department of electrical and ecse-330b electronic circuits ... electronics... · outline of chapter...

Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I

BJTs 1

Outline of Chapter 5• 1- Introduction to The Bipolar Junction Transistor• 2- Active Mode Operation of BJT• 3- DC Analysis of Active Mode BJT Circuits• 4- BJT as an Amplifier• 5- BJT Small Signal Models• 6- CEA, CEA with RE, CBA, & CCA • 7- Integrated Circuit Amplifiers


BJTs 2

Small Signal Model• Apply small signal

at base: vs(t)=vbe(t)• Results in signal

current, ic(t), at collector

• Can we generate a small signal model based on what we know so far

)()( tvgti bemc =

Cbemc

Ccc

RtvgtvRitv

)()()(0−==−


BJTs 3

Small Signal Model: vbe controls ic

• In response to signal input between base and emitter (vbe), signal current flows in collector (ic)

• Can describe using hybrid-π small signal model

gmvbe+-

vbe

B C

E

C

B

Evbe

ic

)()( tvgti bemc = Hybrid-π small signal model


BJTs 4

Output Resistance and Small Signal Model

• For constant VBE and small VCE, BJT in saturation:

ICC

IB

B

IEE

VCE

VBE

+VCE

_

Linear dependence on IC vs. VCE for constant VBEdefined as the Early Effect

Active Mode; Early Effect


BJTs 5

Modeling the Early Effect• Extrapolated curves

intersect at common point (-VA, 0)

• VA is the Early voltage– typically 50 to 100V

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛=

A

CE

T

BESC V

VVVII 1expIC

VCE


BJTs 6

BJT Small Signal Output Resistance

C

A

constvCE

Co I

VVIr

BE

=⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

≡

−

=

1

.

• Derivation of ro in active mode is a small signal approximation that provides expression for BJT output resistance in the active mode:

IC

VCE

VBE

C

Ao I

Vr =


BJTs 7

BJT Small Signal Model With Output Resistance ro

• The model is updated to include the output resistance, ro , between C & E terminals.

• The resistance is in parallel with the current source

gmvbe+-

vbe

B C

E

ro

C

Ao I

Vr =T

Cm V

Ig =


BJTs 8

Small Signal: vbe proportional to ib

• Since there is both a voltage and a current at the base node, there must be an equivalent resistance (V=IR)

• Small signal base current: ib

• Small signal base emitter voltage: vbe

• Define small signal input resistance at base as vbe/ib= rπ

bbe irv ⋅= π


BJTs 9

Derive an Expression for BJT Small Signal Base Resistance – rπ

• Define expression for rπ:

• Make use of linearity:

• Take derivative and simplify:

⎟⎟⎠

⎞⎜⎜⎝

⎛==

T

BESCB V

VIII expββ

1−

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

≡=OPBE

B

b

be

VIr

iv

π

mC

T

OPBE

C

OPBE

B

gIV

VI

VIr ββ

βπ =⋅

=⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

=⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

=−− 11

1

B

T

m IV

gr ==

βπ


BJTs 10

Hybrid-π Small Signal Models

πrvi be

b =

βib

B C

E

rorπibgmvbe+

-vbe

B C

E

rorπ

( ) bbmbem iirgvg βπ ==

B

T

m IV

gr ==

βπ

VCCS based model CCCS based model


BJTs 11

Transistor View: Inclusion of ro and rπ


BJTs 12

Small-Signal: vbe proportional to ie

eebe irv ⋅=

• Since there is both a voltage and a current at the emitter node, there must be an equivalent resistance (V=IR)

• Small signal emitter current: ie• Small signal base emitter

voltage: vbe

• Define small signal input resistance at emitter as vbe/ie= re


BJTs 13

Derive an Expression for BJT Small Signal Emitter Resistance – re

• Define expression for re:

• Make use of linearity:

• Take derivative and simplify:

⎟⎟⎠

⎞⎜⎜⎝

⎛==

T

BESCE V

VIII expαα

1−

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

≡=OPBE

Ee

e

be

VIr

iv

mC

T

OPBE

C

OPBE

Ee gI

VVI

VIr αα

α=

⋅=

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

=⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

=−− 11

1

E

T

me I

Vg

r ==α


BJTs 14

T-Models

gmvbe

+

-vbe

B

C

E

ro

re

αie

B

C

E

ro

reie

VCCS based model CCCS based model

e

bee r

vi = ( ) eeembem iirgvg α==E

T

me I

Vg

r ==α


BJTs 15

Hybrid-π Small Signal Model – Summary

T

Cm V

Ig =C

Ao I

Vr =B

T

IVr =π

• Useful to use model when:– emitter terminal at signal ground– input applied at base

gmvbevbe


BJTs 16

– input applied at base or emitter

T Small Signal Model – Summary

• Useful to use model when:

– emitter terminal not at signal ground

T

Cm V

Ig =C

Ao I

Vr =E

Te I

Vr =

e

beebe

eebbe

rriiriir

ririv

)1()1(;)/(

+=+==

==

ββ

π

π

π

• Note:


BJTs 17

PNP Small Signal Model• Small-signal model for

pnp’s identical to npn• Re-orient the model to

reflect direction of current flow and voltage polarity

• Common mistakes:– Get location of B, E,

and C terminals wrong– DC current flows one way,

signal current flows other way

Note: Vbe = -Veb


BJTs 18

Example: Calculate Common Emitter Voltage Gain

VA

m mg 4.42= Ω= kro 8.70Ω= kr 36.2π

Use Hybrid-π model, and assume DC operating point is such that the following small signal parameters apply:

Ω= kRC 2


BJTs 19

Small Signal Example

X


BJTs 20

Small Signal Example

Cobemout Rrvgv ⋅−=

VVRrgvv

vvA Com

be

out

s

outV /5.82−=⋅−===

bes vv =


BJTs 21

Small Signal Analysis – Comments• Analysis procedure:

– Solve for DC operating point

– Calculate small-signal parameters, gm, rπ, re, ro

– Construct small-signal equivalent circuit

– Compute voltage and current gains, input and output resistances.

• What to do about ro?– Often, including ro

complicates circuit analysis

– Omitting ro from small signal model results in acceptable accuracy

– Sometimes, ro must be included

• The often used rule of thumb: if neither end of ro is at a signal ground, you can ignore it


BJTs 22

Small Signal Approximation

• Small signal analysis requires the use of “small”signals to be valid; how small is “small enough”?

• BJT based on pn junction, thus vbe constraint follows that for diode

• For linear approximation to be valid:

• Works for vbe less than approximately 10mV in amplitude

1<<⋅ T

d

Vnv

1<<T

be

Vv


BJTs 23

What is the Limit on vs in Order to Remain in Small Signal Approximation?

bes vv =• For this circuit, since vs = vbe, vs must remain less than 10 mV in order for small signal model to be valid• What modifications can be made to increase allowable magnitude of vs?


BJTs 24

Outline of Chapter 5

• 1- Introduction to The Bipolar Junction Transistor• 2- Active Mode Operation of BJT• 3- DC Analysis of Active Mode BJT Circuits• 4- BJT as an Amplifier• 5- BJT Small Signal Models• 6- CEA, CEA with RE, CBA, & CCA• 7- Integrated Circuit Amplifiers


BJTs 25

The Common Emitter Amplifier (CEA)• Input at base; output at collector• The emitter has a small-signal

ground and is “common” to both input and output.

• By-pass (red) capacitors and coupling (green) capacitors are used to DC-bias transistor and couple signals.

• Use Hybrid-π model with the output resistance, ro.

01

01

=∞=

∞==

ωω

ω

whenCj

CwhenCj


BJTs 26

CEA DC Analysis – Confirm Active• DC Analysis

– Thevenin:

– Analysis:

mAII EC 82.11

=+

=ββ

VkIV COUT 18.3)1(5 =Ω−=

( ) ( )

18755000//3000

25.153

3553

55

==

=⎟⎠⎞

⎜⎝⎛

+−+⎟

⎠⎞

⎜⎝⎛

+=

EQ

EQ

Rkk

kkk

kV

VkIV EE 515.05)3( =−Ω=

VVV EB 215.17.0 =+=

mAk

RV

I

II

kIRIV

EQ

EQE

EB

EEQBEQ

84.1)3(

1

57.0)1/(

05)3(7.0

=Ω+

+

+−=

+=

=+Ω−−−

β

β


BJTs 27

CEA Voltage Gain

inbe vv = ( )Ω−= krvgv obemout 1

( )Ω−== krgvvA om

in

outVO 1

Ω==

Ω==

==

54945

4.1359

0728.0

C

AO

B

T

T

Cm

IVr

IVr

VA

VIg

π

Voltage gain analysis


BJTs 28

Rin Rout

CEA Input/Output Resistance

Input Resistance:

Ω==

≡

786|| EQIN

in

inIN

RrRivR

π Ω=Ω= 9821krR oOUT

Output resistance: set vin = 0; thus vbe = 0; leads to gmvbe = 0 and thus open circuited; note one node of rotied to ground


BJTs 29

CEA Summary

( )Comin

outVO Rrg

vvA −==

πrRIN =

CoOUT RrR =

• Large gain parameters

• RIN & ROUT both moderate

• RIN & ROUT not ideal for any amplifier configuration

• In practice, not usually used by itself for gain


BJTs 30

CEA with RE

• There is NO small-signal ground in the emitter

• Since there is neither collector nor emitter at signal ground– Use T small-

signal model– Neglect ro

RE=3kΩ


BJTs 31

CEA with RE - Voltage Gain Analysis

• Draw small-signal T-model equivalent circuit.

• Neglect rO

• Voltage gain

inEe

ebe v

Rrrv+

=

Cbemout Rvgv −=

Ee

eCm

in

outVO Rr

rRgvvA

+−==

RC

vin

gmvbe

+

-vbe re

vout

RE


BJTs 32

RIN: the β+1 Reflection Rule

• The β+1 rule takes advantage of the relationship between iEand iB

b

Eeb

b

xbe

in

inIN i

Ririi

vvivR +

=+

=≡ π

• Rule generally applicable only when ro neglected

ib

VXie

EIN RrR )1( ++= βπ

be ii )1( += β

vin

vout

When looking into the base, the input resistance is the base resistance plus (β+1) times total resistance in the emitter


BJTs 33

The β+1 Reflection Rule in Reverse: Looking Into the Emitter

ib

VX

ve

e

Bbee

e

xeb

in

inIN i

Ririi

vvivR

−−−

=−+

=≡

)1( ++=

βB

eINRrRbe ii )1( += β

Veb

-

+

+-

• RB looks (β+1) smaller from emitter perspective

• When looking into the emitter, the input resistance is the emitter resistance PLUS whatever is in the base divided by (β+1)

xebinxebin vvvvvv =−+= ;

vin


BJTs 34

CEA with RE– Input/Output Resistance• Neglect rO

• Input Resistance• Using the β+1 reflection

rule:

• Output resistance: set vin = 0; thus vbe = 0; leads to gmvbe = 0 and thus open circuited; by inspection:

Ω= kROUT 1

Rout( )( )[ ]EeEQIN RrRR ++= 1|| β

Rin


BJTs 35

The CEA With RE – Summary

COUT RR =

moderate

moderate

• Moderate gain due to REwhich reduces gain

• Large RIN good for voltage and transconductanceamplifier configuration

• Moderate ROUT a problem, but fixable

Ee

eCm

in

outVO Rr

rRgvvA

+−==

( )( )EeIN RrR ++= 1β large


BJTs 36

The Common Base Amplifier (CBA)• The input is ve(t)• The output is vc(t)• The base has a small-

signal ground and is “common” to both input and output.

• By-pass capacitors and coupling capacitors are used to DC-bias transistor and couple signals.

• Use T model without the output resistance, ro.

by-pass

coupling


BJTs 37

CBA – Voltage Gain Analysis

inbe vv −=

• Draw small-signal T-model equivalent circuit.

• Neglect rO

• Circuit analysis - voltage gain

)1( Ω−= kvgv bemout

)1( Ω== kgvvA m

in

outVO


BJTs 38

CBA – Short Circuit Current Gain Analysis• Draw small-signal T-model

equivalent circuit.• Neglect rO

• Circuit analysis - current gain

eout ii α−=

⎟⎟⎠

⎞⎜⎜⎝

⎛+

==Ee

E

in

outIS Rr

RiiA α

VX

+

_

_

VX

ineX iii +=

inEe

Ee i

RrRi ⎟⎟

⎠

⎞⎜⎜⎝

⎛+

−=

iX

EXeeX Ririv =−=


BJTs 39

CBA – Input/Output resistance

Ω= kROUT 1

Rout

• Input Resistance

• Output resistance• With vIN = -vbe = 0

EeIN RrR ||=

Rin

LOW input resistance can be useful !!


BJTs 40

The Common Collector Amplifier (CCA)• The input is vb(t)• The output is ve(t)• The collector has a small-

signal ground and is “common” to both input and output.

• By-pass capacitors and coupling capacitors are used to DC-bias transistor and couple signals.

• Use T model with the output resistance, ro.

by-pass

coupling


BJTs 41

CCA – Voltage-Gain Analysis

⎟⎟⎠

⎞⎜⎜⎝

⎛+ΩΩ

=eo

oinout rkr

krvv4//

4//

+

- -+

Since re small, Almost vout=vin

Voltage Division:


BJTs 42

The CCA – Current-Gain Analysis

⎟⎟⎠

⎞⎜⎜⎝

⎛++Ω

Ω+==

)1(88)1(

ββ

ein

outIS rk

kiiA

)1/(;

βα

+=−−==+

exin

xinbeeb

iiiiiiiii

eexin rikiv =Ω= )8(

eout ii =

iX


BJTs 43

CCA - Input/Output Resistance• Input Resistance; by

inspection using β+1 rule:

RIN

HIGH INPUT RESISTANCE

• Output Resistance, vin= 0

EoeOUT RrrR ////=

ROUTLOW OUTPUT RESISTANCE

( )( ){ }EoeIN RrrkR //1//8 ++Ω= β


BJTs 44

CCA Operation – Voltage Buffer• Good voltage buffer

– The VOLTAGE gain is almost unity, and the DC component is only reduced by 0.7V

– Large short circuit current gain

– High input resistance (which reduces loading to the circuits before)

– Low output resistance (which reduces the loading of circuits after)

department of electrical and ecse-330b electronic circuits ... electronics... · outline of chapter...

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