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Now we have looked at a couple of examples
of circuit analysis when the circuit has diodes.
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Of course, I will take a very simple circuit,
but the principles are the same for more complicated
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circuits. Let us take this circuit, I have
a 5.7 volts voltage source, let me call that
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V s. I will call this resistor – R, which
I will say five kilo ohms, and there is a
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diode-D with a voltage V D across it. And
I will say that this diode has a saturation
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current of 10 to the minus 15 amperes. Now
first of all, we can write down the nonlinear
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equation, which is to equate the current in
the resistor; V S minus V D by R to be equal
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to the current in the diode in terms of its
voltage which is I s exponential V D by V
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T minus 1. And if you solve this equation
using Newton-Raphson iteration or any other
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technique, you will find that V D is 0.72
volts or so, and you can also find the current
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here I D by substituting that into V S minus
V D by R, R into the right hand side of this.
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Of course, our interest is not in numerically
solving this nonlinear equation, but to use
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suitable approximations.
Now, the approximation we said we will use
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or we can use is that if there is a substantial
forward current then this V D will be fixed
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to some value, which is V D ON. Of course,
V D equals V D ON, if I D is greater than
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zero; and I D equals zero, if V D is smaller
than V D on. Now, because the characteristic
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is given as this conditional, there are two
possibilities. You have to evaluate both,
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and this is the general principle, so any
diode in the circuit can be in on state or
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the off state. You have to assume the two
cases; you have to check the two cases and
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see which one leads to contradiction, obviously
that is the wrong one, the other one is the
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correct one and for this circuit, it is very
easy.
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But I will just still show you to illustrate
the principle. First, I will assume an ON
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diode, this is where I assumed the diode to
be ON, so which means that the diode voltage
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is 0.7 volt. And if you make the other assumption
that the diode is OFF that case the current
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through the diode is zero, and I can replace
the diode with an open circuit. And let me
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evaluate the two cases; first of all, if I
assume the diode to be ON then I have 0.7
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volt across this, and 5.7 volts here, so the
voltage across this resistor is 5 volts. So
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the current in this is one milli ampere. And
clearly in this case, there is no contradiction,
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because the diode voltage is 0.7 volt, if
there is a forward current flowing and with
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that assumption we calculated this and found
that the forward current is one milli ampere.
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So what we calculate is consistent that.
But let see if we had started off from the
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other assumption that the diode is OFF then
the diode is OFF this is an open circuit,
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no current is flowing through this. So the
voltage across this is zero and the voltage
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between these two terminals which is the voltage
across the diode will be 5.7 volts. Now we
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know from the diode characteristic that the
diode voltage cannot be more than 0.7 volts,
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I am referring to the approximated characteristic.
So there is a horizontal line up to 0.7 volt
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and a vertical line after that so we can easily
see that 5.7 volts is not part of the diode
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characteristic at all. So this tells you that
there is a contradiction, so this is the incorrect
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assumption, and this is the correct one.
And you can just go through the same exercise
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by making this minus 5.7 volt instead 5.7,
and see where you are arrive at a contradiction.
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Now this circuit is extremely simple. The
point of doing this exercise is to go through
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the logical steps and make sure that you understand
every step. Now when you have multiple diodes,
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if you have a circuit with N diodes then there
are two to the N possibilities, that is every
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diode can be ON or OFF, and if you take all
those combinations there will be two raise
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to power N possibilities. And in principle,
you have to check for all of these that is
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if you have five diodes in a circuit, you
have to check for thirty two possibilities.
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But of course, frequently you can very quickly
dismiss some of the possibilities, you will
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able to very easily see the contradiction
without having to analyze them in detail.
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In this circuit with even a very little bit
of experience circuit analysis, you should
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be able to see that current can only go in
this direction and the diode has to be ON.
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So all the in principle there are there are
many possibilities to check, in practice you
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have to check only a few of them.
But the point is to understand the systematic
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method, so that if you if you have to do it,
you have to be able to go through all the
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possibilities systematically, you have to
consider all the possibilities systematically
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and eliminate all the wrong ones.