7- 1st semester_BJT_AC_Analysis (re model)-1.pdf

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1. ACmodelisanequivalentcircuitthatrepresentstheACcharacteristicsofthetransistor.Itisacombination
ofcircuitelements,properlychosen,thatbestapproximatestheactualbehaviorofasemiconductordeviceunder
specificoperatingconditions.
Toanalyzetheworkingofatransistorinamplifiercircuits,itbeneficialtorepresentthedevicesintheform
ofmodelcircuits.Themodelcircuitoftransistorusesmanyinteriorparametersoftransistortodefinetheoperation.
Therearetwomodelscommonlyusedinthesmall-signalacanalysisoftransistornetworks:
1.??????
??????equivalent(dynamicresistance)model.
2.hybridequivalent(h-parameter)model.
TheParameters??????
??????,??????
??????,??????
??????,and??????
??????arethemostimportantparametersfortheanalysisoftheACcharacteristicsofa
transistorcircuit.
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed
TransistorACModeling
1

2. Importantproceduresforacanalysis(smallsignalanalysis)
1.Settingalldcsourcestozeroandreplacingthembyashort-circuitequivalent
2.Replacingallcapacitorsbyashort-circuitequivalent
3.Removingallelementsbypassedbytheshort-circuitequivalentsintroducedbysteps1and2
4.Redrawingthenetworkinamoreconvenientandlogicalform.
5.Definingtheimportantparametersofthetransistormodel.
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed
TransistorACModeling
2

3. University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed 3

4. Common-EmitterConfiguration
Theequivalentcircuitforthecommon-emitterconfigurationwillbeconstructedusingthedevicecharacteristicsanda
numberofapproximations.Startingwiththeinputside,wefindtheappliedvoltage??????
??????isequaltothevoltage??????
??????�
(0.7)withtheinputcurrentbeingthebasecurrent??????
??????.
Ifweredrawthecollectorcharacteristicstohaveaconstant??????(anotherapproximation),theentirecharacteristicsatthe
outputsectioncanbereplacedbyacurrentcontrolledsourcewhosemagnitudeisbetatimesthebasecurrent.
Becausealltheinputandoutputparametersoftheoriginalconfigurationarenowpresent,theequivalentnetworkfor
thecommon-emitterconfigurationhasbeenestablished.
Theequivalentmodelcanbeimprovedbyfirstreplacingthediodebyitsequivalentresistance??????
�=
�??????????????????
??????
�
.
Usingthesubscriptebecausethedeterminingcurrentistheemittercurrentwillresultin??????
�=
�??????????????????
??????
�
??????
??????=
??????
??????
??????
??????
=
??????
????????????
??????
??????
??????
�??????=??????
????????????
??????=??????
�+??????
�??????
??????
??????
�??????=�??????
�+??????
�??????
??????=�+1??????
�??????
??????
??????
??????=
??????
????????????
??????
??????
=
�+1??????
??????�
??????
??????
??????
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed
The??????
�TransistorModel
4

5. Theresultisthattheimpedanceseen“lookinginto”thebaseofthenetworkisaresistorequalto
betatimesthevalueof??????
�.Thecollectoroutputcurrentisstilllinkedtotheinputcurrentbybeta
asshowninthesamefigure.
Theoutputimpedance??????
??????canbecalculatedanditisappearasaresistorinparallelwiththeoutput
asshownintheequivalentcircuit.
Forthecommon-emitterconfigurationthereisa180°phaseshift.
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed 5

6. Common-BaseConfiguration
Thecommon-baseequivalentcircuitwillbedevelopedinmuchthesamemannerasappliedtothe
common-emitterconfiguration.
Fortheacresponse,thediodecanbereplacedbyitsequivalentacresistancedeterminedby
Thenetworkofisanexcellentequivalentcircuitfortheanalysisofmostcommon-baseconfigurations.Itis
similarinmanywaystothatofthecommon-emitterconfiguration.
Ingeneral,common-baseconfigurationshaveverylowinputimpedancebecauseitisessentiallysimply
??????
�.Typicalvaluesextendfromafewohmstoperhaps50Ω.Theoutputimpedance??????
??????willtypicallyextend
intothemegaohmrange.
Becausetheoutputcurrentisoppositetothedefined??????
??????direction,youwillfindintheanalysistofollow
thatthereisnophaseshiftbetweentheinputandoutputvoltages.
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed 6

7. Common Emitter, Fixed Bias Configuration
Circuit analysis
Inputimpedance(??????
??????)
??????
??????=??????
�∖∖????????????
�
(For??????
�largerthan10????????????
�)
??????
??????≅�??????
??????
Outputimpedance(??????
??????)
??????
??????=??????
�∖∖??????
??????
(For??????
??????largerthan10??????
�)
??????
o≅??????
C
Voltagegain(�
??????)
??????
??????=
??????
??????
??????
??????
??????
??????=−�??????
�??????
�∖∖??????
??????
??????
??????=??????
��??????
??????
??????
??????=
??????
??????
??????
??????
=
−�??????
??????�
�∖∖�
??????
�??????
??????�
??????
If??????
??????≫��??????
�,sothattheeffectof??????
??????canbeignored,
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed 7

8. EXAMPLE 1
For the network shown in the Figure determine:
a)Determine ??????
??????.
b)Determine ??????
??????,??????
??????and ??????
??????(with ??????
??????=∞).
c)Repeat parts (b) including (??????
??????=50??????Ω).
Solution:
a) ??????
�=
??????
��−??????
��
�
�
=
12??????−0.7??????
470??????Ω
=24.04????????????
??????
�=�+1??????
�=100+124.04????????????=2.428????????????
??????
??????=
26????????????
????????????
=
26????????????
2.428??????�
=10.71Ω
b) ??????
??????=??????
�∖∖�??????
??????=1.07??????Ω
??????
o=??????
C∖∖??????
o=3??????Ω∖∖∞=??????
C=3??????Ω
??????
??????=
−�
�∖∖�
??????
�
??????
=
−�
�
�
??????
=
−3??????Ω
10.7Ω
=−280.1
c) ??????
o=??????
C∖∖??????
o=3??????Ω∖∖50??????Ω=2.83??????Ω
??????
??????=
−�
�∖∖�
??????
�
??????
=
−3??????Ω∖∖50??????Ω
10.7Ω
=−264.24
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed 8

9. Common Emitter, Voltage Divider Bias Configuration
??????
�and??????
�remainpartoftheinputcircuit,whereas??????
�ispartoftheoutputcircuit.Theparallel
combinationof??????
1and??????
2isdefinedby??????
′
=??????
�∥??????
�.
Inputimpedance(??????
??????)
Forlarge??????
�(largerthan10�??????
??????)??????
??????≅�??????
??????
Outputimpedance(??????
??????)
For??????
olargerthan10R
C) ??????
o≅??????
C
Voltagegain(�
??????)
Electrical Engineering Dept / Year Two / Semester I / Electronic I / Dr. Ahmed M. Mohammed 9

10. EXAMPLE 2
For the network shown in the Figure determine:
a)Determine ??????
??????.
b)Determine ??????
??????,??????
??????and ??????
??????(with ??????
??????=∞).
c)Repeat parts (b) including (??????
??????=50??????Ω).
Solution
a) ??????
�=??????
��.
�
2
�1+�2
=22
8.2??????Ω
56+8.2??????Ω
=2.81??????
??????
�=??????
�−??????
��=2.81−0.7=2.11??????
??????
�=
??????�
��
=
2.11??????
1.5??????Ω
=1.41????????????
??????
??????=
26????????????
1.41??????�
=18.44Ω
b) ??????
′
=??????
1∥??????
2=7.15??????Ω
??????
??????=??????
′
∖∖�??????
??????=1.35??????Ω
??????
o=??????
C∖∖??????
o=??????
C=6.8??????Ω
??????
??????=
−��∖∖�??????
�
??????
=
−��
�
??????
=
−6.8??????Ω
18.44Ω
=−368.76
c)???
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed 10

11. CE Emitter-Base Configuration with ??????
�(Unbypassedcircuit analysis)
Applying Kirchhoff’s voltage law to the input side
??????
??????=??????
��??????
??????+??????
????????????
�
??????
??????=??????
��??????
??????+(�+1)??????
�??????
�
the input impedance looking into the network to the right of ??????
�is:-
??????
�=
??????
??????
??????
??????
=
??????
??????[��
??????+�+1�
�]
??????
??????
=�??????
??????+�+1??????
�
for
for
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed 11

12. Unbypassed circuit analysis
Input impedance (??????
??????).
??????
??????=??????
�∥??????
??????
Output impedance (??????
??????)
??????
??????=??????
�
Voltage gain (�
??????)
??????
??????=??????
�??????
�
??????
??????=−??????
????????????
�=−�??????
�??????
�
??????
??????=
????????????
??????
??????
=
−�????????????��
????????????????????????
=
−���
????????????
??????
??????=
−���
�(�??????+��)
=
−??????�
??????�+??????�
??????
??????≅
−??????�
??????�
for
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed12

13. EXAMPLE 3
For the network, determine: (a) r
e,Z
i,Z
o,andA
vwithout C
E(unbypassed),
(b) Repeat the analysis with C
Ein place (bypassed).
solution
a) ??????
�=
??????
��−??????
��
��+(�+1)��
=
20−0.7
470??????Ω+121(0.56??????Ω)
=35.89????????????
??????
�=�+1??????
�=4.34????????????
??????
??????=
26????????????
??????
�
=5.99Ω
??????
�=�??????
??????+??????
�=67.92??????Ω
??????
??????=??????
�∥??????
�=59.34??????Ω
??????
??????=??????
�=2.2??????Ω
??????
??????=
????????????
??????
??????
=
−���
??????
??????
=−3.89
b)??????
�=�??????
??????
??????
??????=??????
�∥??????
�=??????
�∥�??????
??????=717.7Ω
??????
??????=??????
�=2.2??????Ω
??????
??????=
????????????
??????
??????
=
−��
�
??????
=−367.28
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed 13

14. EXAMPLE 4
ForthenetworkofFigure,withC
Eunconnected(Unbypassed),determine:
a)r
e,Z
i,Z
o,andA
v. b)RepeattheanalysiswithC
Einplace(bypassed).
Solution (a) (Unbypassed)
DC analysis: -??????
�=??????
��.
�2
�1+�2
=1.6??????
??????
�=??????
�−??????
��=0.9??????
??????
�=
??????�
��
=1.324????????????
??????
??????=
26????????????
??????�
=19.64Ω
ACanalysis??????
′
=??????
1∥??????
2=9??????Ω
??????
�=�(??????
??????+??????
�)=210(19.64+0.68??????)=146.924??????Ω
??????
??????=??????
′
∥??????
�=8.47??????Ω
??????
??????=??????
�=2.2??????Ω
??????
??????=
−??????�
??????�+??????�
=−�.��
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed 14

15. Solution(b)(bypassed)
DCanalysis(thesameasinsection(a))
ACanalysis
??????
�=�(??????
??????+??????
�)=146.924??????Ω
??????
??????=??????
′
∥??????
�=2.83??????Ω
??????
??????=??????
�∥??????
??????=2.2??????Ω∥50??????Ω
??????
??????=
−��∥�??????
�??????
=−
2.2????????????∥50????????????
19.64
=
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed15

16. Note
Anothervariationofanemitter-biasconfigurationisshownbelow.Forthedcanalysis,theemitter
resistance(??????
�)is(??????
�1+??????
�2),whereasfortheacanalysis,theresistor(??????
�)intheequationsaboveis
simply(??????
�1)with(??????
�2)bypassedbyC.
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed16

17. Collector Feedback Configuration
Thecollectorfeedbacknetworkofthefigurebelowemploysafeedbackpathfromcollectortobaseto
increasethestabilityofthesystemasdiscussedin(DCanalysis).However,thesimplemaneuverof
connectingaresistorfrombasetocollectorratherthanbasetodcsupplyhasasignificanteffectonthe
levelofdifficultyencounteredwhenanalyzing(ac)thenetwork.
Substitutingtheequivalentcircuitandredrawingthenetworkresultsintheconfigurationshownbelow.
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed17

18. Collector Feedback Configuration
Inputimpedance(??????
??????)
??????
??????=
??????
??????
??????
??????
??????
??????=??????
��??????
??????
??????
??????=??????
�−??????
′
??????
′
=
????????????−??????
??????
��
??????
??????=−??????
????????????
�=−(??????
′
+�??????
�)??????
�
??????
′
=
−(??????
′
+�??????
??????)��−??????
??????��??????
��
??????
′
=
−??????
′
��
�
�
−
�??????
??????��
�
�
−
�??????
??????�??????
�
�
Bysimplifying
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed18
??????
′
1+
??????
�
??????
�
=−�??????
�
??????
�+??????
??????
??????
�
??????
′
=−�??????
�
(�
�+�
??????)
��+��
??????
??????=??????
�+�??????
�
(��+�??????)
��+��
??????
??????=??????
�1+�
�
�+�
??????
��+��
??????
??????=
??????
??????��??????
??????
??????1+�
??????
�
+????????????
??????
�
+??????
�
=
��??????
1+�
??????
�
+????????????
??????
�
+??????
�
Since??????
�≫≫??????
??????
??????
??????=
�??????
1
??????
+
??????
�
??????
�
+??????
�

19. Collector Feedback Configuration
Output impedance (??????
??????)
If (??????
??????)is set to zero as required to define ??????
??????, the network will appear as shown below. The effect of (�??????
??????)is
removed, and (??????
�)appears in parallel with (??????
�)and :-
Z
??????=??????
�∕∕??????
�
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed19

20. Collector Feedback Configuration
Voltage gain (�
??????)
??????
??????=
????????????
??????
??????
??????
??????=??????
��??????
??????
??????
??????=−??????
????????????
�=−(??????
′
+�??????
�)??????
�
??????
??????=−(−�??????
�
(��+�??????)
��+��
+�??????
�)??????
�
??????
??????=−�??????
�(1−
��+�??????
��+��
)??????
�
??????
??????=
−�??????
??????(1−
??????
�
+????????????
??????
�
+??????
�
)��
??????
??????��??????
??????
??????=−1−
��+�??????
�
�+�
�
��
�
??????
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed20
Since??????
�≫≫??????
??????
??????
??????=−1−
�
�
��+��
�
�
�??????
??????
??????=−
��
�
�+�
�
��
�
??????
the negative sign indicates a 180°phase shift
between ??????
??????and ??????
??????.

21. Collector Feedback Configuration with ??????
�
For the configuration of the figure shown below, the following equations are use to determine the variables
of interest.
Input impedance (??????
??????)
??????
??????=
��
1
??????
+
??????
�
+??????
�
??????
�
Output impedance (??????
??????)
Z
??????=??????
C∕∕??????
�
Voltage gain(�
??????)
�
??????=−
��
��
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed21

22. Common-Base Configuration
Thecommon-baseconfigurationischaracterizedashavingarelativelylowinputandahighoutputimpedanceanda
currentgainlessthan1.Thevoltagegain,however,canbequitelarge.ThestandardconfigurationappearsinFigure
bellow,withthecommon-base??????
�equivalentmodelsubstituted.
inputimpedance??????
??????
??????
??????=??????
�∥??????
??????
Outputimpedance??????
??????
??????
??????=??????
�
Voltagegain�
??????
??????
??????=??????
????????????
??????
??????
??????=−??????
????????????
�=�??????
????????????
�
??????
??????=
??????
??????
??????
??????
=
�??????
??????�
�
??????
??????�
??????
??????
??????=
���
�??????
≅
�
�
�
??????
(for�=1)
Current gain �
??????
??????
i=
I
??????
I
??????
=−α=−1
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed22

23. EXAMPLE 5
ForthenetworkshownintheFigure,determine:-r
e,Z
i,Z
o,A
vandA
i.
solution
??????
�=
??????��−??????��
�
�
=1.3????????????
??????
??????=
26????????????
??????�
=
26????????????
1.3??????�
=20Ω
??????
??????=??????
�∥??????
??????=19.61Ω
??????
??????=??????
�=5kΩ
??????
??????=
????????????
??????
??????
=
���
�
??????
=245
??????
i=−α=−0.98
University of Technology / Electrical Engineering Dept/ Electronic I / Dr.Ahmed M. Mohammed 23

24. CommonCollector(Emitter-Follower)Configuration
WhentheoutputistakenfromtheemitterterminalofthetransistorasshowninFigure,the
networkisreferredtoasanemitter-follower.Theoutputvoltageisalwaysslightlylessthanthe
inputsignalduetothedropfrombasetoemitter,buttheapproximationA
v=1isusuallyagood
one.Unlikethecollectorvoltage,theemittervoltageisinphasewiththesignalV
i.Thatis,both
V
oandV
iattaintheirpositiveandnegativepeakvaluesatthesametime.ThefactthatV
o
“follows”themagnitudeofV
iwithanin-phaserelationshipaccountsfortheterminologyemitter-
follower.
University of Technology / Electrical Engineering Dept/ Electronic I / Dr.Ahmed M. Mohammed 24

25. Substitutingthe??????
??????equivalentcircuitintothenetworkoffigureaboveresultsthenetworkoffigurebelow.
Theinputimpedanceisdeterminedinthesamemannerasdescribedearlierinthislecture.
inputimpedance??????
??????
??????
??????=??????
�∥??????
�
??????
�≅�(??????
??????+??????
�)
outputimpedance??????
??????
I
b=
??????
i
Z
b
??????
??????=�+1??????
�⇒⇒⇒??????
??????=�+1
??????
i
Z
b
SubstitutingforZ
bgives;-??????
??????=
�+1??????
i
�(�??????+��)
Solvingfor�+1≅�andsettheinputvoltagetozero
??????
??????=
�+1??????
i
�(�??????+��)
=
??????
??????
�??????+��
??????
o=??????
�∥??????
??????
??????
o≅??????
?????? for??????
�≫??????
??????
Voltagegain�
??????
A
v=
??????o
??????
i
=
RE
RE+re
A
v=
??????
o
??????
i
≅1 for(??????
�≫??????
??????)
University of Technology / Electrical Engineering Dept/ Electronic I / Dr.Ahmed M. Mohammed 25

26. Effect of ??????
??????and ??????
�
Alltheparametersdeterminedbeforehavebeenforanunloadedamplifierwiththeinput
voltageconnecteddirectlytoaterminalofthetransistor.Nowtheeffectofapplyingaloadtothe
outputterminalandtheeffectofusingasourcewithaninternalresistancewillbeinvestigated.
Asshowninthenetworkbelow.
??????
??????NL=
??????
??????
??????
??????
??????
??????L=
??????
??????
??????
??????
??????
??????s=
??????
??????
??????
s
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed 26

27. Theloadedvoltagegainofanamplifierisalwayslessthantheno-loadgain.
Inotherwords,theadditionofaloadresistor??????
??????totheconfigurationwillalwayshavetheeffectof
reducingthegainbelowtheno-loadlevel.
Thegainobtainedwithasourceresistanceinplacewillalwaysbelessthanthatobtainedunderloaded
orunloadedconditionsduetothedropinappliedvoltageacrossthesourceresistance.
Intotal,therefore,thehighestgainisobtainedunderno-loadconditionsandthelowestgainwithasource
impedanceandloadinplace.Thatis:
For the same configuration ??????
??????????????????>??????
????????????>??????
??????�
Foraparticulardesign,thelargerthelevelof(??????
??????),thegreateristhelevelofacgain.
Inotherwords,thelargertheloadresistance,thecloseritistoanopen-circuitapproximationthatwould
resultinthehigherno-loadgain.
Inaddition:
Foraparticularamplifier,thesmallertheinternalresistanceofthesignalsource,thegreateristhe
overallgain.
Inotherwords,thecloserthesourceresistanceistoashort-circuitapproximation,the
greateristhegainbecausetheeffectofRswillessentiallybeeliminated.
Foranynetworkthathavecouplingcapacitors,thesourceandloadresistancedonotaffectthedc
biasinglevels.
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed27

28. ForCommonEmitterConfiguration
??????
??????=??????
B∥β??????
?????? ??????
??????NL=
????????????
??????
??????
=
−��∥�o
re
??????
o=??????
C∥??????
o ??????
??????L=
????????????
??????
??????
=
−��∥RL∥�o
re
??????
??????
′
=??????
C∥??????
o∥R
L ??????
??????s=
????????????
??????s
=
????????????
??????
i
×
??????
i
??????s
=??????
??????L×
Z
i
Z
i+Rs
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed 28

29. For(emitter-follower)CommonCollectorConfiguration
??????
??????=??????
�∥??????
�
??????
�≅�[??????
??????+(??????
�∥R
L)]
??????
o=??????
�∥??????
??????
??????
??????
′
=??????
�∥R
L∥??????
??????
A
vNL=
RE
RE+re
A
vL=
RE∥RL
(RE∥RL)+re
??????
??????s=
????????????
??????s
=
????????????
??????
i
×
??????
i
??????s
=??????
??????L×
Z
i
Z
i+Rs
University of Technology / Electrical Engineering Dept / Electronic I / Dr. Ahmed M. Mohammed29