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In this lesson, we will discuss the diode
model. And the model I am referring to now
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is what is known as the large signal model.
It simply refers to the fact that we are dealing
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with total quantities that is, the total voltage
across the diode and the total current in
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the diode, and not incremental values over
certain operating point.
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This is the diode symbol and we have the anode
and cathode. By convention I will define the
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voltage across the diode to be positive at
the anode terminal, the value of V D of course
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can be anything. And the current I D will
be flowing into the anode as per passive sign
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convention. Now we already have seen a model
for this. The diode current is I s times exponential
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diode voltage by thermal voltage minus one,
where I s is the reverse saturation current.
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And V t which is K T by q is the thermal voltage,
and if you substitute the value as for three
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hundred Kelvin or room temperature, this is
approximately 25 milli volts. And we also
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know what the characteristic look likes graphically;
the current can be substantial, when V D is
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positive; and it will saturate to minus I
s, when V D is negative. And of course, the
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current is zero, when the diode voltage is
zero. Now, even with this expression for the
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diode current and even for very simple circuits,
evaluation becomes very difficult, because
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you have to solve equations numerically. So,
we have a number of approximation to this,
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which I am going to discuss now.
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So, one of the first thing to do sometimes
this is very convenient is to neglect this
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one, when compared to this. And of course,
this works only when this term is very large,
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and when is it very large when V D is large
and positive. When I say large and positive
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V D must be much more than the thermal voltage.
In this case, clearly the exponential of this
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is much more than this. For a V D of a few
thermal voltages, this turns out to be correct
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right; couple of 100 milli volts is all we
need. And in this case, the diode current
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can be approximated to be I s exponential
V D by V t. Of course, it must be remembered
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that this holds only when V D is much more
than the thermal voltage.
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Now, if you do plot this, what happens is
in this region where the current it substantial,
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you will get approximately the same value.
One crucial difference between the exact expression
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and this is that a new expression does not
go to zero when V D equals zero. So, this
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means that if you plot this characteristic,
there will be a part in the second quadrant
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which means that the devices is not passive.
Of course the reality is that near the origin,
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near V D equal to zero, this expression should
not even be used; it is only an approximation.
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And another approximation frequently used
is that because the reverse bias current is
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so small, this value of I s is quite small
and again when I say small compared to currents
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you normally see in forward bias. Then you
assume that there is no current flowing through
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the diode, that is in reverse bias there is
no current in the diode. This is one of the
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approximation that is frequently used. Of
course, we have still left with the nonlinear
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equation and this is useful for certain classes
of circuits, but still even for simple arbitrary
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circuits, you have to solve nonlinear equations,
and we would like to avoid that for hand calculations.
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So, the next approximation that you see is
that if you look at this part of the curve,
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curve is quite steep. I am plotting I D versus
V D and curve is very steep. So, what you
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can say is that in this part of the curve,
the diode voltage does not changed much, it
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of course changes. In fact, I will use this
approximate expression to find the expression
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for the diode voltage. So, V D will be the
thermal voltage times the natural logarithm
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of the diode current by the saturation current.
So, now let say I D is doubled, I D becomes
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2 I D then this changes to V t ln 2 I D by
I s, which is basically the old value of V
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t ln I D by I s plus V t times the natural
logarithm of two. And if you calculate this,
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it will come out to be approximately 17.5
milli volts. So, even doubling the current,
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changes the diode voltage only by something
less than 20 milli volts.
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So, we can make a reasonable approximation
that for a range of currents the diode voltage
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is constant that is we assumed the characteristic
to be exactly vertical where the diode voltage
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is not changing at all. Of course, this gives
you very bad errors when you come close to
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the origin but that is ok; we assume that
the diode is operating somewhere here. So,
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we say essentially the next level of approximation
is to say that the diode voltage is the constant
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when there is some current flowing in the
forward direction. And also we know that the
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current is very small in the reverse bias
region and we already approximated that to
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zero earlier, that is we assumed characteristic
of this type and we can continue that all
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the way till here. So, we assume that there
is zero current up to this point, and at this
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point, the voltage will be constant and it
can carry any current.
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So, the next level of approximation is as
follows. Forward bias which means that
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substantial I D flowing, of course in the
forward direction. In the reverse direction,
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substantial current cannot flow in the diode
at all. So, in this case, what happens, V
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D is some constant, which is denoted by V
D ON. And what is the value of this constant,
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essentially the way you work out this constant
value is you have certain types of diodes
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that you normally use, and you have certain
range of currents that you normally operated,
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and for that you just look for a reasonable
value. And it turns out that the reasonable
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value for this is point seven volt. Now, this
does not have to be the case, if you operate
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diodes with very small currents, it could
be smaller than this; and also in diodes,
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which carry very large currents, it could
be more than this even as much as one volt.
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But we will assume that it is 0.7 volts. But
the important thing is that it is assumed
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to be a constant regardless of the value of
current.
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And then I will call it reverse bias, basically
when the diode is OFF. By the way I refer
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to this as the diode being OFF, and I shouldnâ€™t
really call this reverse bias, because V D
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is not necessarily negative, it also includes
V D less than 0.7 volts. So, this means that
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if V D is less than 0.7 volts, this means
the current will be zero. If V D is less than
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V D ON, the current will be zero. The forward
bias is when the diode is ON, but it looks
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like some kind of switch where you can go
from OFF state, where there is no current;
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to ON state, where the voltage is constant
and it can support any current. Now this is
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fine, this is in fact what we will use for
our large signal calculations.
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And there will be some cases where we can
approximate this even further, let say we
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have circuits where the voltages are much
larger than point seven volts, it turns out
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that you can approximate this as having zero
current when V D is negative. And having a
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zero voltage, when there is any current flowing
through it that is we make an even cruder
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approximation for V D ON by setting into zero
volts that is the diode behaves like a short
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circuit when there is a positive current flowing
and the diode behaves like an open circuit,
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when a reverse voltage is applied. If you
remember I versus V of a short circuit, is
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as follows. It is this, it will have zero
voltage regardless of the current that is
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flowing, and the I-V characteristic of an
open circuit, it is like that. It will have
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zero current regardless of the voltage across
it.
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Now the diode is the combination of these
two. It is an open circuit in this part in
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reverse bias region; and a short circuit in
the forward bias region, so that is another
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approximation to the diode characteristics.
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So, to summarize, we have the exact characteristics
of the diode; and this exact, I will put in
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quotes because this is still an idealize version
of the diode characteristic. And in a practical
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diode, you will have other non-ideal features,
but as far as we are concern this is the exact
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characteristics. And this is valid for all
values of V D, and then we have the first
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level of approximation where we say that I
D is just the exponential without this minus
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one term, when V D is much more than V t;
and it is zero, when V D is less than zero.
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And we have a second level of approximation
where we say that if there is current flowing
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through the diode at all, forward current
flowing through the diode, then the diode
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voltage is some constant V D ON, which we
will take as zero point seven volts.
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And if the voltage happens to be less than
V D ON, then the I D will be exactly equal
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to zero; and in this model that the diode
voltage cannot be more than V D ON. And in
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even cruder version of this is to say that
if I D is more than zero, V D is zero; and
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if V D is less than zero, I D equals zero.
So, this is the ON diode, and that is the
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OFF diode. In this course, and generally in
many courses for hand calculations, you will
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end up using this as a reasonable approximation.