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BJT AC AnalysisBJT AC Analysis
Chapter 5
Boylestad
Electronic Devices and Circuit TheoryElectronic Devices and Circuit Theory
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
BJT Transistor Modeling
A model is an equivalent circuit that represents the AC characteristics of the transistor.
A model uses circuit elements that approximate the behavior of the transistor.
There are two models commonly used in small signal AC analysis of a transistor:
re model
Hybrid equivalent model
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
The re Transistor Model
BJTs are basically current-controlled devices; therefore the re model uses a diode and a current source to duplicate the behavior of the transistor.
One disadvantage to this model is its sensitivity to the DC level. This model is designed for specific circuit conditions.
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Common-Base Configuration
ee I
mV26 r
ei rZ
oZ
e
L
e
LV r
R
r
RA
1iA
Input impedance:
Output impedance:
Voltage gain:
Current gain:
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Common-Emitter Configuration
bbe II I 1
ee I
mV26 r
The diode re model can be replaced by the resistor re.
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Common-Emitter Configuration
ei rZ
oo rZ
e
LV r
RA
oriA
Input impedance:
Output impedance:
Voltage gain:
Current gain:
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Common-Collector Configuration
ei rZ )1(
Eeo RrZ ||
eE
EV rR
RA
1βAi
Input impedance:
Output impedance:
Voltage gain:
Current gain:
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
The Hybrid Equivalent Model
Hybrid parameters are developed and used for modeling the transistor. These parameters can be found on a transistor’s specification sheet:
hi = input resistancehr = reverse transfer voltage ratio (Vi/Vo) 0 hf = forward transfer current ratio (Io/Ii)ho = output conductance
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Simplified General h-Parameter Model
hi = input resistancehf = forward transfer current ratio (Io/Ii)
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
re vs. h-Parameter Model
acfe
eie
βh
βrh
Common-Emitter
Common-Base
1
αh
rh
fb
eib
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
The Hybrid Model
The hybrid pi model is most useful for analysis of high-frequency transistor applications.
At lower frequencies the hybrid pi model closely approximate the re parameters, and can be replaced by them.
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Common-Emitter Fixed-Bias Configuration
The input is applied to the baseThe output is taken from the collector
High input impedanceLow output impedance
High voltage and current gain
Phase shift between input and output is 180
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Common-Emitter Fixed-Bias Configuration
AC equivalent
re,model
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Common-Emitter Fixed-Bias Calculations
Co Rre
Cv
e
oC
i
ov
r
RA
r
)||r(R
V
VA
10
eBCo βr, RRri
eBCo
oB
i
oi
βA
)βr)(RR(r
rβR
I
IA
1010
C
iVi R
ZAA Current gain
from voltage gain:
Input
impedance:
Output
impedance:
Voltage gain:
Current gain:
eE βrRei
eBi
βrZ
||β|RZ
10
Co
O
RrCo
Co
RZ
||rRZ
10
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Common-Emitter Voltage-Divider Bias
re model requires you to determine , re, and ro.
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Common-Emitter Voltage-Divider Bias Calculations
Input impedance
ei
21
βr||RZ
R||RR
Output impedance
Co 10RrCo
oCo
RZ
r||RZ
Voltage gain
Co 10Rre
C
i
ov
e
oC
i
ov
r
R
V
VA
r
r||R
V
VA
Current gain
eCo
Co
r10R ,10Rri
oi
10Rrei
oi
eCo
o
i
oi
I
IA
rR
R
I
IA
)rR)(R(r
rR
I
IA
Current gain from Av
C
ivi R
ZAA
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Common-Emitter Emitter-Bias Configuration
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Impedance Calculations
Eb
Eeb
Eeb
bBi
RZ
)R(rZ
1)R(rZ
Z||RZ
Input impedance:
Output impedance:
Co RZ
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Gain Calculations
Current gain from Av:
Voltage gain:
Current gain:
Eb
Eeb
RZE
C
i
ov
)R(rZEe
C
i
ov
b
C
i
ov
R
R
V
VA
Rr
R
V
VA
Z
R
V
VA
bB
B
i
oi ZR
R
I
IA
C
ivi R
ZAA
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Emitter-Follower Configuration
This is also known as the common-collector configuration.The input is applied to the base and the output is taken from the emitter.There is no phase shift between input and output.
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Impedance Calculations
Input impedance:
Output impedance:eE rReo
eEo
rZ
||rRZ
Eb
Eeb
Eeb
b Bi
βRZ
)Rβ(rZ
)R(ββrZ
||ZRZ
1
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Gain Calculations
Current gain from voltage gain:
Voltage gain:
Current gain:
EeEeE Rr, RrRi
ov
eE
E
i
ov
V
VA
rR
R
V
VA
1
bB
Bi ZR
βRA
E
ivi R
ZAA
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Common-Base ConfigurationThe input is applied to the emitter
The output is taken from the collector
Low input impedance.High output impedance
Current gain less than unity
Very high voltage gain
No phase shift between input and output
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Calculations
eEi r||RZ
Co RZ
e
C
e
C
i
ov r
R
r
R
V
VA
1I
IA
i
oi
Input impedance:
Output impedance:
Voltage gain:
Current gain:
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Common-Emitter Collector Feedback Configuration
• A variation of the common-emitter fixed-bias configuration• Input is applied to the base• Output is taken from the collector• There is a 180 phase shift between the input and output
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Calculations
F
C
ei
RR
β
rZ
1
FCo R||RZ
e
C
i
ov r
R
V
VA
C
F
i
oi
CF
F
i
oi
R
R
I
IA
βRR
βR
I
IA
Input impedance:
Output impedance:
Voltage gain:
Current gain:
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Collector DC FeedbackConfiguration
• The input is applied to the base
• The output is taken from the collector
• There is a 180 phase shift between input and output
This is a variation of the common-emitter, fixed-bias configuration
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Calculations
F
C
ei
RR
β
rZ
1
FCo ||RRZ
e
C
i
ov r
R
V
VA
C
F
i
oi
CF
F
i
oi
R
R
I
IA
RR
R
I
IA
Input impedance:
Output impedance:
Voltage gain:
Current gain:
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Two-Port Systems Approach
ooTh RZZ
With Vi set to 0 V:
The voltage across the open terminals is:
where AvNL is the no-load voltage gain
ivNLTh VAE
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Effect of Load Impedance on Gain
L
ivi R
ZAA
This model can be applied to any current- or voltage-controlled amplifier.
Adding a load reduces the gain of the amplifier:
vNLoL
L
i
ov A
RR
R
V
VA
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Effect of Source Impedance on Gain
The amplitude of the applied signal that reaches the input of the amplifier is:
si
sii RR
VRV
vNLsi
i
s
ovs A
RR
R
V
VA
The internal resistance of the signal source reduces the overall gain:
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Combined Effects of RS and RL on Voltage Gain
Effects of RL:
Effects of RL and RS:
L
ivi
oL
vNLL
i
ov
R
RAA
RR
AR
V
VA
L
isvsis
vNLoL
L
si
i
s
ovs
R
RRAA
ARR
R
RR
R
V
VA
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Cascaded Systems
• The output of one amplifier is the input to the next amplifier
• The overall voltage gain is determined by the product of gains of the individual stages
• The DC bias circuits are isolated from each other by the coupling capacitors
• The DC calculations are independent of the cascading
• The AC calculations for gain and impedance are interdependent
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
R-C Coupled BJT Amplifiers
Co RZ
Input impedance, first stage:
Output impedance, second stage:
Voltage gain:
ei RRRZ |||| 21
21
2
211
||||||
vvv
e
Cv
e
eCv
AAA
r
RA
r
RRRRA
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Cascode Connection
This example is a CE–CB combination. This arrangement provides high input impedance but a low voltage gain.
The low voltage gain of the input stage reduces the Miller input capacitance, making this combination suitable for high-frequency applications.
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Darlington Connection
The Darlington circuit provides very high current gain, equal to the product of the individual current gains:
D = 1 2
The practical significance is that the circuit provides a very high input impedance.
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
DC Bias of Darlington Circuits
BDBDE III )1(
EEE RIV
EDB
BECCB RR
VVI
Base current:
Emitter current:
Emitter voltage:
Base voltage:
BEEB VVV
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Feedback Pair
This is a two-transistor circuit that operates like a Darlington pair, but it is not a Darlington pair.
It has similar characteristics: • High current gain• Voltage gain near unity• Low output impedance• High input impedance
The difference is that a Darlington uses a pair of like transistors, whereas the feedback-pair configuration uses complementary transistors.
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Current Mirror Circuits
Current mirror circuits provide constant current in integrated circuits.
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Current Source Circuits
Constant-current sources can be built using FETs, BJTs, and combinations of these devices.
IE ICE
BEZE R
VVII
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Current Source Circuits
VGS = 0VID = IDSS = 10 mA
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Fixed-Bias
ieBi hRZ ||
oeCo hRZ /1||
ie
oCfe
i
ov h
ehRh
V
VA
/1||
fei
oi h
I
IA
Input impedance:
Output impedance:
Voltage gain:
Current gain:
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Voltage-Divider Configuration
ie
fei hR
RhA
iei h||RZ
Co RZ
ie
oeCfev h
1/h||RhA
Input impedance:
Output impedance:
Voltage gaingain:
Current gain:
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Emitter-Follower Configuration
boi
Efeb
Z||RZ
RhZ
boi
Efeb
ZRZ
RhZ
||
Input impedance:
Output impedance:
Voltage gain:
Current gain:
fe
ieEo h
hRZ ||
feieE
E
i
ov hhR
R
V
VA
/
E
ivi
bB
Bfei
R
ZAA
ZR
RhA
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Common-Base Configuration
ibEi h||RZ
Co RZ
ib
Cfb
i
ov h
Rh
V
VA
1hI
IA fb
i
oi
Input impedance:
Output impedance:
Voltage gain:
Current gain:
Electronic Devices and Circuit TheoryBoylestad
© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Ch.5 Summary
Troubleshooting
Check the DC bias voltages
If not correct, check power supply, resistors, transistor. Also check the coupling capacitor between amplifier stages.
Check the AC voltages
If not correct check transistor, capacitors and the loading effect of the next stage.