1 00:00:01,930 --> 00:00:06,060 Now we have looked at a couple of examples of circuit analysis when the circuit has diodes. 2 00:00:06,060 --> 00:00:17,990 Of course, I will take a very simple circuit, but the principles are the same for more complicated 3 00:00:17,990 --> 00:00:32,349 circuits. Let us take this circuit, I have a 5.7 volts voltage source, let me call that 4 00:00:32,349 --> 00:00:36,960 V s. I will call this resistor – R, which I will say five kilo ohms, and there is a 5 00:00:36,960 --> 00:00:42,390 diode-D with a voltage V D across it. And I will say that this diode has a saturation 6 00:00:42,390 --> 00:00:53,590 current of 10 to the minus 15 amperes. Now first of all, we can write down the nonlinear 7 00:00:53,590 --> 00:01:00,879 equation, which is to equate the current in the resistor; V S minus V D by R to be equal 8 00:01:00,879 --> 00:01:07,940 to the current in the diode in terms of its voltage which is I s exponential V D by V 9 00:01:07,940 --> 00:01:18,250 T minus 1. And if you solve this equation using Newton-Raphson iteration or any other 10 00:01:18,250 --> 00:01:29,030 technique, you will find that V D is 0.72 volts or so, and you can also find the current 11 00:01:29,030 --> 00:01:39,380 here I D by substituting that into V S minus V D by R, R into the right hand side of this. 12 00:01:39,380 --> 00:01:45,500 Of course, our interest is not in numerically solving this nonlinear equation, but to use 13 00:01:45,500 --> 00:01:53,250 suitable approximations. Now, the approximation we said we will use 14 00:01:53,250 --> 00:02:00,159 or we can use is that if there is a substantial forward current then this V D will be fixed 15 00:02:00,159 --> 00:02:19,269 to some value, which is V D ON. Of course, V D equals V D ON, if I D is greater than 16 00:02:19,269 --> 00:02:28,709 zero; and I D equals zero, if V D is smaller than V D on. Now, because the characteristic 17 00:02:28,709 --> 00:02:34,969 is given as this conditional, there are two possibilities. You have to evaluate both, 18 00:02:34,969 --> 00:02:39,900 and this is the general principle, so any diode in the circuit can be in on state or 19 00:02:39,900 --> 00:02:45,499 the off state. You have to assume the two cases; you have to check the two cases and 20 00:02:45,499 --> 00:02:50,120 see which one leads to contradiction, obviously that is the wrong one, the other one is the 21 00:02:50,120 --> 00:02:52,659 correct one and for this circuit, it is very easy. 22 00:02:52,659 --> 00:03:12,319 But I will just still show you to illustrate the principle. First, I will assume an ON 23 00:03:12,319 --> 00:03:20,169 diode, this is where I assumed the diode to be ON, so which means that the diode voltage 24 00:03:20,169 --> 00:03:35,870 is 0.7 volt. And if you make the other assumption that the diode is OFF that case the current 25 00:03:35,870 --> 00:03:52,669 through the diode is zero, and I can replace the diode with an open circuit. And let me 26 00:03:52,669 --> 00:04:00,510 evaluate the two cases; first of all, if I assume the diode to be ON then I have 0.7 27 00:04:00,510 --> 00:04:07,819 volt across this, and 5.7 volts here, so the voltage across this resistor is 5 volts. So 28 00:04:07,819 --> 00:04:14,680 the current in this is one milli ampere. And clearly in this case, there is no contradiction, 29 00:04:14,680 --> 00:04:19,549 because the diode voltage is 0.7 volt, if there is a forward current flowing and with 30 00:04:19,549 --> 00:04:24,110 that assumption we calculated this and found that the forward current is one milli ampere. 31 00:04:24,110 --> 00:04:28,190 So what we calculate is consistent that. But let see if we had started off from the 32 00:04:28,190 --> 00:04:35,090 other assumption that the diode is OFF then the diode is OFF this is an open circuit, 33 00:04:35,090 --> 00:04:41,849 no current is flowing through this. So the voltage across this is zero and the voltage 34 00:04:41,849 --> 00:04:48,260 between these two terminals which is the voltage across the diode will be 5.7 volts. Now we 35 00:04:48,260 --> 00:04:53,490 know from the diode characteristic that the diode voltage cannot be more than 0.7 volts, 36 00:04:53,490 --> 00:05:00,690 I am referring to the approximated characteristic. So there is a horizontal line up to 0.7 volt 37 00:05:00,690 --> 00:05:05,389 and a vertical line after that so we can easily see that 5.7 volts is not part of the diode 38 00:05:05,389 --> 00:05:17,889 characteristic at all. So this tells you that there is a contradiction, so this is the incorrect 39 00:05:17,889 --> 00:05:22,330 assumption, and this is the correct one. And you can just go through the same exercise 40 00:05:22,330 --> 00:05:29,530 by making this minus 5.7 volt instead 5.7, and see where you are arrive at a contradiction. 41 00:05:29,530 --> 00:05:34,319 Now this circuit is extremely simple. The point of doing this exercise is to go through 42 00:05:34,319 --> 00:05:44,360 the logical steps and make sure that you understand every step. Now when you have multiple diodes, 43 00:05:44,360 --> 00:05:59,370 if you have a circuit with N diodes then there are two to the N possibilities, that is every 44 00:05:59,370 --> 00:06:03,969 diode can be ON or OFF, and if you take all those combinations there will be two raise 45 00:06:03,969 --> 00:06:08,120 to power N possibilities. And in principle, you have to check for all of these that is 46 00:06:08,120 --> 00:06:11,930 if you have five diodes in a circuit, you have to check for thirty two possibilities. 47 00:06:11,930 --> 00:06:16,820 But of course, frequently you can very quickly dismiss some of the possibilities, you will 48 00:06:16,820 --> 00:06:24,530 able to very easily see the contradiction without having to analyze them in detail. 49 00:06:24,530 --> 00:06:29,599 In this circuit with even a very little bit of experience circuit analysis, you should 50 00:06:29,599 --> 00:06:35,520 be able to see that current can only go in this direction and the diode has to be ON. 51 00:06:35,520 --> 00:06:39,680 So all the in principle there are there are many possibilities to check, in practice you 52 00:06:39,680 --> 00:06:44,319 have to check only a few of them. But the point is to understand the systematic 53 00:06:44,319 --> 00:06:50,999 method, so that if you if you have to do it, you have to be able to go through all the 54 00:06:50,999 --> 00:06:55,400 possibilities systematically, you have to consider all the possibilities systematically 55 00:06:55,400 --> 00:06:57,889 and eliminate all the wrong ones.