Mandalay Technological University

Department of Electronic Engineering

EcE-22011 ,Basic Analog Devices II

Chapter-6
BJT Amplifier
Lecture - 1
Daw Mya Sandar Aung
Lecturer
Daw Phue Wai Phyo, Tutor
 DEPARTMENT OF
ELECTRONIC
CHAPTER OUTLINE ENGINEERING

❖AMPLIFIER OPERATION
❖TRANSISTOR AC MODELS
❖THE COMMON-EMITTER AMPLIFIER
❖THE COMMON-COLLECTOR AMPLIFIER
❖THE COMMON-BASE AMPLIFIER
❖MULTISTAGE AMPLIFIERS
❖THE DIFFERENTIAL AMPLIFIER

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 DEPARTMENT OF
ELECTRONIC
OBJECTIVES ENGINEERING

❖ Describe amplifier operation

❖ Discuss transistor models
❖ Describe and analyze the operation of common-emitter amplifiers
❖ Describe and analyze the operation of common-collector amplifiers
❖ Describe and analyze the operation of common-base amplifiers
❖ Describe and analyze the operation of multistage amplifiers
❖ Discuss the differential amplifier and its operation

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 DEPARTMENT OF
ELECTRONIC
INTRODUCTION ENGINEERING

❖ An amplifier is used to increase the signal level. It is used to get a larger signal output
from a small signal input.
❖ To make the transistor work as an amplifier, it is to be biased to operate in active region.
❖ It means base-emitter junction is forward biased and base-collector junction is reverse
biased.

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 DEPARTMENT OF
ELECTRONIC
Bipolar Junction Transistors (BJT) ENGINEERING

❖ The BJT is constructed with three doped semiconductor regions separated by two pn
junctions, as shown in the epitaxial planar structure in Figure(1).
❖ The three regions are called emitter, base, and collector.
❖ Physical representations of the two types of BJTs are shown in Figure 1 (b) and (c).
One type consists of two n regions separated by a p region (npn), and the other type
consists of two p regions separated by an n region (pnp)

Figure 2 BJT symbol and current

Figure 1 BJT construction.
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 DEPARTMENT OF
ELECTRONIC
AMPLIFIER OPERATION ENGINEERING

❖ The biasing of a transistor is purely a dc operation.

❖ The purpose of biasing is to establish a Q-point about which variations in current and voltage
can occur in response to an ac input signal.
❖ In applications where small signal voltages must be amplified— such as from an antenna or a
microphone—variations about the Q-point are relatively small.
❖ Amplifiers designed to handle these small ac signals are often referred to as small-signal
amplifiers.

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 DEPARTMENT OF
ELECTRONIC
THE COMMON-EMITTER AMPLIFIER ENGINEERING

❖ Three amplifier configurations are the common-emitter,

the common-base, and the common-collector.

❖ The common-emitter (CE) configuration has the emitter as

the common terminal, or ground, to an ac signal.

❖ CE amplifiers exhibit high voltage gain and high current

gain.

❖ The input signal, 𝑉𝑖𝑛 , is capacitively coupled to the base

terminal, the output signal, 𝑉𝑜𝑢𝑡 , is capacitively coupled
from the collector to the load. Figure 3 A common-emitter amplifier

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 DEPARTMENT OF
ELECTRONIC
A GRAPHICAL PICTURE ENGINEERING

• The operation just described can be illustrated graphically on the ac load line, as shown in Figure 6–2.
• The sinusoidal voltage at the base produces a base current that varies above and below the Q-point
on the ac load line, as shown by the arrows.

FIGURE 4 Graphical ac load line operation

of the amplifier showing the
variation of the base current,
collector current, and collector-
to-emitter voltage about their dc
Q-point values. 𝐼𝑏 and 𝐼𝑐 are on
different scales.

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 DEPARTMENT OF
ELECTRONIC
TRANSISTOR AC MODELS ENGINEERING

❖ To visualize the operation of a transistor in an amplifier circuit, it is often useful to

represent the device by a model circuit.
❖ A transistor model circuit uses various internal transistor parameters to represent its
operation.
❖ Transistor models are described in this section based on resistance or r parameters.
❖ Another system of parameters, called h parameters, is briefly described.

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 DEPARTMENT OF
ELECTRONIC
r Parameters ENGINEERING

• The five r parameters commonly used for BJTs are given in Table 6–1.
• The italic lowercase letter r with a prime denotes resistances internal to the transistor.

TABLE 6–1 r parameters

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 DEPARTMENT OF
ELECTRONIC
r-Parameter Transistor Model ENGINEERING

• An r-parameter model for a BJT is shown in Figure 3.

• For most general analysis work, it can be simplified as follows: The effect of the ac base resistance
is usually small enough to neglect, so it can be replaced by a short.
• The ac collector resistance is usually several hundred kilo-ohms and can be replaced by an open.
• The resulting simplified r-parameter equivalent circuit is shown in Figure 5.

FIGURE 5 r-parameters transistor model.

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 DEPARTMENT OF
ELECTRONIC
ENGINEERING

❖The interpretation of this model circuit in terms of a transistor’s ac operation is as follows: A

resistance appears between the emitter and base terminals.
❖ This is the resistance “seen” looking into the emitter of a forward-biased transistor.
❖The collector effectively acts as a dependent current source of or, equivalently, represented by the
diamond-shaped symbol.
❖These factors are shown with a transistor symbol in Figure 6.

FIGURE 6 Relation of transistor symbol to

r-parameter model

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 DEPARTMENT OF
ELECTRONIC
DETERMINING 𝑟𝑒′ BY A FORMULA ENGINEERING

❖For amplifier analysis, the ac emitter resistance, is the most important of the r parameters.
❖To calculate the approximate value,
❖The Shockley equation for the base-emitter pn junction is I E = I R (eVQ / KT − 1)
Where, I E = total forward current across the base-emitter junction
IR = reverse saturation current
V =voltage across the depletion layer
Q = charge on an electron
k = number known as Boltzmann’s constant
T = absolute temperature
Q 1.62 10−19
At ambient temperature = = 40 so,
kT 1.38 10−23  293.16

I E = I R (eV 40 − 1)

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 DEPARTMENT OF
Continued: ELECTRONIC
ENGINEERING

Differentiating,
dI E
= 40 I R eV 40
dV
Sin ce I R eV 40 = I E + I R
dI E
= 40 ( I E + I R )
dV
Assuming I R I E ,
dI E
= 40 I E
dV
dV
The ac resistance re of the base-emitter junction can be expressed as .
dI E
dV 1 25mV
re = = =
dI E 40 I E IE
25𝑚𝑉
Equation 6–1 𝑟𝑒′ ≅
𝐼𝐸

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 DEPARTMENT OF
ELECTRONIC
DC Analysis ENGINEERING

❖To analyze the amplifier in Figure 6–6, the dc bias values must first be determined.
❖To do this, a dc equivalent circuit is developed by removing the coupling and bypass
capacitors because they appear open as far as the dc bias is concerned.
❖ This also removes the load resistor and signal source.
❖The dc equivalent circuit is shown in Figure 7.

FIGURE 7 DC equivalent circuit for the amplifier.

𝑅𝑇𝐻
𝑉𝑇𝐻 𝑉𝐵𝐸

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 DEPARTMENT OF
ELECTRONIC
DC Analysis ENGINEERING

❖Theveninizing the bias circuit and applying Kirchhoff’s voltage law to the base-emitter
circuit,
𝑅1 𝑅2 (6.8 𝑘Ω)(22 𝑘Ω)
𝑅𝑇𝐻 = = = 5.19 𝑘Ω
𝑅1 +𝑅2 6.8 𝑘Ω+22 𝑘Ω
𝑅2 6.8 𝑘Ω
𝑉𝑇𝐻 = 𝑉𝐶𝐶 = 12 𝑉 = 2.83 𝑉
𝑅1 +𝑅2 6.8 𝑘Ω+22 𝑘Ω
𝑉𝑇𝐻 −𝑉𝐵𝐸 2.83 𝑉−0.7 𝑉
𝐼𝐸 = = = 3.58 𝑚𝐴
𝑅𝐸 +𝑅𝑇𝐻 Τ𝛽𝐷𝐶 560 Ω+34.6 Ω

𝐼𝐶 ≅ 𝐼𝐸 = 3.58 𝑚𝐴
𝑉𝐸 = 𝐼𝐸 𝑅𝐸 = 3.58𝑚𝐴 560Ω = 2 𝑉
𝑉𝐵 = 𝑉𝐸 + 0.7 𝑉 = 2.7 𝑉
𝑉𝐶 = 𝑉𝐶𝐶 − 𝐼𝐶 𝑅𝐶 = 12𝑉 − 3.58𝑚𝐴 1.0𝑘Ω = 8.42𝑉
𝑉𝐶𝐸 = 𝑉𝐶 − 𝑉𝐸 = 8.42𝑉 − 2𝑉 = 6.42𝑉

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 DEPARTMENT OF
ELECTRONIC
AC Analysis ENGINEERING

❖To analyze the ac signal operation of an amplifier, an ac equivalent circuit is developed as follows:
1. The capacitors 𝐶1 , 𝐶2 , and 𝐶3 are replaced by effective shorts because their values are selected so
that 𝑋𝐶 is negligible at the signal frequency and can be considered to be 0V.
2. The dc source is replaced by ground.

FIGURE 8 AC equivalent circuit for the amplifier in Figure 3

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 DEPARTMENT OF
Signal (AC) Voltage at the Base ELECTRONIC
ENGINEERING

FIGURE 9 AC equivalent of the base circuit.

This is illustrated in Figure 9(a) and is simplified by combining 𝑅1 , 𝑅2 , and 𝑅𝑖𝑛(𝑏𝑎𝑠𝑒) in parallel to get the
total input resistance, 𝑅𝑖𝑛(𝑡𝑜𝑡) , which is the resistance by an ac source connected to the input, as shown in
Figure 9(b).
The total input resistance is expressed by the following formula:
𝑅𝑖𝑛(𝑡𝑜𝑡) = 𝑅1 ∥ 𝑅2 ∥ 𝑅𝑖𝑛(𝑏𝑎𝑠𝑒) Equation 6–2
❖In the figure, the source voltage, 𝑉𝑠 , is divided down by 𝑅𝑠 (source resistance) and 𝑅𝑖𝑛(𝑡𝑜𝑡) so that the
signal voltage at the base of the transistor is found by the voltage-divider formula as follows:
𝑅𝑖𝑛(𝑡𝑜𝑡)
𝑉𝑏 = ( )𝑉
𝑅𝑠 + 𝑅𝑖𝑛(𝑡𝑜𝑡) 𝑠
➢ If 𝑅𝑠 ≪ 𝑅𝑖𝑛(𝑡𝑜𝑡) ,then 𝑉𝑏 ≅ 𝑉𝑠 where 𝑉𝑏 is the input voltage, 𝑉𝑖𝑛 , to the amplifier.

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 DEPARTMENT OF
ELECTRONIC
Input Resistance at the Base ENGINEERING

❖To develop an expression for the ac input resistance looking in at the base, use the
simplified r-parameter model of the transistor.
❖ Figure 6-9 shows the transistor model connected to the external collector resistor, 𝑅𝑐 .
❖The input resistance looking in at the base is
𝑉𝑖𝑛 𝑉𝑏
𝑅𝑖𝑛(𝑏𝑎𝑠𝑒) = =
𝐼𝑖𝑛 𝐼𝑏
The base voltage is 𝑉𝑏 = 𝐼𝑒 𝑟𝑒′
𝐼𝑒
And since 𝐼𝑒 ≅ 𝐼𝑐 , 𝐼𝑏 ≅
𝛽𝑎𝑐
𝑉𝑏 𝐼𝑒 𝑟𝑒′
Substituting for 𝑉𝑏 and 𝐼𝑏 , 𝑅𝑖𝑛(𝑏𝑎𝑠𝑒) = =
𝐼𝑏 𝐼𝑒 ∕𝛽𝑎𝑐
FIGURE 10 r-parameter transistor model
Cancelling 𝐼𝑒 ,
connected to external circuit.
𝑅𝑖𝑛(𝑏𝑎𝑠𝑒) = 𝛽𝑎𝑐 𝑟𝑒′ Equation 6-3

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 DEPARTMENT OF
ELECTRONIC
Output Resistance ENGINEERING

❖ The output resistance of the common-emitter amplifier is the resistance looking in at the collector
and is approximately equal to the collector resistor.

𝑅𝑜𝑢𝑡 ≅ 𝑅𝑐 Equation 6-4

❖ Actually, but since the internal ac collector resistance of the transistor, is typically much larger
than 𝑅𝐶 , the approximation is usually valid.

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 DEPARTMENT OF
EXAMPLE 6-3 Determine the signal voltage at the base of the transistor in Figure 6-10. ELECTRONIC
This circuit is the ac equivalent of the amplifier in Figure 6–8 with a 10 ENGINEERING
m 𝑉𝑟𝑚𝑠 , signal source 𝐼𝐸 was previously found to be 3.80 mA.

FIGURE 6–11

Solution
First, determine the ac emitter resistance.
′
25𝑚𝑉 25𝑚𝑉
𝑟𝑒 ≅ =
𝐼𝐸 3.80𝑚𝐴
Then, 𝑅𝑖𝑛(𝑏𝑎𝑠𝑒) = 𝛽𝑎𝑐 𝑟𝑒′ = 160 6.58Ω = 1.05𝑘Ω
1
𝑅𝑖𝑛(𝑡𝑜𝑡) = 𝑅1 ∥ 𝑅2 ∥ 𝑅𝑖𝑛(𝑏𝑎𝑠𝑒) = 1 1 1 = 873Ω
+ +
22𝑘Ω 6.8𝑘Ω 1.05𝑘Ω
𝑅𝑖𝑛(𝑡𝑜𝑡) 873Ω
𝑉𝑏 = 𝑉𝑠 = = 10𝑚𝑉
𝑅𝑠 +𝑅𝑖𝑛(𝑡𝑜𝑡) 1173Ω

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 DEPARTMENT OF
ELECTRONIC
Voltage Gain ENGINEERING

• The ac voltage gain expression for the common-emitter amplifier is developed

using the model circuit in Figure 12.
• The gain is the ratio of ac output voltage at the collector (𝑉𝑐 ) to ac input voltage
at the base (𝑉𝑏 ).
𝑉𝑜𝑢𝑡 𝑉𝑐
𝐴𝑣 = =
𝑉𝑖𝑛 𝑉𝑏
Notice in the figure that 𝑉𝑐 = 𝛼𝑎𝑐 𝐼𝐸 𝑅𝐶 ≅ 𝐼𝑒 𝑅𝑐 and 𝑉𝑏 = 𝐼𝑒 𝑟𝑒′ .
Therefore,
𝐼𝑒 𝑅𝑐
𝐴𝑣 =
𝐼𝑒 𝑟𝑒′
FIGURE 12 Model circuit for
The 𝐼𝑒 terms cancel, so obtaining ac voltage
𝑅𝐶 gain.
𝐴𝑣 = Equation 6-5
𝑟𝑒′

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 DEPARTMENT OF
ELECTRONIC
Attenuation ENGINEERING

• Attenuation is the reduction in signal voltage as it passes through a circuit and

corresponds to a gain of less than 1.
• To get the overall gain of the amplifier from the source voltage to collector, the
attenuation (reduction in signal voltage) of the input circuit must be included.

Vs Rs + Rin (tot )
Attenuation = =
Vb Rin (tot )

• The overall voltage gain of the amplifier

Reciprocal of the attenuation FIGURE 13

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 DEPARTMENT OF
ELECTRONIC
Voltage Gain Without the Bypass Capacitor ENGINEERING

• The bypass capacitor affects ac voltage gain, let’s remove it from the circuit in Figure 6–14
and compare voltage gains.
• Without the bypass capacitor, the emitter is no longer at ac ground.
• Instead, 𝑅𝐸 is seen by the ac signal between the emitter and ground and effectively adds to 𝑟𝑒′
in the voltage gain formula.

𝑅𝐶
𝐴𝑣 = Equation 6-6
𝑟𝑒′ + 𝑅𝐸

• The effect of 𝑅𝐸 is to decrease the ac voltage gain.

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 DEPARTMENT OF
EXAMPLE 6–5 Calculate the base-to-collector voltage gain of the amplifier in Figure ELECTRONIC
6–14 both without and with an emitter bypass capacitor if there is no ENGINEERING
load resistor.

Solution,
From Example 6–3,𝑟𝑒′ = 6.58Ω for this same amplifier. Without 𝐶2 , the gain is

𝑅𝐶 1.0𝑘Ω
𝐴𝑣 = = = 1.76
𝑟𝑒′ 𝑅𝐸 567Ω

With 𝐶2 , the gain is

𝑅𝐶 1.0𝑘Ω 𝑅𝐶 1.0𝑘Ω
𝐴𝑣 = = = 152 𝐴𝑣 = = = 152
𝑟𝑒′ 6.58Ω 𝑟𝑒′ 6.58Ω

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 DEPARTMENT OF
ELECTRONIC
Effect of a Load on the Voltage Gain ENGINEERING

❖A load is the amount of current drawn from the output of an amplifier or other circuit through a load
resistance.
❖When a resistor, 𝑅𝐿 , is connected to the output through the coupling capacitor 𝐶3 , as shown in
Figure 6–15(a), it creates a load on the circuit.
❖ The collector resistance at the signal frequency is effectively 𝑅𝐶 in parallel with 𝑅𝐿 .
❖ Remember, the upper end of 𝑅𝐶 is effectively at ac ground.
❖ The ac equivalent circuit is shown in Figure 13.
❖The total ac collector resistance is
𝑅𝐶 𝑅𝐿
❖𝑅𝑐 =
𝑅𝐶 +𝑅𝐿
❖Replacing 𝑅𝐶 with 𝑅𝑐 in the voltage gain expression gives
𝑅𝑐
❖ 𝐴𝑣 = Equation 6-7
𝑟𝑒′

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 DEPARTMENT OF
• When because of 𝑅𝐿 , the voltage gain is reduced. ELECTRONIC
ENGINEERING
• However, if 𝑅𝐿 ≫ 𝑅𝐶 ,then 𝑅𝑐 ≅ 𝑅𝐶 and the load has very little effect on the gain.

FIGURE 14 A common-emitter amplifier with an ac (capacitively) coupled

load.

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 DEPARTMENT OF
EXAMPLE 6-6 Calculate the base-to-collector voltage gain of the amplifier in Figure ELECTRONIC
6–16 when a load resistance of is connected to the output. The emitter ENGINEERING
is effectively bypassed and 𝑟𝑒′ = 6.58Ω

Solution,
The ac collector resistance is

𝑅𝐶 𝑅𝐿 (1.0𝑘Ω)(5𝑘Ω)
𝑅𝑐 = = = 833Ω = 833Ω
𝑅𝐶 + 𝑅𝐿 6𝑘Ω
Therefore,

𝑅𝑐 833Ω
𝐴𝑣 = = = 127
𝑟𝑒′ 6.58Ω

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 DEPARTMENT OF
ELECTRONIC
Stability of the Voltage Gain ENGINEERING

❖Stability is a measure of how well an amplifier maintains its design values over changes in temperature
or for a transistor with a different 𝛽.
❖ Although bypassing 𝑅𝐸 does produce the maximum voltage gain, there is a stability problem because
the ac voltage gain is dependent on 𝑟𝑒′ since 𝐴𝑣 = 𝑅𝐶 Τ𝑟𝑒′ .
❖With no bypass capacitor, the gain is decreased because 𝑅𝐸 is now in the ac circuit
❖ (𝐴𝑣 = 𝑅𝐶 Τ(𝑟𝑒′ + 𝑅𝐸 )).
❖However, with 𝑅𝐸 unbypassed, the gain is much less dependent on 𝑟𝑒′ .
❖If 𝑅𝐸 ≫ 𝑟𝑒′ , the gain is essentially independent of 𝑟𝑒′ because

𝑅𝐶
𝐴𝑣 ≅
𝑅𝐸

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 DEPARTMENT OF
ELECTRONIC
Current Gain ENGINEERING

• The current gain from base to collector is 𝐼𝑐 Τ𝐼𝑏 𝑜𝑟 𝛽𝑎𝑐 .

• However, the overall current gain of the common-emitter amplifier is

𝐼
𝐴𝑖 = 𝐼𝑐 Equation 6–10
𝑠

• 𝐼𝑠 is the total signal input current produced by the source, part of which
(𝐼𝑏 ) is base current and part of which (𝐼𝑏𝑖𝑎𝑠 ) goes through the bias circuit
(𝑅1 ∥ 𝑅2 ) as shown in Figure 6–24.
• The source “sees” a total resistance of 𝑅𝑠 + 𝑅𝑖𝑛(𝑡𝑜𝑡) .
• The total current produced by the source is
𝑉𝑠 FIGURE 15 Signal currents (directions
𝐼𝑠 = shown are for the positive half-
𝑅𝑠 + 𝑅𝑖𝑛(𝑡𝑜𝑡)
cycle of 𝑉𝑠 .

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 DEPARTMENT OF
ELECTRONIC
Power Gain ENGINEERING

❖The overall power gain is the product of the overall voltage gain (𝐴′𝑣 ) and the overall
current gain (𝐴𝑖 ).

𝐴𝑝 = 𝐴′𝑣 𝐴𝑖 Equation 6–11

Where 𝐴′𝑣 = 𝑉𝑐 Τ𝑉𝑠 .

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 DEPARTMENT OF
ELECTRONIC
ENGINEERING

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