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C
B
E
Dr. D G Borse
The BJT – Bipolar Junction Transistor
Note: Normally Emitter layer is heavily doped, Base layer is lightly
doped and Collector layer has Moderate doping.
The Two Types of BJT Transistors:
npn
pnp
E
n
p
n
C
E
C
Cross Section
p
n
p
C
Cross Section
B
C
B
B
B
Schematic
Symbol
Schematic
Symbol
E
• Collector doping is usually ~ 109
• Base doping is slightly higher ~ 1010 – 1011
• Emitter doping is much higher ~ 1017
Dr. D G Borse
E
BJT Current & Voltage - Equations
IE
E
-
VCE +
IC
-
IE
-
VBE
IB
C
E
VEC
+
VEB
VBC
-
C
+
VCB
IB
-
+
+
+
IC
-
B
B
npn
pnp
IE = IB + IC
IE = IB + IC
VCE = -VBC + VBE
VEC = VEB - VCB
Dr. D G Borse
n
I co
VCB
-
Inc
+
-
p- Electrons
+ Holes
+
VBE -
Ipe
Ine
n+
Bulk-recombination
Current
Figure : Current flow (components) for an n-p-n BJT in the active region.
NOTE: Most of the current is due to electrons moving from the emitter through base to the
collector. Base current consists of holes crossing from the base into the emitter and of holes
that recombine with electrons in the base.
Dr. D G Borse
Physical Structure
• Consists of 3 alternate layers of n- and ptype semiconductor called emitter (E),
base (B) and collector (C).
• Majority of current enters collector,
crosses base region and exits through
emitter. A small current also enters base
terminal, crosses base-emitter junction
and exits through emitter.
• Carrier transport in the active base
region directly beneath the heavily
doped (n+) emitter dominates i-v
characteristics of BJT.
Dr. D G Borse
Ic
C
Recombination
VCB +
- - - - -- n
- - - - - - - - - -
_
- Electrons
B
+
+
_
- + -
- - - - + - -p
-
-
IB
VBE
- - - --- - - -
- - -- -
- - - - - - - - -
E
Dr. D G Borse
IE
n
+ Holes
For CB Transistor IE= Ine+ Ipe
Ic= Inc- Ico
Bulkrecombination
current
ICO
Inc
And Ic= - αIE + ICo
CB Current Gain, α ═ (Ic- Ico) .
(IE- 0)
For CE Trans., IC = βIb + (1+β) Ico
where β ═ α ,
1- α is CE Gain
Ipe
Ine
Figure: An npn transistor with variable biasing sources (common-emitter configuration).
Dr. D G Borse
Common-Emitter
Circuit Diagram
VCE
IC
VC
+
_
Collector-Current Curves
IC
Active
Region
IB
C
IB
Region of Description
Operation
Active
Small base current
controls a large
collector current
VCE
Saturation Region
Saturation VCE(sat) ~ 0.2V, VCE
increases with IC
Cutoff
Cutoff Region
IB = 0
Achieved by reducing IB
to 0, Ideally, IC will also
be equal to 0.
Dr. D G Borse
BJT’s have three regions of operation:
1) Active - BJT acts like an amplifier (most common use)
2) Saturation - BJT acts like a short circuit
BJT is used as a switch by switching
3) Cutoff - BJT acts like an open circuit
between these two regions.
IC(mA)
Saturation Region
IB = 200 mA
30
When analyzing a DC
BJT circuit, the BJT
is replaced by one of
the DC circuit models
shown below.
C
Active Region
IB = 150 mA
22.5
B
E
IB = 100 mA
15
IB = 50 mA
7.5
Cutoff Region
IB = 0
0
VCE (V)
0
5
10
15
20
DC Models for a BJT:
C
C
C
rsat
IB
B
B
+
_
B
+
_
b dc IB
ICEO
b dc IB
Vo
+
_
RBB
Vo
Vo
E
E
Active Region Model #1
Saturat ion Region Model
Dr. D G Borse
E
Active Region Model #2
Ro
DC b and DC 
b = Common-emitter current gain
 = Common-base current gain
b = IC
 = IC
IB
IE
The relationships between the two parameters are:
=
b
b=
b+1

1-
Note:  and b are sometimes referred to as dc and bdc
because the relationships being dealt with in the BJT
are DC.
Dr. D G Borse
Output characteristics: npn BJT (typical)
IC(mA)
b dc =
IB = 200 mA
30
Note: The PE review text
sometimes uses dc instead of bdc.
They are related as follows:
IB = 150 mA
22.5
IB = 100 mA
15
IB = 50 mA
7.5
IB = 0
0
0
5
10
15
20
Input characteristics: npn BJT (typical)
IC
= h FE
IB
 dc =
b dc
b dc + 1
b dc 
 dc
1 -  dc
VCE (V)
• Find the approximate values
of bdc and dc from the graph.
IB(mA)
VCE = 0.5 V
200
VCE = 0
VCE > 1 V
150
The input characteristics look like the characteristics of a
forward-biased diode. Note that VBE varies only slightly,
so we often ignore these characteristics and assume:
Common approximation: VBE = Vo = 0.65 to 0.7V
100
Note: Two key specifications for the BJT are
50
Bdc and Vo (or assume Vo is about 0.7 V)
0
VBE (V)
0
0.5
1.0
Dr. D G Borse
Figure: Common-emitter characteristics displaying exaggerated secondary effects.
Dr. D G Borse
Figure: Common-emitter characteristics displaying exaggerated secondary effects.
Dr. D G Borse
Various Regions (Modes) of Operation of BJT
Active:
• Most important mode of operation
• Central to amplifier operation
• The region where current curves are practically flat
Saturation: • Barrier potential of the junctions cancel each other out
causing a virtual short (behaves as on state Switch)
Cutoff:
• Current reduced to zero
• Ideal transistor behaves like an open switch
* Note: There is also a mode of operation called
inverse active mode, but it is rarely used.
Dr. D G Borse
BJT Trans-conductance Curve
For Typical NPN Transistor 1
Collector Current:
IC
IC =  IES eVBE/VT
8 mA
Transconductance:
(slope of the curve)
6 mA
gm =
IC /
VBE
IES = The reverse saturation current
of the B-E Junction.
4 mA
VT = kT/q = 26 mV (@ T=300oK)
 = the emission coefficient and is
usually ~1
2 mA
0.7 V
VBE
Dr. D G Borse
Three Possible Configurations of BJT
Biasing the transistor refers to applying voltages to the
transistor to achieve certain operating conditions.
1. Common-Base Configuration (CB) : input = VEB & IE
output = VCB & IC
2. Common-Emitter Configuration (CE): input = VBE & IB
output= VCE & IC
3. Common-Collector Configuration (CC) :input = VBC & IB
(Also known as Emitter follower)
Dr. D G Borse
output = VEC & IE
Common-Base BJT Configuration
Circuit Diagram: NPN Transistor
C
IC
VCE
VCB
The Table Below lists assumptions
that can be made for the attributes
of the common-base BJT circuit in
the different regions of operation.
Given for a Silicon NPN transistor.
Region of
Operation
IC
Active
bIB
Saturation
Max
Cutoff
~0
VCE
E
VBE
+
_
+
_
IB
B
VCB
VBE
=VBE+VCE ~0.7V
~0V
IE
VBE
VCB
 0V
C-B
Bias
E-B
Bias
Rev. Fwd.
~0.7V -0.7V<VCE<0 Fwd. Fwd.
=VBE+VCE  0V
Dr. D G Borse
 0V
Rev.
None
/Rev.
Common-Base (CB) Characteristics
Although the Common-Base configuration is not the most
common configuration, it is often helpful in the understanding
operation of BJT
Vc- Ic (output) Characteristic Curves
IC mA
Breakdown Reg.
Saturation Region
6
0.8V
Active
Region
IE
4
IE=2mA
2
IE=1mA
2V
4V
6V
Dr. D G Borse
8V
Cutoff
IE = 0
VCB
Common-Collector BJT Characteristics
Emitter-Current Curves
The CommonCollector biasing
circuit is basically
equivalent to the
common-emitter
biased circuit except
instead of looking at
IC as a function of VCE
and IB we are looking
at IE.
Also, since  ~ 1, and
 = IC/IE that means
IC~IE
IE
Active
Region
IB
VCE
Saturation Region
Cutoff Region
IB = 0
Dr. D G Borse
n p n Transistor: Forward Active Mode Currents
Base current is given by
IC=

I
F
20  b
IB=

V



I
co
BE  1
I  C 
exp
 V

B b

b 
T 
F
F




 500 is forward common-emitter
current gain
Emitter current is given by
VBE
IE=
Forward Collector current is







V


I  I co exp BE  1
C
V  
T  






V

I co 


BE  1
I I I 
exp
 V

E
B  
C

T




F
b
is forward common-
F  1.0
0.95   
base current gain
F b 1
F
Ico is reverse saturation current In this forward active operation region,
I
1018A  Ico 10 9 A
VT = kT/q =25 mV at room temperature
Dr. D G Borse
I
C b
B
I
F
I
C 
E
F
Various Biasing Circuits used for BJT
• Fixed Bias Circuit
• Collector to Base Bias Circuit
• Potential Divider Bias Circuit
Dr. D G Borse
The Thermal Stability of Operating Point SIco
The Thermal Stability Factor : SIco
SIco = ∂Ic
∂Ico V , β
be
This equation signifies that Ic Changes SIco times as fast as Ico
Differentiating the equation of Collector Current IC & rearranging
the terms we can write
SIco ═ 1+β
1- β (∂Ib/∂IC)
It may be noted that Lower is the value of SIco better is the stability
Dr. D G Borse
The Fixed Bias Circuit
15 V
15 V
The Thermal Stability Factor : SIco
SIco = ∂Ic
∂Ico Vbe, β
General Equation of SIco Comes out to be
200 k
RC
Rb
1k
C
B
SIco ═
1+β
1- β (∂Ib/∂IC)
RC
Applying KVL through Base Circuit we
can write,
Ib Rb+ Vbe= Vcc
Ib
E
Diff w. r. t. IC, we get (∂Ib / ∂Ic) = 0
SIco= (1+β) is very large
Indicating high un-stability
Dr. D G Borse
The Collector to Base Bias Circuit
VCC
RC
The General Equation for Thermal
Stability Factor,
SIco = ∂Ic
∂Ico
Vbe, β
Comes out to be
SIco ═
Ic
RF
Ib
Applying KVL through base circuit
C
we can write (Ib+ IC) RC + Ib Rb+ Vbe= Vcc
Diff. w. r. t. IC we get
B
+ V
BE
1+β
1- β (∂Ib/∂IC)
-
E
IE
(∂Ib / ∂Ic) = - RC / (Rb + RC)
Therefore, SIco ═
(1+ β)
1+ [βRC/(RC+ Rb)]
Which is less than (1+β), signifying better
thermal stability
Dr. D G Borse
The Potential Devider Bias Circuit
VCC
R1
Ib
The General Equation for Thermal Stability
Factor,
SIco ═
1+β
VCC
1- β (∂Ib/∂IC)
RC
IC
C
Applying KVL through input base circuit
B
we can write IbRTh + IE RE+ Vbe= VTh
E
R2
IC
VCC
Thevenin
Equivalent Ckt
Ib
(∂Ib / ∂Ic) = - RE / (RTh + RE)
Therefore,
1 b
SIco 
RE 

1 b
 RE  RTh 
RC
IC
This shows that SIco is inversely proportional
to RE and
It is less than (1+β), signifying better thermal
stability
C
B
RTh
E
+
_
Therefore, IbRTh + (IC+ Ib) RE+ VBE= VTh
Diff. w. r. t. IC & rearranging we get
RE
VTh
RE
Thevenins
Equivalent Voltage
Self-bias Resistor
Rth = R1*R2 & Vth = Vcc R2
R1+R2
R1+R2
Dr. D G Borse
A Practical C E Amplifier Circuit
VCC
VCC
Input Signal Source
R1
RC
io
C
Co
ii
Rs
+
vs
+
Ci
+
B
E
vi
_
R2
RE
_
Common Emitter (CE) Amplifier
Dr. D G Borse
RL
CE
vo
_
BJT Amplifier (continued)
If changes in operating currents and
voltages are small enough, then IC
and VCE waveforms are undistorted
replicas of the input signal.
A small voltage change at the base
causes a large voltage change at the
collector. The voltage gain is given
by:
~
~ vce 1.65180
 206180  206
An 8 mV peak change in vBE gives a 5 Av  ~ 
v
0.0080
mA change in iB and a 0.5 mA change in
be
iC.
The minus sign indicates a 1800
The 0.5 mA change in iC gives a 1.65 V phase shift between input and
change in vCE .
output signals.
Dr. D G Borse
A Practical BJT Amplifier using Coupling and Bypass
Capacitors
In a practical amplifier design, C1 and C3 are
large coupling capacitors or dc blocking
capacitors, their reactance (XC = |ZC| = 1/wC) at
signal frequency is negligible. They are effective
open circuits for the circuit when DC bias is
considered.
C2 is a bypass capacitor. It provides a low
impedance path for ac current from emitter to
ground. It effectively removes RE (required for
good Q-point stability) from the circuit when ac
signals are considered.
•
•
AC coupling through capacitors is used to inject an ac input signal
and extract the ac output signal without disturbing the DC Q-point
Capacitors provide negligible impedance at frequencies of interest
and provide open circuits at dc.
Dr. D G Borse
D C Equivalent for the BJT Amplifier (Step1)
DC Equivalent Circuit
• All capacitors in the original amplifier circuit are replaced by open
circuits, disconnecting vI, RI, and R3 from the circuit and leaving RE
intact. The the transistor Q will be replaced by its DC model.
Dr. D G Borse
A C Equivalent for the BJT Amplifier (Step 2)
R1IIR2=RB
Ro
Rin
• Coupling capacitor CC and Emitter bypass capacitor CE are replaced by short
circuits.
• DC voltage supply is replaced with short circuits, which in this case is connected
to ground.
Dr. D G Borse
A C Equivalent for the BJT Amplifier
(continued)
All externally connected capacitors are assumed
as short circuited elements for ac signal
R  R R 10kΩ 30kΩ
B
1 2
R  R R  4.3kΩ 100kΩ
C 3
• By combining parallel resistors into equivalent RB and R, the equivalent AC
circuit above is constructed. Here, the transistor will be replaced by its
equivalent small-signal AC model (to be developed).
Dr. D G Borse
A C Analysis of CE Amplifier
1) Determine DC operating point and
Step 1
calculate small signal parameters
2) Draw the AC equivalent circuit of Amp.
• DC Voltage sources are shorted to ground
• DC Current sources are open circuited
Step
2
• Large capacitors are short circuits
• Large inductors are open circuits
Step
3
3) Use a Thevenin circuit (sometimes a
Norton) where necessary. Ideally the
base should be a single resistor + a single
source. Do not confuse this with the DC
Thevenin you did in step 1.
Step
4
4) Replace transistor with small signal model
5) Simplify the circuit as much as necessary.
Steps to Analyze a Transistor Amplifier
Step
5
6) Calculate the small signal parameters and
gain etc.
Dr. D G Borse
π-model
used
Hybrid-Pi Model for the BJT
• The hybrid-pi small-signal model is the
intrinsic low-frequency representation of
the BJT.
• The small-signal parameters are
controlled by the Q-point and are
independent of the geometry of the BJT.
Transconductance:
I
gm  C ,VT  KT
q
V
T
Input resistance: Rin
b oV
bo
T
r 

I
gm
C
Output resistance:
V V
ro  A CE
I
C
Where, VA is Early Voltage
(VA=100V for npn)
Dr. D G Borse
Hybrid Parameter Model
Ii
Io
Linear Two
port Device
Vi
Vo
Ii
1
Vi
Io
hi
hrVo
hfIi
ho
1'
2
Vo
2'
Vi  h11Ii  h12Vo  hi I i  hrVo
I o  h21Ii  h22Vo  h f I i  hoVo
Dr. D G Borse
h-Parameters
Vi
h11 
Ii
Io
h21 
Ii
Vo  0
Vi
h12 
Vo
Ii  0
Vo  0
Io
h22 
Vo
Ii  0
h11 = hi = Input Resistance
h12 = hr = Reverse Transfer Voltage Ratio
h21 = hf = Forward Transfer Current Ratio
h22 = ho = Output Admittance
Dr. D G Borse
Three Small signal Models of CE Transistor
The Mid-frequency small-signal models
ib
ic
c
b
+
vbe
hie
Alternate names:
h fe = b ac = b o = b
+
hrevce
+
_
hfe ib
hoe
vce
_
_
e
e
h-parameter model
ib
ic
c
b
+
vbe
+
r
_
+
v
gmv
rd
vce
_
_
38.92
IC (Note: Uses DC value of I C )
n
where n = 1 (typical, Si BJT)
gm =
rd =
h re = 0
r = h ie =
e
e
hybrid- model
ib
ic
c
b
+
vbe
+
bre
bib
vce
_
_
e
e
re model
1
h oe
b o = h fe
re =
bo
gm
26 mV
(Note: uses DC value of I B )
IB
b o = h fe
b o re = h ie
h re = 0
h oe = 0, or use rd =
Dr. D G Borse
1
h oe
BJT Mid-frequency Analysis using the hybrid- model:
VCC
VCC
R1
A common emitter (CE) amplifier
RC
io
The mid-frequency circuit is drawn as follows:
• the coupling capacitors (Ci and Co) and the
bypass capacitor (CE) are short circuits
• short the DC supply voltage (superposition)
• replace the BJT with the hybrid- model
The resulting mid-frequency circuit is shown below
C
Co
ii
Rs
+
+
+
B
Ci
E
vs
vi
R2
_
RL
RE
CE
vo
_
_
is
ii
b
RS
+
vs
+
RTh
vi
_
_
e
io
c
+
r
v
+
gmv
rrod
RC
RL
_
_
mid-frequency CE amplifier circuit
e
v
A  o   g R ' , where, R '  r R R ,
v v
m L
L
o L C
i
i
An a c Equivalent Circuit
vo
 Z 
i 
A  o o i A 
vs v
v Z  R 
v v
s
i
s
s
 i
v
v
v
A  o Z  i  R r , where, R  R R
i
i I
Th 
Th
1 2
i
i
i
Z
o
v

v
r
o
i
o
o v o
i
Dr. D G Borse
R
C
Details of Small-Signal Analysis for Gain Av (Using Π-model)


 v   g v  R R r 
o
m be  C 3 o 

Rs
R
Rs
L
From input circuit
R
r R
R ,  R C R3
C
o
3
L
 v
v
 o
A  o 

v
v
v
i
 be
 v 
 be 

 v 


 i 
v  I R   g v  R
 m be  L
o o L


 
 vi  RB r  

 
v

be
 R   R r 


 S
 B  



R r


B


 A  g R 
v
m L




 RS   RB r  


Dr. D G Borse
C-E Amplifier Input Resistance
• The input resistance, the total resistance
looking into the amplifier at coupling
capacitor C1, represents the total
resistance presented to the AC source.
v x  ix ( R r )
B
vx
R 
 R r  R R r
B
1 2
in i
x
Dr. D G Borse
C-E Amplifier Output Resistance
• The output resistance is the total equivalent
resistance looking into the output of the
amplifier at coupling capacitor C3. The input
source is set to 0 and a test source is applied
at the output.
v
v
ix  x  x  gm v
be
R
ro
C
But vbe=0.
v
Rout  x  R ro  R
C
C
ix
since ro is usually >> RC.
Dr. D G Borse
High-Frequency Response – BJT Amplifiers
Capacitances that will affect the high-frequency response:
• Cbe, Cbc, Cce – internal capacitances
• Cwi, Cwo – wiring capacitances
• CS, CC – coupling capacitors
• CE – bypass capacitor
Dr. D G Borse
Frequency Response of Amplifiers
The voltage gain of an amplifier is typically flat over the mid-frequency
range, but drops drastically for low or high frequencies. A typical
frequency response is shown below.
For a CE BJT: (shown on lower right)
• low-frequency drop-off is due to CE, Ci and Co
• high-frequency drop-off is due to device capacitances Cp and Cm
(combined to form Ctotal)
• Each capacitor forms a break point (simple pole or zero) with a break
frequency of the form f=1/(2pREqC), where REq is the resistance seen by
the capacitor
• CE usually yields the highest low-frequency break
which establishes fLow.
LM(A vi ) = 20log(v o/vi) [in dB]
LM Response for a General Amplifier
20log(A vi(mid))
3dB
BW
f
fLOW
Dr. D G Borse
fHIGH
Amplifier Power Dissipation
• Static power dissipation in amplifiers is determined from their DC
equivalent circuits.
Total power dissipated in C-B
and E-B junctions is: P V I V I
D CE C BE B
V V V
where
CE CB BE

Total power supplied is:
P  V  I  I , where I  I  I
S
CC  C 2 
2 1 B
V
CC
I 
and I 
1 R R
B R
1
2
V
EQ
EQ

b
The difference is the power dissipated by the bias resistors.
Dr. D G Borse
V
 F
BE
 1
R
 E
Dr. D G Borse
Figure 4.36a Emitter follower.
Dr. D G Borse
An Emitter Follower (CC Amplifier) Amplifier
Figure Emitter follower.
Very high input Resistance
Very low out put Resistance
Unity Voltage gain with no phase shift
High current gain
Can be used for impedance matching or a
circuit for providing electrical isolation
Dr. D G Borse
Figure 4.36b Emitter follower.
Dr. D G Borse
Figure 4.36c Emitter follower.
Dr. D G Borse



Capacitor Selection for the CE Amplifier
1
1
Zc 
Capacitive Reactance Xc  Z c 
where w  2f
jwC
wC
The key objective in design is to make the capacitive reactance
much smaller at the operating frequency f than the associated
resistance that must be coupled or bypassed.








X R r Make X  0.01 R r for < 1% gain error.
c1
B
c1
B
X  0 Make X 1 for <1% gain error.
c2
c2


X R Make X  0.01R  for <1% gain error.
c3
3
c3
 3 

Dr. D G Borse
Summary of Two-Port Parameters for
CE/CS, CB/CG, CC/CD
Dr. D G Borse
A Small Signal h-parameter Model of C E - Transistor
= h11
Vce*h12
Dr. D G Borse
A Simple MOSFET Amplifier
The MOSFET is biased in the saturation region by dc voltage sources VGS and
VDS = 10 V. The DC Q-point is set at (VDS, IDS) = (4.8 V, 1.56 mA) with VGS =
3.5 V.
Total gate-source voltage is:
v V  vgs
GS GS
A 1 V p-p change in vGS gives a 1.25 mA p-p change in iDS and a 4 V p-p change
in vDS. Notice the characteristic non-linear I/O relationship compared to the BJT.
Dr. D G Borse
Eber-Moll BJT Model
The Eber-Moll Model for BJTs is fairly complex, but it is
valid in all regions of BJT operation. The circuit diagram
below shows all the components of the Eber-Moll Model:
E
IE
IC
RIC
RIE
IF
IR
IB
B
Dr. D G Borse
C
Eber-Moll BJT Model
R = Common-base current gain (in forward active mode)
F = Common-base current gain (in inverse active mode)
IES = Reverse-Saturation Current of B-E Junction
ICS = Reverse-Saturation Current of B-C Junction
IC = FIF – IR
IB = IE - IC
IE = IF - RIR
IF = IES [exp(qVBE/kT) – 1] IR = IC [exp (qVBC/kT) – 1]
 If IES & ICS are not given, they can be determined using various
BJT parameters.
Dr. D G Borse
Small Signal BJT Equivalent Circuit
The small-signal model can be used when the BJT is in the active region.
The small-signal active-region model for a CB circuit is shown below:
iB
iC
B
biB
r
r = (b + 1) * VT
IE
@  = 1 and T = 25C
r = (b + 1) * 0.026
IE
iE
E
Recall:
b = IC / IB
Dr. D G Borse
C
The Early Effect (Early Voltage)
IC
Note: Common-Emitter
Configuration
IB
-VA
VCE
Green = Ideal IC
Orange = Actual IC (IC’)
IC’ = IC
VCE + 1
VA
Dr. D G Borse
Early Effect Example
Given: The common-emitter circuit below with IB = 25mA,
VCC = 15V, b = 100 and VA = 80.
Find:
a) The ideal collector current
b) The actual collector current
Circuit Diagram
IC
VCE
b = 100 = IC/IB
a)
VCC
+
_
IC = 100 * IB = 100 * (25x10-6 A)
IB
IC = 2.5 mA
b)
IC’ = IC
VCE + 1
VA
= 2.5x10-3
15 + 1
80
IC’ = 2.96 mA
Dr. D G Borse
= 2.96 mA
Breakdown Voltage
The maximum voltage that the BJT can withstand.
BVCEO =
BVCBO =
The breakdown voltage for a common-emitter
biased circuit. This breakdown voltage usually
ranges from ~20-1000 Volts.
The breakdown voltage for a common-base biased
circuit. This breakdown voltage is usually much
higher than BVCEO and has a minimum value of ~60
Volts.
Breakdown Voltage is Determined By:
•
•
The Base Width
Material Being Used
•
Doping Levels
•
Biasing Voltage
Dr. D G Borse
Potential-Divider Bias Circuit with Emitter Feedback
Most popular biasing circuit.
Problem: bdc can vary over a wide range for BJT’s (even with the same part number)
Solution: Adding the feedback resistor RE. How large should RE be? Let’s see.
VCC
VCC
VCC
R1
RC
RC
C
C
B
B
Substituting the active region model into
the circuit to the left and analyzing the
circuit yields the following well known
equation:
RTh
E
E
+
_
R2
RE
Voltage divider biasing
circuit with emitter
feedback
IC =
VTh
RE
Replacing the input circuit by a
Thevenin equivalent circuit yields:
 R2 
VTh = VCC 
 and R Th = R1 R 2
 R1 + R 2 
b dc  VTh - Vo  + ICEO  R Th + R E 
R Th +  b dc + 1 R E
where ICEO =  b dc + 1 ICBO
ICEO has little effect and is often
neglected yielding the simpler
relationship:
b dc  VTh - Vo 
IC =
R Th +  b dc + 1 R E
Test for stability: For a stable Q-point w.r.t. variations in bdc choose:
R Th <<  bdc + 1 R E
Why? Because then
b dc  VTh - Vo 
b  V - Vo 
IC =
 dc Th
R Th +  b dc + 1 R E
 b dc + 1 R E
Dr. D G Borse

 VTh
- Vo 
(independent of b dc )
RE
PE-Electrical Review Course - Class 4 (Transistors)
Example :
15 V
15 V
200 k
1k
Find the Q-point for the biasing circuit shown below.
The BJT has the following specifications:
bdc = 100, rsat = 100  (Vo not specified, so assume Vo = 0.7 V)
C
B
E
Example :
Repeat Example 3 if RC is changed from 1k to 2.2k.
Dr. D G Borse
PE-Electrical Review Course - Class 4 (Transistors)
Example
18 V
18 V
30 k
10 k
C
Determine the Q-point for the biasing circuit shown.
The BJT has the following specifications:
bdc varies from 50 to 400, Vo = 0.7 V, ICBO = 10 nA
Solution:
Case 1: bdc = 50
B
E
15 k
8k
Case 2: bdc = 400 Similar to Case 1 above. Results are: IC = 0.659 mA, VCE =
6.14 V Summary:
bdc
50
400
IC
VCE
Dr. D G Borse
PE-Electrical Review Course - Class 4 (Transistors)
VCC
BJT Amplifier Configurations
and Relationships:
VCC
R1
RC
io
C
Using the hybrid- model.
Co
ii
Rs
+
+
+
B
Ci
E
vs
vi
R2
_
RL
RE
CE
_
_
Common Emitter (CE) Amplifier
E
ii
Rs
+
C
io
Co
Ci
B
+
vi
vs
RE
RL
R1
_
C2
R2
-g m R
R 'L
rd R C R L
Zi
R Th r
vo
Zo
rd R C
VCC
AI
AP
C
ii
+
Ci
B
rd R C
 Zi 
 Zi 
A vi 
 A vi 

 R s + Zi 
 R s + Zi 
Z 
Z 
A vi  i 
A vi  i 
 RL 
 RL 
A vi A I
A vi A I
CC
r
1 + b o  R 'L
+ 1 + b o  R 'L
RE RL
R Th  r + 1 + b o  R 'L 
 r + R Th R S 
RE  

 1 + b o  
 Zi 
A vi 

 R s + Zi 
Z 
A vi  i 
 RL 
where R Th = R1 R 2
io
E
Co
vs
rd R C R L
1
R E r
gm
_
R1
Rs
gmR
'
L
VCC
Common Base (CB) Amplifier
+
'
L
A vi
A vs
VCC
CB
+
RC
_
CE
vo
vi
_
R2
RE
+
RL
_
vo
_
Common Collector (CC) Amplifier (also called “emitter-follower”)
Dr. D G Borse
Note: The biasing circuit is
the same for each amplifier.
A vi A I
Figure 4.16 The pnp BJT.
Dr. D G Borse
Figure 4.17 Common-emitter characteristics for a pnp BJT.
Dr. D G Borse
Figure 4.18 Common-emitter amplifier for Exercise 4.8.
Dr. D G Borse
Figure 4.19a BJT large-signal models. (Note: Values shown are appropriate for typical small-signal silicon devices at
a temperature of 300K.
Dr. D G Borse
Figure 4.19b BJT large-signal models. (Note: Values shown are appropriate for typical small-signal silicon devices at
a temperature of 300K.
Dr. D G Borse
Figure 4.19c BJT large-signal models. (Note: Values shown are appropriate for typical small-signal silicon devices at
a temperature of 300K.
Dr. D G Borse
Dr. D G Borse