COURSE MATERIAL

ELECTRONIC DEVICES AND CIRCUITS

SUBJECT
(EC23APC302)

UNIT 3

COURSE B.TECH

DEPARTMENT ECE

SEMESTER 21

PREPARED BY M.POORNIMA
(Faculty Name/s) Assistant Professor

Version V-1

PREPARED / REVISED DATE 08-11-2024

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1. Course Objectives
The objectives of this course is
1. To understand the basic principles of all semiconductor devices.
2. To be able to solve problems related to diode circuits, and amplifier circuits.
3. To analyse diode circuits, various biasing and small signal equivalent circuits of
amplifiers.
4. To be able to compare the performance of BJTs and MOSFETs.
5. To design rectifier circuits and various amplifier circuits using BJTs and MOSFETs.
2. Prerequisites
Students should have knowledge on
1. Network Analysis
2. Applied Physics2

3. Syllabus
UNIT 3
Small-Signal Operation and Models, The Collector Current and the
Transconductance, The Base Current and the Input Resistance at the Base, The
Emitter Current and the Input Resistance at the Emitter, Voltage gain,
The Hybrid-π model and T model, Performing small -signal analysis directly on the
circuit diagram.

Basic B J T a m p l i f i e r c o n f i g u r a t i o n s : Three b a s i c c o n f i g u r a t i o n s - T h e
C o m m o n E m i t t e r amplifier without and with emitter resistance, Common Base
amplifier and Common collector amplifier, Comparison of three configurations.
4. Course outcomes
After completion of this subject, students will be able to
1. Understand principle of operation, characteristics and applications of
Semiconductor diodes, Bipolar Junction Transistor and MOSFETs.
2. Apply the basic principles for solving the problems related to Semiconductor
diodes, BJTs, and MOSFETs.
3. Analyze diode circuits for different rectifiers, and also analyze biasing circuits of
BJTs, and MOSFETs.
4. Design diode circuits and amplifiers using BJTs, and MOSFETs.
5. Compare the performance of various semiconductor devices.

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 5. Co-PO / PSO Mapping

EDC PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 P10 PO11 PO12 PSO1 PSO2

CO1 3 2 1 3 2

CO2 3 3 3 2 3 3

CO3 3 3 2 2 3 3

CO4 3 3 3 2 2 3

CO5 3 3 2 2 3 3

6. Lesson Plan

Lecture No. Weeks Topics to be covered References

Small-Signal Operation and Models, The Collector Current and the
1 T1
Transconductance
2 The Base Current and the Input Resistance at the Base, T1

3 The Emitter Current and the Input Resistance at the Emitter T1

4 Voltage gain T1

5 The Hybrid-π model and T model T1

6 Performing small -signal analysis directly on the circuit diagram T1

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T h e C o m m o n E m i t t e r amplifier without and with emitter
7 T1
resistance
8 Common Base amplifier T1

9 3 Common collector amplifier, Comparison of three configurations T1

7. Activity Based Learning

1. Through project based teaching learning to apply the theoretical concepts.

2. Through worksheets is used to facilitate project based learning by
strengthening the fundamental concepts during classroom teaching

8. Lecture Notes
3.1 Small-Signal Operation and Models

Having learned the basis for the operation of the BJT as an amplifier, we now
take a closer look at the small-signal operation of the transistor. Toward that
end, consider once more the conceptual amplifier circuit shown in Fig. 3.1(a).
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Here the base–emitter junction is forward biased by a dc voltage VBE (battery).
The reverse bias of the collector–base junction is established by connecting the
collector to another power supply of voltage VCC through a resistor RC. The
input signal to be amplified is represented by the voltage source vbe that is
superimposed on VBE.
We consider first the dc bias conditions by setting the signal vbe to zero. The
circuit reduces to that in Fig. 3.1(b), and we can write the following
relationships for the dc cur-rents and voltages

Figure 3.1 (a) Conceptual circuit to illustrate the operation of the

transistor as an amplifier. (b) The circuit of (a) with the signal source vbe
eliminated for dc (bias) analysis.

Obviously, for active-mode operation, VC should be greater than (VB 0.4)

by an amount that allows for the required signal swing at the collector.

3.1.1 The Collector Current and the Transconductance

If a signal vbe is applied as shown in Fig. 3.1(a), the total instantaneous base–
emitter volt- age vBE becomes

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Correspondingly, the collector current becomes

C
Now, if vbe < VT, we may approximate Eq. 5) as

Here we have expanded the exponential in Eq. 5) in a series and retained only
the first two terms. This approximation, which is valid only for vbe less than
approximately 10 mV, is referred to as the small-signal approximation. Under this
approximation, the total collector current is given by Eq. (6) and can be
rewritten

Thus the collector current is composed of the dc bias value IC and a signal
component ic ,

This equation relates the signal current in the collector to the corresponding
base–emitter signal voltage. It can be rewritten as

where gm is called the transconductance, and from Eq. (8), it is given by

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We observe that the transconductance of the BJT is directly proportional to

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the collector bias current IC. Thus to obtain a constant predictable value for
gm, we need a constant predictable IC. Finally, we note that BJTs have
relatively high transconductance); for instance, at IC = 1 mA, gm = 40 mA/V.
A graphical interpretation for gm is given in Fig. 3.2, where it is shown that
gm is equal to the slope of the iC –vBE characteristic curve at iC = IC (i.e., at
the bias point Q). Thus,

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Figure 3.2 Linear operation of the transistor under the small-signal condition: A
small signal vbe with a triangular waveform is superimposed on the dc voltage
VBE. It gives rise to a collector signal current ic, also of triangular waveform,
superimposed on the dc current IC. Here, ic = gmvbe, where gm is the slope of
the iC –vBE curve at the bias point Q

The small-signal approximation implies keeping the signal amplitude

sufficiently small that operation is restricted to an almost-linear segment of the
iC–vBE exponential curve. Increasing the signal amplitude will result in the
collector current having components nonlinearly related to vbe. This, of
course, is the same approximation that we discussed in the context of the
amplifier transfer curve.

The analysis above suggests that for small signals (vbe << VT), the transistor

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behaves as a voltage-controlled current source. The input port of this
controlled source is between base and emitter, and the output port is
between collector and emitter. The transconductance of the controlled
source is gm, and the output resistance is infinite. The latter ideal property is a
result of our first-order model of transistor operation in which the collector
voltage has no effect on the collector current in the active mode. As we
have seen, practical BJTs have finite output resistance because of the Early
effect. The effect of the output resistance on amplifier performance will be
considered later.

3.1.2 The Base Current and the Input Resistance at the Base
To determine the resistance seen by vbe, we first evaluate the total base
current iB using Eq. (7), as follows:

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where IB is equal to IC / β and the signal component ib is given by

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Substituting for IC / VT by gm gives

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The small-signal input resistance between base and emitter, looking into
the base, is denoted by rπ and is defined as

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 Thus rπ is directly dependent on β and is inversely proportional to the bias current
IC . Substituting for gm in Eq. (16) from Eq. (10) and replacing IC /β by IB gives
an alternative expression for rπ ,

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3.1.3 The Emitter Current and the Input Resistance at the Emitter

The total emitter current iE can be determined from

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Comparison with Eq. (10) reveals that

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The relationship between rπ and re can be found by as

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Figure 3.3 illustrates the definition of rπ and re.

Figure 3.3 illustrating the definition of rπ and re.

3.1.4 Voltage Gain

We have established above that the transistor senses the base–emitter signal vbe
and causes a proportional current gmvbe to flow in the collector lead at a high
(ideally infinite) impedance level. In this way the transistor is acting as a voltage-
controlled current source. To obtain an output voltage signal, we may force this
current to flow through a resistor, as is done in Fig. 3.1(a). Then the total collector
voltage vCE will be

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Here the quantity VCE is the dc bias voltage at the collector, and the signal
voltage is given by

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Here again we note that because gm is directly proportional to the collector

bias current, the gain will be as stable as the collector bias current is made.
Substituting for gm from Eq. (10) enables us to express the gain in the form

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3.1.5 The Hybrid-π Model

An equivalent circuit model for the BJT is shown in Fig. 3.4(a). This model
represents the BJT as a voltage-controlled current source and explicitly includes
the input resistance looking into the base, rπ. The model obviously yields ic =
gmvbe and Not so obvious, however, is the fact that the model also yields the
correct expression for ie . This can be shown as follows: At the emitter node we
have

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This results in the alternative equivalent-circuit model shown in Fig. 3.4(b). Here
the transistor is represented as a current-controlled current source, with the
control current being ib.

Figure 3.4 Two slightly different versions of the hybrid-π model for the small-signal
operation of the BJT. The equivalent circuit in (a) represents the BJT as a
voltage-controlled current source (a transconductance amplifier), and that in
(b) represents the BJT as a current-controlled current source (a current
amplifier).

The two models of Fig. 3.4 are simplified versions of what is known as the hybrid-
π model. This is the most widely used model for the BJT. It is important to note
that the small-signal equivalent circuits of Fig. 3.4 model the operation of the BJT
at a given bias point. This should be obvious from the fact that the model
parameters gm and rπ depend on the value of the dc bias current IC , as
indicated in Fig. 3.4.

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3.1.6 The T Model

Although the hybrid-π model (in one of its two variants shown in Fig. 3.4 can be
used to carry out small-signal analysis of any transistor circuit, there are situations
in which an alternative model, shown in Fig. 3.5 is much more convenient. This
model, called the T model, is shown in two versions in Fig. 3.5. The model of Fig.
3.5 (a) represents the BJT as a voltage-controlled current source with the control
voltage being vbe. Here, however, the resistance between base and emitter,
looking into the emitter, is explicitly shown. From Fig. 3.5(a) we see clearly that
the model yields the correct expressions for ic and ie. For ib we note that at the
base node we have

Figure 3.5 Two slightly different versions of what is known as the T model of the
BJT. The circuit in (a) is a voltage-controlled current source representation and
that in (b) is a current-controlled current source representation. These models
explicitly show the emitter resistance re rather than the base resistance rπ
featured in the hybrid-π model.

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as should be the case.

If in the model of Fig. 3.5(a) the current of the controlled source is expressed in
terms of the emitter current as

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we obtain the alternative T model shown in Fig. 3.5(b).

3.2 Basic BJT Amplifier Configurations

The Three Basic Configurations
There are three basic configurations for connecting the BJT as an amplifier.
Each of these configurations is obtained by connecting one of the three BJT
terminals to ground, thus creating a two-port network with the grounded
terminal being common to the input and output ports. Figure 3.6 shows the
resulting three configurations with the biasing arrangements omitted. In the
circuit of 3.6a the emitter terminal is connected to ground, the input voltage
signal is applied between the base and ground, and the output voltage signal
is taken between the collector and ground, across the resistance . This
configuration, therefore, is called the grounded-emitter or common-

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emitter(CE)amplifier. It is by far the most popular BJT amplifier configuration

Figure 3.6 The three basic configurations of BJT amplifier. The biasing
arrangements are not shown.

The common-base (CB) or grounded-base amplifier is shown in Fig. 3.6(b). It is

obtained by connecting the base to ground, applying the input between the
emitter and ground, and taking the output across the resistance connected
between the collector and ground. Finally, Fig. 3.6(c) shows the common-
collector (CC) or grounded-collector amplifier. It is obtained by connecting the
collector terminal to ground, applying the input voltage signal between base
and ground, and taking the output voltage signal between the emitter and
ground, across a load resistance. For reasons that will become apparent shortly,
this configuration is more commonly called the emitter follower. Our study of the
three basic BJT amplifier configurations will reveal that each has distinctly
different attributes and hence areas of application

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3.3 The Common-Emitter (CE) Amplifier

Of the three basic BJT amplifier configurations, the common emitter is the most
widely used. Typically, in an amplifier formed by cascading a number of stages,
the bulk of the voltage gain is obtained by using one or more common-emitter
stages in the cascade.
Figure 3.7(a) shows a common-emitter amplifier (with the biasing
arrangement omitted) fed with a signal source vsig having a source resistance
Rsig . We wish to analyse the circuit to determine Rin, Avo, Ro , and Gv. For this
purpose we shall assume that RC is part of the amplifier; thus if a load resistance
RL is connected to the amplifier output, it appears in par- allel with RC.
Characteristic Parameters of the CE Amplifier Replacing the BJT with its hybrid-
model, we obtain the CE amplifier equivalent circuit shown in Fig. 3.7(b). We
shall use this equivalent circuit to determine the characteristic parameters of
the amplifier Rin , Avo , and Ro as follows.

The input resistance Rin is found by inspection to be

Figure 3.7 (a) Common-emitter amplifier fed with a signal vsig from a generator with a
resistance Rsig.
Figure 3.7 (b) The common-emitter amplifier circuit with the BJT replaced with its hybrid-
model.

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29

30

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Overall Voltage Gain

To determine the overall voltage gain𝐺𝑉 we first determine the fraction of that
appears at the amplifier input proper, that is, ;

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Depending on the relative values of rπ and Rsig, significant loss of signal

strength can occur at the input, which is obviously undesirable and can be
avoided by raising the input
Resistance, as discussed above. At this point, we should remind the reader that
to maintain a reasonably linear operation, vi should not exceed about 5 mV to
10 mV, which poses a con straint on the value of vsig.
If a load resistance RL is connected to the output terminal of the amplifier, this
resistance will appear in parallel with RC . It follows that the voltage gain Av can
be obtained by simply replacing RC in the expression of Avo in Eq. (29) by RC
// RL ,

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3.4 The Common-Emitter Amplifier with an Emitter Resistance

Including a resistance in the emitter as shown in Fig. 3.8(a) can lead to

significant changes in the amplifier characteristics. Thus, such a resistor can be
an effective design tool for tailoring the amplifier characteristics to fit the design
requirements.

Analysis of the circuit in Fig. 3.8(a) can be performed by replacing the BJT with
one of its small-signal models. Although any one of the models can be used, the
most convenient for this application is one of the two T models. This is because
the resistance in the emitter will appear in series with the emitter resistance of
the T model and can thus be added to it, simplifying the analysis considerably.
In fact, whenever there is a resistance in the emitter lead, the T model should
prove more convenient to use than the hybrid- model.

Replacing the BJT with the T model results in the amplifier small-signal,
equivalent-circuit model shown in Fig. 3.8(b). Note that we have not included
the BJT output resistance; because this would complicate the analysis
considerably. Since for the discrete amplifier at hand it turns out that the effect
of on circuit performance is small, we shall not include it in the analysis here.

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Figure 3.8 The CE amplifier with an emitter resistance Re; (a) Circuit without bias
details; (b) Equivalent circuit with the BJT replaed with its T model.

To determine the amplifier input resistance we note from Fig. 3.8(b) that

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This is a very important result. It states that the input resistance looking into the
base is β+1 times the total resistance in the emitter, and is known as the
resistance-reflection rule. The factor β+1 arises because the base current is 1 /
β+1 times the emitter current. The expression for Rin in Eq. (36) shows clearly that
including a resistance Re in the emitter can substantially increase Rin . Indeed,
the value of Rin is increased by the ratio

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Thus, including Re reduces the voltage gain by the factor ( 1 + gm Re ), which is

the same factor by which Rin is increased. This points out an interesting trade-off
between gain and input resistance, a trade-off that the designer can exercise
through the choice of an appropriate value for Re.
The output resistance Ro can be found from the circuit in Fig. 3.8(b) by
inspection:
Ro = RC

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3.5 The Common-Base (CB) Amplifier

Figure 3.9(a) shows a common-base amplifier with the biasing circuit omitted.
The amplifier is fed with a signal source characterized by vsig and Rsig . Since
Rsig appears in series with the emitter, it is more convenient to represent the
transistor with the T model than with the hybrid- model. Doing this, we obtain
the amplifier equivalent circuit shown in Fig. 3.9(b). Note that we have not
included ro. This is because including ro would complicate the analysis
consider- ably, for it would appear between the output and input of the
amplifier. Fortunately, it turns out that the effect of ro on the performance of a
discrete CB amplifier is very small.

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figure 3.9 (a) CB amplifier with bias details omitted; (b) Amplifier equivalent
circuit with the BJT represented by its T Model.

From inspection of the equivalent circuit in Fig. 3.9(b), we see that the input
resistance is

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The output resistance of the CB circuit can be found by inspection of the circuit
in Fig. 3.9(b) as

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3.6 The Common-Collector Amplifier or Emitter Follower

Figure 3.10(a) shows a common- collector amplifier or emitter follower, as we will
refer to it henceforth. Note that the biasing circuit is not shown. The emitter
follower is fed with a signal source ( vsig, Rsig ) and has a load resistance RL
connected between emitter and ground. To keep things simple, we are as-
suming that RL includes both the actual load and any other resistance that may
be present be- tween emitter and ground. Normally the actual RL would be
much lower in value than such other resistances and thus would dominate.
Since the BJT has a resistance connected in its emitter, it is most convenient to
use the T model to represent the BJT. Doing this results in the emitter-follower
equivalent circuit shown in Fig. 3.10(b). We have included simply because it is
very easy to do so. However, note that appears in parallel with , and in discrete
circuits is much larger than and can thus be neglected. The resulting simplified

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circuit shown in Fig. 3.10(c), can now be used to determine the characteristic
parameters of the amplifier.

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Figure 3.10 (a) Common-collector amplifier or emitter-follower. (b) Equivalent circuit obtained
by replacing the BJT with its T model. Note that ro appears in parallel with RL. Since in discrete
circuits r0 � RL, we shall neglect it, thus obtaining the simplified circuit in (c).

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a result that we could have written directly, utilizing the resistance-reflection

rule. Note that as expected the emitter follower takes the low load resistance
and reflects it to the base side, where the signal source is, after increasing its
value by a factor β+1. It is this impedance transformation property of the emitter
follower that makes it useful in connecting a low- resistance load to a high-
resistance source, that is, to implement a buffer amplifier.

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To determine Ro, refer to Fig. 3.10(c) and look back into the emitter (i.e., behind
or excluding RL ) while setting vi = 0 (i.e., grounding the base). You will see re of
the BJT, thus

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3.7 Summary and Comparisons

For easy reference and to enable comparisons, we present in Table the
formulas for determining the characteristic parameters of discrete BJT amplifiers.
Note that ro has been neglected throughout. As has already been mentioned,
this is possible in discrete-circuit amplifiers. In addition to the remarks made
throughout this section about the characteristics
and applicability of the various configurations, we make the following
concluding points.
1. The CE configuration is the one best suited for realizing the bulk of the gain
required in an amplifier. Depending on the magnitude of the gain required, either
a single stage or a cascade of two or three stages can be used.
2. Including a resistor Re in the emitter lead of the CE stage provides a number of
perfor mance improvements at the expense of gain reduction.
3. The low input resistance of the CB amplifier makes it useful only in specific
applications. As we shall see in previous chapters, it has a much better high-
frequency response than the CE amplifier. This superiority will make it useful as a
high-frequency amplifier, especially when combined with the CE circuit.
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4.The emitter follower finds application as a voltage buffer for connecting a
high- resistance source to a low-resistance load and as the output stage in a
multistage amplifier, where its purpose is to equip the amplifier with a low
output-resistance.

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