24.2 Bipolar Transistors
699
I E = α I I C + (1 − α I α N ) I F
(24.26a)
I C = α N I E − (1 − α I α N ) I R .
(24.26b)
Under normal operation we have
I E = I F
(24.27a)
I C = α N I E .
(24.27b)
The model can be refined and made more realistic by including the effect of series resistances and
depletion-layer capacitances, increasing the number of parameters to eight. The Early effect (see next
section) can be included by adding a further current source. This level is the ‘standard’ Ebers-Moll
model with a total of nine parameters. Further parameters can be added. However, as is always the
case with simulations, there is a tradeoff between the simplicity of the model and to what detail a real
situation is approximated.
24.2.4 Current–Voltage Characteristics
In Fig. 24.8, the hole density in the base (of a pnp transistor) is shown for various voltage conditions.
In Fig. 24.9, the I –V characteristics of a bipolar transistor in common base and common collector
circuit are shown. In the common base circuit (Fig. 24.9a), the collector current is practically equal
to the emitter current and is almost independent of the collector–base voltage. From (24.26b), the
dependence of the collector current on the collector–base voltage is given (within the Ebers-Moll
model) as
I C = α N I E − (1 − α I α N )I R0
exp (βV CB ) − 1
.
(24.28)
V CB is in the reverse direction. Therefore, the second term is zero for normal operating conditions.
Since α N 1, the collector current is almost equal to the emitter current.
Even at V CB = 0 (the case of (Fig. 24.8c), holes are extracted from the base since ∂ p/∂x| x=w > 0.
A small forward voltage must be applied to the collector–base diode in order to make the current zero,
Fig. 24.8 Hole density
(linear scale) in the base
region (the neutral part of
the base ranges from 0 to
w) of a pnp transistor for
various voltages. a normal
voltages, V CB = const. and
various V EB (in forward
direction). b V EB = const.
and various values of V CB .
c Various values of
V EB > 0, V CB = 0. d Both
pn-junctions in forward
direction. e Conditions for
I C0 and I
C0 . f both
junctions in reverse
direction. Adapted
from [574]
p
x
p n0
0
w
V EB =0
p
x
p n0
0
ww'
p
p
x
p n0
0
w
V EB =0
p
x
p n0
0
w
I C =0
I C >0
p
x
p n0
0
w
p
x
p n0
0
w
I C0
I C0
V EB =0
'
(a)
(b)
(c)
(d)
(e)
(f)
699
I E = α I I C + (1 − α I α N ) I F
(24.26a)
I C = α N I E − (1 − α I α N ) I R .
(24.26b)
Under normal operation we have
I E = I F
(24.27a)
I C = α N I E .
(24.27b)
The model can be refined and made more realistic by including the effect of series resistances and
depletion-layer capacitances, increasing the number of parameters to eight. The Early effect (see next
section) can be included by adding a further current source. This level is the ‘standard’ Ebers-Moll
model with a total of nine parameters. Further parameters can be added. However, as is always the
case with simulations, there is a tradeoff between the simplicity of the model and to what detail a real
situation is approximated.
24.2.4 Current–Voltage Characteristics
In Fig. 24.8, the hole density in the base (of a pnp transistor) is shown for various voltage conditions.
In Fig. 24.9, the I –V characteristics of a bipolar transistor in common base and common collector
circuit are shown. In the common base circuit (Fig. 24.9a), the collector current is practically equal
to the emitter current and is almost independent of the collector–base voltage. From (24.26b), the
dependence of the collector current on the collector–base voltage is given (within the Ebers-Moll
model) as
I C = α N I E − (1 − α I α N )I R0
exp (βV CB ) − 1
.
(24.28)
V CB is in the reverse direction. Therefore, the second term is zero for normal operating conditions.
Since α N 1, the collector current is almost equal to the emitter current.
Even at V CB = 0 (the case of (Fig. 24.8c), holes are extracted from the base since ∂ p/∂x| x=w > 0.
A small forward voltage must be applied to the collector–base diode in order to make the current zero,
Fig. 24.8 Hole density
(linear scale) in the base
region (the neutral part of
the base ranges from 0 to
w) of a pnp transistor for
various voltages. a normal
voltages, V CB = const. and
various V EB (in forward
direction). b V EB = const.
and various values of V CB .
c Various values of
V EB > 0, V CB = 0. d Both
pn-junctions in forward
direction. e Conditions for
I C0 and I
C0 . f both
junctions in reverse
direction. Adapted
from [574]
p
x
p n0
0
w
V EB =0
p
x
p n0
0
ww'
p
p
x
p n0
0
w
V EB =0
p
x
p n0
0
w
I C =0
I C >0
p
x
p n0
0
w
p
x
p n0
0
w
I C0
I C0
V EB =0
'
(a)
(b)
(c)
(d)
(e)
(f)