out 81 00:10:43,980 --> 00:10:52,540 that you can approximate this as having zero current when V D is negative. And having a 82 00:10:52,540 --> 00:11:05,220 zero voltage, when there is any current flowing through it that is we make an even cruder 83 00:11:05,220 --> 00:11:22,140 approximation for V D ON by setting into zero volts that is the diode behaves like a short 84 00:11:22,140 --> 00:11:27,620 circuit when there is a positive current flowing and the diode behaves like an open circuit, 85 00:11:27,620 --> 00:11:40,810 when a reverse voltage is applied. If you remember I versus V of a short circuit, is 86 00:11:40,810 --> 00:11:51,670 as follows. It is this, it will have zero voltage regardless of the current that is 87 00:11:51,670 --> 00:12:10,480 flowing, and the I-V characteristic of an open circuit, it is like that. It will have 88 00:12:10,480 --> 00:12:13,670 zero current regardless of the voltage across it. 89 00:12:13,670 --> 00:12:20,149 Now the diode is the combination of these two. It is an open circuit in this part in 90 00:12:20,149 --> 00:12:24,360 reverse bias region; and a short circuit in the forward bias region, so that is another 91 00:12:24,360 --> 00:12:27,220 approximation to the diode characteristics. 92 00:12:27,220 --> 00:12:36,839 So, to summarize, we have the exact characteristics of the diode; and this exact, I will put in 93 00:12:36,839 --> 00:12:42,200 quotes because this is still an idealize version of the diode characteristic. And in a practical 94 00:12:42,200 --> 00:12:48,460 diode, you will have other non-ideal features, but as far as we are concern this is the exact 95 00:12:48,460 --> 00:13:00,510 characteristics. And this is valid for all values of V D, and then we have the first 96 00:13:00,510 --> 00:13:07,440 level of approximation where we say that I D is just the exponential without this minus 97 00:13:07,440 --> 00:13:18,390 one term, when V D is much more than V t; and it is zero, when V D is less than zero. 98 00:13:18,390 --> 00:13:29,110 And we have a second level of approximation where we say that if there is current flowing 99 00:13:29,110 --> 00:13:33,240 through the diode at all, forward current flowing through the diode, then the diode 100 00:13:33,240 --> 00:13:39,430 voltage is some constant V D ON, which we will take as zero point seven volts. 101 00:13:39,430 --> 00:13:47,279 And if the voltage happens to be less than V D ON, then the I D will be exactly equal 102 00:13:47,279 --> 00:13:55,200 to zero; and in this model that the diode voltage cannot be more than V D ON. And in 103 00:13:55,200 --> 00:14:02,899 even cruder version of this is to say that if I D is more than zero, V D is zero; and 104 00:14:02,899 --> 00:14:13,670 if V D is less than zero, I D equals zero. So, this is the ON diode, and that is the 105 00:14:13,670 --> 00:14:25,360 OFF diode. In this course, and generally in many courses for hand calculations, you will 106 00:14:25,360 --> 00:14:29,340 end up using this as a reasonable approximation.