# 3 Transistor Parameters

```3. Transistor Parameters
3.1 Introduction
Several parameters can be defined for the bipolar junction
transistor, which act as figures of merit in quantifying its performance.
Most of these, but not all, are measured and specified for the forward
active mode of operation. Some parameters differentiate between
electron and hole currents but these are not of particular interest in
this discussion and attention is confined to those that are based on the
terminal currents of the device. These can be deduced from the
physical model shown in Fig. 3.1, which formed the basis of the EbersMoll model.
The Ebers-Moll Equations are given as:
IE  IES(eVBE/VT  1)  RICS(eVBC/VT  1)
IC  F IES(eVBE/VT  1)  ICS (eVBC/VT  1)
IB  (1  F )IES(eVBE/VT  1)  (1  R )ICS (eVBC/VT  1)
3.2 Forward Transfer Ratio
This is defined for the forward active mode of operation as the ratio of
the collector and emitter terminal currents. In the forward active mode
the base-collector junction is reverse biased so that
hence the currents approximate to:
eV
BC
/ VT
 0
IE  IESe VBE/VT
IC  F IESe VBE/VT   F IE
IB  (1  F )IESe VBE/VT  (1   F )IE
Then:
IC FIES e VBE/VT
Foward Transfer Ratio 

 F
IE
IES e VBE/VT
1
and
IB
(1-αF)IF
(1-αR)IR
αFIF
IF
IE
B
n
E
p
n
αRIR
C
IC
IR
Fig. 3.1 Model Showing Forward and Reverse Current Components
Base
Current
IF
Variation in
excess carriers
present due to
changing base
current
E
Fig. 3.2
C
B
Minority Carrier Concentration in the Base Region
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3.3 Forward Current Gain, βF
Under steady-state conditions in the forward active mode, the
volume of minority charge stored in the base region is constant. The
greater part of this is charge in transit to the collector which forms the
electronic component of the collector current. A small percentage of
the minority charge continually recombines with majority carriers
which are replaced with holes supplied by an external base current.
Since the base region is very thin and is sandwiched between the two
junctions, it is not surprising that the volume of minority charge
present in the base exercises a profound influence on the behaviour of
the transistor.
In fact, the excess minority charge in the base region can be
forced to change by modulating the base current with an external
signal. The atomic forces operating cause both the recombining charge
and the charge in transit to the collector to vary in sympathy. The
junction voltages will adjust, in response to the currents flowing, to
conform to the exponential laws governing them. However, since the
charge in transit to the collector is much greater than the
recombination charge, a greater change in absolute charge terms is
induced in the collector current than is present in the base current due
to the signal. Hence, the transistor is seen to amplify the input signal
to the base as shown in Fig. 3.3.
small input
IC
signal
RC
C
amplified output
B
IB
signal developed
E
Fig. 3.3 The Current Amplifying Property of the Bipolar Transistor
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This current amplifying property is described by the current gain of the
transistor in the forward active mode which is taken simply as the
ratio of the collector and base currents. Hence:
Foward Current Gain
IC
FIES eVBE/VT
F
F 


IB (1 - F )IES e VBE/VT 1 - F
Alternatively:
F 
IC
IC
IC/IE
F



IB IE  IC 1  IC/IE 1  F
Typical values of  F range from 40-100 for integrated transistors but
can be as high as 300 – 500 for discrete devices.
3.4 Reverse Transfer Ratio and Current Gain, αR, βR
The above parameters can also be defined for the reverse active mode
when the B-E junction is reverse biased and the B-C junction is
forward biased. However, these parameters are not of great interest
as the transistor is very inefficient from an amplifying point of view in
this mode. Typically αR = 0.1 - 0.5 and βR = 0.1 – 1.0.
B
This is the average amount of time a minority carrier can survive after
being injected into the base region before recombining with a majority
carrier. It depends on the physical properties of the device, such as the
doping concentration and the dimensions. Typically  B = 50 - 100ns.
3.6 Forward Transit Time,
F
This is the average time it takes a minority carrier injected into the
base region to make the transition to the collector region when the
transistor is operating in the forward active mode. It can be shown
that:
2
Wb2
1W 
F 
  b  b
2Db 2  Lb 
Typically
F
= 0.1 – 0.5ns
The above parameters will be used in the analysis of static and
dynamic performance of the transistor as a circuit switching element.
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