Download - 5_BJT Small Signal
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Sem I 0809/rosdiyana
Chapter 5:BJT Small-Signal Analysis
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Contents
1. Common-Emitter fixed-bias configuration2. Voltage divider bias3. CE Emitter bias4. Emitter-follower configuration5. Common-base configuration
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• re transistor model – employs a diode and controlled current source to duplicate the behavior of a transistor in the region of interest.
• The re and hybrid models will be used to analyze small-signal AC analysis of standard transistor network configurations.
Ex: Common-base, common-emitter and common-collector configurations.
• The network analyzed represent the majority of those appearing in practice today.
BJT Small Signal Analysis
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AC equivalent of a network is obtained by:
1. Setting all DC sources to zero
2. Replacing all capacitors by s/c equiv.
3. Redraw the network in more convenient and logical form
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1/5: Common-Emitter (CE) Fixed-Bias Configuration
The input (Vi) is applied to the base and the output (Vo) is from the collector.
The Common-Emitter is characterized as having high input impedance and low output impedance with a high voltage and current gain.
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Removing DC effects of VCC and Capacitors
Common-Emitter (CE) Fixed-Bias Configuration
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re Model
Determine , re, and ro: and ro: look in the specification sheet for the transistor or test the transistor using a curve tracer.re: calculate re using dc analysis:
Ee I
26mVr
Common-Emitter (CE) Fixed-Bias Configuration
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Impedance Calculations
Input Impedance: Output Impedance:
eBi r||RZ
eB ei r10RrZ
Or||RZ Co
c o 10roZ RRc
Common-Emitter (CE) Fixed-Bias Configuration
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Gain Calculations
Voltage Gain (Av):
Current Gain (Ai):
Current Gain from Voltage Gain:
e
oC
i
ov r
)r||(R
V
VA
Coe
Cv 10Rrr
RA
)r)(RR(r
rR
I
IA
eBCo
oB
i
oi
eBCoi r10R ,10RrA
C
ivi R
ZAA
Common-Emitter (CE) Fixed-Bias Configuration
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Voltage Gain
e
CvCo
e
oC
eb
oCbv
eb i
oCbO
i
Ov
r
RA 10Ror r if
r
)r||(R
βrI
)r||(RβIA
βrIV
)r||(RβIV
V
VA
Common-Emitter (CE) Fixed-Bias Configuration
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Current gain
C
ivi
Bo
Bo
i
oi
eBCo
eBCo
Bo
i
oi
eB
B
Co
o
i
b
b
o
i
oi
eB
B
i
b
eB
iBb
Co
o
b
o
Co
boo
R
ZAA
ooequation t thisusecan or we
βRr
βRr
I
IA
,βr10R and 10R r if
βrRRr
βRr
I
IA
βrR
R
Rr
βr
I
I
I
I
I
IA
βrR
R
I
I and
βrR
IRI
Rr
βr
I
I and
Rr
βIrI
circuitsoutput andinput the toruledivider -current
theapplyingby determined isgain current The
Common-Emitter (CE) Fixed-Bias Configuration
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Phase Relationship
The phase relationship between input and output is 180 degrees. The negative sign used in the voltage gain formulas indicates the inversion.
Common-Emitter (CE) Fixed-Bias Configuration
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2/5 CE – Voltage-Divider Bias Configuration
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re Model
You still need to determine , re, and ro.
CE – Voltage-Divider Bias Configuration
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Impedance Calculations
Input Impedance: Output Impedance:
21
2121
RR
RRR||RR
er||RZi
oC r||RZo
C C 10RroRZo
CE – Voltage-Divider Bias Configuration
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Gain Calculations
Voltage Gain (Av):
Current Gain (Ai):
Current Gain from Voltage Gain:
e
oC
i
ov r
r||R
V
VA
Coe
C
i
ov 10Rrr
R
V
VA
)rR)(R(r
rR
I
IA
eCo
o
i
oi
Coei
oi 10RrrR
Rβ
I
IA
eCoi
oi r10R ,10RrI
IA
C
ivi R
ZAA
CE – Voltage-Divider Bias Configuration
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Voltage Gain
e
C vCo
e
oC v
oCe
io
e
ib
oCbO
r
RA 10Ror r if
r
)r ||(RA
)r ||(Rβr
VβV
βr
VI
)r ||)(RI (βV
CE – Voltage-Divider Bias Configuration
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Current gain
e
eo
o
i
oi
Co
eCo
o
i
oi
B21
βrR'
βR'
βrR'r
rβR'
I
IA
,R10rfor
βrR'Rr
rβR'
I
IA
RR||RR'
format. same thehave
gain willcurrent for theequation the,R' the
for except ion,configurat bias-fixedemitter -
common that similar to so isnetwork thesince
CE – Voltage-Divider Bias Configuration
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C
iVi
i
oi
i
oi
e
R
ZAA
optionan as
I
IA
R'
βR'
I
IA
,r10R' if And
CE – Voltage-Divider Bias Configuration
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Phase Relationship
A CE amplifier configuration will always have a phase relationship between input and output is 180 degrees. This is independent of the DC bias.
CE – Voltage-Divider Bias Configuration
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3/5. CE Emitter-Bias Configuration
Unbypassed RE
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re Model
Again you need to determine , re.
CE Emitter-Bias Configuration
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Impedance Calculations
Input Impedance: Output Impedance:
Eeb 1)R(rZ
)R(rZ Eeb
eE Eb rRRZ
bBi Z||RZ Co RZ
CE Emitter-Bias Configuration
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Defining the input impedance of a transistor with an unbypassed emitter resistor
Eb
eE
Eeb
Eeb
ib
Ebebi
Eeebi
βRZ
toreduced becan aboveeqn ,ran greater thmuch is R since
βRβrZ
1,an greater thnormally is β since
R)1β(βrI
VZ
RI)1β(βrIV
RIβrIV
:sideinput the toKVL Applying
CE Emitter-Bias Configuration
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Voltage Gain (Av):
Current Gain (Ai):
Current Gain from Voltage Gain:
Gain Calculations
b
C
i
ov Z
R
V
VA
)R(rZRr
R
V
VA
EebEe
C
i
ov
EbE
C
i
ov RZR
R
V
VA
bB
B
i
oi ZR
R
I
IA
C
ivi R
ZAA
or
CE Emitter-Bias Configuration
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Voltage Gain
E
C
i
oV
Eb
Ee
C
i
oV
Eeb
b
C
i
oV
Cb
i
CbCoo
b
ib
R
R
V
VA
βRion Zapproximat for the and
Rr
R
V
VA
gives )Rβ(r Zngsubstituti
Z
βR
V
VA
RZ
Vβ
RβIRIV
Z
VI
CE Emitter-Bias Configuration
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Current Gain
CR
ZAA
ZR
R
I
I
I
I
I
IA
I
I
II
ZR
R
I
I
ZR
IRI
:inresult llcircuit wiinput the toruledivider -current theApplying .II
ion approximat permit the to Z toclose often too is R of magnitude The
ivi
bB
B
i
b
b
o
i
oi
b
o
bo
bB
B
i
b
bB
iBb
ib
bB
CE Emitter-Bias Configuration
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Phase RelationshipA CE amplifier configuration will always have a phase relationship between input and output is 180 degrees. This is independent of the DC bias.
CE Emitter-Bias Configuration
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Bypassed RE
This is the same circuit as the CE fixed-bias configuration and therefore can be solved using the same re model.
4/5. CE Emitter-Bias Configuration
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Emitter-Follower Configuration
You may recognize this as the Common-Collector configuration. Indeed they are the same circuit. Note the input is on the base and the output is from the emitter.
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re Model
You still need to determine and re.
Emitter-Follower Configuration
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Impedance Calculations
Input Impedance:
bBi Z||RZ
Eeb 1)R(rZ
)R(rZ Eeb
Eb RZ
Emitter-Follower Configuration
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Calculation for the current Ie
Ee
ie
eee
Ee
i
Ee
ie
b
b
ibe
b
ib
Rr
VI
rβ
βr1)β(
βr and
β1)β(but R1)β(
βrV
1)Rβ(βr
1)Vβ(I
gives for Z gsubtitutin
Z
V1)β(1)Iβ(I
Z
VI
Emitter-Follower Configuration
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Impedance Calculations (cont’d)Output Impedance:
eEo r||RZ eE
eo rRrZ
Ee
ie Rr
VI
ionconfiguratfollower emitter for the impedenceoutput theDefining
Emitter-Follower Configuration
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Gain CalculationsVoltage Gain (Av):
Current Gain (Ai):
Current Gain from Voltage Gain:
eE
E
i
ov rR
R
V
VA
EeEeEi
ov RrR ,rR 1
V
VA
bB
Bi ZR
RA
E
ivi R
ZAA
Emitter-Follower Configuration
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Voltage gain
1V
VA
RrR
,ran greater thmuch usually R
rR
R
V
VA
rR
VRV
i
ov
EeE
eE
eE
E
i
ov
eE
iEo
Emitter-Follower Configuration
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Current Gain
E
ivi
bB
Bi
bB
B
i
b
b
o
i
oi
b
o
beo
bB
B
i
b
bB
iBb
R
ZAAor
ZR
RA
,)1( since
ZR
R)1(
I
I
I
I
I
IA
)1(I
I
I)1(II
ZR
R
I
I
ZR
IRI
Emitter-Follower Configuration
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Phase RelationshipA CC amplifier or Emitter Follower configuration has no phase shift between input and output.
Vo
Emitter-Follower Configuration
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5/5. Common-Base (CB) Configuration
The input (Vi) is applied to the emitter and the output (Vo) is from the collector.
The Common-Base is characterized as having low input impedance and high output impedance with a current gain less than 1 and a very high voltage gain.
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re Model
You will need to determine and re.
Common-Base (CB) Configuration
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Impedance Calculations
Input Impedance: Output Impedance:
eEi r||RZ Co RZ
Common-Base (CB) Configuration
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Gain Calculations
Voltage Gain (Av):
Current Gain (Ai):
e
C
e
C
i
ov r
R
r
R
V
VA
1I
IA
i
oi
Common-Base (CB) Configuration
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Voltage & Current gain
e
C
e
C
i
oV
Ce
io
e
ie
Ce
CcCoo
r
R
r
Rα
V
VA
Rr
VαV
r
VI
RαI
)RI(RIV
1I
IA
III
II
i
oi
ieo
ie
Common-Base (CB) Configuration
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Phase Relationship
A CB amplifier configuration has no phase shift between input and output.
Vo
Common-Base (CB) Configuration