Analisador paramétrico de Transisistores (Parametric BJT analyzer)
•
0 recomendaciones•309 vistas
Relatório de trabalho realizado no âmbito do projeto final. Deve ser lido em conjunto com os anexos - Testador paramétrico de transistores.
Recomendados
Recomendados
Más contenido relacionado
La actualidad más candente
La actualidad más candente (20)
Destacado
Destacado (18)
Más de Fernando Rui Campos
Más de Fernando Rui Campos (20)
Analisador paramétrico de Transisistores (Parametric BJT analyzer)
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
- 7. V +'1+ .&)63I&+ +&%4- &?&,'21)1+ 1 2.1 '&./&%1'2%1 /%&)&?6(6)1 &('%& N & !"N + +:2&.1+ )& 5-,-+ )- +6+'&.1 +4- -+ 1/%&+&('1)-+ (1+ )21+ ?6<2%1+ +&<26('&+ D@&% ?6< & ?6< E -+ &+:2&.1+ &. ,12+1 (4- +& &(,-('%1. %&/%&+&('1)-+ (&. 1 156.&('134- (&. 1 /%-<%1.134- %&156=1)1 ! " # $%#&" ' ( () ( * + , # - . / 00 1 2 3+ 3+ . 4 " # - 3+ 1 $ ?6< * 61<%1.1 )& 5-,-+ )&'1591)-
- 8. F ?6< * +:2&.1 <&%15 )& 5-,-+
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≈∆ "N 7/5(<(&,2*0 2% *'=1&(, 1./56?6,1)-% )& /-'O(,61 A 2'656=1)- &. )-6+ ,6%,26'-+ 6()&/&()&('&+K 2. /1%1 <&%1% 1 '&(+4- &('%& - ,-5&,'-% & - &.6++-% )- '%1(+7+'-% &. '&+'& & - +&<2()- /1%1 <&%1% 1 '&(+4- 1/56,1)1 R +17)1 )1 ,A5251 )& &5'6&%
- 11. 1 6./5&.&('134- /%8'6,1 -/'-2*+& /&51 2'656=134- )- 1./56?6,1)-% )& /-'O(,61 " "> )1)- +2/-%'1% 1+ '&(+I&+ & ,-%%&('&+ &(@-5@6)1+ (1 A5251 )& &5'6&% )& 1,-%)- ,-. 1+ +21+ ,1%1,'&%7+'6,1+ '656=1%1.*+& '&(+I&+ )& 156.&('134- +6.A'%6,1+ )& L ! )& .-)- 1 :2& &. ,1+- )& +1'2%134- )- 1./56?6,1)-% )& /-'O(,61 1 '&(+4- R &('%1)1 )1 ,A5251 (4- &B,&)1 - @15-% .8B6.- 1).6'6)- /-% &+'1 '&(+4- )& 156.&('134- .7(6.1 )&+'& 1./56?6,1)-% A )& ! (0&4('*+ 2% /0*'%&-.* 2, &?545, 2% %5'(%0 /%-'&,34- )1 ,A5251 A ,-(+'6'27)1 /-% )-6+ ,6%,26'-+ 6()&/&()&('&+K /%6.&6%- A 2. ,6%,26'- ,-./1%1)-% %&<&(&%1'6@- :2& )&'&,'1 +& 1 '&./&%1'2%1 .8B6.1 )1 ,A5251 DF N E> +& &(,-('%1 (- 56.61% 102+'1)- DF"N E . ,1+- )1 '&./&%1'2%1 +&% 1'6(<6)1> 1,'21%8 2. '%1(+7+'-% ,20- %&+25'1)- +&%8 1 )6.6(2634- )1 '&(+4- )& &('%1)1 )- ./56?6,1)-% /&%1,6-(15 )& -'O(,61 -.- ,-(+&:2O(,61 1 '&(+4- (1 &('%1)1 )1 ,A5251 )6.6(26%8 1;%2/'1.&('& /%-'&<&()- 1++6. 1 ,A5251 )& &@&('215 &.;151.&('- 'A%.6,- +&<2()- /%-'&<& 1 ,A5251 (1 &@&('2156)1)& )& &B6+'6%&. @15-%&+ )& '&(+4- &. .S)25- +2/&%6-%&+ 1 1/%-B6.1)1.&('& & ,-%%&('&+ +2/&%6-%&+ 1 >F /%-,&++- )& /%-'&,34- 2'656=1)- ,-(+6+'& (2.1 /-('& )& )7-)-+ &. +A%6& :2& ?2(,6-(1 /1%1 '&(+I&+ /-+6'6@1+ & (&<1'6@1+ )& .-)- 1 :2& &. ,-()63I&+ )& '&(+4- 6(?&%6-%&+ 1 > (4- &B6+'1 6(?52O(,61 (- ,6%,26'- %1+*0 % ,&*12(&(*1,2*0 2, '%7/%0,'40, ,7#(%1'% -(+'6'27)- /-% 2. +&(+-% )& '&./&%1'2%1 D ZE & 1,-()6,6-(1)-% )& +6(15 :2& &+'1;&5&,& -+ @15-%&+ )& '&(+4- /%-/-%,6-(16+ R '&./&%1'2%1 1.;6&('& )& ?-%.1 1 +&%&. .&)6)1+ /&5- ,-(@&%+-% G 1%1 &?&,'21% 1 6('&%?1,& 1- C -/'-2*+& /-% 2'656=1% 2. 1./56?6,1)-% -/&%1,6-(15 (1 .-('1<&. )& 1./56?6,1)-% (4- 6(@&%+-% & %&?&%6% :2& - +&(+-% 1/%&+&('1 2.1 ?2(34- ,1%1,'&%7+'6,1 " " − = ∆ ∆ ! ! /1%1 [ ]"∈ "
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≅(( ?6< * 61<%1.1 )& 5-,-+ ,-('%-51)-% &. .1591 ?&,91)1 +'& ,-('%-5- %&[(& 1+ 1,3I&+ /%-/-%,6-(15> 6('&<%15 & )&%6@1'6@1> - :2& +& '%1)2= R /1%'6)1 /&51 &B6+'O(,61 )& 2.1 ?2(34- )& '%1(+?&%O(,61 ,-. )-6+ =&%-+ 102+'8@&6+> 2. <1(9- ( 6<215.&('& 102+'8@&5 & 2. /S5- (1 -%6<&. ?2(34- )& '%1(+?&%O(,61 )- ,-('%-51)-% A )1)1 /-%K EDED ( ++= &()-K * -(+'1('& )& '&./- )- &?&6'- )&%6@1'6@- * -(+'1('& )& '&./- )- &?&6'- 6('&<%15
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−= _* ^ −= ^ −=
- 17. V *7,2*0 &*7 1)%0+*0 EEDEDEDDED FV! !!!! ++−= 1%1 -;'&% ,-&?6,6&('&+ 6<216+ )1+ @8%61+ '&(+I&+ )- +-.1)-%> FV! == K EEDEDEDDED ! !!!! ++−= & F () −= ED ED! −= * /&%134- &?&,'21)1 /&5- ('&<%1)-% EDED! −= * /&%134- &?&,'21)1 /&5- )6?&%&(,61)-% EDED! −= * /&%134- &?&,'21)1 /&5- -('- )& -.1 -(+6)&%1()- F () −= > +2;+'6'26()- ED! > ED! & ED! -;'A.*+&K EDEDED F (! ) ++ = ++= '%6;26()- = -;'A.*+&> ++ = (! )ED >5&45* 2*+ ,0G7%'0*+ 2* *1'0*5,2*0 /S+ 1 -;'&(34- )1 ?2(34- ,1%1,'&%7+'6,1 &. .1591 1;&%'1> )1+ ,1%1,'&%7+'6,1+ &5A,'%6,1+ )1 ,A5251 D1(&B- `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
- 18. F +'& ,-./-%'1.&('- /-)& +&% 1/%-B6.1)- 1 2. +6+'&.1 )& /%6.&6%1 -%)&. ,-. 1'%1+-> +&()- 1 ?2(34- )& '%1(+?&%O(,61 )1)1 /&51 &B/%&++4-K ED + = − , ?6< * 2%@1 )& %&1,34- )- /%-,&++- -.K ` ./56'2)& )- &+,154- ` &./- )& +2;6)1 '6%1)- )1 '1(<&('& R ,2%@1 )& +2;6)1 ` &./- )& 1'%1+- '6%1)- )1 '1(<&('& R ,2%@1 %&5134- A )1)1 /-%K τ = &()- &. ,-('1 1 %&+/-+'1 1- &+,154-> @4-*+& &B'%16% /1%1 +6+'&.1+ &. ,1)&61 1;&%'1 -+ /1%J.&'%-+ &<2()- * + -+ @15-%&+ 1,-(+&591)-+ /1%1 +6+'&.1+ &. ,1)&61 1;&%'1 ,-. &+'& '6/- )& %&+/-+'1 D,2%@1 %&1,34- /%-,&++-E +4- )1)-+ /-%K ( > = ^ = ^ >"= 1 ,2%@1 &B/&%6.&('15 :2& +&%@62 ,-.- %&?&%O(,61 1- .-)&5- D@&% ?6< VE> & 2'656=1()- 1 @1%6134- 1;+-52'1 )& 1./56'2)& 'A%.6,1> -;'A.*+&K V=−≈τ +
- 19. V ≅== N G+ & _ + ?6< * 2%@1 )& %&1,34- -;'6)1 /1%1 1 ,A5251 )& &5'6&% '656=1()- -+ @15-%&+ /1%1 1./56'2)& (4- (-%.156=1)1 1,-(+&591)-+ '&.*+&K > Va>> ===( ^ a === ^ a>">" === > & -+ /1%J.&'%-+ )&'&%.6(1)-+ /-% &+'& .A'-)- )& %&<%1+ -;'A.*+&K ++= ++= ( >">ED !>"ED + = & 1,-%)- ,-. 1 &B'%1,34- )1+ ,1%1,'&%7+'6,1+ &B/&%6.&('16+K E>"D > EGD Va!>"ED + = + = &.*+& &('4- 2. /S5- (1 -%6<&. & )-6+ =&%-+ &. `">
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b (-+ ,6%,26'-+ ,-. 1./56?6,1)-%&+ -/&%1,6-(16+ '%6;26()- - @15-% )& "" Qb 1 FV! == > %&+25'1 ""a"a F.1B .1B === ! b> & """"aa.6( .6( === ! Qb /'-2*+& /&51 ,-5-,134- &. +A%6& )& 2.1 %&+6+'O(,61 )& ""Qb &. +A%6& ,-. 2. /-'&(,6S.&'%- .25'6*@-5'1 )& b • *1'0*5* %0(),'()* & = ,-. = +,-59&()- 2. ,-()&(+1)-% )& _ >VY > '&.*+& _ b • *1'0*5* 1'%90,5 == %;6'%1()- _ >V2 )& ?-%.1 1 '&%.-+ @15-%&+ )& c_ b> ,15,251()- > ! "aV> − = ^ = Qb
- 21. • *7,2*0 &*7 1)%0+*0 % ,1H* 0*/*0&(*1,5K 1=&()- !_ V_ F_ _ ""Qb> 1'%6;262*+& - @15-% )& _ b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
- 22. +'(7,-.* 2* *2%5* 2, &?545, 2% %5'(%0 %7 7,5H, ,#%0', ++2.62*+& 2. .-)&5- 56(&1% & 6(@1%61('& (- '&./- /1%1 1 ,A5251 )& &5'6&% 4- ,-(9&,&()- - .-)&5- '&S%6,- )1 ?2(34- )& '%1(+?&%O(,61 )1 ,A5251 )& &5'6&% &+'1 ?-6 &+'6.1)1 /-% 1/%-B6.134-> 1 /1%'6% )& )1)-+ &B/&%6.&('16+ 1%1 -;'&(34- )- .-)&5- D6)&('6?6,134- )- +6+'&.1E -;'&@&*+& 1 %&+/-+'1 '%1(+6'S%61 1 /1%'6% )1 &B,6'134- )- +6+'&.1 /-% 2. &+,154- V] & 1,-%)- ,-. -+ )1)-+ -;'6)-+ &B/&%6.&('15.&('& 1 %&+/-+'1 1- &+,154- 6()6,61 +&% %&/%&+&('1)1 /-% 2. +-.1'S%6- )& &B/-(&(,616+K EDED ++++∞= −−− -- γβα & ' &B/%&++4- :2& ,1%1,'&%6=1 1 &B6+'O(,61 )& /S5-+ & =&%-+ %&16+ (2.1 /-++7@&5 ?2(34- )& '%1(+?&%O(,61 )- +6+'&.1 &. &+'2)- & +2;'%16%.-+ 1 D E - @15-% ?6(15 & 1++2.6()- :2& α− A - /S5- )& .16-% @15-% /-)&%&.-+ %&+,%&@&% 1 &B/%&++4- 1/%-B6.1)1K -- α− ≅∞− EDED D E -2 16()1K [ ]-- """ 5-<5-<ED5-< α−≅∞− D E &()- >"5-< " = > '&%&.-+ :2&K [ ]-- α>"5-<ED5-< "" −≅∞− D E ;'A.*+& 1++6. 1 &:2134- )& 2.1 %&,'1 ,20- )&,56@& )&'&%.6(1 - ,-&?6,6&('& α & 1 -%)&(1)1 (1 -%6<&. )&'&%.6(1 - ,-&?6,6&('& + ,-&?6,6&('&+ & β )1 &:2134- D E +4- -;'6)-+ )& ?-%.1 1(85-<1 & R &B/%&++4- D E +2;'%16%.-+ 1<-%1 - α− +∞ED /-)&%&.-+ &+,%&@&% 1 &B/%&++4- 1/%-B6.1)1K -- βα −− ≅+∞− EEDDED D E %-,&)&()- '15 ,-.- &. D E & D E /1%1 &+'1 (-@1 &B/%&++4-> -;'&%&.-+ -+ @15-%&+ )& β & +'& /%-,&)6.&('- A %&/&'6)-> /1%1 -+ -2'%-+ /1%J.&'%-+ E>>D δ > 1'A :2& 1 /%&,6+4- )-+ )1)-+ (4- /&%.6'1 (-@1 6'&%134-
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− = D!E &. :2&K + * &./&%1'2%1 (-%.156=1)1 )1 1.-+'%1 * &./&%1'2%1 )1 1.-+'%1 1 %&/%&+&('1% . * &./&%1'2%1 ?6(15 )1 &B/&%6O(,61 * &./&%1'2%1 6(6,615 )1 &B/&%6O(,61 '&./- &('%& 1.-+'%1<&(+ ?-6 )& 2. +&<2()- & ,-(+'1('& (1+ @8%61+ &B/&%6O(,61+ /S+ 1 +21 %&156=134-> +&5&,,6-(-2*+& 1:2&51 :2& +&%@6%61 )& %&?&%O(,61 ++6.> ?-6 &+,-596)1 )& ?-%.1 &./7%6,1 1 :2& 1/%&+&('1@1 2. ,-./-%'1.&('- .16+ /%SB6.- )1 .A)61 )1+ &B/&%6O(,61+ %&156=1)1+ D@&% ?6< !E
- 24. # $ % ! &' " ( 9 9! 9. 9: 9 9 9! ! ! ) * +" # - 0 .; " # 4 :! <; < !; &0 .; ' ?6< ! ` &+/-+'1 1- &+,154- &. .1591 1;&%'1 ,A5251 &5'6&% &156=-2*+& 1 ,-./1%134- )1 %&+/-+'1 '%1(+6'S%61 1- &+,154- -;'6)1 &B/&%6.&('15.&('& ,-. 1 )- .-)&5- &+'6.1)- D@&% ?6< VE & " , - $ 9 9 9! 9 9. 9 9: 9< 9 9= 9 ! ! ) * +" # - 2 # - ?6< V * -./1%134- &('%& .-)&5- &+'6.1)- & &B/&%6O(,61
- 25. '656=1()- )1)-+ &B'%17)-+ )& 2.1 )1+ &B/&%6O(,61+ %&156=1)1+ ?-6 &?&,'21)1 1 %&/%&+&('134- <%8?6,1 )1 ?2(34- )& .-)- 1 &+'6.1%*+& @15-% )- ,-&?6,6&('& & α ?6< F * ;'&(34- )- ?1,'-% (1 6)&('6?6,134- )- +6+'&.1 "V!!>""!V>"dEDd5-< +−=− += /- 0- >"dd "V!!>" == )1)- :2& EDED -- <∞ &('4- "dd < /&5- :2& >−= FV>" >"a dd"5-<dd"5-< = ∆ − = . α & +2;'%16% α + 1-+ )1)-+ & +& ?-% &?&,'21)1 1 %&/%&+&('134- )- %&+25'1)-> /-)&%*+&*8 &+'6.1% - @15-% )- ?1,'-% K dEEDEDDd"5-< - α− +− F>"" V F>" == − " 6./56?6,1()- -;'A.*+&K = ">
- 26. ! > % 0 .: :? 0 < ! ! % . 0 0 : 0 . 0 ! 0 0 0 : 0 . 0 ! ! ! . / ," @ & ' ?6< * ;'&(34- )- ?1,'-% (1 6)&('6?6,134- )- +6+'&.1 !!V> >"a dd"5-<dd"5-< >"a = ∆ − = ∆ ∆ = . β @15-% )& 5-< "d D"Ed A -;'6)- /&5- @15-% )1 -%)&(1)1 (1 -%6<&.> +&()- )& *">V F -.;6(1()- -+ %&+25'1)-+ -;'6)-+ /1%1 -+ ,-&?6,6&('&+ α> & β> ?-6 )&'&%.6(1)1 1 ?2(34- )& '%1(+?&%O(,61 )- .-)&5- &+'6.1)- - >!!!"> FV >">EDe −− +−= /56,1()- 1 '%1(+?-%.1)1 )& 1/51,& 1 EDe- K E!!!>D >" EFV>"D > ED f + + + −=' > 1 /1%'6% )- @15-% )& f ED' -;'A.*+& - @15-% &+/&%1)- )& ' , G ED ED f f = '%1@A+ )1 2'656=134- )& /%-<%1.134- &. 1' 1;# )6+/-(7@&5 (- 1(&B- %&?&%&('& R ,-./-(&('& )& /%-<%1.134- (-.&1)1.&('& 1'%1@A+ )-+ & ;'&% + -5-+ > -;'A.*+& 1+ ?2(3I&+ )& '%1(+?&%O(,61K V>"F> VV>"!>"> ED V ++ +− = − ,
- 27. V &+/%&=1()- - ?1,'-% )& +&<2()1 -%)&. )- (2.&%1)-% & +6./56?6,1()- -;'A.*+&K E!!V>EDFV>"D EVV>D!>" ED ++ −− =, DVE 1 ?6< " &+'8 %&/%&+&('1)1 1 %&+/-+'1 1- &+,154- )- .-)&5- &+'6.1)- %&/%&+&('1)- /-% ED f , K ?6< " * &+/-+'1 1- &+,154- )& .-)&5- & 1,-%)- ,-. 1 &+'6.134- )- .-)&5-> )1 ,A5251 &. .1591 1;&%'1 & 2'656=1()- - +6+'&.1 )& ,-('%-5- /-% %&156.&('134-> %&/%&+&('1)- (1 ?6< > +6.25-2*+& 1 %&+/-+'1 )- +6+'&.1 ,-. -+ +&<26('&+ /1%J.&'%-+ 6(6,616+K D E_ > # D E_ > E!!!>EDFV>"D EVV>D!>" ED ++ −− =, 16 2'656=1%*+& - % )& .-)- 1 -;'&%*+& 2.1 -%)&. )& <%1()&=1 )- <1(9- /%-/-%,6-(15> /1%1 - :215 - +6+'&.1 16()1 A &+'8@&5> (4- +& 2'656=1()- - '&%.- 6('&<%15 & )&%6@1'6@-
- 28. F 5 0 ED'ED ED ED, ED# ?6< * 61<%1.1 )& 5-,-+ )& 6+'&.1 )& -('%-5- /-% &156.&('134- ED * 6(15 )& %&?&%O(,61 D E* -('%-51)-% G -./&(+1)-% # D E ` 2(34- )& '%1(+?&%O(,61 &(+-% , D E ` 2(34- )& '%1(+?&%O(,61 )1 ,1)&61 )& 1,34-> 6+'&.1 1 ,-('%-51% ?&,'2-2*+& 1 +6.25134- ,-. 2. <1(9- /%-/-%,6-(15 :2& ,-5-,1++& - +6+'&.1 &. .-)- ,%6'6,1.&('& &+'8@&5 D/S5-+ (- &6B- 6.1<6(8%6-E & 1,-%)- ,-. - +6+'&.1> %&/%&+&('1)- D@&% ?6< E & /1%J.&'%-+ 6(6,616+ )&?6(6)-+ (- /-('- 1('&%6-% -;'&@&*+& - +&<26('& )61<%1.1 )& @1(+ D % EK % K ?6< * % +6+'&.1
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−− =, K 0. 0 0! 0 ! . 0 ! 0 ! 0 0 0 ! ! ! =. ==< ==. . ! === = . =.==. === === === ==< = . ? @ 8 & ' "A? ?6< * % +6+'&.1 &. .1591 ?&,91)1 /1%1 .-)&5- &+'6.1)- &
- 30. " ?&,'21()- 1 %&/%&+&('134- )1 %&+/&,'6@1 %&+/-+'1 1- &+,154-K & ' ! ! . . 0 ! ! . : ! ?6< * &+/-+'1 )- +6+'&.1 1- &+,154- & 1,-%)- ,-. 1 1(856+& )- % > - +6+'&.1> 1/S+ 1 6('%-)234- )& )-6+ =&%-+ %&16+ & 2. /S5- (1 -%6<&. D,-. 1 6('%-)234- )- ,-('%-51)-% E> ?6,-2 ,-. )-6+ /S5-+ )-.6(1('&+ ,-./5&B-+ ,-(02<1)-+ 6.251()- 1 15'&%134- )- <1(9- &+'8'6,- D.1('&()- - /S5- (1 -%6<&. & -+ )-6+ =&%-+ &. `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−= !V"V> - ,1+- &. :2& 1 '&./&%1'2%1 )& '&+'& A 6(?&%6-% R '&./&%1'2%1 )- )6++6/1)-% -;'&@&*+& 1 +&<26('& &B/%&++4-K 0- +−= V>"
- 32. 4 ( 5 *1&%/-.* 2* /0*90,7, & 1,-%)- ,-. 1 &+/&,6?6,134-> '-%(-2*+& (&,&++8%61 1 2'656=134- )& @8%61+ 56(<21<&(+ )& /%-<%1.134-> /1%1 6./5&.&('134- )- /%-0&,'- & :2& +& %&?&%&(,61. (- &+:2&.1 1/%&+&('1)- D@&% ?6< E " # B C D "D 2 7 3+ * E 3+ 7 3+ A 3+ + * D "D F " A 4 3+ 2 4 @ A A A 3+ 2 @ : ?6< * &/%&+&('134- &+:2&.8'6,1 )1+ 56(<21<&(+ )& /%-<%1.134- 2'656=1)1+
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
- 34. 7/5%7%1',-.* 1)1 1 (&,&++6)1)& )& ,-.2(6,134- &('%& 1 1/56,134- & - C > 6./5&.&('-2*+& - /%-'-,-5- )& ,-.2(6,13I&+ 1'%1@A+ )& 2. ,-(02('- )& ,-.1()-+ )& 1,-%)- ,-. - &+/&,6?6,1)- ,-. - D@&% 1;&51 E ,-(02('- )& ,-.1()-+ 6./5&.&('1)-+ ?-6 - +&<26('&K *7,12* ,0G7%'0*+ #$%&'()* K K K K -%%&('& &. . ] %-<%1.1% 1 ,-%%&('& )& 1+& K g &./&%1'2%1 N ] 6++6/1)-%> .;6&('&> A5251 ?&,'21% 5&6'2%1 '&./&%1'2%1+ K K g -%%&('& -5&,'-% ?&,'21% 5&6'2%1 ,-%%&('& ,-5&,'-% 15K155 &(92. 156;%134- )- &:26/1.&('- a g &(92. 1%1,'&%7+'6,1+ -.2(6,134- +A%6& a g &(92. &+'& )- 6(+'%2.&('- &(92. )&('6?6,134- )- 6(+'%2.&('- K &./&%1'2%1 &. N ] %-<%1.1% '&./&%1'2%1 )& '&+'& K K K K &(+4- &. ] %-<%1.1% '&(+4- )& ,-5&,'-% h K K X g &(92. ;'&(34- )& &%%- -,-%%6)- h K g &(92. 1'1 )1 (-%.1 6./5&.&('1)1 1;&51 * 6+'1 )& ,-.1()-+ 6./5&.&('1)-+ +6+'&.1 6./5&.&('1)- '&. +&(+-%&+ & 1,'21)-%&+ &> (- ,1+- )-+ 1,'21)-%&+> 1 ,-.2(6,134- &('%& - C & -+ ,6%,26'-+ )& 1,'2134- 1++-,61)-+ %&,-%%& R 2'656=134- )& ,-(@&%+-%&+ 6<6'15G (15S<6,- &+,-591 %&,162 +-;%& - ,-(@&%+-% .-)&5- V! F )& F ;6'+> :2& '&. ,-.- 2.1 )1+ +21+ ,1%1,'&%7+'6,1 1 /-++6;656)1)& )1 '&(+4- )& +17)1 /-)&% @1%61% &('%& M & ` %&51'6@1.&('& R '&(+4- )& " +'1 ,1%1,'&%7+'6,1 A (&,&++8%61 /1%1 1 6./5&.&('134- &?&,'21)1 (1 <&%134- )1 ,-%%&('& )& ;1+&> '&(+4- )& ,-5&,'-% & 16()1 )1 /%-<%1.134- )1 '&./&%1'2%1 )1 ,A5251
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• &(+4- ,-5&,'-% &.6++-%> • -%%&('& ,-5&,'-% .8B6.1> • -%%&('& )& ;1+& .8B6.1> • 1++- ,-%%&('& )& ;1+&> • 1++- '&(+4- ,-5&,'-% &.6++-%> • -'O(,61 .8B6.1> -. 1 6('&%?1,& ,-. - 2'656=1)-% D@&% 1(&B-+ +&,34- ('&%?1,& 1' 1;# * &(2 /%6(,6/15E ?6,1 )6+/-(7@&5 1 15'&%134- )-+ @15-%&+ /-% )&?&6'- )&?6(6)-+ /1%1 - '&+'& )- '%1(+7+'-%
- 36. ! " C $ G* 2 @ 4 8 * F # A 3+ " 4 F C 3+ E 3+ ( ( A 3+ F 3+ * * " ( 3+ 4 " # 3+ " & ' * 1 ( * ( 8 * ( A H 8? 7 * 3+ # 8 * 2 A I# * J 3+ E 3+ K " # ( ( ( ?6< * 52B-<%1.1 <&%15 )& 6./5&.&('134- ,S)6<- &. 1' 1;#
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i> i +'& )&56.6'1)-% /-)& +&% ?1,65.&('& 15'&%1)- D ` :26+6,1- 1)-+ . @1%68@&5 +&/1%1)-%E &+'%2'2%1 <&%15 )& ,-./-%'1.&('- )- /%-<%1.1> :21()- )1 %&,-591 )& 1.-+'%1+ %&156=1)1+ )2%1('& 1 &B/&%6O(,61 &(,-('%1*+&> )&?6(6)1 D@&% ?6< E
- 38. F " C E 8 * " L + 4 2 A G? I L 4 9 9 - 3+ 9 G? ( 8 * " & ' 2 & 4 M M 1 ' 2 7 * 3+ # 8 * % A ? G? A N ( ?6< * ./5&.&('134- 1:26+634- )& )1)-+
- 39. *07,'* (&H%(0*+ &*7 /,0G7%'0*+ 2% ,J4(+(-.* 1/56,134- <%1@1 &. '%O+ ?6,9&6%-+ )& 1,-%)- ,-. -+ ?-%.1'-+ D@&% 1;&51 & E -+ )1)-+ (&,&++8%6-+ R /-+'&%6-% %&156=134- )-+ <%8?6,-+ /%&+&('&+ (1 1/56,134- %&156=1)1 + (-.&+ )-+ ?6,9&6%-+ & -+ ?-%.1'-+ +4- -+ +&<26('&+K -.& ?6,9&6%- * *9 ,2*+ 2,' -%.1'- )- ?6,9&6%-* 1%J.&'%- ! " &./&%1'2%1 .;6&('& &./&%1'2%1 6++6/1)-% &./&%1'2%1 A5251 &./&%1'2%1 &+'& &./- .-+'%1<&. (6)1)& . . N N N N + 1;&51 * &+,%634- & -%)&. )-+ ,1./-+ )6+/-(7@&6+ (- ?6,9&6%- -< 1)-+ )1' +'& ?6,9&6%- A ,2.251'6@-> -2 +&01> 1+ (-@1+ &B/&%6O(,61+ +4- 1)6,6-(1)1+ 1- ?6(15 )- ?6,9&6%- ?6,9&6%- ,%61)- &. ,1)1 &B/&%6O(,61 )&+6<(1*+& /-% *)*+ ,2*+ 2,' & '&. - .&+.- ?-%.1'- )- ?6,9&6%- *9 ,2*+ 2,' 16()1 ,%61)- 2. ?6,9&6%- D@&% 1;&51 E ,-. 1 &@-5234- )1 '&./&%1'2%1 )1 ,A5251 )&+)& 1 '&./&%1'2%1 6(6,615 1'A R '&./&%1'2%1 ?6(15> ,-. - -;0&,'6@- )& +& &?&,'21% 1 1(856+& )1 &@-5234- )- /&%7-)- '%1(+6'S%6- )1 '&./&%1'2%1 (1 ,A5251 )& &5'6&% -.& )- ?6,9&6%-* *9 %'%&', %7/%0,'40, 2,' -%.1'- )- ?6,9&6%-* 1%J.&'%- &./&%1'2%1 .;6&('& &./&%1'2%1 6++6/1)-% &./&%1'2%1 A5251 &./&%1'2%1 &+'& &./- .-+'%1<&. (6)1)& N N N N + 1;&51 * &+,%634- & -%)&. )-+ ,1./-+ )6+/-(7@&6+ (- ?6,9&6%- -< &'&,'1 &./&%1'2%1 )1'
- 40. " K2(9* 2* (&0* *1'0*5,2*0 & ?-%.1 1 /-)&% 56<1%*+& - 1' 1;# 1- ,S)6<- )- C > 6./5&.&('-2*+& - ,S)6<- :2&> )& 1,-%)- ,-. - +'1()1%) > %&,&;& -+ ,-.1()-+ & 1,'21 (- &:26/1.&('-> '15 ,-.- %&/%&+&('1)- <&(&%6,1.&('& D@&% ?6< E " C $ G* * 4 2 @ 4 # D ND ( 3+ " 8 * 3+ + D D ( 4 * N 8 * 3+ + D D ( " " " & ' " " " & ' " " * F ?6< * S)6<- 2'656=1)- (- C
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j -%)&.> /-)& &B'%16%*+& )1 -;+&%@134- )1 ?6<2%1> 2'656=1()- -+ @15-%&+ )1 &B/&%6O(,61> &('%& -2'%-+> -+ +&<26('&+ /1%J.&'%-+K * &./- )& /6,- ≈ > * &./- )& ,%&+,6.&('- * !≈ >
- 42. * &./- )& &+'1;&5&,6.&('- !≈ > 15,251.*+& -+ %&+'1('&+ /1%J.&'%-+ 1'%1@A+ )1 1(856+& )1 ?6<2%1 %&+/&,'6@1 D@&% ?6< E> & -;'A.*+&K * -;%&*&5&@134-> ED EDED ""DkE +∞ +∞− = - -- > k > ""DkE = − = * &%7-)- )1+ -+,6513I&+ π = > &/%&+&('1()- - 6(+'1('& )& '&./- /1%1 - :215 -,-%%& - N .8B6.- )& -D E %&+25'1 &('4-K == π -2 a= a == * %&:2O(,61 )1+ -+,6513I&+ 1.-%'&,6)1+> ! F>"== π %1)G+ ;'6)-+ -+ @15-%&+ &B/&%6.&('16+ %&51'6@-+ R %&+/-+'1 )- +6+'&.1 1- &+,154- /1%1 @8%61+ '&./&%1'2%1+ )& '&+'& D&('%& N & !"N E> - @15-% )1 +-;%&*&5&@134- DkE +6'21* +& (- 6('&%@15- &('%& " & Fk> /1%1 2. '&./- )& &+'1;&5&,6.&('- D E &('%& V+ 1 "N & "+ 1 !"N D@&% ?6<2%1+ 1(&B- %&+25'1)-+ ?6(16+E + @15-%&+ -;'6)-+ /1%1 1 +-;%&*&5&@134- 2'656=1()- 2. ,-('%-51)-% > & (- ,1+- )& +&%&. 1/56,1)1+ 1+ %&<%1+ )& * + &+'1%4- (2. 6('&%@15- )& "k 1 !"k )- @15-% .8B6.- )1 %&+/-+'1 1- &+,154- ] &+'& ,1+- - @15-% )& +-;%&*&5&@134- @1%61 &('%& " & Fk> - :2& 6()6,61 :2& - /%-,&++- )- A'-)- )1 2%@1 )& %&1,34- )& * + 2'656=1)- /-)& +&% 1/56,1)- (&+'& .-)&5- )& A5251 )& &5'6&% . -2'%- /1%J.&'%- 6./-%'1('& A - @15-% .8B6.- )1 '&./&%1'2%1 +2/-%'1)1 /&51 ,A5251 )& &5'6&% :2&> )& 1,-%)- ,-. 1 &+/&,6?6,134- )- ?1;%6,1('&> A )& F N 1%1 - ,1+- &. :2& 1 '&./&%1'2%1 )& '&+'& A )& !"N & ,-(+6)&%1()- - @15-% )& +-;%&*&5&@134- -;'6)- &B/&%6.&('15.&('& '&.*+&K
- 43. NF>a!".1B ==−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
- 44. %7/%0,'40, 2, &?545, 1%1 ,-(9&,&% -+ &%%-+ %&51'6@-+ )1 '&./&%1'2%1> 2'656=1%1.*+& -+ ,-.1()-+ /%&@61.&('& 6./5&.&('1)-+ ++6.> /-% ,1)1 5&6'2%1 )& '&./&%1'2%1 )&('%- )1 <1.1 )& '&./&%1'2%1+ )& 6('&%&++&> ?-%1. &(@61)-+ )-6+ ,-.1()-+K /%6.&6%- ,-. 1 +6('1B& )&?6(6)1 )- '6/- K &. :2& %&/%&+&('1 1 '&./&%1'2%1 )& '&+'& ^ - +&<2()- :2& )&@&%8 +&% &(@61)- 1/S+ 1 ,&%'6?6,134- )& :2& 1 '&./&%1'2%1 (1 ,A5251 +& &(,-('%1 (2.1 @6=6(91(31 &+'1;&5&,6)1 DMG* kE )- @15-% ?6(15 )1 %&+/-+'1 A K g /S+ 1 /%-<%1.134- (- C )1+ ?2(3I&+ ,1%1,'&%7+'6,1+ D@&% ?6< E -;'6@&%1.*+& -+ +&<26('&+ &%%-+ &B/&%6.&('16+ /1%1 2. 6('&%@15- )& '&./&%1'2%1+ &('%& N & !"N & /1%1 2.1 '&./&%1'2%1 1.;6&('& )& "N K 8 * *G 0 9 0.9 0 9 0!9 0 9 9 9 !9 9 .9 9 ! ! . . : : " )3&* #6)7* 8 * ?6< * %%- %&51'6@- '&./&%1'2%1 D'&./ )6++6/1)-% &('%& F>VN & > N E O.*+&> 1++6.> &%%-+ %&51'6@-+ (- 6('&%@15- &('%& k & k )- @15-% ?6(15 /%-<%1.1)- +'&+ &%%-+ &(,-('%1.*+& )&('%- )-+ @15-%&+ &B/&,'8@&6+ /1%1 - +6+'&.1 /%-0&,'1)-
- 45. %+'%+ +(+'%7, &*7/5%'* & 1,-%)- ,-. - /%-0&,'- &51;-%1)- /-)&.-+ @1%61% '%O+ /1%J.&'%-+ )- '%1(+7+'-%> 1 +1;&%K • -%%&('& )& 1+& • &(+4- )& ,-5&,'-%*&.6++-% ! " • &./&%1'2%1 )& '&+'& )- '%1(+7+'-% ?&,'21%1.*+& -+ +&<26('&+ '&+'&+ /1%1 -;'&(34- )1+ ,1%1,'&%7+'6,1+ )- K * %-<%1.134- )1 &B/&%6O(,61 1 2.1 '&./&%1'2%1 )&?6(6)1 &('%& -+ N & -+ !"N * ;'&(34- )1 ,-%%&('& )& ,-5&,'-% .1('&()- 1 -%%&('& ,-(+'1('& & @1%61()- 1 '&(+4- )& ,-5&,'-% * 1%6134- )1 ,-%%&('& )& ;1+&> @1%61()- 1 '&(+4- )& ,-5&,'-% '656=1()- - )&+&(@-5@6)- (- /%-0&,'- -;'6@&%1.*+&> /1%1 - '%1(+7+'-% )- '6/- V> -+ +&<26('&+ %&+25'1)-+ D1.-+'%1+ %&,-596)1+ (- ?6,9&6%- -<)1)-+ )1'EK 40), 2, ),0(,-.* 2% )%0+4+ &*7 &*1+',1'% /%&+&('& <%8?6,- D@&% ?6< E ?-6 -;'6)- +&5&,,6-(1()- 1 1.-+'%1 /1%1 2. ! "_* & 2. @15-% )& '&./&%1'2%1 )& '&+'& )&?6(6)1 .S)25- )- @15-% )- )&,56@& )8 2.1 6()6,134- +-;%& - @15-% )- 3" /1%1 1 '&./&%1'2%1 &. '&+'&> ,-. -+ @15-%&+ )& & )&?6(6)-+
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
- 47. V " * $ 8 $ 8 ? %0!$ & . ; ' ! . : < 0! 0 9 0 9: 0 9. 0 9! 0 0 9 0 9: 0 9. 0 9! $ 8O$P Q"QOP " % " %! " % ?6< * 2%@1 ,1%1,'&%7+'6,1 _?D! "E /1%1 '%1(+7+'-% V O,0(,-.* 2% &*7 '%7/%0,'40, <%8?6,- D@&% ?6< !E %&/%&+&('1 1 @1%6134- )- <1(9- /1%1 2.1 <1.1 )& '&./&%1'2%1+ &('%& N & !"N )& 1,-%)- ,-. - ,%6'A%6- )& ! " & ,-(+'1('&K + %0# 6 " +&# .= /:; + > % : : ? 5 :< . ! ! ! . : < " )3&* %0# 8 @ C 3+ ?6< ! * 2%@1 ,1%1,'&%7+'6,1 9 _?D E
- 48. F . 1(&B- (1 +&,34- % 3 &(,-('%1.*+& )6+/-(7@&6+ 2.1 +A%6& )& <%8?6,-+ -;'6)-+ 1 /1%'6% )1 1/56,134- %&156=1)1 &. 1' 1;# %7/%0,'40, 2% '%+'% /S+ - '&./- )& &+'1;&5&,6.&('- -;'6@&%1.*+& -+ +&<26('&+ %&+25'1)-+ &B/&%6.&('16+ /1%1 2.1 &B/&%6O(,61 ,-. '&./&%1'2%1 /%-<%1.1)1 )& "N <%8?6,- +&<26('& 1/%&+&('1> /1%1 2.1 '&./&%1'2%1 )& '&+'& )&?6(6)1> 1 @1%6134- )1 '&./&%1'2%1 )2%1('& 2.1 &B/&%6O(,61 D@&% ?6< VEK " &' " 6 5 . . 9! . 9. . 9: . 9 .! .!9! .!9. .!9: .!9 ! . : < 5 ) * "&'")3&* 9 R 9 R !9 R 9 R .9 R 9 R :9 R <9 R #6)7* . ; 8 * ORP ?6< V * B&./5- )1 @1%6134- )1 '&./&%1'2%1 )2%1('& 2.1 &B/&%6O(,61 1 1(856+& )1 ?6<2%1 D@&% ?6< VE> &B6+'& 2. 6('&%@15- )& @1%6134- )1 '&./&%1'2%1> '-.1()- ,-.- %&?&%O(,61 1 '&./&%1'2%1 )& >VN )& *"> N 1 M"> N & %&?&%6% :2& /1%1 1 '&./&%1'2%1 )& "N - &%%- %&51'6@- -;'6)- D@&% ?6< E> 1/-('1@1 /1%1 1 -;'&(34- )- @15-% ?6(15 ,-. 2. &%%- )& > k> 6()6,1()- 1++6. :2& 1 '&./&%1'2%1 ?6(15 +&%8 +2/&%6-% R '&./&%1'2%1 /%-<%1.1)1 & ?-% '-.1)1 ,-.- %&?&%O(,61 1 '&./&%1'2%1 /%-<%1.1)1 D "N E &('4- - )&+@6- A (- .7(6.- )& > N & ,-.- .8B6.- )& >!N +'&+ @15-%&+ ,-(?6%.1. 1++6. -+ @15-%&+ &B/&%6.&('16+ -;'6)-+ (- '&+'& )& ;5-,-+ + +15'-+ -;+&%@1)-+ (1+ 1.-+'%1+ )1 '&./&%1'2%1 )1 ,A5251 'O. 1 @&% ,-. %&+-5234- )- +6+'&.1
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l+ )& .16+ )& F ;6'+& 1%1 12.&('1% 1 /%&,6+4- (1 5&6'2%1 )1 ,-%%&('& )& ,-5&,'-% )&@&%8 +&% 2'656=1)- 2. ,-(@&%+-% (15S<6,-G 6<6'15 ,-. .16+ )& F ;6'+ (7@&5 )- &+'2)- )- ,-('%-51)-% (4- ?-%1. &51;-%1)1+ (&+'& %&51'S%6- 1+ ,2%@1+ ,-('%6;26('&+ )1 1,34- 6('&<%15> )&%6@1'6@1> 1++6. ,-.- 1 2'656=134- )& 'A,(6,1+ )& ,-('%-5- 15'&%(1'6@1+ 1- &+'2)- )- +6+'&.1 &. .1591 ?&,91)1> )1)- (4- +&% - -;0&,'6@- )- '%1;159-
- 50. " &+'%2'2%1 )& & ?5&B6;656)1)& )-+ /%-<%1.1+ /&%.6'&> (1 (-++1 /&%+/&,'6@1> &+'2)-+ ?2'2%-+> (-.&1)1.&('&K • '656=134- )& ,-('%-51)-%&+ 1(15S<6,-+ )- '6/-K > > > (- ,-('%-5- )& ,A5251+ )& &5'6&% • +'2)- )1 %&+/-+'1 )- +6+'&.1 &. .1591 1;&%'1 • )&('6?6,134- )& 6+'&.1+ • +'2)- )& 15<-%6'.-+ )& -('%-5- • +'2)- )- /%-'-,-5- • %6134- )& .-)&5-+ )& '%1(+7+'-%&+ ,-. &B/-%'134- /1%1 ) " 1 /1%'6% )-+ )1)-+ -;'6)-+ &. ?6,9&6%- •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
- 51. @ #0# A & 98 8B 0 L N > +1;&5 * (1,(+ % (+'%7,+ 6+;-1K +,-51% )6'-%1> "" L N > H1'+296Q- ` 19%1H,0(, 2% *1'0*5% *2%01*K j &) 6- )& 1(&6%-K %&('6,& Z155 %1+65> L N > 5;&%' ` 0(1&(/(* 2% 5%&'0K1(&, -5 > !j ) * , %1m Z655> %1) %-? % (< Z&%.7(6- 21%'& 1.-+ L N > 26+^ > Z&(%6:2&* 0*$%&'* 2, 1'%0<,&% 2% 0,1+7(++.* /,0, , (9,-.* /*0 (#0, P/'(&, %1'0% , +',-.* 2% ,+% % , +',-.* %1'0,5 -6.;%1K (+'6'2'- )& &5&,-.2(6,13I&+ L N 1%5-m,-(+25' " 2' "" ] 9''/KGGmmm .1%5-m ,-.G &,9(6,15 (?-G'9&.-&5&,'%6,n,--5&%n+&5&,'6-(n/ 9'. 9''/KGGmmm .1%5-m ,-.G &,9(6,15 (?-G'&,n.-2('6(<n.&'9-)n/%-,&)2%&+ 9'. L N 6<9'P1@&,-(+25' 1( "" ] 9''/KGGmmm 56<9'm1@& ,-.G+&,'n+2//-%'G56;%1%oG +G -,2.&('+G /)? L NP Z 5&,'%-(6,+* 9 == L@N > 27+ ` (194,9%7 > > 6+;-1 L N > 561 ` ,' ,#I 6 412,7%1'*+ 2% 0*90,7,-.*K )6'-%1 L CN > 296)6( ,-(+25' 2( "" ] )6+/-(7@&5 (1 L,,SSS A ,TA U ,"888 V # ! ., :, . L N Z > %-? 1%5-+ 5;&%'- 2(&+ * 5%&'0K1(&, 2* +',2* K5(2* 1,25)1)& 6O(,61+ & &,(-5-<61 * (6@ -@1 )& 6+;-1> 4556^ L N > %-? -)%6<- B (+/*+('()*+ %7(&*124'*0%+ 1,25)1)& 6O(,61+ & &,(-5-<61 * (6@ -@1 )& 6+;-1> "" ^ L N > %-? % 1%'6(B ,0,7%'%0 :'0,&'(*1 ,12 *2%5(19 *< (/*5,0 0,1+(+'*0+ H Z> -o15 (+'6'2'& -? &,9(-5-<o ` '-,Q9-5.> "" ^ L N h > -;&%'^ Z Hh> -26+ ` (+/*+('()*+ 5%&'0K1(&*+ % %*0(, 2% (0&4('*+7 :26('1 &) > )6'-%1 ?6561)1* %&('6,&* Z155 )- %1+65> L N > 5&B1()%&^ > 1%5-+* *7* +&0%)%0 47, %+%K j &) > )63I&+ 751;-> )1 > 6+;-1> "" L N > j +1;&5* 1>5(+% 2% (+'%7,+ (1%,0%+> %&++ > 6+;-1 L N %1(Q56(> P * %%2#,&Q *1'0*5 *< R1,7(& R+'%7+> ))6+-(*P&+5&o