This document provides an overview of the I-V characteristics and Ebers-Moll model of bipolar junction transistors (BJTs). It discusses the input and output characteristics of BJTs in common base and common emitter configurations. The Early effect is described as well as the concepts of base punch through, load line analysis, and the four modes of BJT operation according to the Ebers-Moll model: forward active, reverse active, cutoff, and saturation. Different biasing schemes for BJTs are also summarized including fixed, collector base, emitter, and voltage divider biasing.

1. Analog & Digital Electronics
Course No: PH-218
BJT
Lec-6: I-V characteristics and Ebers-Moll Model
Course Instructors:
Dr. A. P. VAJPEYI
Department of Physics,
Indian Institute of Technology Guwahati, India 1

2. I-V Characteristics of BJT under common base configuration
Common Base configuration
IE
2
Input characteristics Output characteristics
Input characteristics are like a normal forward biased diode.
As the CB junction is reverse biased, the current IC is independent of collector
voltage and depends only upon the emitter current IE. The collector current is almost
constant and work as a current source.
When IE=0 , IC=ICB0 is the leakage current caused by the minority carriers crossing
the pn-junction.

3. I-V Characteristics of BJT common emitter configuration
Input characteristics Output characteristics
npn common emitter
VCE
VBE
IC
IB
3
Input characteristics are like a normal forward biased diode.
As the CE junction is reverse biased, the current IC is independent of collector
voltage and depends only upon the base current IB.
In real diode, the collector current slightly increases with increase in collector
emitter voltage(Early effect).
At low value of VCE, the CBJ becomes forward-biased and the transistor enters the
saturation region.

4. Early Effect (Base width modulation)
VA is called the Early voltage and
ranges from about 50 V to 100 V.
Observed by James Early






+
=






A
CE
kT
eV
s
C
V
V
e
I
I
BE
1
Early effect can be modeled as
4
When VCB increases:
depletion region of CBJ widens
so the effective base width decreases (base-width modulation)
VCB VCB
o
CE
c
C
r
V
I
I +
= '
)
exp(
Is
'
kT
eV
I BE
c =
where

5. Base punch through
if reverse bias voltage of C-B junction is keep on increasing, a situation arises
where E-B and C-B space charge regions touch each other, and the width of the
quasi-neutral base region becomes zero, Known as base punch through.
5
Any increase in VCB beyond the punch-through point lowers the E-B potential
barrier and allows a large injection of carriers from the emitter directly into the
collector.
If punch-through occurs, the maximum voltage (VCB0 or VCE0) that can be applied
to a BJT is limited.

6. RC
VBB
VCC
+
vBE
+
-
VCE
IB
IE
IC
RB
DC Load Line Analysis
6
-
Application of KVL in output (CE)circuit:
VCE = VCC – ICRC ; is called Load line equation.
When IC = 0, VCE = VCC ; When VCE = 0, IC = VCC/RC
The operating point Q (VCEQ, ICEQ) is determined by finding the intersection
point of load line and BJT output characteristics for a particular value of base
current.

7. Ebers-Moll Model (Large-Signal Model)
The Ebers-Moll (EM) model is a large-signal model for BJT. It relates the
transistor d.c terminal currents to voltages.
EM model is low frequency (static) model based on the fact that BJT is
composed of two pn junctions – EB and CB junction.
Therefore terminal currents of BJT can be expressed as a superposition
of the currents due to the two pn junctions.
D : E-B junction diode
7
DE : E-B junction diode
DC : C-B junction diode
)
1
(
ISE −
= T
BE
V
V
DE e
I )
1
(
ISC −
= T
BC
V
V
DC e
I
)
1
(
)
1
(
I
I S
C
−
=
−
=
= T
BE
T
BE
V
V
SE
V
V
DE e
I
e
I
α
α

8. Ebers-Moll Model (Large-Signal Model)
Forward Active Mode
Reverse Active Mode
8
DC
R
F
B
DC
F
C
DC
R
E
I
I
I
I
I
I
)
1
(
)I
1
(
I
I
DE
DC
DE
α
α
α
α
−
+
−
=
+
−
=
−
=
)
1
(
I
)
1
(
)
1
(
)
1
(
I
S
S
−
−
−
=
−
−
−
=
T
BC
T
BE
T
BC
T
BE
V
V
R
V
V
S
C
V
V
S
V
V
F
E
e
e
I
I
e
I
e
I
α
α

9. Ebers-Moll Model (Large-Signal Model)
BJT Forward Active Mode
BE forward-biased,
BC reverse-biased:
9
BJT Reverse Active Mode
BE reverse-biased,
BC forward-biased:

10. BJT Cut-off Mode
BE reverse-biased,
BC reverse-biased:
Ebers-Moll Model (Large-Signal Model)
10
BJT Saturation Mode
BE forward-biased,
BC forward-biased:

11. BJT with input ac signal
11

12. Biasing schemes for BJT
Biasing refers to the application of D.C. voltages to setup the operating
point in such a way that output signal is undistorted throughout the whole
operation.
Also once selected properly, the Q point should not shift because of
change of IC due to
(i) β variation
(ii) Temperature variation
12
(ii) Temperature variation
Different biasing schemes
(i) Fixed bias (base resistor biasing)
(ii) Collector base bias
(iii) Emitter bias
(iv) Voltage divider bias

13. DC
R
F
B
DC
F
C
DC
R
E
I
I
I
I
I
I
)
1
(
)I
1
(
I
I
DE
DC
DE
α
α
α
α
−
+
−
=
+
−
=
−
=
13
)
1
(
I
)
1
(
)
1
(
)
1
(
I
S
S
−
−
−
=
−
−
−
=
T
BC
T
BE
T
BC
T
BE
V
V
R
V
V
S
C
V
V
S
V
V
F
E
e
e
I
I
e
I
e
I
α
α