6. bjt small signal
TRANSCRIPT
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BJT Small-Signal Analysis
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Contents
Common-Emitter fixed-bias configuration Voltage divider bias CE Emitter bias Emitter-follower configuration Common-base configuration Collector-feedback configuration Hybrid equivalent circuit and model
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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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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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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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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.
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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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
![Page 45: 6. BJT Small Signal](https://reader033.vdocuments.mx/reader033/viewer/2022061108/54500af4b1af9f19098b495d/html5/thumbnails/45.jpg)
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
![Page 46: 6. BJT Small Signal](https://reader033.vdocuments.mx/reader033/viewer/2022061108/54500af4b1af9f19098b495d/html5/thumbnails/46.jpg)
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
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Collector DC Feedback Configuration
The network has a dc feedback resistor for increased stability, yet the capacitor C3 willshift portions of the feedback resistance to the input and output sections of the networkin the ac domain. The portion of RF shifted to the input or output side will be determinedby the desired ac input and output resistance levels.
![Page 49: 6. BJT Small Signal](https://reader033.vdocuments.mx/reader033/viewer/2022061108/54500af4b1af9f19098b495d/html5/thumbnails/49.jpg)
Substituting the re equivalent circuit into the ac equivalent network
eβr||RZ F1i oF2Co r||R||RZ
2|| FCo RRZ
Collector DC Feedback Configuration
Impedance Calculations
Input Impedance: Output Impedance:
![Page 50: 6. BJT Small Signal](https://reader033.vdocuments.mx/reader033/viewer/2022061108/54500af4b1af9f19098b495d/html5/thumbnails/50.jpg)
Voltage Gain
e
CF2
i
ov
Co
e
CF2o
i
ov
e
io
e
ib
bo
CF2o
r
R||R
V
VA
,10Rrfor
r
R||R||r
V
VA
R'βr
VβV
βr
VI
R'βIV
R||R||rR'
Collector DC Feedback Configuration
![Page 51: 6. BJT Small Signal](https://reader033.vdocuments.mx/reader033/viewer/2022061108/54500af4b1af9f19098b495d/html5/thumbnails/51.jpg)
Current Gain
C
iV
i
oi
F2o
Ci
oi
CF2oF1
F2oF1
i
oi
F1eF1eF1
eF1C
F1
i
oi
eF
F1
Ci
b
b
o
i
oi
Cb
o
C
bo
F2o
eF
F
i
b
eF
iFb
R
ZA
I
IA or
R||rR
1
β
I
IA
RR||rR
)R||(rβR
I
IA
RβrR,βrn larger thamuch usually is R since
βrRRR'
βRR'
I
IA
βrR
R.
RR'
βR'
I
I.
I
I
I
IA
,gain current the
RR'
βR'
I
Ior
RR'
βIR'I
R||rR' using sideoutput for the and
βrR
R
I
Ior
βrR
IRI
sideinput For the
Collector DC Feedback Configuration
![Page 52: 6. BJT Small Signal](https://reader033.vdocuments.mx/reader033/viewer/2022061108/54500af4b1af9f19098b495d/html5/thumbnails/52.jpg)
Approximate Hybrid Equivalent Circuit
The h-parameters can be derived from the re model:
hie = re hib = rehfe = hfb = -hoe = 1/ro
The h-parameters are also found in the specification sheet for the transistor.
![Page 53: 6. BJT Small Signal](https://reader033.vdocuments.mx/reader033/viewer/2022061108/54500af4b1af9f19098b495d/html5/thumbnails/53.jpg)
Hybrid equivalent model re equivalent model
Approximate Common-Emitter Equivalent Circuit
![Page 54: 6. BJT Small Signal](https://reader033.vdocuments.mx/reader033/viewer/2022061108/54500af4b1af9f19098b495d/html5/thumbnails/54.jpg)
Hybrid equivalent model re equivalent model
Approximate Common-Base Equivalent Circuit
![Page 55: 6. BJT Small Signal](https://reader033.vdocuments.mx/reader033/viewer/2022061108/54500af4b1af9f19098b495d/html5/thumbnails/55.jpg)
Troubleshooting
1. Check the DC bias voltages – if not correct check power supply, resistors, transistor. Also check to ensure that the coupling capacitor between amplifier stages is OK.
2. Check the AC voltages – if not correct check transistor, capacitors and the loading effect of the next stage.
![Page 56: 6. BJT Small Signal](https://reader033.vdocuments.mx/reader033/viewer/2022061108/54500af4b1af9f19098b495d/html5/thumbnails/56.jpg)
Practical Applications
• Audio Mixer
• Preamplifier
• Random-Noise Generator
• Sound Modulated Light Source
![Page 57: 6. BJT Small Signal](https://reader033.vdocuments.mx/reader033/viewer/2022061108/54500af4b1af9f19098b495d/html5/thumbnails/57.jpg)
Assignment #1
1. Derive the formulas for Zi, Zo, AV and Ai in a CE Emitter-Bias Configuration with unbypassed RE and Emitter Follower Configulation with the effect of ro. Show your equivalent circuit and complete derivations. You can use approximations to simply your answers.
2. Derive and solve for the value of Zi, Zo, AV and Ai.
![Page 58: 6. BJT Small Signal](https://reader033.vdocuments.mx/reader033/viewer/2022061108/54500af4b1af9f19098b495d/html5/thumbnails/58.jpg)
3. Determine Zi, Zo, AV and Ai.