BJT’s
Forward Characteristics
Reverse Characteristics
ENGR 311
–
Electronic Devices and Circuits
October 26, 2000
Transistor Model: Current Amplifier
A Summary For Clarification (assume npn for the following general r
ules/properties
–
for pnp reverse
polarities)
Rules / Properties
1
–
The collector must be positive than the emitter.
2
–
The base

emitter and base

collector circuits behave like diodes. Normally the base

emitter diode is
conducting and the base

collect
or diode is reverse

biased
3
–
When 1 and 2 are obeyed Ic is proportional to Ib (Ic = beta . Ib)
Both Ib and Ic follow to the emitter.
Note: the collector current is not due to forward conduction of the base

collector diode; that diode is reverse

biased.
Just think of it as “transistor action.”
Property 3 gives the transistor its usefulness: a small current flowing into the base controls a much larger
current flowing into the collector.
Note the effect of property 2. This means you can’t go sticking a v
oltage across the base

emitter terminals,
because an enormous current will flow if the base is more positive than the emitter by more than about 0.6 to
0.8 volt. This rule also implies that an operating transistor has Vb = ~ Ve + 0.6 (Vb = Ve + Vbe) (for a
n npn).
Let me emphasize again that you should not try to think of the collector current as diode conduction. It isn’t,
because the collector

base diode normally has voltages applied across it in a reverse direction. Furthermore,
collector current varies
very little with collector voltage (it behaves like a not

too

great current source), unlike
forward diode conduction, where the current rises very rapidly with applied voltage.
Current flow
The forward bias on the base

emitter junction will cause curren
t flow across this junction. Current will consist
of two components: electrons injected from the emitter into the base, and holes from the base into the emitter.
The electrons injected from the emitter into the base are minority carriers in the p

type bas
e region. Because
the base is usually very thin the excess minority carriers (electron) concentration in the base will have an
almost straight

line profile. The electrons will reach the boundary of the collector

base depletion region.
Because the collector
is more positive than the base these electrons will be swept across the CB junction region
into the collector. They are then “collected” to constitute the collector current. By convention the direction of
ic will be opposite to that of the electron flow;
thus ic will flow into the collector terminal.
Ic
–
Vce Characteristic for an npn Transistor
Ic

Vbe Characteristics
Biasing
For common emitter amplifier
ENGR 311

BJTs
–
Exercises

October 29, 2001
Examples
Soluti
on
Example 1

Beta = 100, vBE = 0.7V at
iC = 1mA. Design circuit so that a
current of 2mA flows through the
collector and a voltage of +5V appears at
the collector.
Example 2

In the circuit below vC =

0.7V. If Beta = 50, find IE, IB, IC and
VC.
Example 3
–
In the circuit below, Vb =
1V, VE = 1.7V. What are alfa and beta
for this transistor? What voltage VC do
you expect at the collector.
Example 4

Beta = 100
–
Determine all
node voltages and branch currents.
Example 5
Determine the voltages at all nodes and current through all branches.
Assume beta 1 and beta2 = 200. Assume Q1 is in the active mode.
ENGR 311

Graphical Representation of Transistor Characteristics

Oc
tober 31, 2001
Conceptual circuit for measuring the
i
C

v
CE
characteristics of the BJT.
(b)
The
i
C

v
CE
characteristics of a practical BJT.
The
i
C

v
CB
characteristics for an npn transistor in the active mode
Determine the voltages at all nodes and the currents at all branches in the circuit below.
Solution
The Transistor As An Amplifier
–
DC Conditions
The Collector Current and The Transconductance
Th
e Base Current and the Input Resistance at the Base
(a) Conceptual circuit to illustrate the op
eration of the transistor of an amplifier.
(b)
The circuit
of (a) with the signal source
v
be
eliminated for dc (bias) analysis.
Transistor as An Amplifier

Small Signal Approximation
Transconductance (gm), Input Resistance at the Base (r
), Input Resistance at the Emitter (re), Voltage Gain
Exercise 4.22 and 4.23
Small

Signal Equivalent Circuits Models
Amplifier Circuit Without DC Sources
Hybrid

The T Model
Application of the Small

Signal Equivalent Circuits
1
2
3
4
5
Example 4.9
DC
Analysis
Small

Signal Analysis
Example 4.11
Determine voltage gain in the circuit below
DC Analysis
Small

Signal Model
Small

Signal Analysis Directly on Circuit
Graphical Analysis
Graphical determinati
on of the signal components
v
be
,
i
b
,
i
c
, and
v
ce
when a signal component
v
i
is
superimposed on the dc voltage
V
BB
.
Biasing The BJT For Discrete

Circuit Design
Basic Single

Stage BJT Amplifier Configurations
Minority

Carrier
Transport In the Base Region
i
T
= qADn. dn/dx =

qADnn. (nbo/Wb). [exp(vbe/Vt)
–
exp(vbc/Vt)]
Is = qADn.(nbo/Wb) = (qADn.ni^2 )/Nab.Wb
nbo = equilibrium electron density
A = cross

sectional area of the base region
Wb = base width
Dn = diffusit
y (cm^2/s)
Nab = doping concentration in base of transistor’
ni = intrinsic

carrier concentration (10^10.cm^3)
nbo = ni^2 / Nab
Base Transit Time
To turn the BJT minority

carrier charge must be introduced into the base to establish the gradient.
The
forward transit time tau

f represents the time constant associated with storing the required charge Q in the
base region and is defined by
Q/I
T
Diffusion Capacitance
For the base

emitter voltage and hence the collector current in the BJT to change
, the charge stored in the base
region also must change.
This change in charge with vbe can be modeled by a capacitance C
D
CD = (Ic/V
T
).
f
Frequency Dependence of the Common

Emitter Current Gain
Beta

cutoff Frequency
Transconductance
Relates changes in ic to changes in vbe
gm = dic/dvbe (@Q

point)
gm = Ic /V
T
C
D
= gm.
f
The Early Effect
(James Early form Bell Labs
)
Experimentally demonstrated that when the output curves are extrapolated back to a point of zero collector
current, the curves all intersect at a constant voltage point vce =

V
A
Modeling the Early Effect
ic
Betaf
ib
Tolerances in Bias Ci
rcuits
Worst Case Analysis
Study the operation of the transistor considering tolerances (worst case anaysis) in the circuit. Assume that the
12V power supply has a 5% tolerance and the resistors have 10% tolerance. Assume also that the volta
ge drop
in R
EQ
can be neglected, and beta is large.
V
EQ
(max, min)
I
C
(max, min)
V
CE
(max, min)
Monte Carlo Analysis
Perform Monte Carlo Analysis on previous circuit assuming the random values to
Vcc, R1, R2, Rc, Re, and beta. (Use Excel and/or
Pspice).
Calculate
V
EQ
R
EQ
I
B
I
C
I
E
V
C
= V
CC
–
I
C
.R
C
–
I
E
.R
E
Electronic Devices and Circuits
–
11/5/00
Monte Carlo Analysis
–
Using Pspice
Probe Output
Ic(Q), Ib(Q), Vce
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