13 ae bjt-ii amplifiers

26
Analogue Electronics Paolo Colantonio A.A. 2015-16 Università degli Studi di Roma Tor Vergata Dipartimento di Ingegneria Elettronica

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Page 1: 13 AE BJT-II Amplifiers

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)

Page 2: 13 AE BJT-II Amplifiers

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)

Page 3: 13 AE BJT-II Amplifiers

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)

Page 4: 13 AE BJT-II Amplifiers

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)

Page 5: 13 AE BJT-II Amplifiers

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)

Page 6: 13 AE BJT-II Amplifiers

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)

Page 7: 13 AE BJT-II Amplifiers

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)

Page 8: 13 AE BJT-II Amplifiers

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)

Page 9: 13 AE BJT-II Amplifiers

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)

Page 10: 13 AE BJT-II Amplifiers

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)

Page 11: 13 AE BJT-II Amplifiers

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)

Page 12: 13 AE BJT-II Amplifiers

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)

Page 13: 13 AE BJT-II Amplifiers

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)

Page 14: 13 AE BJT-II Amplifiers

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)

Page 15: 13 AE BJT-II Amplifiers

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)

Page 16: 13 AE BJT-II Amplifiers

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)

Page 17: 13 AE BJT-II Amplifiers

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)

Page 18: 13 AE BJT-II Amplifiers

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)

Page 19: 13 AE BJT-II Amplifiers

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)

Page 20: 13 AE BJT-II Amplifiers

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)

Page 21: 13 AE BJT-II Amplifiers

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)

Page 22: 13 AE BJT-II Amplifiers

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)

Page 23: 13 AE BJT-II Amplifiers

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)

Page 24: 13 AE BJT-II Amplifiers

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)

Page 25: 13 AE BJT-II Amplifiers

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)

Page 26: 13 AE BJT-II Amplifiers

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)