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24 Transistors
Fig. 24.7 Ebers-Moll
model of a transistor, ‘E’:
emitter, ‘C’: collector and
‘B’: base. Currents are
shown for a pnp transistor.
a Basic model (grey area in
b, c), b model with series
resistances and
depletion-layer
capacitances, c model
additionally including the
Early effect (V A : Early
voltage)
(a)
(b)
(c)
I C = α N I F − I R
(24.24b)
I B = (1 − α N )I F + (1 − α I )I R .
(24.24c)
The last equation is obtained from (24.24a,b) using (24.12). By comparison with (24.21a,b) and
(24.23a–d) we find
I F0 = ˆ
a 11
(24.25a)
I R0 = −ˆ a 22
(24.25b)
α I = ˆ
a 12 /I R0
(24.25c)
α N = ˆ
a 21 /I F0 = −ˆ a 12 /I F0 = −α I I R0 /I F0 .
(24.25d)
The constants α N and α I are the forward (‘normal’) (α N = α 0 from (24.13)) and reverse (‘inverted’)
gains in the common base circuit, respectively. Both constants are larger than zero. Typically, α N ≈
0.98 . . . 0.998 1 and α I ≈ 0.5 . . . 0.9 < α N . The model has three independent parameters, e.g. α N ,
I F0 and I R0 . Equations (24.24a,b) can be rewritten as