5_bjt small signal
TRANSCRIPT
Sem I 0809/rosdiyana
Chapter 5:BJT Small-Signal Analysis
Contents
1. Common-Emitter fixed-bias configuration2. Voltage divider bias3. CE Emitter bias4. Emitter-follower configuration5. Common-base configuration
• 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
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
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.
Removing DC effects of VCC and Capacitors
Common-Emitter (CE) Fixed-Bias Configuration
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
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
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
Voltage Gain
e
CvCo
e
oC
eb
oCbv
eb i
oCbO
i
Ov
r
RA 10Ror r if
r
)r||(R
βrI
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βrIV
)r||(RβIV
V
VA
Common-Emitter (CE) Fixed-Bias Configuration
Current gain
C
ivi
Bo
Bo
i
oi
eBCo
eBCo
Bo
i
oi
eB
B
Co
o
i
b
b
o
i
oi
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B
i
b
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iBb
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o
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o
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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
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
2/5 CE – Voltage-Divider Bias Configuration
re Model
You still need to determine , re, and ro.
CE – Voltage-Divider Bias Configuration
Impedance Calculations
Input Impedance: Output Impedance:
21
2121
RR
RRR||RR
er||RZi
oC r||RZo
C C 10RroRZo
CE – Voltage-Divider Bias Configuration
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
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
Current gain
e
eo
o
i
oi
Co
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oi
B21
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βR'
βrR'r
rβR'
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RR||RR'
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for except ion,configurat bias-fixedemitter -
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CE – Voltage-Divider Bias Configuration
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iVi
i
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i
oi
e
R
ZAA
optionan as
I
IA
R'
βR'
I
IA
,r10R' if And
CE – Voltage-Divider Bias Configuration
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
3/5. CE Emitter-Bias Configuration
Unbypassed RE
re Model
Again you need to determine , re.
CE Emitter-Bias Configuration
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
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
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
Voltage Gain
E
C
i
oV
Eb
Ee
C
i
oV
Eeb
b
C
i
oV
Cb
i
CbCoo
b
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R
V
VA
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R
V
VA
gives )Rβ(r Zngsubstituti
Z
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V
VA
RZ
Vβ
RβIRIV
Z
VI
CE Emitter-Bias Configuration
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
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
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
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.
re Model
You still need to determine and re.
Emitter-Follower Configuration
Impedance Calculations
Input Impedance:
bBi Z||RZ
Eeb 1)R(rZ
)R(rZ Eeb
Eb RZ
Emitter-Follower Configuration
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
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
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
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
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
Phase RelationshipA CC amplifier or Emitter Follower configuration has no phase shift between input and output.
Vo
Emitter-Follower Configuration
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.
re Model
You will need to determine and re.
Common-Base (CB) Configuration
Impedance Calculations
Input Impedance: Output Impedance:
eEi r||RZ Co RZ
Common-Base (CB) Configuration
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
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
Phase Relationship
A CB amplifier configuration has no phase shift between input and output.
Vo
Common-Base (CB) Configuration