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1

SingleSingle StageStage Amplifier,Amplifier, CharacterizingCharacterizing BJTBJTAmplifiers,Amplifiers, CE,CE, CCCC andand CGCG Amplifiers,Amplifiers, BJTBJT InternalInternal

1

CapacitancesCapacitances andand HighHigh FrequencyFrequency Model,Model,FrequencyFrequency ResponseResponse ofof CE,CE, BJTBJT logiclogic InverterInverter..

Lecture # 8Lecture # 8

Single Stage AmplifierSingle Stage Amplifier

3 Configurations, Common Emitter, Common Base and Common Collector. In the following circuit a constant current biasing isselected, we would also like to select the base resistance to be large to have large input resistance and at the same time we would liketo limit the voltage drop across base resistance also more importantly the variability of this drop due to variations in the beta value fordifferent transistors of the same type. The dc voltage VB basically, determines the allowable signal swing at the collector.

Copyright © 2004 by Oxford University Press, Inc.2

Basic structure of the circuit used to realize single-stage, discrete-circuit BJT amplifier configurations.

2

Exercise 5.41Exercise 5.41


Characterizing BJT AmplifiersCharacterizing BJT Amplifiers

Amplifier can be unilateralunilateral or nonnon--unilateralunilateral, basically a non-unilateral amplifier is the one in which Rin may depend on RLand Rout may depend on Rsig, in contrast for unilateral amplifierthere is no such dependency, as Rin = Ri and Rout = Ro.


3

DefinitionsDefinitions

Ri

ovo

Ri

iin

iA

vvA

ivR

L

L

≡

≡

∞=

∞=

≡

≡

≡

oi

i

ov

i

iin

iiA

vvA

ivRInput resistance with no load:

Open circuit gain:

Input resistance:

Voltage gain:

Current gain:

sig

ov

vx

xo

Ri

om

Ri

ois

vvG

ivR

viG

iiA

i

L

L

≡

≡

≡

≡

=

=

=

0

0

0

∞=

=

≡

≡

L

sig

Rsig

ovo

vx

xout

ii

vvG

ivR

i

0

Short circuit gain:

Short circuit trans-conductance:

Output resistance of amplifier proper:

Overall voltage gain:

Current gain:

Output resistance :

Open circuit Overall voltage gain:

Lini RAARv


outL

Lvovvo

sigi

ivo

oL

Lvo

sigin

invomvo

oL

Lvov

sigin

in

sig

i

RRRGGA

RRRG

RRRA

RRRGRGA

RRAA

RRvv

+=

+=

++==

+=

+=

Example 5.17Example 5.17

iminouto

vvivovo

AGRRRGARGA


4



Common Emitter AmplifierCommon Emitter AmplifierUnilateral or Non-Unilateral

& ooutiin RRRR ==

Signal Ground, by pass capacitor (µF – 10 of µF)


(a) A common-emitter amplifier using the structure. (b) Equivalent circuit obtained by replacing the transistor with its hybrid-π model.

5

Common Emitter AmplifierCommon Emitter Amplifier

)||()||(

moderate) tolow as considered ,k few of range in the is(It normally

grounded isemitter since base, theinto looking resistanceinput theis

||

sig

sigi

BsigB

sigin

sigin

sigi

in

Bib

ib

ibBi

iin

rRr

vv

rRRrR

vR

RRv

v

rRrRrR

R

RRivR

+≅

+=

+=

Ω≅>>=

=≡

ππ

ππ

π

ππ


load tosource from-Gain --- )||||()||(

)||( slightly), resistanceoutput thereduce ( , ||

10%)by gain thereduce ( usually )||( )(gain circuit open )||||(

)||||(

LComsigB

Bv

CoutooCout

ooCCmvo

ComvoLLComv

LComo

i

g

RRrgRrR

rRG

RRrrRRrrRRgA

RrgARRRrgARRrvgv

vv

+=

≅=<<−≅

−=∞=−=−=

=

π

π

π

π



6


π

π

RRrgArRgRgA

rRRVIg

IVrRrgA

rRRRR

LC

Bminmis

oCout

T

Cm

C

AoComvo

ibibBin

)||||()||(

||

, ),||(

)( )||(

−=−=−=

=

==−=

==


ππ

πππ

ππ

ππ

π β

vRRgvRRrgVAV

vvrRvRr

rv

RrRRrRRrg

RrRrRG

RRrgA

LCmLComivo

iBsigsig

sig

LCoLCom

sigB

Bv

LComv

)||()||||(ˆˆ

)||(

)||||()||||()||(

)||()||||(

==−=

=→+

=

+=

+=

Common Emitter Amplifier with Emitter Common Emitter Amplifier with Emitter ResistanceResistance


(a) A common-emitter amplifier with an emitter resistance Re. (b) Equivalent circuit obtained by replacing the transistor with its T model. Theadvantage of using T model is that the re resistance is placed in series with the emitter resistance so it can just be added and it simplifies thedesign.

7

Common Emitter Amplifier with Emitter Common Emitter Amplifier with Emitter ResistanceResistance

)1()1(

||

eeb

b

iib

ibBin

iii

ivR

RRR

=−=

≡

=

βα

)1(

)1( )()||(

)()||(

)||( )||(

11)1(

))(1()(

)(

:factor aby increased is that means This ))(1( ,)(

)1(

em

Cmv

ee

LC

ee

LCv

LCeLCCo

eme

e

e

ee

eib

eib

ibeeibee

ie

eb

RRRg

RgA

RrRR

RrRRA

RRiRRiv

RgrR

rRr

RwithoutRincludedRwithR

RRrRRr

vi

=+

=

≅+

−≅+

−=

−=−=

+=+=+

++=

−−−

++=+

=

+

ααα

ββ

β

β


))(1()||(

eesig

LCv

Cout

RrRRRG

RR

+++=

=

ββ

The input resistance Rib is increased by a factor (1 + gmRe).

Th lt i f b t ll t i d d b

Characteristics ComparisonCharacteristics Comparison

The voltage gain from base to collector is reduced by a factor of (1 + gmRe).

For the same non-linear distortion, the input signal vi can be increased by the factor (1 + gmRe).

The over all voltage gain is less dependent on the value of beta.

Th hi h f i i ifi tl i d


The high frequency response is significantly improved.

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Common Base AmplifierCommon Base Amplifier

The gain of the CB amplifier is similar to CE, however, over all gain can be different, the low input resistanceof CB can severely affect/attenuate the input signal as:

We can see if Rsig is of the order of re, otherwise signal transmission factor vi/vsig can be very small, one of theapplication of CB is using to amplify high frequency signal that appears on coaxial cable, to stop the reflectionon the cable CB has to have an input resistance equal to the characteristics resistance of the cable, which is the

f i l bl h i i i h 0 h

esig

e

isig

i

sig

ii

isig

sigi rR

rRR

RvvR

RRv

v+

=+

=+

= ,

case for coaxial cables having resistance in the range 50 tp 75 ohms.


(a) A common-base amplifier using the basic structure shown earlier. (b) Equivalent circuit obtained by replacing the transistor with its T model.

9

Common Base AmplifierCommon Base Amplifier

)||(ein

esig

e

sig

i

RRivrR

rRr

vv

≅=

+=

α

sametheofisIfemitterinresistancetotaltocollectorin theresistance totalof ratio just the isgain allover thesince

)||( )||(

with multplying factor isgain allover The

)||()||(

)||(

esig

LCLCm

esig

ev

vsig

i

LCme

LC

i

ov

e

ie

LCeo

R

rRRRRRg

rRrG

Avv

RRgr

RRvvA

rvias

RRiv

+=

+=

==≡

−=

−≅

α

α

α


small. be gain will and asorder

sametheofisIfemitter.in resistance totaltocollector in the

LC

sig

RR

R

Common Base Amplifier SummaryCommon Base Amplifier Summary

CB has a low input resistance.The short circuit gain is near to unity.The open circuit gain is positive and equal in magnitude toCE amplifier (gmRC).CB has high output resistance.Because of the low input resistance CB is not attractive,however, it is used in special applications.


10

Exercise 5.45 & 5.46Exercise 5.45 & 5.46


CC Amplifier (Emitter Follower)CC Amplifier (Emitter Follower)


(a) An emitter-follower circuit based on the basic structure. (b) Small-signal equivalent circuit of the emitter follower with the transistor replaced by its T model augmented with ro. (c) The circuit in (b) redrawn to emphasize that ro is in parallel with RL. This simplifies the analysis considerably.

11

CC Amplifier CC Amplifier

The CC is unlike CE & CB as it is not a unilateral amplifier, the input resistance depend upon RL and the output resistance depends upon Rsig.


CC AmplifierCC Amplifier

The emitter resistance has a series resistance equal to (ro || RL).


(a) An equivalent circuit of the emitter follower obtained from the previous slide (c) by reflecting all resistances in the emitter to the base side.

(b) The circuit in (a) after application of Thévenin theorem to the input circuit composed of vsig, Rsig, and RB.

12

CC AmplifierCC Amplifier


(a) An alternate equivalent circuit of the emitter follower obtained by reflecting all base-circuit resistances to the emitter side. (b) The circuit in (a) after application of Thévenin theorem to the input circuit composed of vsig, Rsig / (β 1 1), and RB / (β 1 1).

CC Amplifier SummaryCC Amplifier Summary

As only a small fraction of the input signalappears between base and emitter, so it exhibitlinear operation over a wide range, however, therep g , ,is an upper limit imposed on the value of theoutput signal amplitude by transistor cutoff.

Increasing vsig beyond this value will go intocuttoff and the signal will be clipped off.

v

Lsig G

IRV =ˆ


Thévenin equivalent circuit of the output of the emitter follower.This circuit can be used to find vo and hence the overall voltagegain vo/vsig for any desired RL.

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CC Amplifier SummaryCC Amplifier Summary

Emitter follower has high input resistance and a low output resistance.

Voltage gain is small but close to unity.

Current gain is relatively large.

It is useful for applications where a high resistance source is to be connected with alow resistance load (last stage or output stage of a multistage amplifier.

This way its purpose is to provide a low output resistance and not the voltage gain.




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BJT Internal CapacitorsBJT Internal Capacitors

Base Charging Capacitor or Diffusion Capacitance Cde.

Base Emitter Junction Capacitance Cje.

Collector Base junction Capacitance Cμ.


Base Charging CapacitanceBase Charging Capacitance

As iC is dependent on vBE and iC is exponentially related to vBE,therefore, charge storage mechanism represent a non linearcapacitive effect.

T

CFmF

BE

CF

BE

nde

CFCn

n

VIg

dvdi

dvdQC

iiD

WQ

τττ

τ

====

==2

2


15

Base Emitter Junction CapacitanceBase Emitter Junction Capacitance

m

BE

jeoje

V

CC

1 ⎟⎟⎞

⎜⎜⎛+

=

jeoje

je

oejejeo

oe

CC

Cm

VCC

V

2

to;edapproximat isit

so , of prediction accurate providenot doesequation above the, mode active in the biasedforward is EBJ becauseout that It turns 0.5V). (typically EBJ theoft coefficien grading theis

V), 0.9 (typically in voltagebuilt EBJ theis voltage,zeroat of value theis where

≅

⎟⎟⎠

⎜⎜⎝


jeoje

Collector Base Junction CapacitanceCollector Base Junction Capacitance

C

V). 0.5 - 0.2 (typically CBJ theoft coefficien grading theis V), 0.75 (typically in voltagebuilt CBJ theis voltage,zeroat of value theis where

1

mVCC

VV

CC

oco

m

oc

CB

o

μμ

μμ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=


16

High Frequency HybridHigh Frequency Hybrid--ππ ModelModel

rAlso,ohms.oftensfewaoftypicallyisitregion,emitterunder theterminalbaseinternalfictitious theand terminalbase ebetween thregion base theof materialsilicon theof resistance theis

pF. few a topF a offraction a of range in the is as wherepF, of tensfew topF few of range in the is

x

jede

rr

CCCCC

μπ

π

<<

+=


(given). specified isfrequency vs)( ofbehaviour rather the ,specify not doessheet data The

r Also,ohms.oftensfewaoftypicallyisit region,emitter under the terminalbase internal x

fehC

r

βπ

π<<

Frequency Response of CEFrequency Response of CE


(a) Capacitively coupled common-emitter amplifier. (b) Sketch of the magnitude of the gain of the CE amplifier versus frequency. The graph delineates the three frequency bands relevant to frequency-response determination.

17

Expression for Expression for hhfefe(s) ≈ (s) ≈ IIcc/I/Ibb. .

.at frequency dB-3 a with response pole single

a has thus, of valuefrequency low theis )(1

0

0

β

πμπ

ββ

β

gw

ww

hrCCs

h

m

fe

fe

=

=

++=


)(2 μπ

μπ

π CCgf

CCw

mT

T

+=

+=

BJT High Frequency ModelBJT High Frequency Model


0

0

2 2

jejemFdejede

T

m

mC

Ao

T

Cm

CCgCCCCf

gCCg

rIV

rVIg

≅=+=

=+===

τπ

β

π

μππ

18

High Frequency ResponseHigh Frequency Response


Determining the high-frequency response of the CE amplifier: (a) equivalent circuit; (b) the circuit of (a) simplified at both the input side and the output side; (c) equivalent circuit with Cμ replaced at the input side with the equivalent capacitance Ceq; (d) sketch of the frequency-response plot, which is that of a low-pass STC circuit.

Low Frequency ResponseLow Frequency Response


Analysis of the low-frequency response of the CE amplifier: (a) amplifier circuit with dc sources removed; (b) the effect of CC1 is determined with CE and CC2 assumed to be acting as perfect short circuits;

19

Transfer Characteristics of BJT InverterTransfer Characteristics of BJT Inverter


Sketch of the voltage transfer characteristic of the inverter circuit for the case RB = 10 kΩ, RC = 1 kΩ, β = 50, and VCC = 5 V. For the calculation of the coordinates of X and Y, refer to the text.

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