# BJT-1-examples

Electronics - Devices

Oct 7, 2013 (4 years and 9 months ago)

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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

-

exp(vbc/Vt)]

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