What is the re-model of npn common base transistor?

Answer 1

Thus if we go back to the

circuit model for the common emitter transistor, and

re-draw it as a small signal model it would look

something like Figure 1. Here we have replaced the

diode with a linear element (a resistor, called

rπ)

and we have changed the notation for the currents from

IB

and

IC

to

ib

and

ic

respectively, to remind us that we are now talking about small signal

ac quantities, not large signal ones. The bias currents

IB

and

IC

are still flowing through the device (and we will leave it to ELEC 342

to discuss how these are generated and set up) but they do not appear

in the small signal model. This model is only used to figure out how

the transistor behaves for the ac signal going through it, not have

it responds to large DC values.

Figure 1: Small signal linear model for the common emitter transistor

Figure 1 (3.16.png)

Now

rπ

the equivalent small signal resistance of the base-emitter diode

is given simply by the inverse of the conductance of the

equivalent diode. Remember, we found

rπ===1qkTIB1qkTICββ40IC

(1)

where we have used the fact that

IC=βIB

and

qkT=40V-1.

As we said earlier, typical values for βin a standard bipolar transistor will be around

100. Thus, for a typical collector bias current of

IC=1mA,

rπ

will be about 2.5 kΩ.

There is one more item we should consider in putting together our

model for the bipolar transistor. We did not get things completely

right when we drew the common emitter characteristic curves for the

transistor. There is a somewhat subtle effect going on when

VCE

is increased. Remember, we said that the current coming out of the

collector is not effected by how big the drop was in the reverse

biased base-collector junction. The collector current just depends

on how many electrons are injected into the base by the emitter,

and how many of them make it across the base to the base-collector

junction. As the base-collector reverse bias is increased (by

increasing

VCE

the depletion width of the base-collector junction increases as

well. This has the effect of making the base region somewhat

shorter. This means that a few more electrons are able to make it

across the base region without recombining and as a result

α and hence

β increase somewhat. This then

means that

IC

goes up slightly with increasing

VCE.

The effect is called base width modulation.

Let us now include that effect in the common emitter

characteristic curves. As you can see in Figure 3,

there is now a slope to the

IC(VCE)

curve, with

IC

increasing somewhat as

VCE

increases. The effect has been somewhat exaggerated in Figure 2, and I will now make the slope even bigger so

that we may define a new quantity, called the Early

Voltage.

Figure 2: Common emitter response with base-width modulation

effectFigure 2 (3.17b.png)

Figure 3: Finding the Early VoltageFigure 3 (3.18b.png)

Back in the very beginning of the transistor era, an engineer

at Bell Labs, Jim Early, predicted that there would be a slope to the

IC

curves, and that they would all project back to the same

intersection point on the horizontal axis. Having made that

prediction, Jim went down into the lab, made the measurement, and

confirmed his prediction, thus showing that the theory of

transistor behavior was being properly understood. The point of

intersection of the

VCE

axis is known as the Early Voltage. Since

the symbol

VE,

for the emitter voltage was already taken, they had to label the

Early Voltage

VA

instead. (Even though the intersection point in on the negative

half of the

VCE

axis,

VA

is universally quoted as a positive number.)

How can we model the sloping I-V curve? We can do almost the

same thing as we did with the solar cell. The horizontal part of

the curve is still a current source, and the sloped part is

simply a resistor in parallel with it. Here is a graphical

explanation in Figure 4.

Figure 4: Combining a current course and a resistor in parallelFigure 4 (3.19.png)

Usually, the slope is much less than we have shown here, and so

for any given value of

IC,

we can just take the slope of the line as

ICVA,

and hence the resistance, which is usually called

ro

is just

VAIc.

Thus, we add

ro

to the small signal model for the bipolar transistor. This is

shown in Figure 5. In a good quality modern

transistor, the Early Voltage,

VA

will be on the order of 150-250 Volts. So if we let

VA=200,

and we imagine that we have our transistor biased at 1 mA, then

ro==200V1mA200kΩ

(2)

which is usually much larger than most of the other resistors you

will encounter in a typical circuit. In most instances,

ro

can be ignored with no problem. If you get into high impedance

circuits however, as you might find in a instrumentation

amplifier, then

vbe

has to be taken into account.

Figure 5: Including ro in the small signal linear modelFigure 5 (3.20.png)

Sometimes it is advantageous to use a mutual transconductance

model instead of a current gain model for the transistor. If we

call the input small signal voltage

vbe,

then obviously

ib==vberπvbeβ40IC

(3)

But

ic=βib=βvbeβ40IC=40ICvbe≡gmvbe

(4)

Where

gm

is called the mutual transconductance of the transistor.

Notice that β

has completely cancelled out in the expression for

gm

and that

gm

depends only upon the bias current,

IC,

flowing through the collector and not on any of the physical

properties of the transistor itself!

Figure 6: Transconductance small signal linear modelFigure 6 (3.21.png)

Finally, there is one last physical consideration we should make

concerning the operation of the bipolar transistor. The

base-collector junction is reverse biased. We know that if we

apply too much reverse bias to a pn junction, it can breakdown

through avalanche multiplication. Breakdown in a transistor is

somewhat "softer" than for a simple diode, because once a small

amount of avalanche multiplication starts, extra holes are

generated within the base-collector junction. These holes fall up,

into the base, where they act as additional base current, which,

in turn, causes

IC

to increase. This is shown in Figure 7.

Figure 7: Ionization at the base-collector junction causes additional

base currentFigure 7 (3.22.png)

A set of characteristic curves for a transistor going into

breakdown is also shown in Figure 8.

Figure 8: Bipolar Transistor going into breakdownFigure 8 (3.23b.png)

Well, we have learned quite a bit about bipolar transistors in a

very short space. Go back over this chapter and see if you can

pick out the two or three most important ideas of equations which

would make up a set of "facts" that you could stick away in you

head someplace. Do this so you will always have them to refer to

when the subject of bipolars comes up (In say, a job interview or

something!).