378
Compact Models for Integrated Circuit Design
given by I C /I E for V BE  > 0. Similarly, for the reverse-biased CB pn-junction, a
reverse current, I R , flows through the CB pn-junction and a current, α R I R , flows
through the EB pn-junction, where α R is the reverse current gain and is given
by I E /I C for V BC  < 0. Then from Figure 11.7a, the terminal currents are given by
I
I
I
I
I I
E
F
R R
C
F F
R
= − +
=
−
α
α
(11.1)
The physical concept described in Figure  11.7 can be represented by an
equivalent circuit shown in Figure 11.8.
Figure 11.8 represents the basic npn-BJT model for circuit CAD and is known
as the basic Ebers–Moll or EM1 BJT model. From Figure 11.8 the terminal currents are given by
I
I
I
E
F
R R
= − + α
(11.2)
α F I F
α R I R
E
I E
I F
I R
B
I B
C
I C
FIGURE 11.8
The basic Ebers–Moll model for an npn-BJT: the basic model is obtained by considering two backto-back pn-junctions. Here, α F I F and α R I R are the current sources at the CB and EB pn-junctions,
respectively.
(a)
(b)
E
E
n+
n+
p
B
B
C
I F
I E
E
I E
C
I C
C
I C
I B
B I B
I R
α F I F
α R I R
FIGURE 11.7
An ideal npn-BJT structure used to derive the basic Ebers–Moll model: (a) the transistor
configuration with carrier injection due to the applied biases and (b) the npn-BJT structure
represented by two back-to-back pn-junctions.