13 ae bjt-ii amplifiers
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Analogue ElectronicsPaolo Colantonio
AA 2015-16
Universitagrave degli Studi di Roma Tor VergataDipartimento di Ingegneria Elettronica
P Colantonio ndash Analogue Electronics 2|26AA 201516
Bias issuesbull The DC bias point is affected by thermal issue due to the active device parameter
variations with temperature
bull Both ICO and VBE vary with the temperature thus resulting in a variation of IC
P Colantonio ndash Analogue Electronics 3|26AA 201516
Bias issues
bull To reduce thermal issue a feedback solution could be adopted
R1
R2
RC
RE
VCC
vi
IC
IE
IBCB1
+
-
bull If the bias current IC is increasing then the voltage drop across RE is increasing alsobull Consequently the base‐emitter voltage VBE is decreasingbull Accounting for the device input characteristics the base current IB will be reducedbull Thus the device output current (IC=HFEIB) will be reducedbull However as we will see later the resistor RE will reduce the AC gain therefore
typically it is short circuited by a parallel capacitance
P Colantonio ndash Analogue Electronics 4|26AA 201516
Thermal compensation techniquesbull By adding in the circuit some element that is bias dependent thus able to reproduce
the same variation of VBE IC0 (and b) it is possible to compensate the IC variation
R1
RC
V CC
I C
IE
I B
+
-
I0 VBE
Compensation of IC0 bull I0 is the diode reverse saturated current
bull Assuming
VCCgtgtVBEgtgt1
P Colantonio ndash Analogue Electronics 5|26AA 201516
Thermal compensation techniquesbull In the integrated implementation since the resistor RE requires a by‐pass capacitance to
allow higher gain and this capacitance could be very high a different approach is adopted
Compensation in integrated circuits bull The transistor Q1 resembles a diode being VCE1=VBE1
bull Its collector current IC1 is given by
R1
RC
V CC
IC2
IB2IB1
I
Q1
VBE1
Q2IC1
vi
vo
VBE2
bull Assuming VCCgtgtVBE1 and (IB1+IB2)ltltIC1
bull If the two transistors are similar accountingfor VBE1=VBE2 and R1=RC then the bias currentIC2 is constant
P Colantonio ndash Analogue Electronics 6|26AA 201516
Thermal compensation techniquesCompensation in integrated circuits bull The addiction of the two resistors R2 e R3 improves the circuit behaviorbull In this case in fact are the biasing currents IB1 and IB2 instead of VBE1 and VBE2 to control
the DC behavior of Q1 and Q2
R1
RC
V CC
IC2
IBIB
I
Q1
VBE1
Q2IC1
vo
VBE2
vi
R3
R2=R3
bull If R2=R3 then
bull By a suitable selection of parameter andaccounting that Q1=Q2 it is possible to obtain
bull Moreover selecting RC=12R1 then
P Colantonio ndash Analogue Electronics 7|26AA 201516
BJT equivalent AC modelbull Assuming a generic two port a representation is made by assuming some electrical
quantities as independent variables while the remaining ones are dependent
v2
i2Rg i1
v1vg
bull In particular starting from the set of equation
bull By a series expansion around the quiescent bias point (ie Taylor or McLaurin )
P Colantonio ndash Analogue Electronics 8|26AA 201516
BJT equivalent AC modelbull If a first order approximation is considered
bull Defining
bull An hybrid representation can be obtained
P Colantonio ndash Analogue Electronics 9|26AA 201516
BJT equivalent AC model
v2
i2Rg i1
v1vg
bull In particular referring to the Common Emitter configuration
Input resistance with the output short circuited (ohms)
Voltage gain‐1 with the input open (dimensionless)
Forward current gain with the output short circuited (dimensionless)
Output conductance with the input open (ohms‐1)
P Colantonio ndash Analogue Electronics 10|26AA 201516
The hybrid modelbull The previous equation can be represented by an equivalent circuit model (hybrid model)
P Colantonio ndash Analogue Electronics 11|26AA 201516
Physical meaning of model parameters
tIC
B
BVV
cos
tVB
B
CIV
cos
IB=200μA
160
120
80
40Col
lect
or c
urre
nt I C
mA
Collector-emitter voltage VCE V
10
20
30
40
0 2 4 86 10 12
tVB
C
CII
cos
tIC
C
BVI
cos
Cor
rent
e di
bas
e I B
mA
Base voltage VBE V
0804 060
04
02
06
Typical values
IBBV
CVC1V
C2V = C2V C1-V
hferarr n10 ndash n 100 hrerarr 10-3 ndash 10-4
hierarr 103 ndash 104 Ω hoerarr 10-5 ndash 10-4
P Colantonio ndash Analogue Electronics 12|26AA 201516
Simplified modelbull Accounting for the h parameter values the model can be further simplified assuming
bull Thus obtaining the following model (similar to FET)
bull Accounting for the ldquodioderdquo behavior of the base‐emitter junction it is possible to define
P Colantonio ndash Analogue Electronics 13|26AA 201516
Amplifier configurationbull The basic amplifier configuration are named according to the BJT pin that is common to
both input and output networks
VCC
+ vce
+
-
vs
VBB
iB
RS B
vBE
RLC
E
iC
Common Emitter (CE)
vs
+ iB
RS B
vBE
VCC
RL
C
E
iC
Ri
Vo
Ro
C
Common Collector (CC)
vCB=vo
vs
RS E
vi=vBE
RL
C iC
BVCC
+
Common Base (CB)
P Colantonio ndash Analogue Electronics 14|26AA 201516
Analysis Approachesbull For each configuration the equivalent hybrid model can be used by assuming for the [h]
parameters the corresponding values ie the second letter of the subscript represent thedevice configuration
Common Emitter (CE)bull hie hfe hre hoe
Rs
vs +RL
E
CB
[hje]
Common Collector (CC)bull hic hfc hrc hoc
Rs
vs +RL
E
C
B
[hjc]
Common Base (CB)bull hib hfb hrb hob
Rs
vs +RL
E C
B
[hjb]bull With this appraoch the [h] parameters
assume different values but theamplifier relationships (voltage gaininput and output resistance) have thesame ldquoformrdquo
P Colantonio ndash Analogue Electronics 15|26AA 201516
Analysis Approachesbull A different approach is based on the adoption of the same BJT equivalent model (ie CE
[h] parameters hxe)bull In this case the expressions are different
Common Emitter (CE) Common Collector (CC)
Common Base (CB)
Rs
vs +RL
E
CBRs
vs +RL
E
CB
Rs
vs +RL
E
CB
P Colantonio ndash Analogue Electronics 16|26AA 201516
Analysis ApproachesRs
vsZL
1
1
2
2
V1 V2
Y0Zi
Two-portactive
network(transistor)
I1 I2IL
Rs
vsZL
1
1
2
2
V1 V2
Y0Zi
I1 I2IL
hohfI1+
hrV2
hi
Approximate conversion formulas for hybrid parameters
1rchieic hh
fefc hh 1 oeoc hh
fe
ieib h
hh
1
fe
oeob h
hh
1 fe
fefb h
hh
1
refe
oeierb h
hhhh
1
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 2|26AA 201516
Bias issuesbull The DC bias point is affected by thermal issue due to the active device parameter
variations with temperature
bull Both ICO and VBE vary with the temperature thus resulting in a variation of IC
P Colantonio ndash Analogue Electronics 3|26AA 201516
Bias issues
bull To reduce thermal issue a feedback solution could be adopted
R1
R2
RC
RE
VCC
vi
IC
IE
IBCB1
+
-
bull If the bias current IC is increasing then the voltage drop across RE is increasing alsobull Consequently the base‐emitter voltage VBE is decreasingbull Accounting for the device input characteristics the base current IB will be reducedbull Thus the device output current (IC=HFEIB) will be reducedbull However as we will see later the resistor RE will reduce the AC gain therefore
typically it is short circuited by a parallel capacitance
P Colantonio ndash Analogue Electronics 4|26AA 201516
Thermal compensation techniquesbull By adding in the circuit some element that is bias dependent thus able to reproduce
the same variation of VBE IC0 (and b) it is possible to compensate the IC variation
R1
RC
V CC
I C
IE
I B
+
-
I0 VBE
Compensation of IC0 bull I0 is the diode reverse saturated current
bull Assuming
VCCgtgtVBEgtgt1
P Colantonio ndash Analogue Electronics 5|26AA 201516
Thermal compensation techniquesbull In the integrated implementation since the resistor RE requires a by‐pass capacitance to
allow higher gain and this capacitance could be very high a different approach is adopted
Compensation in integrated circuits bull The transistor Q1 resembles a diode being VCE1=VBE1
bull Its collector current IC1 is given by
R1
RC
V CC
IC2
IB2IB1
I
Q1
VBE1
Q2IC1
vi
vo
VBE2
bull Assuming VCCgtgtVBE1 and (IB1+IB2)ltltIC1
bull If the two transistors are similar accountingfor VBE1=VBE2 and R1=RC then the bias currentIC2 is constant
P Colantonio ndash Analogue Electronics 6|26AA 201516
Thermal compensation techniquesCompensation in integrated circuits bull The addiction of the two resistors R2 e R3 improves the circuit behaviorbull In this case in fact are the biasing currents IB1 and IB2 instead of VBE1 and VBE2 to control
the DC behavior of Q1 and Q2
R1
RC
V CC
IC2
IBIB
I
Q1
VBE1
Q2IC1
vo
VBE2
vi
R3
R2=R3
bull If R2=R3 then
bull By a suitable selection of parameter andaccounting that Q1=Q2 it is possible to obtain
bull Moreover selecting RC=12R1 then
P Colantonio ndash Analogue Electronics 7|26AA 201516
BJT equivalent AC modelbull Assuming a generic two port a representation is made by assuming some electrical
quantities as independent variables while the remaining ones are dependent
v2
i2Rg i1
v1vg
bull In particular starting from the set of equation
bull By a series expansion around the quiescent bias point (ie Taylor or McLaurin )
P Colantonio ndash Analogue Electronics 8|26AA 201516
BJT equivalent AC modelbull If a first order approximation is considered
bull Defining
bull An hybrid representation can be obtained
P Colantonio ndash Analogue Electronics 9|26AA 201516
BJT equivalent AC model
v2
i2Rg i1
v1vg
bull In particular referring to the Common Emitter configuration
Input resistance with the output short circuited (ohms)
Voltage gain‐1 with the input open (dimensionless)
Forward current gain with the output short circuited (dimensionless)
Output conductance with the input open (ohms‐1)
P Colantonio ndash Analogue Electronics 10|26AA 201516
The hybrid modelbull The previous equation can be represented by an equivalent circuit model (hybrid model)
P Colantonio ndash Analogue Electronics 11|26AA 201516
Physical meaning of model parameters
tIC
B
BVV
cos
tVB
B
CIV
cos
IB=200μA
160
120
80
40Col
lect
or c
urre
nt I C
mA
Collector-emitter voltage VCE V
10
20
30
40
0 2 4 86 10 12
tVB
C
CII
cos
tIC
C
BVI
cos
Cor
rent
e di
bas
e I B
mA
Base voltage VBE V
0804 060
04
02
06
Typical values
IBBV
CVC1V
C2V = C2V C1-V
hferarr n10 ndash n 100 hrerarr 10-3 ndash 10-4
hierarr 103 ndash 104 Ω hoerarr 10-5 ndash 10-4
P Colantonio ndash Analogue Electronics 12|26AA 201516
Simplified modelbull Accounting for the h parameter values the model can be further simplified assuming
bull Thus obtaining the following model (similar to FET)
bull Accounting for the ldquodioderdquo behavior of the base‐emitter junction it is possible to define
P Colantonio ndash Analogue Electronics 13|26AA 201516
Amplifier configurationbull The basic amplifier configuration are named according to the BJT pin that is common to
both input and output networks
VCC
+ vce
+
-
vs
VBB
iB
RS B
vBE
RLC
E
iC
Common Emitter (CE)
vs
+ iB
RS B
vBE
VCC
RL
C
E
iC
Ri
Vo
Ro
C
Common Collector (CC)
vCB=vo
vs
RS E
vi=vBE
RL
C iC
BVCC
+
Common Base (CB)
P Colantonio ndash Analogue Electronics 14|26AA 201516
Analysis Approachesbull For each configuration the equivalent hybrid model can be used by assuming for the [h]
parameters the corresponding values ie the second letter of the subscript represent thedevice configuration
Common Emitter (CE)bull hie hfe hre hoe
Rs
vs +RL
E
CB
[hje]
Common Collector (CC)bull hic hfc hrc hoc
Rs
vs +RL
E
C
B
[hjc]
Common Base (CB)bull hib hfb hrb hob
Rs
vs +RL
E C
B
[hjb]bull With this appraoch the [h] parameters
assume different values but theamplifier relationships (voltage gaininput and output resistance) have thesame ldquoformrdquo
P Colantonio ndash Analogue Electronics 15|26AA 201516
Analysis Approachesbull A different approach is based on the adoption of the same BJT equivalent model (ie CE
[h] parameters hxe)bull In this case the expressions are different
Common Emitter (CE) Common Collector (CC)
Common Base (CB)
Rs
vs +RL
E
CBRs
vs +RL
E
CB
Rs
vs +RL
E
CB
P Colantonio ndash Analogue Electronics 16|26AA 201516
Analysis ApproachesRs
vsZL
1
1
2
2
V1 V2
Y0Zi
Two-portactive
network(transistor)
I1 I2IL
Rs
vsZL
1
1
2
2
V1 V2
Y0Zi
I1 I2IL
hohfI1+
hrV2
hi
Approximate conversion formulas for hybrid parameters
1rchieic hh
fefc hh 1 oeoc hh
fe
ieib h
hh
1
fe
oeob h
hh
1 fe
fefb h
hh
1
refe
oeierb h
hhhh
1
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 3|26AA 201516
Bias issues
bull To reduce thermal issue a feedback solution could be adopted
R1
R2
RC
RE
VCC
vi
IC
IE
IBCB1
+
-
bull If the bias current IC is increasing then the voltage drop across RE is increasing alsobull Consequently the base‐emitter voltage VBE is decreasingbull Accounting for the device input characteristics the base current IB will be reducedbull Thus the device output current (IC=HFEIB) will be reducedbull However as we will see later the resistor RE will reduce the AC gain therefore
typically it is short circuited by a parallel capacitance
P Colantonio ndash Analogue Electronics 4|26AA 201516
Thermal compensation techniquesbull By adding in the circuit some element that is bias dependent thus able to reproduce
the same variation of VBE IC0 (and b) it is possible to compensate the IC variation
R1
RC
V CC
I C
IE
I B
+
-
I0 VBE
Compensation of IC0 bull I0 is the diode reverse saturated current
bull Assuming
VCCgtgtVBEgtgt1
P Colantonio ndash Analogue Electronics 5|26AA 201516
Thermal compensation techniquesbull In the integrated implementation since the resistor RE requires a by‐pass capacitance to
allow higher gain and this capacitance could be very high a different approach is adopted
Compensation in integrated circuits bull The transistor Q1 resembles a diode being VCE1=VBE1
bull Its collector current IC1 is given by
R1
RC
V CC
IC2
IB2IB1
I
Q1
VBE1
Q2IC1
vi
vo
VBE2
bull Assuming VCCgtgtVBE1 and (IB1+IB2)ltltIC1
bull If the two transistors are similar accountingfor VBE1=VBE2 and R1=RC then the bias currentIC2 is constant
P Colantonio ndash Analogue Electronics 6|26AA 201516
Thermal compensation techniquesCompensation in integrated circuits bull The addiction of the two resistors R2 e R3 improves the circuit behaviorbull In this case in fact are the biasing currents IB1 and IB2 instead of VBE1 and VBE2 to control
the DC behavior of Q1 and Q2
R1
RC
V CC
IC2
IBIB
I
Q1
VBE1
Q2IC1
vo
VBE2
vi
R3
R2=R3
bull If R2=R3 then
bull By a suitable selection of parameter andaccounting that Q1=Q2 it is possible to obtain
bull Moreover selecting RC=12R1 then
P Colantonio ndash Analogue Electronics 7|26AA 201516
BJT equivalent AC modelbull Assuming a generic two port a representation is made by assuming some electrical
quantities as independent variables while the remaining ones are dependent
v2
i2Rg i1
v1vg
bull In particular starting from the set of equation
bull By a series expansion around the quiescent bias point (ie Taylor or McLaurin )
P Colantonio ndash Analogue Electronics 8|26AA 201516
BJT equivalent AC modelbull If a first order approximation is considered
bull Defining
bull An hybrid representation can be obtained
P Colantonio ndash Analogue Electronics 9|26AA 201516
BJT equivalent AC model
v2
i2Rg i1
v1vg
bull In particular referring to the Common Emitter configuration
Input resistance with the output short circuited (ohms)
Voltage gain‐1 with the input open (dimensionless)
Forward current gain with the output short circuited (dimensionless)
Output conductance with the input open (ohms‐1)
P Colantonio ndash Analogue Electronics 10|26AA 201516
The hybrid modelbull The previous equation can be represented by an equivalent circuit model (hybrid model)
P Colantonio ndash Analogue Electronics 11|26AA 201516
Physical meaning of model parameters
tIC
B
BVV
cos
tVB
B
CIV
cos
IB=200μA
160
120
80
40Col
lect
or c
urre
nt I C
mA
Collector-emitter voltage VCE V
10
20
30
40
0 2 4 86 10 12
tVB
C
CII
cos
tIC
C
BVI
cos
Cor
rent
e di
bas
e I B
mA
Base voltage VBE V
0804 060
04
02
06
Typical values
IBBV
CVC1V
C2V = C2V C1-V
hferarr n10 ndash n 100 hrerarr 10-3 ndash 10-4
hierarr 103 ndash 104 Ω hoerarr 10-5 ndash 10-4
P Colantonio ndash Analogue Electronics 12|26AA 201516
Simplified modelbull Accounting for the h parameter values the model can be further simplified assuming
bull Thus obtaining the following model (similar to FET)
bull Accounting for the ldquodioderdquo behavior of the base‐emitter junction it is possible to define
P Colantonio ndash Analogue Electronics 13|26AA 201516
Amplifier configurationbull The basic amplifier configuration are named according to the BJT pin that is common to
both input and output networks
VCC
+ vce
+
-
vs
VBB
iB
RS B
vBE
RLC
E
iC
Common Emitter (CE)
vs
+ iB
RS B
vBE
VCC
RL
C
E
iC
Ri
Vo
Ro
C
Common Collector (CC)
vCB=vo
vs
RS E
vi=vBE
RL
C iC
BVCC
+
Common Base (CB)
P Colantonio ndash Analogue Electronics 14|26AA 201516
Analysis Approachesbull For each configuration the equivalent hybrid model can be used by assuming for the [h]
parameters the corresponding values ie the second letter of the subscript represent thedevice configuration
Common Emitter (CE)bull hie hfe hre hoe
Rs
vs +RL
E
CB
[hje]
Common Collector (CC)bull hic hfc hrc hoc
Rs
vs +RL
E
C
B
[hjc]
Common Base (CB)bull hib hfb hrb hob
Rs
vs +RL
E C
B
[hjb]bull With this appraoch the [h] parameters
assume different values but theamplifier relationships (voltage gaininput and output resistance) have thesame ldquoformrdquo
P Colantonio ndash Analogue Electronics 15|26AA 201516
Analysis Approachesbull A different approach is based on the adoption of the same BJT equivalent model (ie CE
[h] parameters hxe)bull In this case the expressions are different
Common Emitter (CE) Common Collector (CC)
Common Base (CB)
Rs
vs +RL
E
CBRs
vs +RL
E
CB
Rs
vs +RL
E
CB
P Colantonio ndash Analogue Electronics 16|26AA 201516
Analysis ApproachesRs
vsZL
1
1
2
2
V1 V2
Y0Zi
Two-portactive
network(transistor)
I1 I2IL
Rs
vsZL
1
1
2
2
V1 V2
Y0Zi
I1 I2IL
hohfI1+
hrV2
hi
Approximate conversion formulas for hybrid parameters
1rchieic hh
fefc hh 1 oeoc hh
fe
ieib h
hh
1
fe
oeob h
hh
1 fe
fefb h
hh
1
refe
oeierb h
hhhh
1
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 4|26AA 201516
Thermal compensation techniquesbull By adding in the circuit some element that is bias dependent thus able to reproduce
the same variation of VBE IC0 (and b) it is possible to compensate the IC variation
R1
RC
V CC
I C
IE
I B
+
-
I0 VBE
Compensation of IC0 bull I0 is the diode reverse saturated current
bull Assuming
VCCgtgtVBEgtgt1
P Colantonio ndash Analogue Electronics 5|26AA 201516
Thermal compensation techniquesbull In the integrated implementation since the resistor RE requires a by‐pass capacitance to
allow higher gain and this capacitance could be very high a different approach is adopted
Compensation in integrated circuits bull The transistor Q1 resembles a diode being VCE1=VBE1
bull Its collector current IC1 is given by
R1
RC
V CC
IC2
IB2IB1
I
Q1
VBE1
Q2IC1
vi
vo
VBE2
bull Assuming VCCgtgtVBE1 and (IB1+IB2)ltltIC1
bull If the two transistors are similar accountingfor VBE1=VBE2 and R1=RC then the bias currentIC2 is constant
P Colantonio ndash Analogue Electronics 6|26AA 201516
Thermal compensation techniquesCompensation in integrated circuits bull The addiction of the two resistors R2 e R3 improves the circuit behaviorbull In this case in fact are the biasing currents IB1 and IB2 instead of VBE1 and VBE2 to control
the DC behavior of Q1 and Q2
R1
RC
V CC
IC2
IBIB
I
Q1
VBE1
Q2IC1
vo
VBE2
vi
R3
R2=R3
bull If R2=R3 then
bull By a suitable selection of parameter andaccounting that Q1=Q2 it is possible to obtain
bull Moreover selecting RC=12R1 then
P Colantonio ndash Analogue Electronics 7|26AA 201516
BJT equivalent AC modelbull Assuming a generic two port a representation is made by assuming some electrical
quantities as independent variables while the remaining ones are dependent
v2
i2Rg i1
v1vg
bull In particular starting from the set of equation
bull By a series expansion around the quiescent bias point (ie Taylor or McLaurin )
P Colantonio ndash Analogue Electronics 8|26AA 201516
BJT equivalent AC modelbull If a first order approximation is considered
bull Defining
bull An hybrid representation can be obtained
P Colantonio ndash Analogue Electronics 9|26AA 201516
BJT equivalent AC model
v2
i2Rg i1
v1vg
bull In particular referring to the Common Emitter configuration
Input resistance with the output short circuited (ohms)
Voltage gain‐1 with the input open (dimensionless)
Forward current gain with the output short circuited (dimensionless)
Output conductance with the input open (ohms‐1)
P Colantonio ndash Analogue Electronics 10|26AA 201516
The hybrid modelbull The previous equation can be represented by an equivalent circuit model (hybrid model)
P Colantonio ndash Analogue Electronics 11|26AA 201516
Physical meaning of model parameters
tIC
B
BVV
cos
tVB
B
CIV
cos
IB=200μA
160
120
80
40Col
lect
or c
urre
nt I C
mA
Collector-emitter voltage VCE V
10
20
30
40
0 2 4 86 10 12
tVB
C
CII
cos
tIC
C
BVI
cos
Cor
rent
e di
bas
e I B
mA
Base voltage VBE V
0804 060
04
02
06
Typical values
IBBV
CVC1V
C2V = C2V C1-V
hferarr n10 ndash n 100 hrerarr 10-3 ndash 10-4
hierarr 103 ndash 104 Ω hoerarr 10-5 ndash 10-4
P Colantonio ndash Analogue Electronics 12|26AA 201516
Simplified modelbull Accounting for the h parameter values the model can be further simplified assuming
bull Thus obtaining the following model (similar to FET)
bull Accounting for the ldquodioderdquo behavior of the base‐emitter junction it is possible to define
P Colantonio ndash Analogue Electronics 13|26AA 201516
Amplifier configurationbull The basic amplifier configuration are named according to the BJT pin that is common to
both input and output networks
VCC
+ vce
+
-
vs
VBB
iB
RS B
vBE
RLC
E
iC
Common Emitter (CE)
vs
+ iB
RS B
vBE
VCC
RL
C
E
iC
Ri
Vo
Ro
C
Common Collector (CC)
vCB=vo
vs
RS E
vi=vBE
RL
C iC
BVCC
+
Common Base (CB)
P Colantonio ndash Analogue Electronics 14|26AA 201516
Analysis Approachesbull For each configuration the equivalent hybrid model can be used by assuming for the [h]
parameters the corresponding values ie the second letter of the subscript represent thedevice configuration
Common Emitter (CE)bull hie hfe hre hoe
Rs
vs +RL
E
CB
[hje]
Common Collector (CC)bull hic hfc hrc hoc
Rs
vs +RL
E
C
B
[hjc]
Common Base (CB)bull hib hfb hrb hob
Rs
vs +RL
E C
B
[hjb]bull With this appraoch the [h] parameters
assume different values but theamplifier relationships (voltage gaininput and output resistance) have thesame ldquoformrdquo
P Colantonio ndash Analogue Electronics 15|26AA 201516
Analysis Approachesbull A different approach is based on the adoption of the same BJT equivalent model (ie CE
[h] parameters hxe)bull In this case the expressions are different
Common Emitter (CE) Common Collector (CC)
Common Base (CB)
Rs
vs +RL
E
CBRs
vs +RL
E
CB
Rs
vs +RL
E
CB
P Colantonio ndash Analogue Electronics 16|26AA 201516
Analysis ApproachesRs
vsZL
1
1
2
2
V1 V2
Y0Zi
Two-portactive
network(transistor)
I1 I2IL
Rs
vsZL
1
1
2
2
V1 V2
Y0Zi
I1 I2IL
hohfI1+
hrV2
hi
Approximate conversion formulas for hybrid parameters
1rchieic hh
fefc hh 1 oeoc hh
fe
ieib h
hh
1
fe
oeob h
hh
1 fe
fefb h
hh
1
refe
oeierb h
hhhh
1
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 5|26AA 201516
Thermal compensation techniquesbull In the integrated implementation since the resistor RE requires a by‐pass capacitance to
allow higher gain and this capacitance could be very high a different approach is adopted
Compensation in integrated circuits bull The transistor Q1 resembles a diode being VCE1=VBE1
bull Its collector current IC1 is given by
R1
RC
V CC
IC2
IB2IB1
I
Q1
VBE1
Q2IC1
vi
vo
VBE2
bull Assuming VCCgtgtVBE1 and (IB1+IB2)ltltIC1
bull If the two transistors are similar accountingfor VBE1=VBE2 and R1=RC then the bias currentIC2 is constant
P Colantonio ndash Analogue Electronics 6|26AA 201516
Thermal compensation techniquesCompensation in integrated circuits bull The addiction of the two resistors R2 e R3 improves the circuit behaviorbull In this case in fact are the biasing currents IB1 and IB2 instead of VBE1 and VBE2 to control
the DC behavior of Q1 and Q2
R1
RC
V CC
IC2
IBIB
I
Q1
VBE1
Q2IC1
vo
VBE2
vi
R3
R2=R3
bull If R2=R3 then
bull By a suitable selection of parameter andaccounting that Q1=Q2 it is possible to obtain
bull Moreover selecting RC=12R1 then
P Colantonio ndash Analogue Electronics 7|26AA 201516
BJT equivalent AC modelbull Assuming a generic two port a representation is made by assuming some electrical
quantities as independent variables while the remaining ones are dependent
v2
i2Rg i1
v1vg
bull In particular starting from the set of equation
bull By a series expansion around the quiescent bias point (ie Taylor or McLaurin )
P Colantonio ndash Analogue Electronics 8|26AA 201516
BJT equivalent AC modelbull If a first order approximation is considered
bull Defining
bull An hybrid representation can be obtained
P Colantonio ndash Analogue Electronics 9|26AA 201516
BJT equivalent AC model
v2
i2Rg i1
v1vg
bull In particular referring to the Common Emitter configuration
Input resistance with the output short circuited (ohms)
Voltage gain‐1 with the input open (dimensionless)
Forward current gain with the output short circuited (dimensionless)
Output conductance with the input open (ohms‐1)
P Colantonio ndash Analogue Electronics 10|26AA 201516
The hybrid modelbull The previous equation can be represented by an equivalent circuit model (hybrid model)
P Colantonio ndash Analogue Electronics 11|26AA 201516
Physical meaning of model parameters
tIC
B
BVV
cos
tVB
B
CIV
cos
IB=200μA
160
120
80
40Col
lect
or c
urre
nt I C
mA
Collector-emitter voltage VCE V
10
20
30
40
0 2 4 86 10 12
tVB
C
CII
cos
tIC
C
BVI
cos
Cor
rent
e di
bas
e I B
mA
Base voltage VBE V
0804 060
04
02
06
Typical values
IBBV
CVC1V
C2V = C2V C1-V
hferarr n10 ndash n 100 hrerarr 10-3 ndash 10-4
hierarr 103 ndash 104 Ω hoerarr 10-5 ndash 10-4
P Colantonio ndash Analogue Electronics 12|26AA 201516
Simplified modelbull Accounting for the h parameter values the model can be further simplified assuming
bull Thus obtaining the following model (similar to FET)
bull Accounting for the ldquodioderdquo behavior of the base‐emitter junction it is possible to define
P Colantonio ndash Analogue Electronics 13|26AA 201516
Amplifier configurationbull The basic amplifier configuration are named according to the BJT pin that is common to
both input and output networks
VCC
+ vce
+
-
vs
VBB
iB
RS B
vBE
RLC
E
iC
Common Emitter (CE)
vs
+ iB
RS B
vBE
VCC
RL
C
E
iC
Ri
Vo
Ro
C
Common Collector (CC)
vCB=vo
vs
RS E
vi=vBE
RL
C iC
BVCC
+
Common Base (CB)
P Colantonio ndash Analogue Electronics 14|26AA 201516
Analysis Approachesbull For each configuration the equivalent hybrid model can be used by assuming for the [h]
parameters the corresponding values ie the second letter of the subscript represent thedevice configuration
Common Emitter (CE)bull hie hfe hre hoe
Rs
vs +RL
E
CB
[hje]
Common Collector (CC)bull hic hfc hrc hoc
Rs
vs +RL
E
C
B
[hjc]
Common Base (CB)bull hib hfb hrb hob
Rs
vs +RL
E C
B
[hjb]bull With this appraoch the [h] parameters
assume different values but theamplifier relationships (voltage gaininput and output resistance) have thesame ldquoformrdquo
P Colantonio ndash Analogue Electronics 15|26AA 201516
Analysis Approachesbull A different approach is based on the adoption of the same BJT equivalent model (ie CE
[h] parameters hxe)bull In this case the expressions are different
Common Emitter (CE) Common Collector (CC)
Common Base (CB)
Rs
vs +RL
E
CBRs
vs +RL
E
CB
Rs
vs +RL
E
CB
P Colantonio ndash Analogue Electronics 16|26AA 201516
Analysis ApproachesRs
vsZL
1
1
2
2
V1 V2
Y0Zi
Two-portactive
network(transistor)
I1 I2IL
Rs
vsZL
1
1
2
2
V1 V2
Y0Zi
I1 I2IL
hohfI1+
hrV2
hi
Approximate conversion formulas for hybrid parameters
1rchieic hh
fefc hh 1 oeoc hh
fe
ieib h
hh
1
fe
oeob h
hh
1 fe
fefb h
hh
1
refe
oeierb h
hhhh
1
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 6|26AA 201516
Thermal compensation techniquesCompensation in integrated circuits bull The addiction of the two resistors R2 e R3 improves the circuit behaviorbull In this case in fact are the biasing currents IB1 and IB2 instead of VBE1 and VBE2 to control
the DC behavior of Q1 and Q2
R1
RC
V CC
IC2
IBIB
I
Q1
VBE1
Q2IC1
vo
VBE2
vi
R3
R2=R3
bull If R2=R3 then
bull By a suitable selection of parameter andaccounting that Q1=Q2 it is possible to obtain
bull Moreover selecting RC=12R1 then
P Colantonio ndash Analogue Electronics 7|26AA 201516
BJT equivalent AC modelbull Assuming a generic two port a representation is made by assuming some electrical
quantities as independent variables while the remaining ones are dependent
v2
i2Rg i1
v1vg
bull In particular starting from the set of equation
bull By a series expansion around the quiescent bias point (ie Taylor or McLaurin )
P Colantonio ndash Analogue Electronics 8|26AA 201516
BJT equivalent AC modelbull If a first order approximation is considered
bull Defining
bull An hybrid representation can be obtained
P Colantonio ndash Analogue Electronics 9|26AA 201516
BJT equivalent AC model
v2
i2Rg i1
v1vg
bull In particular referring to the Common Emitter configuration
Input resistance with the output short circuited (ohms)
Voltage gain‐1 with the input open (dimensionless)
Forward current gain with the output short circuited (dimensionless)
Output conductance with the input open (ohms‐1)
P Colantonio ndash Analogue Electronics 10|26AA 201516
The hybrid modelbull The previous equation can be represented by an equivalent circuit model (hybrid model)
P Colantonio ndash Analogue Electronics 11|26AA 201516
Physical meaning of model parameters
tIC
B
BVV
cos
tVB
B
CIV
cos
IB=200μA
160
120
80
40Col
lect
or c
urre
nt I C
mA
Collector-emitter voltage VCE V
10
20
30
40
0 2 4 86 10 12
tVB
C
CII
cos
tIC
C
BVI
cos
Cor
rent
e di
bas
e I B
mA
Base voltage VBE V
0804 060
04
02
06
Typical values
IBBV
CVC1V
C2V = C2V C1-V
hferarr n10 ndash n 100 hrerarr 10-3 ndash 10-4
hierarr 103 ndash 104 Ω hoerarr 10-5 ndash 10-4
P Colantonio ndash Analogue Electronics 12|26AA 201516
Simplified modelbull Accounting for the h parameter values the model can be further simplified assuming
bull Thus obtaining the following model (similar to FET)
bull Accounting for the ldquodioderdquo behavior of the base‐emitter junction it is possible to define
P Colantonio ndash Analogue Electronics 13|26AA 201516
Amplifier configurationbull The basic amplifier configuration are named according to the BJT pin that is common to
both input and output networks
VCC
+ vce
+
-
vs
VBB
iB
RS B
vBE
RLC
E
iC
Common Emitter (CE)
vs
+ iB
RS B
vBE
VCC
RL
C
E
iC
Ri
Vo
Ro
C
Common Collector (CC)
vCB=vo
vs
RS E
vi=vBE
RL
C iC
BVCC
+
Common Base (CB)
P Colantonio ndash Analogue Electronics 14|26AA 201516
Analysis Approachesbull For each configuration the equivalent hybrid model can be used by assuming for the [h]
parameters the corresponding values ie the second letter of the subscript represent thedevice configuration
Common Emitter (CE)bull hie hfe hre hoe
Rs
vs +RL
E
CB
[hje]
Common Collector (CC)bull hic hfc hrc hoc
Rs
vs +RL
E
C
B
[hjc]
Common Base (CB)bull hib hfb hrb hob
Rs
vs +RL
E C
B
[hjb]bull With this appraoch the [h] parameters
assume different values but theamplifier relationships (voltage gaininput and output resistance) have thesame ldquoformrdquo
P Colantonio ndash Analogue Electronics 15|26AA 201516
Analysis Approachesbull A different approach is based on the adoption of the same BJT equivalent model (ie CE
[h] parameters hxe)bull In this case the expressions are different
Common Emitter (CE) Common Collector (CC)
Common Base (CB)
Rs
vs +RL
E
CBRs
vs +RL
E
CB
Rs
vs +RL
E
CB
P Colantonio ndash Analogue Electronics 16|26AA 201516
Analysis ApproachesRs
vsZL
1
1
2
2
V1 V2
Y0Zi
Two-portactive
network(transistor)
I1 I2IL
Rs
vsZL
1
1
2
2
V1 V2
Y0Zi
I1 I2IL
hohfI1+
hrV2
hi
Approximate conversion formulas for hybrid parameters
1rchieic hh
fefc hh 1 oeoc hh
fe
ieib h
hh
1
fe
oeob h
hh
1 fe
fefb h
hh
1
refe
oeierb h
hhhh
1
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 7|26AA 201516
BJT equivalent AC modelbull Assuming a generic two port a representation is made by assuming some electrical
quantities as independent variables while the remaining ones are dependent
v2
i2Rg i1
v1vg
bull In particular starting from the set of equation
bull By a series expansion around the quiescent bias point (ie Taylor or McLaurin )
P Colantonio ndash Analogue Electronics 8|26AA 201516
BJT equivalent AC modelbull If a first order approximation is considered
bull Defining
bull An hybrid representation can be obtained
P Colantonio ndash Analogue Electronics 9|26AA 201516
BJT equivalent AC model
v2
i2Rg i1
v1vg
bull In particular referring to the Common Emitter configuration
Input resistance with the output short circuited (ohms)
Voltage gain‐1 with the input open (dimensionless)
Forward current gain with the output short circuited (dimensionless)
Output conductance with the input open (ohms‐1)
P Colantonio ndash Analogue Electronics 10|26AA 201516
The hybrid modelbull The previous equation can be represented by an equivalent circuit model (hybrid model)
P Colantonio ndash Analogue Electronics 11|26AA 201516
Physical meaning of model parameters
tIC
B
BVV
cos
tVB
B
CIV
cos
IB=200μA
160
120
80
40Col
lect
or c
urre
nt I C
mA
Collector-emitter voltage VCE V
10
20
30
40
0 2 4 86 10 12
tVB
C
CII
cos
tIC
C
BVI
cos
Cor
rent
e di
bas
e I B
mA
Base voltage VBE V
0804 060
04
02
06
Typical values
IBBV
CVC1V
C2V = C2V C1-V
hferarr n10 ndash n 100 hrerarr 10-3 ndash 10-4
hierarr 103 ndash 104 Ω hoerarr 10-5 ndash 10-4
P Colantonio ndash Analogue Electronics 12|26AA 201516
Simplified modelbull Accounting for the h parameter values the model can be further simplified assuming
bull Thus obtaining the following model (similar to FET)
bull Accounting for the ldquodioderdquo behavior of the base‐emitter junction it is possible to define
P Colantonio ndash Analogue Electronics 13|26AA 201516
Amplifier configurationbull The basic amplifier configuration are named according to the BJT pin that is common to
both input and output networks
VCC
+ vce
+
-
vs
VBB
iB
RS B
vBE
RLC
E
iC
Common Emitter (CE)
vs
+ iB
RS B
vBE
VCC
RL
C
E
iC
Ri
Vo
Ro
C
Common Collector (CC)
vCB=vo
vs
RS E
vi=vBE
RL
C iC
BVCC
+
Common Base (CB)
P Colantonio ndash Analogue Electronics 14|26AA 201516
Analysis Approachesbull For each configuration the equivalent hybrid model can be used by assuming for the [h]
parameters the corresponding values ie the second letter of the subscript represent thedevice configuration
Common Emitter (CE)bull hie hfe hre hoe
Rs
vs +RL
E
CB
[hje]
Common Collector (CC)bull hic hfc hrc hoc
Rs
vs +RL
E
C
B
[hjc]
Common Base (CB)bull hib hfb hrb hob
Rs
vs +RL
E C
B
[hjb]bull With this appraoch the [h] parameters
assume different values but theamplifier relationships (voltage gaininput and output resistance) have thesame ldquoformrdquo
P Colantonio ndash Analogue Electronics 15|26AA 201516
Analysis Approachesbull A different approach is based on the adoption of the same BJT equivalent model (ie CE
[h] parameters hxe)bull In this case the expressions are different
Common Emitter (CE) Common Collector (CC)
Common Base (CB)
Rs
vs +RL
E
CBRs
vs +RL
E
CB
Rs
vs +RL
E
CB
P Colantonio ndash Analogue Electronics 16|26AA 201516
Analysis ApproachesRs
vsZL
1
1
2
2
V1 V2
Y0Zi
Two-portactive
network(transistor)
I1 I2IL
Rs
vsZL
1
1
2
2
V1 V2
Y0Zi
I1 I2IL
hohfI1+
hrV2
hi
Approximate conversion formulas for hybrid parameters
1rchieic hh
fefc hh 1 oeoc hh
fe
ieib h
hh
1
fe
oeob h
hh
1 fe
fefb h
hh
1
refe
oeierb h
hhhh
1
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 8|26AA 201516
BJT equivalent AC modelbull If a first order approximation is considered
bull Defining
bull An hybrid representation can be obtained
P Colantonio ndash Analogue Electronics 9|26AA 201516
BJT equivalent AC model
v2
i2Rg i1
v1vg
bull In particular referring to the Common Emitter configuration
Input resistance with the output short circuited (ohms)
Voltage gain‐1 with the input open (dimensionless)
Forward current gain with the output short circuited (dimensionless)
Output conductance with the input open (ohms‐1)
P Colantonio ndash Analogue Electronics 10|26AA 201516
The hybrid modelbull The previous equation can be represented by an equivalent circuit model (hybrid model)
P Colantonio ndash Analogue Electronics 11|26AA 201516
Physical meaning of model parameters
tIC
B
BVV
cos
tVB
B
CIV
cos
IB=200μA
160
120
80
40Col
lect
or c
urre
nt I C
mA
Collector-emitter voltage VCE V
10
20
30
40
0 2 4 86 10 12
tVB
C
CII
cos
tIC
C
BVI
cos
Cor
rent
e di
bas
e I B
mA
Base voltage VBE V
0804 060
04
02
06
Typical values
IBBV
CVC1V
C2V = C2V C1-V
hferarr n10 ndash n 100 hrerarr 10-3 ndash 10-4
hierarr 103 ndash 104 Ω hoerarr 10-5 ndash 10-4
P Colantonio ndash Analogue Electronics 12|26AA 201516
Simplified modelbull Accounting for the h parameter values the model can be further simplified assuming
bull Thus obtaining the following model (similar to FET)
bull Accounting for the ldquodioderdquo behavior of the base‐emitter junction it is possible to define
P Colantonio ndash Analogue Electronics 13|26AA 201516
Amplifier configurationbull The basic amplifier configuration are named according to the BJT pin that is common to
both input and output networks
VCC
+ vce
+
-
vs
VBB
iB
RS B
vBE
RLC
E
iC
Common Emitter (CE)
vs
+ iB
RS B
vBE
VCC
RL
C
E
iC
Ri
Vo
Ro
C
Common Collector (CC)
vCB=vo
vs
RS E
vi=vBE
RL
C iC
BVCC
+
Common Base (CB)
P Colantonio ndash Analogue Electronics 14|26AA 201516
Analysis Approachesbull For each configuration the equivalent hybrid model can be used by assuming for the [h]
parameters the corresponding values ie the second letter of the subscript represent thedevice configuration
Common Emitter (CE)bull hie hfe hre hoe
Rs
vs +RL
E
CB
[hje]
Common Collector (CC)bull hic hfc hrc hoc
Rs
vs +RL
E
C
B
[hjc]
Common Base (CB)bull hib hfb hrb hob
Rs
vs +RL
E C
B
[hjb]bull With this appraoch the [h] parameters
assume different values but theamplifier relationships (voltage gaininput and output resistance) have thesame ldquoformrdquo
P Colantonio ndash Analogue Electronics 15|26AA 201516
Analysis Approachesbull A different approach is based on the adoption of the same BJT equivalent model (ie CE
[h] parameters hxe)bull In this case the expressions are different
Common Emitter (CE) Common Collector (CC)
Common Base (CB)
Rs
vs +RL
E
CBRs
vs +RL
E
CB
Rs
vs +RL
E
CB
P Colantonio ndash Analogue Electronics 16|26AA 201516
Analysis ApproachesRs
vsZL
1
1
2
2
V1 V2
Y0Zi
Two-portactive
network(transistor)
I1 I2IL
Rs
vsZL
1
1
2
2
V1 V2
Y0Zi
I1 I2IL
hohfI1+
hrV2
hi
Approximate conversion formulas for hybrid parameters
1rchieic hh
fefc hh 1 oeoc hh
fe
ieib h
hh
1
fe
oeob h
hh
1 fe
fefb h
hh
1
refe
oeierb h
hhhh
1
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 9|26AA 201516
BJT equivalent AC model
v2
i2Rg i1
v1vg
bull In particular referring to the Common Emitter configuration
Input resistance with the output short circuited (ohms)
Voltage gain‐1 with the input open (dimensionless)
Forward current gain with the output short circuited (dimensionless)
Output conductance with the input open (ohms‐1)
P Colantonio ndash Analogue Electronics 10|26AA 201516
The hybrid modelbull The previous equation can be represented by an equivalent circuit model (hybrid model)
P Colantonio ndash Analogue Electronics 11|26AA 201516
Physical meaning of model parameters
tIC
B
BVV
cos
tVB
B
CIV
cos
IB=200μA
160
120
80
40Col
lect
or c
urre
nt I C
mA
Collector-emitter voltage VCE V
10
20
30
40
0 2 4 86 10 12
tVB
C
CII
cos
tIC
C
BVI
cos
Cor
rent
e di
bas
e I B
mA
Base voltage VBE V
0804 060
04
02
06
Typical values
IBBV
CVC1V
C2V = C2V C1-V
hferarr n10 ndash n 100 hrerarr 10-3 ndash 10-4
hierarr 103 ndash 104 Ω hoerarr 10-5 ndash 10-4
P Colantonio ndash Analogue Electronics 12|26AA 201516
Simplified modelbull Accounting for the h parameter values the model can be further simplified assuming
bull Thus obtaining the following model (similar to FET)
bull Accounting for the ldquodioderdquo behavior of the base‐emitter junction it is possible to define
P Colantonio ndash Analogue Electronics 13|26AA 201516
Amplifier configurationbull The basic amplifier configuration are named according to the BJT pin that is common to
both input and output networks
VCC
+ vce
+
-
vs
VBB
iB
RS B
vBE
RLC
E
iC
Common Emitter (CE)
vs
+ iB
RS B
vBE
VCC
RL
C
E
iC
Ri
Vo
Ro
C
Common Collector (CC)
vCB=vo
vs
RS E
vi=vBE
RL
C iC
BVCC
+
Common Base (CB)
P Colantonio ndash Analogue Electronics 14|26AA 201516
Analysis Approachesbull For each configuration the equivalent hybrid model can be used by assuming for the [h]
parameters the corresponding values ie the second letter of the subscript represent thedevice configuration
Common Emitter (CE)bull hie hfe hre hoe
Rs
vs +RL
E
CB
[hje]
Common Collector (CC)bull hic hfc hrc hoc
Rs
vs +RL
E
C
B
[hjc]
Common Base (CB)bull hib hfb hrb hob
Rs
vs +RL
E C
B
[hjb]bull With this appraoch the [h] parameters
assume different values but theamplifier relationships (voltage gaininput and output resistance) have thesame ldquoformrdquo
P Colantonio ndash Analogue Electronics 15|26AA 201516
Analysis Approachesbull A different approach is based on the adoption of the same BJT equivalent model (ie CE
[h] parameters hxe)bull In this case the expressions are different
Common Emitter (CE) Common Collector (CC)
Common Base (CB)
Rs
vs +RL
E
CBRs
vs +RL
E
CB
Rs
vs +RL
E
CB
P Colantonio ndash Analogue Electronics 16|26AA 201516
Analysis ApproachesRs
vsZL
1
1
2
2
V1 V2
Y0Zi
Two-portactive
network(transistor)
I1 I2IL
Rs
vsZL
1
1
2
2
V1 V2
Y0Zi
I1 I2IL
hohfI1+
hrV2
hi
Approximate conversion formulas for hybrid parameters
1rchieic hh
fefc hh 1 oeoc hh
fe
ieib h
hh
1
fe
oeob h
hh
1 fe
fefb h
hh
1
refe
oeierb h
hhhh
1
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 10|26AA 201516
The hybrid modelbull The previous equation can be represented by an equivalent circuit model (hybrid model)
P Colantonio ndash Analogue Electronics 11|26AA 201516
Physical meaning of model parameters
tIC
B
BVV
cos
tVB
B
CIV
cos
IB=200μA
160
120
80
40Col
lect
or c
urre
nt I C
mA
Collector-emitter voltage VCE V
10
20
30
40
0 2 4 86 10 12
tVB
C
CII
cos
tIC
C
BVI
cos
Cor
rent
e di
bas
e I B
mA
Base voltage VBE V
0804 060
04
02
06
Typical values
IBBV
CVC1V
C2V = C2V C1-V
hferarr n10 ndash n 100 hrerarr 10-3 ndash 10-4
hierarr 103 ndash 104 Ω hoerarr 10-5 ndash 10-4
P Colantonio ndash Analogue Electronics 12|26AA 201516
Simplified modelbull Accounting for the h parameter values the model can be further simplified assuming
bull Thus obtaining the following model (similar to FET)
bull Accounting for the ldquodioderdquo behavior of the base‐emitter junction it is possible to define
P Colantonio ndash Analogue Electronics 13|26AA 201516
Amplifier configurationbull The basic amplifier configuration are named according to the BJT pin that is common to
both input and output networks
VCC
+ vce
+
-
vs
VBB
iB
RS B
vBE
RLC
E
iC
Common Emitter (CE)
vs
+ iB
RS B
vBE
VCC
RL
C
E
iC
Ri
Vo
Ro
C
Common Collector (CC)
vCB=vo
vs
RS E
vi=vBE
RL
C iC
BVCC
+
Common Base (CB)
P Colantonio ndash Analogue Electronics 14|26AA 201516
Analysis Approachesbull For each configuration the equivalent hybrid model can be used by assuming for the [h]
parameters the corresponding values ie the second letter of the subscript represent thedevice configuration
Common Emitter (CE)bull hie hfe hre hoe
Rs
vs +RL
E
CB
[hje]
Common Collector (CC)bull hic hfc hrc hoc
Rs
vs +RL
E
C
B
[hjc]
Common Base (CB)bull hib hfb hrb hob
Rs
vs +RL
E C
B
[hjb]bull With this appraoch the [h] parameters
assume different values but theamplifier relationships (voltage gaininput and output resistance) have thesame ldquoformrdquo
P Colantonio ndash Analogue Electronics 15|26AA 201516
Analysis Approachesbull A different approach is based on the adoption of the same BJT equivalent model (ie CE
[h] parameters hxe)bull In this case the expressions are different
Common Emitter (CE) Common Collector (CC)
Common Base (CB)
Rs
vs +RL
E
CBRs
vs +RL
E
CB
Rs
vs +RL
E
CB
P Colantonio ndash Analogue Electronics 16|26AA 201516
Analysis ApproachesRs
vsZL
1
1
2
2
V1 V2
Y0Zi
Two-portactive
network(transistor)
I1 I2IL
Rs
vsZL
1
1
2
2
V1 V2
Y0Zi
I1 I2IL
hohfI1+
hrV2
hi
Approximate conversion formulas for hybrid parameters
1rchieic hh
fefc hh 1 oeoc hh
fe
ieib h
hh
1
fe
oeob h
hh
1 fe
fefb h
hh
1
refe
oeierb h
hhhh
1
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 11|26AA 201516
Physical meaning of model parameters
tIC
B
BVV
cos
tVB
B
CIV
cos
IB=200μA
160
120
80
40Col
lect
or c
urre
nt I C
mA
Collector-emitter voltage VCE V
10
20
30
40
0 2 4 86 10 12
tVB
C
CII
cos
tIC
C
BVI
cos
Cor
rent
e di
bas
e I B
mA
Base voltage VBE V
0804 060
04
02
06
Typical values
IBBV
CVC1V
C2V = C2V C1-V
hferarr n10 ndash n 100 hrerarr 10-3 ndash 10-4
hierarr 103 ndash 104 Ω hoerarr 10-5 ndash 10-4
P Colantonio ndash Analogue Electronics 12|26AA 201516
Simplified modelbull Accounting for the h parameter values the model can be further simplified assuming
bull Thus obtaining the following model (similar to FET)
bull Accounting for the ldquodioderdquo behavior of the base‐emitter junction it is possible to define
P Colantonio ndash Analogue Electronics 13|26AA 201516
Amplifier configurationbull The basic amplifier configuration are named according to the BJT pin that is common to
both input and output networks
VCC
+ vce
+
-
vs
VBB
iB
RS B
vBE
RLC
E
iC
Common Emitter (CE)
vs
+ iB
RS B
vBE
VCC
RL
C
E
iC
Ri
Vo
Ro
C
Common Collector (CC)
vCB=vo
vs
RS E
vi=vBE
RL
C iC
BVCC
+
Common Base (CB)
P Colantonio ndash Analogue Electronics 14|26AA 201516
Analysis Approachesbull For each configuration the equivalent hybrid model can be used by assuming for the [h]
parameters the corresponding values ie the second letter of the subscript represent thedevice configuration
Common Emitter (CE)bull hie hfe hre hoe
Rs
vs +RL
E
CB
[hje]
Common Collector (CC)bull hic hfc hrc hoc
Rs
vs +RL
E
C
B
[hjc]
Common Base (CB)bull hib hfb hrb hob
Rs
vs +RL
E C
B
[hjb]bull With this appraoch the [h] parameters
assume different values but theamplifier relationships (voltage gaininput and output resistance) have thesame ldquoformrdquo
P Colantonio ndash Analogue Electronics 15|26AA 201516
Analysis Approachesbull A different approach is based on the adoption of the same BJT equivalent model (ie CE
[h] parameters hxe)bull In this case the expressions are different
Common Emitter (CE) Common Collector (CC)
Common Base (CB)
Rs
vs +RL
E
CBRs
vs +RL
E
CB
Rs
vs +RL
E
CB
P Colantonio ndash Analogue Electronics 16|26AA 201516
Analysis ApproachesRs
vsZL
1
1
2
2
V1 V2
Y0Zi
Two-portactive
network(transistor)
I1 I2IL
Rs
vsZL
1
1
2
2
V1 V2
Y0Zi
I1 I2IL
hohfI1+
hrV2
hi
Approximate conversion formulas for hybrid parameters
1rchieic hh
fefc hh 1 oeoc hh
fe
ieib h
hh
1
fe
oeob h
hh
1 fe
fefb h
hh
1
refe
oeierb h
hhhh
1
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 12|26AA 201516
Simplified modelbull Accounting for the h parameter values the model can be further simplified assuming
bull Thus obtaining the following model (similar to FET)
bull Accounting for the ldquodioderdquo behavior of the base‐emitter junction it is possible to define
P Colantonio ndash Analogue Electronics 13|26AA 201516
Amplifier configurationbull The basic amplifier configuration are named according to the BJT pin that is common to
both input and output networks
VCC
+ vce
+
-
vs
VBB
iB
RS B
vBE
RLC
E
iC
Common Emitter (CE)
vs
+ iB
RS B
vBE
VCC
RL
C
E
iC
Ri
Vo
Ro
C
Common Collector (CC)
vCB=vo
vs
RS E
vi=vBE
RL
C iC
BVCC
+
Common Base (CB)
P Colantonio ndash Analogue Electronics 14|26AA 201516
Analysis Approachesbull For each configuration the equivalent hybrid model can be used by assuming for the [h]
parameters the corresponding values ie the second letter of the subscript represent thedevice configuration
Common Emitter (CE)bull hie hfe hre hoe
Rs
vs +RL
E
CB
[hje]
Common Collector (CC)bull hic hfc hrc hoc
Rs
vs +RL
E
C
B
[hjc]
Common Base (CB)bull hib hfb hrb hob
Rs
vs +RL
E C
B
[hjb]bull With this appraoch the [h] parameters
assume different values but theamplifier relationships (voltage gaininput and output resistance) have thesame ldquoformrdquo
P Colantonio ndash Analogue Electronics 15|26AA 201516
Analysis Approachesbull A different approach is based on the adoption of the same BJT equivalent model (ie CE
[h] parameters hxe)bull In this case the expressions are different
Common Emitter (CE) Common Collector (CC)
Common Base (CB)
Rs
vs +RL
E
CBRs
vs +RL
E
CB
Rs
vs +RL
E
CB
P Colantonio ndash Analogue Electronics 16|26AA 201516
Analysis ApproachesRs
vsZL
1
1
2
2
V1 V2
Y0Zi
Two-portactive
network(transistor)
I1 I2IL
Rs
vsZL
1
1
2
2
V1 V2
Y0Zi
I1 I2IL
hohfI1+
hrV2
hi
Approximate conversion formulas for hybrid parameters
1rchieic hh
fefc hh 1 oeoc hh
fe
ieib h
hh
1
fe
oeob h
hh
1 fe
fefb h
hh
1
refe
oeierb h
hhhh
1
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 13|26AA 201516
Amplifier configurationbull The basic amplifier configuration are named according to the BJT pin that is common to
both input and output networks
VCC
+ vce
+
-
vs
VBB
iB
RS B
vBE
RLC
E
iC
Common Emitter (CE)
vs
+ iB
RS B
vBE
VCC
RL
C
E
iC
Ri
Vo
Ro
C
Common Collector (CC)
vCB=vo
vs
RS E
vi=vBE
RL
C iC
BVCC
+
Common Base (CB)
P Colantonio ndash Analogue Electronics 14|26AA 201516
Analysis Approachesbull For each configuration the equivalent hybrid model can be used by assuming for the [h]
parameters the corresponding values ie the second letter of the subscript represent thedevice configuration
Common Emitter (CE)bull hie hfe hre hoe
Rs
vs +RL
E
CB
[hje]
Common Collector (CC)bull hic hfc hrc hoc
Rs
vs +RL
E
C
B
[hjc]
Common Base (CB)bull hib hfb hrb hob
Rs
vs +RL
E C
B
[hjb]bull With this appraoch the [h] parameters
assume different values but theamplifier relationships (voltage gaininput and output resistance) have thesame ldquoformrdquo
P Colantonio ndash Analogue Electronics 15|26AA 201516
Analysis Approachesbull A different approach is based on the adoption of the same BJT equivalent model (ie CE
[h] parameters hxe)bull In this case the expressions are different
Common Emitter (CE) Common Collector (CC)
Common Base (CB)
Rs
vs +RL
E
CBRs
vs +RL
E
CB
Rs
vs +RL
E
CB
P Colantonio ndash Analogue Electronics 16|26AA 201516
Analysis ApproachesRs
vsZL
1
1
2
2
V1 V2
Y0Zi
Two-portactive
network(transistor)
I1 I2IL
Rs
vsZL
1
1
2
2
V1 V2
Y0Zi
I1 I2IL
hohfI1+
hrV2
hi
Approximate conversion formulas for hybrid parameters
1rchieic hh
fefc hh 1 oeoc hh
fe
ieib h
hh
1
fe
oeob h
hh
1 fe
fefb h
hh
1
refe
oeierb h
hhhh
1
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 14|26AA 201516
Analysis Approachesbull For each configuration the equivalent hybrid model can be used by assuming for the [h]
parameters the corresponding values ie the second letter of the subscript represent thedevice configuration
Common Emitter (CE)bull hie hfe hre hoe
Rs
vs +RL
E
CB
[hje]
Common Collector (CC)bull hic hfc hrc hoc
Rs
vs +RL
E
C
B
[hjc]
Common Base (CB)bull hib hfb hrb hob
Rs
vs +RL
E C
B
[hjb]bull With this appraoch the [h] parameters
assume different values but theamplifier relationships (voltage gaininput and output resistance) have thesame ldquoformrdquo
P Colantonio ndash Analogue Electronics 15|26AA 201516
Analysis Approachesbull A different approach is based on the adoption of the same BJT equivalent model (ie CE
[h] parameters hxe)bull In this case the expressions are different
Common Emitter (CE) Common Collector (CC)
Common Base (CB)
Rs
vs +RL
E
CBRs
vs +RL
E
CB
Rs
vs +RL
E
CB
P Colantonio ndash Analogue Electronics 16|26AA 201516
Analysis ApproachesRs
vsZL
1
1
2
2
V1 V2
Y0Zi
Two-portactive
network(transistor)
I1 I2IL
Rs
vsZL
1
1
2
2
V1 V2
Y0Zi
I1 I2IL
hohfI1+
hrV2
hi
Approximate conversion formulas for hybrid parameters
1rchieic hh
fefc hh 1 oeoc hh
fe
ieib h
hh
1
fe
oeob h
hh
1 fe
fefb h
hh
1
refe
oeierb h
hhhh
1
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 15|26AA 201516
Analysis Approachesbull A different approach is based on the adoption of the same BJT equivalent model (ie CE
[h] parameters hxe)bull In this case the expressions are different
Common Emitter (CE) Common Collector (CC)
Common Base (CB)
Rs
vs +RL
E
CBRs
vs +RL
E
CB
Rs
vs +RL
E
CB
P Colantonio ndash Analogue Electronics 16|26AA 201516
Analysis ApproachesRs
vsZL
1
1
2
2
V1 V2
Y0Zi
Two-portactive
network(transistor)
I1 I2IL
Rs
vsZL
1
1
2
2
V1 V2
Y0Zi
I1 I2IL
hohfI1+
hrV2
hi
Approximate conversion formulas for hybrid parameters
1rchieic hh
fefc hh 1 oeoc hh
fe
ieib h
hh
1
fe
oeob h
hh
1 fe
fefb h
hh
1
refe
oeierb h
hhhh
1
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 16|26AA 201516
Analysis ApproachesRs
vsZL
1
1
2
2
V1 V2
Y0Zi
Two-portactive
network(transistor)
I1 I2IL
Rs
vsZL
1
1
2
2
V1 V2
Y0Zi
I1 I2IL
hohfI1+
hrV2
hi
Approximate conversion formulas for hybrid parameters
1rchieic hh
fefc hh 1 oeoc hh
fe
ieib h
hh
1
fe
oeob h
hh
1 fe
fefb h
hh
1
refe
oeierb h
hhhh
1
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 17|26AA 201516
DC analysis of a simple amplifierbull Consider the following circuit from which we want determine the quiescent collector
current and the quiescent output voltage given that the hFE of the transistor is 100
bull The base‐emitter voltage VBE is approximately 07V
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 18|26AA 201516
Common Emitter Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 19|26AA 201516
Common Collector Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 20|26AA 201516
Common Base Amplifier
bull Small signal equivalent circuit
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 21|26AA 201516
Phase Splitterbull Small signal equivalent circuit
bull If RE=RC then AV1=‐AV2
bull The output resistances are different
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 22|26AA 201516
Summary
CE CC CB CE (with RE)
CC (with RC)
AV -hfeRLhie 1 hfeRLhie -hfeRC[hie+(1+hfe)RE]
(1+hfe)RE[hie+(1+hfe)RE]
Rin hie hie+(1+hfe)RL hie(1+hfe) hie+(1+hfe)RE hie+(1+hfe)RE
Rout hie(1+hfe) hie(1+hfe)
AI -hfe 1+hfe 1 -hfeRCRE 1+hfe
Out2 Out1
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 23|26AA 201516
The use of feedback resistorbull As we have seen the use of resistor RE in the CE amplifier is useful to stabilize the
device operating pointbull It is also useful to stabilize the gain behaviour resulting in
bull With feedback the voltage gain is fixed by the resistive components that are twostable and well‐defined passive components
bull Without the feedback the gain is ‐hfeRLhie thus varying with the transistorrsquosoperating condition and its variability (for hie and hfe)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 24|26AA 201516
Use of a decoupling capacitorbull However the use of RE drastically reduces the amplifier voltage gainbull Thus it is quite common to remove the AC feedback by using a decoupling capacitor
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 25|26AA 201516
Use of a decoupling capacitorbull The adoption of decoupling capacitor change the frequency response of amplifiers
CE without feedback
CE with feedback
CE with RE and decoupling capacitor
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
P Colantonio ndash Analogue Electronics 26|26AA 201516
Use of split emitter resistorsbull The total emitter resistance RE1+RE2 can be tailored to suit the biasing requirements of
the circuitbull Only part of this resistance can be decoupled (RE2) to produce the required small‐signal
performance (RCRE1)
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