700
24 Transistors
(a)
8
6
4
2
0
I (mA)
C
V (V)
CB
0
10
20
30
40
50
BV CB0
I C0
I E =6mA
5
4
3
2
1 0
(b)
8
6
4
2
0
I (mA)
C
V (V)
CE
-5
5
1 0
0
BV CE0
I =28µA
B
V A
V (V)
CE
22
18
14
10 2
6
I C0 '
Fig. 24.9 Characteristics (I C vs. V CB ) of a pnp transistor in a common base (CB) circuit (Fig. 24.4a) for various values
of the emitter current as labeled. Adapted from [2050]. b Characteristics in common emitter (CE) circuit (Fig. 24.4b).
Adapted from [2051]
i.e. ∂ p/∂x| x=w = 0 (Fig. 24.8d). The collector saturation current I C0 is measured with an open emitter
side. This current is smaller than the saturation current of the CB diode, since at the emitter side of
the basis a vanishing gradient of the hole density is present (Fig. 24.8e). This reduces the gradient (and
thus the current) at the collector side. The current I C0 is therefore smaller than the collector current
for shorted emitter–base contact (V EB = 0). At high collector voltage, the current increases rapidly at
BV CB0 due to breakdown of the collector–base diode. It can also occur that the width of the neutral
base region w becomes zero (punch-through). In this case, the emitter and collector are short-circuited.
In the common emitter circuit (Fig. 24.9b), there is a high current amplification I C /I B . Note that the
collector current is given in mA and the base current in µA. The current increases with increasing V CE
because the base width w decreases and β 0 increases. There is no saturation of the I –V characteristics
(Early effect [2052]). Instead, the I –V curves look as if they start at a negative collector–emitter
voltage, the so-called Early voltage V A . In the linear regime, the characteristic can be approximated by
I C =
1 +
V CE
V A
β 0 I B .
(24.29)
Here, β 0 is the current gain for V CE ≈ 0.
The physical reason for the increase of the collector current with increasing V CE is the increasing
reverse voltage at the collector–base diode that causes the so-called ‘base-width modulation’, as shown
in Fig. 24.8b. The expansion of the CB depletion layer leads subsequently to a reduction of the neutral
base width w. w will be smaller and smaller compared to the geometrical base width w B . When w
is reduced, the common base gain α 0 (24.19) becomes closer to 1 and the current gain increases.
Therefore, the collector current increases with V CE for a given (fixed) base current. The Early voltage
is the coefficient of the increase of collector current with V CE ,
β 0 I B
V A
=
∂ I C
∂V CE
=
∂ I C
∂V CB
∂V CB
∂V CE
≈
∂ I C
∂V CB
.
(24.30)
For constant base current, the emitter-base voltage is almost constant and the approximation in (24.30)
holds. The dependence of the CB depletion layer width on the base side x
n
C on U CB is given by (21.110a)
for a pnp-transistor. Typical values for the Early voltage are 50–300 V. The modeling of the Early effect
in the SPICE simulation program is discussed in [2053].
24 Transistors
(a)
8
6
4
2
0
I (mA)
C
V (V)
CB
0
10
20
30
40
50
BV CB0
I C0
I E =6mA
5
4
3
2
1 0
(b)
8
6
4
2
0
I (mA)
C
V (V)
CE
-5
5
1 0
0
BV CE0
I =28µA
B
V A
V (V)
CE
22
18
14
10 2
6
I C0 '
Fig. 24.9 Characteristics (I C vs. V CB ) of a pnp transistor in a common base (CB) circuit (Fig. 24.4a) for various values
of the emitter current as labeled. Adapted from [2050]. b Characteristics in common emitter (CE) circuit (Fig. 24.4b).
Adapted from [2051]
i.e. ∂ p/∂x| x=w = 0 (Fig. 24.8d). The collector saturation current I C0 is measured with an open emitter
side. This current is smaller than the saturation current of the CB diode, since at the emitter side of
the basis a vanishing gradient of the hole density is present (Fig. 24.8e). This reduces the gradient (and
thus the current) at the collector side. The current I C0 is therefore smaller than the collector current
for shorted emitter–base contact (V EB = 0). At high collector voltage, the current increases rapidly at
BV CB0 due to breakdown of the collector–base diode. It can also occur that the width of the neutral
base region w becomes zero (punch-through). In this case, the emitter and collector are short-circuited.
In the common emitter circuit (Fig. 24.9b), there is a high current amplification I C /I B . Note that the
collector current is given in mA and the base current in µA. The current increases with increasing V CE
because the base width w decreases and β 0 increases. There is no saturation of the I –V characteristics
(Early effect [2052]). Instead, the I –V curves look as if they start at a negative collector–emitter
voltage, the so-called Early voltage V A . In the linear regime, the characteristic can be approximated by
I C =
1 +
V CE
V A
β 0 I B .
(24.29)
Here, β 0 is the current gain for V CE ≈ 0.
The physical reason for the increase of the collector current with increasing V CE is the increasing
reverse voltage at the collector–base diode that causes the so-called ‘base-width modulation’, as shown
in Fig. 24.8b. The expansion of the CB depletion layer leads subsequently to a reduction of the neutral
base width w. w will be smaller and smaller compared to the geometrical base width w B . When w
is reduced, the common base gain α 0 (24.19) becomes closer to 1 and the current gain increases.
Therefore, the collector current increases with V CE for a given (fixed) base current. The Early voltage
is the coefficient of the increase of collector current with V CE ,
β 0 I B
V A
=
∂ I C
∂V CE
=
∂ I C
∂V CB
∂V CB
∂V CE
≈
∂ I C
∂V CB
.
(24.30)
For constant base current, the emitter-base voltage is almost constant and the approximation in (24.30)
holds. The dependence of the CB depletion layer width on the base side x
n
C on U CB is given by (21.110a)
for a pnp-transistor. Typical values for the Early voltage are 50–300 V. The modeling of the Early effect
in the SPICE simulation program is discussed in [2053].