ECE 442 Solid State Devices Circuits 7. BJT Amplifiers

ECE 342 – Jose Schutt‐Aine 1

ECE 442Solid‐State Devices & Circuits

7. BJT Amplifiers

Jose E. Schutt-AineElectrical & Computer Engineering

University of [email protected]


• Definitions– Used to increase the amplitude of an input signal to a

desired level– This is a fundamental signal processing function– Must be linear (free of distortion) – Shape of signal

preserved

Amplifiers

( ) ( ),o iv t Av t where A is the voltage gain=

vi(t) vo(t)AMP

: ov

i

vVoltage Gain Av

=

( ) :( )

Lp

I

Load Power PPower Gain AInput Power P

=


Amplifiers

: p v iNote A A A=

: oi

i

iCurrent Gain Ai

=

o op

I I

v iAv i

=

20log VVoltage gain in dB A=

20log ICurrent gain in dB A=

10log PPower gain in dB A=

Expressing gain in dB (decibels)


Amplifiers

1 1 2 2DCP V I V I= +

100L

DC

P Power EfficiencyP

η = × =

Since output associated with the signal is larger than the input signal, power must come from DC supply

DC I L dissipatedP P P P+ = +


An amplifier has ±10 V power supplies and an input current of 0.1 mA (sine wave) input voltage 1 V peak-to-peak and an output voltage with a peak of 9V. The load impedance is 1 kΩ and the amp draws 9.5 mA from each power supply. Determine:

- the voltage gain- the current gain- the power gain- the power drawn from supplies- the power dissipated and η

Problem

9 91

ov

i

VAV

= = =

9ˆ 91oI mAk

= =Ω

20log 20log 9 19.1v dB vA A dB− = = =

ˆ 9 90ˆ 0.1o

ii

IAI

= = =The current gain is


Problem

40.5 8100.05

dv

I

PAP

= = =

20log90 39.1i dBA dB− = =

9 9 40.52 2L o rms o rmsPower at Load P V I mW− −= = = =

1 0.1 0.052 2I I rms I rmsPower at input P V I mW− −= = = =

10log810 29.1v dBA dB− = =

10 9.5 10 9.5 190dcP mW= × + × =

dissipated dc I LP P P P= + −

190 0.05 4.05 149.6dissipatedP mW= − − =

100 21.3%L

dc

PP

η = × =


Biasing of Amp

( ) ( )I QI IV t V v t= +

Bias will provide quiescent points for input and output about which variations will take place. Bias maintain amplifier in active region.

( ) ( )o QO oV t V v t= +

( ) ( )o v Iv t A v t=o

vI at Q

dvAdv

=

Amplifier characteristics are determined by bias point


Voltage Amplifier

vo i Lo

L o

A v RvR R

=+

: o vo Lv

i L o

v A RVoltage gain is Av R R= =

+

Want Ro small (as small as possible) to achieve maximum gain ideal Ro=0

ii s

i S

RInput v vR R

=+

Want Ri large ( so vi≈vs) (actually want Ri >> Rs) ideal Ri=∞

: o i Lvo

s i s L o

v R ROverall gain Av R R R R

= ⋅+ +


In some cases, connecting load to source leads to signal attenuation; for this case an amplifier with a high input resistance (greater than source) is needed and low output resistance. Such an amplifier is a buffer amplifier.

Voltage Amplifier


Voltage Amplifier

0

:o

ovo

i i

vOpen Circuit Voltage Gain Av

=

=

: iideal R = ∞0oR =


Current Amplifier

0

:o

ois

i i

iShort Circuit Current Gain Ai

=

=

: 0iideal R =

oR = ∞


Transconductance Amplifier

Short Circuit Transconductance : om

i

iGv

=

: iideal R = ∞

oR = ∞


Transresistance Amplifier

Open Circuit Transresistance : om

i

vRi

=

: 0iideal R =0oR =


Small-Signal Model

• What is a small-signal incremental model?

– Equivalent circuit that only accounts for signal level fluctuations about the DC bias operating points

– Fluctuations are assumed to be small enough so as not to drive the devices out of the proper range of operation

– Assumed to be linear

– Derives from superposition principle


Common Emitter ConfigurationThe emitter current IE can be approximated as:

/BE TV VE SI I e

An incremental conductance ge can be defined as

/BE TV VSE Ee

BE T T

II Ig eV V V∂

≡ = =∂

1 Te

e E

Vrg I

= =

26Usually, 26T eE

mVV mV rI

= ⇒ =

From which we get:

Emitter resistance


Hybrid-π Incremental Model for BJTs

rπ: input resistance looking into the baserx: parasitic series resistance looking into base – ohmic base resistancegm: BJT transconductancero=rce: output collector resistance related to the Early effect


Hybrid-π Parameters

tanC

C Cm

BE TI cons t

i Igv V

=

∂= =∂

:b

vr is defined as riπ

π π =

mb

g vSince i π

β=

m

then rgπβ

=

A Ace o

C B

V Vr r

I Iβ= = =

is associated with the Early effectce or r=

( )1 er rπ β= +

me

grα

=

mg rπβ =

Can show that

1 1m

e

gr rπ

+ =


Common Emitter (CE) Amplifier

Bias: Choose R1 & R2 to set VB VE is then set. Choose RE to set IE~IC. Quiescent point of Vout will be determined by RC. Emitter is an AC short.


Incremental Model for CE Amplifier

1 2BR R R=

Hybrid-π model (ignoring rx)

iin B

i

vR R ri π= =

B inSometimes R r and R rπ π

rπ

E

ro

+

-

gmvπ

vout

RCvin

C

RB

Rsig

+vπ

-

RL

B

+

vi

-

ii io


( )( )

B o C Lo m sig

B sig

R r r R Rv g v

R r Rπ

π

= −+

iv vπ=( )o m o C Lv g v r R Rπ= −

( )ov m o C L

i

vA g r R Rv

= = −

gain from base to collector

, sigB i

sig

v rand if R r v

r Rπ

ππ +

( )sig in sig B

iin sig B sig

v R v R rv

R R R r Rπ

π

= =+ +

CE Amplifier


Open-circuit voltage gain:

( )vo m o CA g r R= −

In most cases o C vo m Cr R A g R⇒ = −

( )( ) ( )B

v m o C LB sig

R rG g r R R

R r Rπ

π

= −+

( )o C Lv

sig

r R RG

r Rπ

β= −

+

and for the case where BR rπ

CE Amplifier


Output Impedance

out C oR R r=

,o C out CIf r R R R

Lv vo

L o

Rfrom which A AR R

⎛ ⎞= ⎜ ⎟+⎝ ⎠

It can be seen that if Rsig >> rπ, the gain will be highly dependent on β. This is not good because of β variations

( ),sig v m C L oIf R r G g R R rπ −

CE Amplifier


CE with External Resistors


( )out m L Cv g v R Rπ= −

xm

E

v vg vR r

ππ

π

= +

1E Bin m E

R Rv g R vr r ππ π

⎛ ⎞= + + +⎜ ⎟⎝ ⎠

( )1

m L C inout

E Bm E

g R R vv R Rg R

r rπ π

= −+ + +


in x Bvv v v Rrπ

ππ

= + +


( ) ( )1

11

MB m L CE B

A g R RR R

r rπ π

β= −

++ +

RE and RB degrade the gain


( ) ( )( )1

m L C m L Cout

in m E E B E B

g r R R g r R Rvv g r R R r R R r R

π π

π π πβ= − = −

+ + + + + +

( )( )1

L CMB

E B

R RA

R r Rπ

ββ

= −+ + +


( )( )

( )

( ) ( )

11

1 1

L CL C

MBBE B

E

R RR R

A r RR r R R ππ

ββ ββ

β β

⎛ ⎞⎜ ⎟+⎝ ⎠= − = −

+ + + + ++ +

The gain can be written as:

( )and since =

1β α

β +

( )L CMB

E e

R RA

R rα

= −+


( )neglecting

1BR

β +


Given VBEON=0.6V, find the gain for the circuit shown

1.5BQV V=

Example

1 2

0.9 0.9 0.91E

E E

I mAR R k

= =+ Ω

1.5 0.6 0.9EQV V V V= − =


1CMB

E e

RA withR rα α= −+

26 28.80.9

Te

E

VrI

= = = Ω

0.9 12 0.9 10 3C outQI mA V V V⇒ = − × =

AC analysis: RE2 is shorted and RE=RE1=100Ω. Since β is not known, use:

10,000 77.5100 28.8MBA = − = −

+

Example (Cont’)

77.5MBA = −


1o m E m E

vv g v R v g Rr rπ

π ππ π

⎛ ⎞ ⎛ ⎞= + = +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

Emitter Follower

1in B b o E m B

vv v R i v v v R g Rr r

ππ π π

π π

⎛ ⎞= + + = + + +⎜ ⎟

⎝ ⎠

Incremental modelcircuit


Emitter follower has unity voltage gain

( )( )

11

11 1

m Em Eo

in m E BBm E

g Rg r Rrv

v g r R r RRg Rr r

ππ

π π

π π

⎛ ⎞+⎜ ⎟ +⎝ ⎠= =

+ + +⎛ ⎞+ + +⎜ ⎟

⎝ ⎠

Emitter Follower

Using mg rπ β=( )

( )1

11

Eo

in E B

Rvv R r Rπ

ββ

+=

+ + +

11 Bin E m

Rv v R gr rππ π

⎡ ⎤⎛ ⎞= + + +⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦


( )1in B Er r R Rπ β= + + +

Emitter Follower – Input Impedance

( )1 / 1//

B E minin

b

v R r R g rvri v r

π π π

π π

⎡ ⎤+ + +⎣ ⎦= =


Emitter Follower – Output Impedance

oB

B

vir Rπ

= −+

o o o m o oo m

E B E B B

v v v g r v vi g vR r R R r R r R

ππ

π π π

= − + = + ++ + +

[ ] ( )1 1 1( 1)m

o o o B EE B B E B

gi v v r R RR r R r R R r Rπ

π π π

β⎡ ⎤

= + + = + + +⎢ ⎥+ + +⎣ ⎦


Using mg rπ β=

( ) ( )( )

/ ( 1)( 1) / ( 1)

E B E Boout

o B E E B

R r R R r Rv Ri r R R R r R

π π

π π

ββ β

+ + += = =

+ + + + + +

( ) / ( 1)out E BR R r Rπ β= + +

' '( 1)( 1) 1

EMB out E

E

rRA and R Rr R

π

π

ββ β+

= =+ + +

Output Impedance (cont’)

If we neglect RB


Common Base Configuration


,i o m C m i Cv v v g v R g v Rπ π= − = − =

o Cm C

i e

v RVoltage gain g Rv r

α= = =

( ) 11o m m

i im

i g v g vCurrent gaini i

g vr

π π

ππ

β αβ

−= = = = =

+⎛ ⎞+ −⎜ ⎟

⎝ ⎠

out CR R= 1inrr π

β=

+

Common Base Configuration


m Cg R

CR

1rπ

β +

/( 1)ER rπ β +

( )1Er Rπ β+ +

1m Cg R−

rπ

CR

CE CB EF

Avo

Rin

Rout

BJT Topologies - Summary

ECE 442 Solid State Devices Circuits 7. BJT Amplifiers

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