Electronic II (ECE235b)
Bipolar Junction Transistor (BJT)
Review
Anestis Dounavis
The University of Western Ontario
Faculty of Engineering Science
Bipolar Junction Transistor (BJT) Review
5.1 Device Structure and Physical Operation

BJT consists of 3 semiconductor regions as shown in Figure 5.1, 5.2.
Figure 5.1 A simplified structure of the npn transistor.
Figure 5.2 A simplified structure of the pnp transistor.
A terminal is connected to each of the 3 semiconductor regions of the transistor, with terminals labeled
emitter (E), base (B) and collector (C).
 The transistor consists of 2 pn junctions, the emitter-base junction (EBJ) and the collectorbase junction (CBJ).
 Depending on the biasing condition, the EBJ and CBJ biasing can be set to forward or reverse,
thus BJTs have 4 modes of operation.
Table 5.1 BJT modes of operation
Mode
EBJ
Cuttoff
Reverse
Active
Forward
Reverse Active
Reverse
Saturation
Forward
CBJ
Reverse
Reverse
Forward
Forward
•
•
•
Active mode or forward active mode is used for analog circuits, example if transistor is to operate as
an amplifier.
Cut off mode and saturation mode are used in digital circuits. Transistors behave as switches (on
or off, highor low)
Reverse active mode has limited application but is conceptually important
5.1.2 Operation of npn Transistor in active mode
Transistor in active mode is shown in Figure 5.3
Figure 5.3 Current flow in an npn transistor biased to operate in the active mode. (Reverse current
components due to drift of thermally generated minority carriers are not shown.)




2 external voltages are applied to establish the required bias conditions for active-mode
operation.
The voltage VBE, causes the p-type base to be higher in potential than the n-type emitter, thus
forward-biasing the emitter-base junction.
The collector-base voltage VCB, causes the n-type collector to be at a higher potential than the ptype base, thus reverse-biasing the collector-base junction.
An npn transistor whose EBJ is forward biased will operate in active mode as long as the
collector voltage does not fall below that of the base by more than approximately 0.4V.
Current flow: In this description only diffusion current is considered. Drift current due to thermally
generated minority carriers are usually very small and can be neglected.
 The forward bias on the EBJ causes current to flow across this junction. Current consists of two
components: electrons injected from the emitter to base and holes injected from the base to
emitter.
 Since the collector is more positive than base, electrons will be swept across the CBJ depletion
region into the collector.
The collector current is expressed as
iC  I S e vBE / VT
(5.3)
IS = saturation current
VT = thermal voltage = 25mV at room temperature.
-------Equation 5.3 is derived from: As in the case of a forward-biased pn junction (Section 3.7.5), the
concentration np(0) will be proportional to
n p (0)  n p 0 e vBE / VT
(5.1)
-----Relationship of currents
i E  i B  iC
iC  i B
i E  (1   )i B
β
iC 
i E  αi E
(β  1)
=is a constant (referred to as the common-emitter gain).
= is a constant (referred to as the common-base current gain)
5.1.6 The pnp Transistor
Figure 5.11, shows a pnp transistor biased to operate in the active mode.
Figure 5.11 Current flow in a pnp transistor biased to operate in the active mode.


The voltage VEB causes the p-type emitter to be higher in potential than the n-type base, thus
forward-biasing the base-emitter junction.
The collector-base junction is reverse-biased by the voltage VBC, which keeps the p-type
collector lower in potential than the n-type base.
Current flow: The current in the pnp device is mainly conducted by holes injected from emitter into
the base as a result of the forward-bias voltage VEB.
 The base current is composed of: 1) electrons injected from base to emitter (iB1) 2) a number of
holes injected into the base will recombine with the majority carriers in the base (electrons) and
will thus be lost (iB2).
 The holes that succeed in reaching the collector-base junction will be attracted by the negative
voltage on the collector
The above description of the current voltage relationship is similar to that of the npn transistor except
that the vBE is replaced by vEB.
iC  I S e vEB / VT
i E  i B  iC
iC  i B
i E  (1   )i B
β
iC 
i E  αi E
(β  1)
5.2 Current-Voltage Characteristics
5.2.1 Circuit Symbols and Conventions
A circuit description of BJT is shown in figure 5.14
Figure 5.14 Voltage polarities and current flow in transistors biased in the active mode.



The polarity of the device (npn or pnp) is indicated by the direction of the arrowhead on the
emitter.
Transistors are biased to operate in the active mode.
An npn transistor whose EBJ is forward biased will operate in active mode as long as the
collector voltage does not fall below that of the base by more than approximately 0.4V.
Example 5.1
Design the circuit so that a current of 2mA flows through the collector and a voltage of +5V appears at
the collector. (transistor: =100 and exhibits a vBE=0.7 at iC=1mA)
Exercises 5.11
For the following circuit VB =1.0V and VE=1.7. What are   and VC?
5.4 BJT Circuits at DC

1.
2.
3.
Assume applied voltages are at DC only.
We use simple model: for npn assume |VBE| = 0.7V.
Neglect the effect of early effect.
If transistor is in saturated mode assume |VCE| = 0.2V.
For pnp assume |VEB| = 0.7V
These assumptions are made to simplify calculations, however better models can be used to obtain
better accuracy.
 Example Accurate results using elaborate models can be obtained using CAD tools such as
SPICE.
Assumption 1: |VBE| = 0.7V
iC  I S e vBE / VT
Figure 5.16 The iC –vBE characteristic for an npn transistor.


For normal current range VBE Vlies in the 0.6V to 0.8V.
In performing rapid first order DC calculations we normally assume VBE is 0.7V
Assumption 2: Early Effect.
Figure 5.19 (a) Conceptual circuit for measuring the iC –vCE characteristics of the BJT. (b) The iC –
vCE characteristics of a practical BJT.






At low values of vCE, as the collector voltage goes below that of the base by more than 0.4V, the
collector-base junction becomes forward biased and the transistor leaves the active mode and
enters saturation mode.
For a given value of vBE, the current iC, is:
iC  I S e vBE / VT
However iC, is not constant as shown in Figure 5.19.
The linear dependence of iC on vBE can be accounted for as follows:
v
i C  I S e v BE / VT (1  CE )
VA
The nonzero slope indicates that the output resistance looking into the collector is not infinite.
The output resistance r0 is
V  VCE VA
ro  A

IC
IC
VA=Early voltage and ranges 50V to 100V, and usually VA >> VCE
It is rarely necessary to include the dependence of iC on vCE in DC bias design and analysis. However,
the finite output resistance r0 can have significant effect on the gain of transistor amplifiers.
Thus large signal model of npn BJT operating in active mode becomes
Figure 5.20 Large-signal equivalent-circuit models of an npn BJT operating in the active mode in the
common-emitter configuration.
Assumption 3: |VCE| = 0.2V.
Figure 5.24 (a) An npn transistor operated in saturation mode with a constant base current IB. (b) The
iC–vCE characteristic curve corresponding to iB = IB. The curve can be approximated by a straight line
of slope 1/RCEsat. (c) Equivalent-circuit representation of the saturated transistor. (d) A simplified
equivalent-circuit model of the saturated transistor.


The iC on vCE characteristic curves of the saturated transistor are shown in Figure 5.24.
This curve can be approximated as a straight line as:
VCEsat  VCEoff  I Csat RCEsat


Typically VCEsat falls in the range of 0.1V to 0.3V.
Usually for DC analysis, a simpler model shown in Figure 5.24(d) suffices to obtain reasonable
results
Example 5.5
Determine the voltages at all nodes and currents through all branches. Assume  is specified to be at
50.
Figure 5.35 Analysis of the circuit for Example 5.5. Note that the circled numbers indicate the order of
the analysis steps.
Example 5.11
Determine the voltages at all nodes and currents through all branches. Assume  = 100.
Figure 5.41 Circuits for Example 5.11.
5.6 Small-Signal Operation and Models
5.6.1 The Collector Current and the Transconductance
Consider the following circuit (Figure 5.48a)
Figure 5.48 (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.
The total base-emitter voltage vBE becomes:
v BE  V BE  vbe

VBE is DC voltage, vbe is AC voltage
Correspondingly, the iC becomes:
iC  I S e vBE / VT  I S e (VBE  vbe ) / VT  I S e VBE / VT e vbe / VT  I C e vbe / VT
where Ic is
I C  I S eVBE / VT
If vbe << VT, we can expand the exponential in a series to approximate iC as
v
i C  I C (1  be )
VT
This approximation is valid if vbe is less than approximately 10mA and is referred to as small signal
analysis.
I
i C  I C  C v be  I C  g m vbe
VT
where gm is called transconductance, g m  I C / VT .
Figure 5.49 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.
A graphical interpretation for gm is given in Figure 5.49, where gm is equal to the slope of iC–vBE
characteristic curve.
5.6.6 The Hybrid -model.
Figure 5.50 The amplifier circuit of Fig. 5.48(a) with the dc sources (VBE and VCC) eliminated (short
circuited). Thus only the signal components are present. Note that this is a representation of the signal
operation of the BJT and not an actual amplifier circuit.
The input resistance at the base can be calculated by
i
I  g m v be I C g m vbe
iB  C  C


 I B  ib




IC
g
I
vbe  m vbe .
where I B  C and i b 
V T


The small signal input resistance between the base and emitter, looking into the base is
v
V

r  be 
 T
ib
gm I B
The small signal iC current is shown to be
I
i C  I C  ic  I C  C vbe  I C  g m v be
VT
Thus the small signal voltages and currents can be modeled as
Figure 5.51 Two slightly different versions of the simplified hybrid-p 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 -model satisfies ic  g m vbe and ib  vbe / r . In addition, the model gives the correct expression
for ie.
v
v
v
vbe
v
ie  ib  ic  be  g m vbe  be (1  g m r )  be (1   ) 
 be
r
r
r
r /(1   ) re
 ib (1   )
A slightly different equivalent model (Figure 5.51b) described in terms of a current controlled current
source can also be derived as:
g m vbe  g m (ib r )  ( g m r )ib  ib
5.6.7 The T Model
Although -model can be used to carry out small-signal analysis of all transistors circuits, there are
situations in which the T-model is more convenient.
 The input resistance at the emitter can be determined as:
i
I i
i E  C  C c  I E  ie


IC
I
IC
vbe  E v be .
and i e 
V T
VT

The small signal input resistance between the base and emitter, looking into the emitter is
v
V

re  be 
 T
ie
gm I E
where I E 
The relationship between  and T input resistance is
vbe  ib r  ie re  r  (ie / ib )re  (   1)re
Thus the small signal voltages and currents can be modeled as
Figure 5.52 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 rp featured in the hybrid-p model.
A slightly different equivalent model (Figure 5.51b) described in terms of a current controlled current
source can also be derived as:
g m vbe  g m (ie re )  ( g m re )ie  ie
5.6.10 Small-Signal Models to Account for Early Effect
To account for Early effect an output resistance ro needs to be included to the small signal models as
shown in Table 5.4.
Table 5.4
5.7.1 The Basic Structure
Figure 5.59 shows the basic circuit utilized to implement the various configurations of the BJT
amplifiers.
Figure 5.59 Basic structure of the circuit used to realize single-stage, discrete-circuit BJT amplifier
configurations
IE
β
I
I IB 

(β  1)
(β  1) (β  1)
=is a constant (referred to as the common-emitter gain).
= is a constant (referred to as the common-base current gain).
 For simplicity: current biasing at the emitter is constant.
I E  I,
I C  αI E  αI 
IE  I B  IE
Exercise 5.41
For Fig. 5.59 let: Vcc=Vee=10V, I=1mA, Rb=100kOhms, Rc=8kOhms and  =100.
 Find all the DC currents and voltages
 Find the values of the BJT small-signal parameters at the bias point (with  =100). The Early
voltage Va=100V
 What are the allowable signal swings at the collector in both directions? (Hint: In the active
region of operation requires vCB >= -0.4V. see page 388)
Figure E5.41