379
Bipolar Junction Transistor Compact Models
I
I I
C
F F
R
=
−
α
(11.3)
I
I
I I
I
I
I
B
F
R R
R
F F
F
F
R
R
= −
+ −
= −
(
) + −
(
)
α
α
α
α
1
1
(11.4)
From Equation 2.119, we can write the expression for the forward electron
current flow through the EB pn-junction as
I
I
I
V
v
F
n E
E S
BE
kT
=
=
−
exp
1
(11.5)
and, the reverse electron current flow through the CB pn-junction as
I
I
I
V
v
R
n C
C S
BC
kT
=
=
−
exp
1
(11.6)
where:
I ES and I CS are the saturation currents of the EB and CB pn-junctions,
respectively
V BE and V BC are the applied voltages at the EB and CB pn-junctions,
respectively
Then from Equations 11.2 through 11.6, the terminal currents for an npn-BJT
can be shown as
I
I
V
v
I
V
v
E
E S
BE
kT
R CS
BC
kT
= −
−
+
−
exp
e xp
1
1
α
(11.7)
And,
I
I
V
v
I
V
v
C
F ES
BE
kT
CS
BC
kT
=
−
−
−
α
exp
e xp
1
1
(11.8)
From the reciprocity property α F I ES = α R I CS ≡ I S , where I S is the reverse saturation current of an npn-BJT device, so we can express Equations 11.7 and 11.8 as
I
I
V
v
I
V
v
E
S
F
BE
kT
S
BC
kT
= −
−
+
−
α
exp
e xp
1
1
(11.9)
And,
I
I
V
v
I
V
v
C
S
BE
kT
S
R
BC
kT
=
−
−
−
exp
e xp
1
1
α
(11.10)
Bipolar Junction Transistor Compact Models
I
I I
C
F F
R
=
−
α
(11.3)
I
I
I I
I
I
I
B
F
R R
R
F F
F
F
R
R
= −
+ −
= −
(
) + −
(
)
α
α
α
α
1
1
(11.4)
From Equation 2.119, we can write the expression for the forward electron
current flow through the EB pn-junction as
I
I
I
V
v
F
n E
E S
BE
kT
=
=
−
exp
1
(11.5)
and, the reverse electron current flow through the CB pn-junction as
I
I
I
V
v
R
n C
C S
BC
kT
=
=
−
exp
1
(11.6)
where:
I ES and I CS are the saturation currents of the EB and CB pn-junctions,
respectively
V BE and V BC are the applied voltages at the EB and CB pn-junctions,
respectively
Then from Equations 11.2 through 11.6, the terminal currents for an npn-BJT
can be shown as
I
I
V
v
I
V
v
E
E S
BE
kT
R CS
BC
kT
= −
−
+
−
exp
e xp
1
1
α
(11.7)
And,
I
I
V
v
I
V
v
C
F ES
BE
kT
CS
BC
kT
=
−
−
−
α
exp
e xp
1
1
(11.8)
From the reciprocity property α F I ES = α R I CS ≡ I S , where I S is the reverse saturation current of an npn-BJT device, so we can express Equations 11.7 and 11.8 as
I
I
V
v
I
V
v
E
S
F
BE
kT
S
BC
kT
= −
−
+
−
α
exp
e xp
1
1
(11.9)
And,
I
I
V
v
I
V
v
C
S
BE
kT
S
R
BC
kT
=
−
−
−
exp
e xp
1
1
α
(11.10)