In

the last class, we understood the functioning of a bipolar junction transistor as an active

device; and we took for our illustration, a PNP transistor like this, and we explained

how the collected current is almost only the emitter current.

Now, for the PNP transistor, the symbol, instead of drawing it like this, the symbol for the

PNP transistor is as shown here.

Here, the direction of the arrow, the arrow is put at the emitter; the direction of the

arrow, always indicates the direction of actual flow of current. Here, if this is forward

biased, emitter base junction is forward biased, the current in this is going to be injected

from the emitter on to the base; actual direction of flow of current. And therefore, arrow is

always put in the emitter. And, the collector is this; and the base is this.

So, this kind of symbol indicates a PNP transistor. In the case of a NPN transistor, the arrow

direction is opposite. Now, as far as the transistor action is concerned, emitter base

junction is forward biased and the collector base junction is reverse biased, so as to

make the entire collector current become equal to the emitter current; and Alpha becomes

very nearly equal to 1. That is, the transistor action.

Current in this is represented as total current, as I E. Almost the entire current, that is

emitter current, becomes part of the collector current. That is transistor action. That is

facilitated by forward biasing base to emitter junction; and doping emitter very heavily;

making the base width very small, so that most of the injected carriers constitute the

total current. And, most of the injected carriers come to this part of the junction; and this

distance is made so small that there is no recombination here so that most of them come,

arrive, at this point junction. And here, there is a field which is aiding them to get

collected very fast because of the fact that it is reverse biased.

So, I C is equal to Alpha times I E, where Alpha is very close to 1. The ideal transistor,

ideal transistor, therefore Alpha is equal to 1. So, which means, almost all the current

gets collected here; and therefore, in the other terminal, there is no current. Base

current is zero in the ideal transistor. In practice, Alpha is typically of the order

of point 98, point 99, typically. So, Alpha is about point 98; this is the order. So,

it is pretty close to 1. Please remember that.

In I C transistors, it can be even made closer to 1 than this. May be, point 995, things

like that. So, transistor action means

. Base current is zero. Actual current equation at this node therefore is, emitter current

is always equal to collector current; plus, we call this, base current. So, this is KirchhoffÕs

law. This has nothing to do with transistor action. In this node, emitter current is always

equal to collector current plus base current.

What is transistor action is

. In an ideal case, Alpha is equal to 1 and I B is therefore equal to zero.

Now, let us look at this characteristic in a pictorial sense. Whatever be the base to

collector voltage, reverse bias voltage, collector current is almost independent of the base

to collector voltage. So, it is independent. It depends only on emitter current. If emitter

current is 1 milliampere, for example, collector current is going to be very nearly 1 milliampere.

So, this is emitter current, this third parameter. So, as emitter current is being varied, how

does collector current vary?

Collector current remains constant at nearly 1 milliampere. If it is 2 milliamperes, emitter

current, the collector current remains constant, independent of base to collector voltage,

which is the reverse bias voltage, in this. It remains constant at 3 milliamperes. It

remains constant at 4 milliamperes.

Now, strictly speaking, beyond this point, this is the point where V BC is equal to zero,

beyond this point, the transistor is said to be in the saturation region; in this region.

Suppose therefore, actually, the current will start falling. So, this point is called saturation

region. Beyond this point, beyond this point, it is cut-off. This is the active region.

This region is called the active region where transistor action takes place; where the relationship

I C is equal to I E; or, I C is equal to Alpha times I E is valid.

Now, therefore, we just say, V CB equal to zero is the border line separating saturation

and active region; and I E equal to zero is the border line separating cut-off and active

region.

Once again, let us consider the other regions. If collector base junction is reverse biased,

emitter base junction is forward biased, it is said to be in the active region. If emitter

base junction is reverse biased and collector base junction is reverse biased, it is said

to be in the cut-off region. So V EB; emitter base junction Ð reverse biased, collector

base junction Ð also, reverse biased, the transistor is said to be in the cut-off. Ideally

speaking, you can therefore consider that these are two junction diodes which are reverse

biased and therefore they are all open.

So, emitter base junction can be treated as open circuit; collector base junction can

be treated as open circuit; so, this transistor is cut-off. Then, we have emitter base junction

Ð forward biased and collector base junction Ð also, forward

biased;...

... the transistor is said to be in the saturation region; that is in this region. Transistor

is said to be in the saturation region.

Then, there is another one. That is, collector base junction Ð forward biased, emitter base

junction Ð reverse biased; transistor is said to be in the inverse mode. Not normal

mode, but is in the inverse mode. This is normal mode transistor action.

And therefore, if collector base is forward biased, emitter base reverse biased, the transistor

is in the inverse mode. In this, transistor action takes place, exists; but, Alpha is

not close to 1. It is not close to 1 because, this transistor has been fabricated specially

to work in this normal mode.

If it is symmetric; if it had been PNP without any care for any special effect regarding

highly doped emitter, etcetera; if it is just PNP and symmetric; then, both could be normal

modes. We can use emitter as collector and collector as emitter. In this case, it is

not so. So, please remember that the characteristic curve for the transistor can be easily obtained.

You yourself can draw it without any hesitation, once you know that .

Therefore it is not necessary, it is not important, that we should keep pictorial view of this.

We can remember these equations very easily and therefore this is just done for this once;

and we are not going to use this information again in our future analysis. So, this graphic

way of representing the output characteristic of the transistor is going to be over with

this. In further discussions, we will not use this. We will strictly use this information.

It is this information which can be easily pictorially represented.

Now, as far as the non-ideality of the transistor is concerned, in the last class itself I have

told you that Alpha is not equal to 1; I C is equal to Alpha times I E. Not only that,

a better approximation is

; because, this junction is reverse biased. There is this reverse saturation current also

flowing in addition to the injected current.

So, this will add on to the collector current; and actual current is going to be Alpha times

the injected current, plus I C naught. Now, this equation can be normally used whenever

we want fairly accurate information about the transistor.

Otherwise, most of the applications, we can just use the information that Alpha is equal

to 1. That is going to simplify the analysis of any of these transistor circuits; particularly

in situations where we have systems built with large number of transistors, where we

would like to only approximately analyze the circuit. And therefore, we would like to quickly

arrive at the results; in which case, the easiest approximation for the transistor is

Alpha is equal to 1.

Now, with Alpha equal to 1, we have shown that I B is equal to zero. Now, look at this

structure. I B is zero. Alpha equal to 1; because of that, I B is zero. And, emitter

base junction is forward biased; which means, V EB, ideally, should be equal to zero. If

it is an ideal diode, emitter base, if it is replaced by a ideal diode drop, will be

zero. Otherwise, it is point 5 to point 7 volts. So, ideally speaking, V EB is equal

to zero, if it is an ideal diode approximation and I B is equal to zero.

So, you can see here that at the input, V EB is going to be very nearly zero and I B

is going to be very nearly zero. This concept of input voltage zero and this current being

zero can be represented later on by an equivalent element. This, we will discuss later. But,

remember that input voltage is zero and this current is zero, in the case of an ideal transistor.

Now, as far as output current is concerned, it can be always anything; but it is dependent

upon the input current I E here. So, it is equal to I E, very nearly equal to I E; and

it can flow into any resistance and develop any potential. So, you have any potential

getting developed at this point, strictly speaking. So, this is a source, dependent

source.

So now, let us consider the other type of transistor, NPN. So far, we had discussed

PNP transistor. So, the other type of transistor, NPN transistor. The transistor action again

occurs according to the same condition; that, base to emitter junction is forward biased

and collector to base junction is reverse biased. But the polarity is just now will

be the opposite. So, base is now made positive with respect to emitter and collector is made

positive with respect to base, in order to achieve transistor action.

So, the equations will remain the same as here. Only the direction is going to be different.

Now, emitter current is going to be, actual direction of current is indicated by the direction

of the arrow; so, it is in this direction. So, the collector current is going towards

the node and base current also will be towards the node; actual direction of the current.

So, the equation still is valid;

. This is the KirchhoffÕs law; this is still valid. Only thing is, emitter current is going

away from the node; collector and base currents are going towards the node.

So, that is the difference between NPN transistor and PNP transistor. Only the biasing is going

to be different; in the sense, bias voltages will be opposite to that of the earlier situation.

But, base to emitter junctions should still be forward biased and collector base junction

should still be reverse biased.

So, in future, in our all our discussions, we will be only using this symbol, these symbols,

for NPN and PNP transistors; and automatically, please remember, the arrow direction will

so actual direction of current will flow in the circuit, if it is biased properly. Now,

let us consider this as a three terminal block. So, assume that this has been put inside a

block, supposed to be the amplifier block. So, we have now a three terminal block available

here. Differently... So, this is the input port and that is the output port. We have

had earlier, the general discussion about two port network and the two ports were independent.

Here, one terminal is common to both input and output. So, this is actually a three terminal

device, obviously, with input port and output port having emitter as common.

In this case, in this device, we have input port and output port with emitter terminal

as common terminal between input and output; so we can call this a common emitter amplifier.

The idea is, this emitter terminal is common between input and output. So, we have a common

emitter amplifier here. Let us now represent this therefore

this way. The input voltage here, V i for this, is same as V BE. The output voltage

is same as V CE. Input current in this case... So, input voltage is equal to V BE. The output

voltage is equal to V CE.

So, E is common, you can see. Input current is same as base current. You can look at this;

this is the base current. And, output current is same as collector current.

You can write down this; this is I E, emitter current; this is base current; this is collector

current.

So, in this common emitter amplifier which is put inside an amplifier block, we can now

represent V i, which we have earlier used for our two port network. Here, it is same

as V BE. V naught, which we have used in our two port network, is same as V CE. I i is

same as I B. I naught is same as I C.

Now, let us consider the ideal transistor situation. So, ideal transistor. In an ideal

transistor, for the transistor action to take place, we must have this forward biased. So,

this has to be forward biased. This junction has to be forward biased. And, if it is an

ideal diode, the junction drop is zero.

So, which means, V i is zero. So, in an ideal transistor, in this case, V i is going to

be very close to zero. In practice, it is about point 5 to point 6 volts. Please remember

that in practice, it is a semiconductor diode and it has a cut-in voltage of about point

5 to point 6 volts; and I i is going to be equal to zero, because ideal transistor, Alpha

is equal to 1.

I C is equal to I E and from our this thing, I C, if it is equal to I E, I B is equal to

zero, according to this. I C is equal to I E; I B is equal to zero, automatically. That

means this is the situation of the input for a common emitter amplifier. V i is equal to

zero, I i is equal to zero; then I C which is nothing but I naught, I C is equal to I

naught, is going to be equal to I E.

So, this is the output current and V CB which is V naught can be any, anything; any

positive voltage.

So, any voltage... V naught can be anything. That means, actually speaking, I can now represent

this by means of an equivalent circuit; the simplest equivalent circuit.

So, we will put down this transistor in terms of its equivalent. I now put here what is

called as some block here; what it says is, this is what is called as a nullor.

What is a nullor? By definition, nullor is something which has current I through it equal

to zero and voltage across it equal to zero. Nullor. Both are nulls.

Current through it equal to zero; that means it will not allow any current to flow through.

And, voltage across it is equal to zero. So, this is called a nullor.

And here, I put a source; which is to say that, this current has to flow through this.

So, this source is something that can deliver any amount of power. That means, any voltage

or any current, depending upon what is applied here. So, this is called a norator. I is anything.

V is anything. This is called a norator.

An ideal transistor therefore, is a combination of nullator and norator, with a junction between

nullator and norator.

This is the simplest equivalent circuit, in terms of networks, for a transistor. Is this

clear? Another thing I have to tell you is, this nullor, is I equal to zero, V equal to

zero; and norator is something with I anything and V anything.

This concept can be made clear by defining an equivalent for simplest things that are

possible in electrical engineering. It is a short circuit and an open circuit. Let us

therefore find out the equivalent for a short circuit in terms of nullators and

norators.

What is a short circuit by definition? Short circuit is something like this. Let us say,

here the voltage is zero and current is anything, not defined. Current can be anything.

That is called a short circuit.

What is an open circuit? For an open circuit, the current is zero. Current through the open

circuit is zero; but voltage can be anything. This voltage can be anything.

Whereas, in a short circuit, current can be anything but voltage equal to zero. Suppose,

therefore, I want a nullator norator equivalent for this. It is very simple. I want a nullator

norator equivalent.

Another thing - according to the theorem, nullators and norators cannot occur individually.

They always occur in pairs; in, for physical existence of these blocks, nullators and norators

occur in pair. Nullors and... nullor or nullator it is called, occur in pairs.

That means, if there is a nullor, there should be a norator corresponding to that, somewhere

in the network. They always occur in pairs. So physically, you cannot have only nullor

existing or norator existing; in which case, equivalent circuit for a short circuit will

be...

This is the equivalent circuit for a short circuit, so that, this nullor makes the voltage

zero, this norator will permit any current to flow through. So, this nullor will make

the voltage zero, and this will permit any current; so effectively, you have a short

circuit.

More importantly, we can have an open circuit in series. This will prevent the current to

flow. So, this will make the current equal to zero. So, nullor will come in series. It

will make the current equal to zero. And therefore, since this is coming in series, the voltage

here can be anything, because of the norator. The voltage across this is zero. The voltage

here can be anything. So, voltage can be anything, current is zero; which is an open circuit.

So, these two are equivalents in terms of nullators and norators for short circuit and

open circuit. Now, for the transistor, what is the equivalent? Nullator and norator will

occur in pair and this end is the collector; this end is the base, and this is the emitter.

The junction point of nullator and norator is the emitter. So, if you have in a network,

nullator and norator forming a junction, such a network can be realized using transistors.

If you have a nullator norator formulating a junction, such a network can be used using,

realized using, transistors. If you do not have such a junction, then, we can formulate

a junction by using these open circuits. Open circuit, putting an open circuit will not

disturb any circuit. So, by putting an open circuit, we can introduce junctions and realize

the bipolar transistor versions of the same network.

So, please remember that we have evaluated from the NPN transistor... for that matter,

we could have started with PNP as well; we would have arrived at the same equivalent.

As far as equivalent circuit is concerned, whether it is NPN or PNP transistor, the same

equivalent circuit is valid.

Now, only thing is that the initial voltage in these cases, we said ideal cases, it is

going to be zero; and practically, we must have this going positive. In the case of the

PNP, it will have to go negative. That is all. So, as far as the equivalent circuit

of a transistor, in its simplest form, is concerned, we can say that, for a common emitter

amplifier, the nullator comes in series at the input and norator comes in series at the

output. And the nullator norator junction is common to both input and output; and that

is the emitter.

We had now discussed the three terminal device, NPN transistor, as common emitter amplifier.

Let us now consider, how in practice, this is biased. So, with respect to emitter as

common, let us consider the supply voltage is V CC positive. So, this is a positive supply

voltage, V CC. Then automatically, this collector is going to be at a higher potential than

the emitter; and, it can be made as high as you please by selecting V CC. So, this V CC

automatically biases, reverse biases this, and simultaneously forward biases this.

So, by using a single supply, if we use emitter as common and put down your voltages, this

would be automatically plus, minus, plus, minus. Even if we keep this base open, the

junction, these two junctions come in series with one another. So, one junction will automatically

get forward biased; that is, emitter base junction. The other one, collector base junction

will automatically get reverse biased. The forward bias junction will take a voltage

of about point 5 to point 6. The rest of it has to come across the collector base junction,

which is adequate for reverse biasing it. So, this is called a single supply biasing

of a transistor.

Now basically, if I keep this base open, what will happen? Let us see. If the base is open,

collector base is reverse biased; emitter base is forward biased

in this arrangement. That means transistor action should take place. Transistor action

takes place. What is transistor action? Transistor action is

.

This is valid; and one thing else also is valid. Base is open; so base current is zero.

So, according to KirchhoffÕs law, I B is zero; therefore I C has to be equal to what?

- I E; because, this current has to be equal to this current.

If that is the case, then you have very interesting thing happening here. Under this kind of biasing

arrangement, we have I C equal to I E. So, replacing that, I C equals Alpha times I C

plus I C naught. Or, I C equals...

. Or,

.

So, there is a collector current now flowing, even though

base is open. There is a collector current flowing because of the leakage current, which

is, I C naught. Not only that, that is amplified by an extent of 1 by 1 minus Alpha. Alpha

is close to 1. So, this factor, 1 by 1 minus Alpha is going to be much greater than 1.

And therefore, this leakage current, under this situation of biasing, is going to be

more than I C naught. If I C naught is of the order of nanoamperes, this might come

under the range of hundreds of nanoamperes.

So, anyway, we are going to ignore the effect of I C naught. It is still very small; and

therefore, we can assume that there is almost no current flowing. I C equal to I C naught

by 1 minus Alpha; that we remember. But, it is going very small; therefore, the voltage

here is going to be very nearly V CC. Or actually, the voltage is V CC, strictly speaking, minus

I C into R C. This is the voltage V CE.

This voltage V CE is going to be V CC minus I C times R C.

This is nothing but V naught, always. So, this equation is always valid. Another equation

is, V i equals V BE, in this, for this circuit.

So now, we can find out the effect of this, let us say, I i. The relationship between

V i and, let us say, I E; this is I E, this is known.

Because,

; minus 1 we will ignore; so it is approximately equal to this, this we know.

Or, I will put it as, equal, minus 1, approximately equal to I E naught exponent V BE by eta V

T.

Let us assume eta to be equal to 1. We have said eta is between 1 and 2. So, I E is equal

to I E naught exponent V BE by V T. This is equal to I E naught exponent... V BE is same

as V i.

So, we have I E. And, what is I C? I C equal to Alpha times I E plus, what? I C naught.

And this I C naught, I am neglecting now; so equal to,

.

Or now, V naught is going to be equal to V CC minus, already we have now I C in terms

of V i; so, Alpha times I E naught; that into

.

This is the non-linear relationship between V naught and V i without making any approximation

whatsoever; except that, I E has been made equal to I E naught exponent V BE by eta V

T, ignoring that 1.

Because emitter base junction is always forward biased, this approximation can always be made.

So, this approximation, in future, will always be made, and I will not repeat it again. We

will take it for granted that

, in the case of transistors. And also, eta equal to 1, we will take; unless otherwise

mentioned. And, in all future situations, we will take

. And, if you plot this... Let us plot this. This will give you V naught versus V i characteristics,

transfer characteristics for the amplifier.

This is the common emitter amplifier. So, NPN transistor, inverter we will call it.

We will see why it is called inverter, presently. So, when this V i is zero, when V i is zero,

this exponent is going to be, I E to power zero, which is 1; and Alpha I E naught RC

is the only drop. I E naught being of the order of nanoamperes, this voltage RC may

be of the order of Kilo ampere; this voltage may not be much. So, this can be ignored;

or, it is slightly less than V CC.

So, it is going to start at very nearly V CC because of the fact that for RC of the

order of Kilo ohms, I E naught of the order of nanoamperes, this voltage is going to be

extremely small. V CC of the order of volts, let us say, here. So, it is slightly less

than V CC. And, it will start with V i becoming substantial.

What is substantial? V i is substantial when there is substantial current flow. That will

happen only when V BE is of the order of point 5 to point 6; so, when this voltage is of

the order of point 5 to point 6. So, this is therefore V naught, sorry, V i. This is

of course V naught. So, V naught will start with V CC; and when it is point 5 to point

6; let us say this is about 1 volt, this is 1 point 5 volts. So, by about point 6 or so,

it will fall off exponentially. Current is going to increase exponentially with input

voltage. So, the voltage will drop; because, this drop will increase. This will keep on

increasing very drastically; keep on increasing...

After a certain point, when this voltage keeps on decreasing, a point will be reached, when,

if this is point 5 to point 6, let us say, and this is zero, it has reached saturation;

because, V CB equal to zero; we said, the transistor has reached saturation.

That means, when V CE becomes about point 5 to point 6, it has just entered saturation.

So, any voltage which is less than, let us say, point 6 or so, will make it go to saturation.

This voltage is going to be extremely small. So, up to this, it is going to be... the transistor

will enter saturation, somewhere here.

So thereafter, both the junctions are going to be forward biased and the transistor is

deep in saturation. So, this characteristic is that of the transistor inverter characteristics.

Why it is called inverter? We can now see that this is the active region. This point;

it might enter saturation. Beyond this point, this is in cut-off; almost. So, this is the

active region. This is the active region.

Now, in this region, you have to operate in order to make the transistor, amplifier. The

transistor should not enter saturation. That transistor should not be in the cut-off. This

should be in the active region. If it is in the active region, it can work as an amplifier.

And, it will be linear, only for small signal changes; because, basically it is non-linear;

it is an exponential relationship. E to power V i by V T can be expanded as E to power x,

1 plus x plus x square by factorial 2 plus x cubed by factorial 3. That way.

So basically, this is equal to V CC minus Alpha I E naught RC into

, exponent x, which is actually speaking, exponent; let us call it as V i Q, some voltage,

which is constant, plus Delta V i. That is, I am changing the voltage by a small amount

around a quiescent voltage.

Why is this being done? Because, this voltage can be increased or decreased. So, I can apply

an AC input, by maintaining, basically, the emitter base junction at a quiescent voltage

of V i Q. This effective voltage should always be of the order of point 5 to point 6. So,

this is going to be V C C minus Alpha I E naught RC exponent V i Q by V T, V i Q by

V T, into exponent Delta V i by V T.

What is small signal? A small signal is that signal at which I can consider this relationship

between input and output, linear. So, when the input voltage is changing by a small amount,

then, I can consider it as small signal. That small amount is comparable to V T. V T is

of the order of 25 millivolts. That means, if this Delta V i is of the order of a few

millivolts, then, it can be considered as small signal. Then, we can expand this as

, so on... Delta V i by V T whole cubed by factorial 3, which is 6.

So, this is the nature of variation of output. These are, I have told you earlier in our

general discussion about amplifier, this is the linear term; this is the offset; this

is the offset, DC offset; this is the linear term; this is the non-linearity; these are

the nonlinearities. We have to have these non-linear terms made as small as possible

for reducing distortion. That means Delta V i by V T should be much less than 1.

This is an important ... for making this common emitter transistor,

a good amplifier. We will discuss further in

the next class. 2