Appunti di ELETTROTECNICA – PARTE 1 - Marcello Rutter

Embed Size (px)

DESCRIPTION

Appunti di ELETTROTECNICA – PARTE 1Edizione Marzo 2010 Marcello Rutter - Politecnico di Milano

Citation preview

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    1/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; 8

    !""#$%& (&

    )*)++,-+)./0.! 1 2!,+) 3

    )(&4&5$6 78945 :;3;

    < 2#%=%/+. "22*/+. #"22#%=%/+"/' */" ./+%#2#%+">.'/% 2%#='/"&% 0%& $'/+%/*+' ?*&+.?%0."&%

    2#%=%/+% /%&&% =&.0% *@@.$."&. 0%& $'#='; -'=='/' #.=*&+"#% *+.&. $'?% #.@%#.?%/+' 2%# .&2#':#"??" ' $'?% #.2"=='; -%# %=2%#.%/>" 2%#='/"&% 0. $A. &. A" =$#.++. /'/ 0%B'/' %==%#%

    #.+%/*+. ='=+.+*+.B. 0%& ?"+%#."&% '#.:./"&% %C ./ 2"#+.$'&"#%C 0%. +%=+. =*::%#.+.;

    D*++' .& ?"+%#."&% $'/+%/*+' ./ E*%=+. "22*/+. F ='::%++' "&&% ?%0%=.?% $'/0.>.'/. 0.

    $'2G#.:A+ 0%&&% #.=2%++.B% @'/+.H

    I -JK

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    2/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; 5

    0>+0?0

    *64&5$6 3 1 0$%95(#4&5$6 8& @&9@#&%& 6A6%%9&@&

    75(#A5 3 1 0A @&9@#&%5 6A6%%9&@5

    N. 2"#+% 0" */ %=%?2.' O"/"&% 0. $.#$*.+' %&%++#.$' P+'#$." 9Q &"?2"0./"C O"++%#."C ./+%##*++'#%R2%# %B.0%/>."#% $'?% .& $.#$*.+' %&%++#.$' =." ./ #%"&+S 2#%=%/+% ./ ':/. "=2%++' 0%&&" B.+"

    E*'+.0."/" P%=; .& $.#$*.+' =+"?2"+' $'/ . $'?2'/%/+.R; /) 0"$0'"-% *1*--$"0% F */ =.=+%?"$'=+.+*.+' 0" */ ./=.%?% 0. 0.=2'=.+.B. %&%++#.$. $'&&%:"+. +#" 0. &'#' ./ ?'0' 0%@./.+'; K% 2"#+.

    0%& $.#$*.+' ='/' $A."?"+% ./ B"#. ?'0.H 0%2#%)*)-"3 &"4#%4"-","3 *1*2*)-" 0"$0'"-.1";

    !%/+#% .& ?'0' 2"#+.$'&"#% ./ $*. ='/' $'//%==% &% 2"#+. 0. */ $.#$*.+' F 0%++" -%#%1%5". &*10"$0'"-%; 4*% $.#$*.+. ='/' .0%/+.$. =% A"//' =+%==. $'?2'/%/+. % =+%==" +'2'&':."; N%OO%/% ./*/ $.#$*.+' %&%++#.$' "BB%/:"/' 0.B%#=. @%/'?%/. @.=.$.C E*%&&. =+*0."+. ='/' &%:"+.2#./$.2"&?%/+% " +#% :#"/0%>>% @'/0"?%/+"&.H 0%$$*)-"3 -*)4"%)" * #%-*)(*;

    75(#A5 : 1 *6 B98$(6446 6A6%%9&@C6 D5$(8E6$%8A&

    1&&" O"=% 0. +*++. . @%/'?%/. $A% "BB%/:'/' ./ */ $.#$*.+' $TF */"

    2#'2#.%+S 0%&&" ?"+%#." $A."?"+" 0.$"0. *1*--$"0. P$A% 2*U %==%#%0.=+./+" ./ $"#.$" 2'=.+.B" % $"#.$" /%:"+.B" , */.+S 0. ?.=*#" L V

    L'*&'?OR; L'#2. ?"+%#."&. 0'+"+. 0. $"#.$" %&%++.$" %=%#$.+"/' +#" 0. &'#'

    ">.'/. " 0.=+"/>" $'/ @'#>% "++#"++.B% % #%2*&=.B%;6. 0%$$*)-* *1*--$"0. P=. ./0.$" =2%==' $'/ !C */.+S 0. ?.=*#" F 1 V 1?2%#%RC "++#"B%#=' */"=*2%#@.$.%C F &" E*"/+.+S 0. $"#.$" %&%++#.$" $A% "++#"B%#=" &" =*2%#@.$.% /%&&T*/.+S 0. +%?2';1++#"B%#=' &" =%>.'/% 0. */ $'#2' $'/0*++'#% $.#$'&" */" $'##%/+% %&%++#.$" 0. */ "?2%#% =%

    2"==" */" E*"/+.+S 0. $"#.$" 2"#. " */ $'*&'?O ./ */ =%$'/0' P8 1 V 8 L W =R; K" $'##%/+%

    %&%++#.$" F */" :#"/0%>>" 0'+"+" 0. =%:/'; N$%&+' .& =%:/'C =. 2*U 0.#% $A% &" $'##%/+% F

    0%4-.)-* )*1 -*2#%'22*#% ./B"#."/+% '22*#% $'/+./*" =% .& B"&'#% 0%&&" $'##%/+% $A% 2"=="./ E*%& 2*/+'F $'=+"/+% /%& +%?2'; 1& $'/+#"#.' =. 0.#S -*2#% ,.$".)-* ' B"#."O.&% /%& +%?2'=% /'/ F $'=+"/+% PE*./0. F */" X 0%& +%?2'R;

    K" -*)4"%)* *1*--$"0.P=. ./0.B" $'/ "C */.+S 0. ?.=*#" F Y V Y'&+R +#" 0*% 2*/+. 0%++. 1 % Z F0%@./.+" $'?% &T%/%#:." /%$%=="#." " =2'=+"#% */" $"#.$" */.+"#." 2'=.+.B" 0"& 2*/+' Z "& 2*/+'

    1 &*/:' */ 2%#$'#=' 2#%@.=="+'; N. '==%#B. $A% &" $'##%/+% F */" :#"/0%>>" 0. =*2%#@.$.% ?%/+#%

    &" +%/=.'/% F */" :#"/0%>>" 0. &./%" PF "22*/+' .& &"B'#' =B'&+' 2%# =2'=+"#% &" $"#.$" 0" $*."OO."?' " $ %&'%(!8 B'&+ V 8 ['*&% W $'*&'?OR; 1/$A% &" +%/=.'/% 2*U "==*?%#% */ =%:/'

    ./ @*/>.'/% 0%&&% $"#"++%#.=+.$A% 0%& =.=+%?" % 0%&&" $'/B%>.'/% *+.&.>>"+";

    ")*V &"B'#' /%$%=="#.' 2%# =2'=+"#% */" $"#.$" */.+"#." 2'=.+.B" \ 0" Z " 1 V9"*)V &"B'#' /%$%=="#.' 2%# =2'=+"#% */" $"#.$" */.+"#." 2'=.+.B" 0" 1 " Z;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    3/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; ]

    Y"&% E*"/+' 0%++' 2%# &" $'##%/+% ./ ?%#.+' "& @"++' $A% &" +%/=.'/% =." B"#."/+% ' ?%/' /%&+%?2';

    ^&. =+#*?%/+. 0. ?.=*#" 0. $'##%/+% % +%/=.'/% ='/' "?2%#'?%+#' % B'&+?%+#'; J&+#% "&&"

    =.?O'&':." P$&"==.B"C 1 ' Y "&&T./+%#/' 0%& $%#$A.' $A% #"@@.:*#" &' =+#*?%/+'R B%/:'/'.&&*=+#"+% &% $"#"++%#.=+.$A% .0%"&. % .& $'&&%:"?%/+'; -%# &T"?2%#'?%+#' .& $'&&%:"?%/+' F &*/:'

    &" &./%"C ./ $"=$"+" $'/ .& 0.=2'=.+.B' P./ =%#.%R % /'/ 0'B%/0' "&+%#"#% .& $.#$*.+'C %==' 0'B#S"B%#% .?2%0%/>" /*&&" P/'/ 0'B#S "=='#O.#% $'##%/+% ?" /%22*#% :%/%#"#/%R; -%# .&

    B'&+?%+#' B"&:'/' &% =+%==% $'/=.0%#">.'/.H . ?'#=%++. 0%& B'&+?%+#' B"//' $'&&%:"+. +#" . 0*%2*/+. 0. $*. =. ./+%/0% ?.=*#"#% &" +%/=.'/% %0 %==' 0%B% %==%#% +"&% 0" /'/ $'/=*?"#% %/%#:."

    P.?2%0%/>" "&+.==.?"R;

    % %&%++#.$A% .=+"/+"/%%; K" #%-*)(. *1*--$"0. "4-.)-.)*. P*;?; _ V _"++C 8

    `"++ V 8 ['*&% W =%$'/0'R =$"?O."+" 0" */ %&%?%/+' $.#$*.+"&% $'/ .& #%=+' 0%&&" #%+% F &"

    E*"/+.+S 0. %/%#:." %&%++#.$" =$"?O."+" 0"&&T%&%?%/+' /%&&T*/.+S 0. +%?2' P+,-. $ %&'%-R; 1/$A%&" 2'+%/>" F 0'+"+" 0. =%:/' 2'.$Aa */ %&%?%/+' $.#$*.+"&% 2*S "=='#O.#% '22*#% %#':"#%

    %/%#:.";

    75(#A5 F 1 .5$@6%%& (& G8H6

    N. @'#/.=$'/' "&$*/. $'/$%++. % +%#?./'&':.% 0. O"=% +.2.$A% 0%. $.#$*.+.; .'/% 0%. $'?2'/%/+.; \*%&&. @'#?"+. 0" 0*% ='&.?'#=%++. P. 2.b $'?*/.R ='/' 0%++. 7"#%1"; M%&&% @.:*#% $A% =%:*'/' B%/:'/' #.2'#+"+. . +%#?./.

    .?2.%:"+. 2%# ./0.B.0*"#% &% 0.%B#=% 2"#+. 0. */ $.#$*.+' @'#?"+' 0" O.2'&.;

    &"+' $.#$*.+"&% V #"?' V =./:'&'

    0.=2'=.+.B'M'0. V 2*/+. 0. $'//%==.'/% +#" .

    0.B%#=. $'?2'/%/+.

    !":&." P8R V 2%#$'#=' $A.*=' ./

    $*. 2*U %==%#% =*00.B.=' .&

    $.#$*.+';

    !":&." P5R; K% ?":&.% 2'=='/'

    %==%#% "#O.+#"#."?%/+% 2%#$'#=%

    ./ =%/=' '#"#.' ' "/+.'#"#.';

    !":&." P]R

    M%&&T"/"&.=. 0%& $.#$*.+' =. B"//' "0 "/"&.>>"#% &% :#"/0%>>% %&%++#.$A% 2.b =.:/.@.$"+.B% 'BB%#'

    E*%&&% $A% #"22#%=%/+"/' :&. =$"?O. 0. =%:/"&% % 2'+%/>" +#" &% 0.B%#=% 2"#+. 0%& $.#$*.+';

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    4/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; c

    L'##%/+% 0. &"+' P&% $'##%/+. $A%2"=="/' /%&&% =%>.'/. 0%. 0.B%#=.

    #"?. 0%& $.#$*.+'R

    D%/=.'/. 0. &"+' P&% +%/=.'/. +#" &%$'22.% 0. ?'#=%++. 0%. =./:'&.

    $'?2'/%/+. 0%& $.#*.+'R

    D%/=.'/. 0. /'0' P&% +%/=.'/. +#"

    ':/. /'0' 0%& #.$#$*.+' % */ /'0'

    2"#+.$'&"#% , %=; %d, $'/ +%/=.'/%

    7 2#%=' $'?% #.@%#.?%/+' % 0%++'

    0. ?"==" ' 0. +%##"R

    K% :#"/0%>>% %&%++#.$A% ='/' :#"/0%>>% 0'+"+% 0. =%:/' % .& =%:/' 0.2%/0% "/$A% 0"&&"$'/B%/>.'/% "0'++"+";

    !/$/)0 12 345567-6 82 !1 "6594

    !7%!32-4 !7 :!;>"

    $"?O."+" 0. =%:/' "=$>?@

    N%OO%/% &% $'/B%/>.'/. =."/' "#O.+#"#.%C =2%=='C 2%# ?'+.B. 0. $"&$'&'C F O%/% #"22#%=%/+"#%

    $'##%/+. % +%/=.'/. 0. &"+' 2%# $."=$*/ $'?2'/%/+% ./ */" #%+%C

    *+.&.>>"/0' &" $'=.00%++" 0%),*)("%)* &*51" '-"1"((.-%$"; N%$'/0' +"&%$'/B%>.'/% =. 2#%/0% $'?% B%#=' 0. #.@%#.?%/+' 0%&&" $'##%/+% /%&

    $'?2'/%/+% E*%&&' =%$'/0' $*. &" $'##%/+% %/+#" /%& ?'#=%++' =%:/"+'

    $'?% 2'=.+.B' /%&&" $'/B%/>.'/% "0'++"+" 2%# &" +%/=.'/%; K" $'/B%>.'/% '22'=+" F 0%++"0%),*)("%)* &*" 5*)*$.-%$" P&" $'##%/+% F *=$%/+% 0"& ?'#=%++' $'/+#"==%:/"+' $'?%

    2'=.+.B' 2%# &" +%/=.'/%R;

    < 2#'O&%?. ./%#%/+. */ $.#$*.+' $'?2'#+"/' &T"/"&.=. % &" =./+%=. $.#$*.+"&%; 68.).1"4" 0"$0'"-.1*

    A" $'?% 'O.%++.B' &" 0%+%#?./">.'/% 0%&&% $'##%/+. % 0%&&% +%/=.'/. %&%++#.$A% /%. $.#$*.+. P/%&&%0.B%#=% 2"#+. $A% &' $'?2'/:'/'R /'/$Aa &% 2'+%/>% =$"?O."+%; 6. 4")-*4" 0"$0'"-.1*#.:*"#0"

    ./B%$% &" $"2"$.+S 0. "==%?O&"#% 'BB%#' 0. ./B%/+"#% $.#$*.+. %&%++#.$. ./ :#"0' 0. ='00.=@"#%0%&&% @*/>.'/"&.+S =2%$.@.$A%;

    K% :#"/0%>>% %&%++#.$A% '==%#B"+% ./ */ $.#$*.+' ='/' +#" &'#' $'##%&"+%; K" 2'+%/>"C $'?% :.S

    B.=+'C F 0"+"C ./ */ $%#+' .=+"/+%C 0"&&" 0%#.B"+" 0%&&T%/%#:." #.=2%++' "& +%?2'; N% ?'&+.2&.$' %0.B.0' +"&% E*"/+.+S 2%# &" $"#.$" %( $A% $.#$'&" /%& $'?2'/%/+% /%&&T./+%#B"&&' 0. +%?2' %-

    '++%/:' &" =%:*%/+% #%&">.'/%H p(t) =dW

    dt=

    dW

    dq

    dq

    dt=vi ; 1OO."?' :.S 0%++' $A% .& =%:/' 0%&&"

    2'+%/>" ./0.$" .& @"++' $A% */ 0.=2'=.+.B' 2*U "=='#O.#% ' %#':"#% 2'+%/>"; N%$'/0' &"$'/B%>.'/% 0%&&T*+.&.>>"+'#% "OO."?' "&&'#" . =%:*%/+. 0*% $"=.H

    6. 0%$$*)-* *)-$. )*1 2%$4*--%0%) 9:;

    !"#$ "B#S =%:/' f E*"/0' &"

    2'+%/>" F %@@%++.B"?%/+%

    "=='#O.+" 0"& $'?2'/%/+%g "B#S=%:/' , E*"/0' &" 2'+%/>" ="#S

    %#':"+" 0"& $'?2'/%/+% "& #%=+'

    0%& $.#$*.+';

    6. 0%$$*)-* *)-$. )*12%$4*--% 0%) "

    ="#S "=='#O.+" 0"&

    $'?2'/%/+%;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    5/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; h

    N% ./ */ $.#$*.+' "OO."?' 0%+%#?./"+' &% +%/=.'/. ". ?'#=%++. % &% $'##%/+. $A% "++#"B%#="/' .

    0.B%#=. $.?2'/%/+. 2'==."?' #.$"B"#% &% %/%#:.% +'+"&. =$"?O."+%;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    6/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; d

    *64&5$6 F 1 *6 A6BB& (& I&9@CC5DD

    75(#A5 3 1 *8 A6BB6 (& I&9@CC5DD (6AA6 @5996$%&

    N. #.$'#0" $'?% &' =$'2' =." ./+#'0*##% ?%+'0. % +%$/.$A% 2%# &" 0%+%#?./">.'/% 0. +%/=.'/. %$'##%/+. 0. &"+' /%. $.#$*.+. %&%++#.$. P0"&&% E*"&. 2'. F .??%0."+' $"&$'&"#% &% 2'+%/>%

    .=+"/+"/%%R; Y%/:'/' ./+#'0'++% E*./0. 0*% &%::. @'/0"?%/+"&. /'+% $'?% &%::. 0. k.#$AA'@@;

    M%&&T%=%?2.' F #.2'#+"+' */ $.#$*.+' $'/ 1Vd P& V /*?%#' 0. &"+. % 7Vc /'0. P/ V/*?%#' 0. /'0.R; .'/. 2'=='/' %==%#% 0%+%#?./"+% 0"& $.#$*.+' /%&&T.2'+%=. $A% %==' =."

    /'+' 'BB%#' $A% =."/' =2%$.@.$"+. +*++. :&. 10.=2'=.+.B. $A% &' $'?2'/:'/' P./ E*%=+' $"=' &% 1%E*">.'/. ='/' 0"+% 0"&&% 1 #%&">.'/. $'=+.+*%/+.R; -%# 0%+%#?./"#% &% "&+#% l1m %E*">.'/.

    ./0.2%/0%/+. F /%$%=="#.' #.$'##%#% " 0*% &%::. @'/0"?%/+"&. P0%0'++% 0"&&" +%'#." :%/%#"&%0%&&T%&%++#'?":/%+.=?'R;

    => 6*55* &" ?"$0@@%AA B?C6 k.#$AA'@@ $*##%/+ &"`D 6*55* &" ?; &*11* 0%$$*)-"E;N." 0"+' */ $.#$*.+' % =."/' =2%$.@.$"+% &% $'/B%/>.'/. 0. =%:/' 2%# +*++% &% $'##%/+. 0. &"+'g =."

    0"+" ./'&+#% */" =*2%#@.$.% $A.*=" $A% +":&. .& $.#$*.+'; K" ='??" "&:%O#.$" 0%&&% $'##%/+. $A%

    "++#"B%#="/' &" =*2%#@.$.% $A.*=" FC ./ ':/. .=+"/+%C *:*"&% " >%#';

    M%&&T%=%?2.' #.2'#+"+' ./ @.:*#"C &" &./%" +#"++%::."+"

    P$%&%=+%R +":&." E*"++#' &"+.; -#%/0%/0' $'?% B%#=' 2'=.+.B'0%&&% $'##%/+.C #.=2%++' "&&" =*2%#@.$.%C E*%&&' %/+#"/+%

    P"++%/>.'/%H ./ E*%=+' $"=' =. ./+%/0% B%#=' 0%&&" $'##%/+%%/+#"/+% /%&&" =*2%#@.$.% 'BB%#' $A% 0"&&T%=+%#/' 0%&&"

    =*2%#@.$.% F 0.#%++' B%#=' &T./+%#/' 0%&&" =*2%#@.$.% , ./ @.:*#"CE*./0.C ='/' 2'=.+.B% &% $'##%/+. !/% !F;R; 1OO."?' E*./0. $A%

    !/ C !G C !? D !F $ B; \*%=+" &%::% 0%#.B" 0"& 2#./$.2.' 0.

    $'/=%#B">.'/% 0%&&" $"#.$" %&%++#.$" %0 "@@%#?"#% $A% B"&% &"kLK %E*.B"&% "0 "@@%#?"#% $A% ./ E*%=+" #%+% &" $"#.$"

    %&%++#.$" =. $'/=%#B" P/'/ =. $#%" % /'/ =. 0.=+#*::%R; \*%=+' +.2' 0. $.#$*.+. ='/' E*%&&. 0" /'.

    =+*0."+.;

    3=.=+% "/$A% */ =%$'/0' %/*/$."+' 0%&&" kLK P$A% 2'. F E*%&&' $A% #.$'#0"B' .'R 0%++' ?C6 .")%&"; N." 0"+' */ $.#$*.+' % =."/' =2%$.@.$"+% &% $'/B%/>.'/. 0. =%:/' 2%# +*++% &% $'##%/+. 0.&"+'; K" ='??" "&:%O#.$" 0%&&% $'##%/+. %/+#"/+. ./ $."=$*/ /'0' FC ./ ':/. .=+"/+%C *:*"&% "

    >%#';

    ^*"#0"/0' "/$'#" */" B'&+" &T%=%?2.' ./ @.:*#"C =. 2#%/0%*/" =*2%#@.$.% $A.*=" $A% $'?2#%/0" .& ='&' /'0' $ P&"

    =*2%#@.$.% +":&. "+#% &"+.R; 122&.$"/0' &" kLK '++%/:' &"

    =%:*%/+% %E*">.'/% P"==*?%/0' $'?% /%:"+.B% &% $'##%/+.

    *=$%/+. 0"& /'0' $R C!EC !?D !F$ B;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    7/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; 6

    N%:*'/' '#" "&$*/% $'/=.0%#">.'/. 0. $"#"++%#% :%/%#"&% P"==*/+% $'?% "==.'?. ?"&:#"0' =%

    /% 2'==" @"#% &" 0.?'=+#">.'/%R;

    KT"22&.$">.'/% 0%&&" kLK "0 */ $.#$*.+' 0. 1 &"+. %0 7/'0. $'/=%/+% &" =$#.++*#" 0. /*?%#'=%

    %E*">.'/. $A% 2%#U /'/ ='/' +*++% ./0.2%/0%/+. +#" 0. &'#'; .'/. ./0.2%/0%/+. $'/=.=+% /%&&' =$#.B%#% &% %E*">.'/.

    2%# 7>//'0. 0.B%#=. 0%& $.#$*.+' P%$$' 2%#$Aa F 2.b @#%E*%/+% #.$'##%#% "&&" kLK ". /'0.R;

    N%$'/0" $'/=.0%#">.'/% :%/%#"&%; K% %E*">.'/. #%&"+.B% "&&T"22&.$">.'/% 0%&&" kLK /'/0.2%/0'/' 0"&&" /"+*#" 2"#+.$'&"#% 0%. $'?2'/%/+. ?" ='&' 0"&&" +'2'&':." 0%& $.#$*.+'

    P'BB%#' 0"& ?'0' ./ $*. . $'?2'/%/+. ='/' $'&&%:"+. +#" 0. &'#'R;

    .'/% 0%&&" kLK ='/'H

    %E*">.'/. "&:%O#.$A%g &./%"#.g $'/ $'%@@.$.%/+. 2"#. " 8C 98 '22*#% 7;

    75(#A5 : 1 *8 A6BB6 (& I&9@CC5DD (6AA6 %6$H&5$&

    K" =%$'/0" &%::% 0. k; %=2#.?% &% #%&">.'/. +#" &% +%/=.'/. 0. &"+' ./ */ $.#$*.+';

    F> 6*55* &" ?"$0@@%AA B?:6 k.#$AA'@@ B'&+":% &"`D 6*55* &" ?; &*11* -*)4"%)"E;N." 0"+' */ $.#$*.+' % =."/' =2%$.@.$"+% &% $'/B%/>.'/. 0. =%:/' 2%# +*++% &% +%/=.'/. 0. +*++. .&"+.g 2#%=' */ E*"&=."=. $"??./' $A.*=' % '#.%/+"+' /%& $.#$*.+'C &" ='??" "&:%O#.$" 0%&&%

    +%/=.'/. ./$'/+#"+% &*/:' .& $"??./' $A.*=' FC ./ ':/. .=+"/+%C *:*"&% " >%#';

    M%&&" $.#$*.+' 0. %=%?2.' ./ @.:*#" =. F 2#%=' .& $"??./'

    $A.*=' $'?2'=+' 0". &"+. /*?%#"+. $'?% 5C ] % h;-%#$'##%/0' .& $"??./' ./ =%/=' "/+.'#"#.' '++%/."?' &"

    =%:*%/+% %E*">.'/% kYKH >"GD"?C"E$ B;

    \*%=+" &%::% F 0%#.B"+" 0"&&% %E*">.'/. :%/%#"&.

    0%&&T%&%++#'?":/%+.=?' %0 F #.:'#'="?%/+% %="++" /%.

    $.#$*.+. =+">.'/"#. P'BB%#' E*%. $.#$*.+. ./ $*. &% :#"/0%>>%%&%++#.$A% /'/ $"?O."/' /%& +%?2'R; 3==" %=2#.?% .& @"++'

    $A% ./ $'/0.>.'/. =+">.'/"#.% .& $"?2' %&%++#.$' F$'/=%#B"+.B' % E*./0. .& &"B'#' /%$%=="#.' 2%# 2'#+"#% */"

    $"#.$" %&%++#.$" 0" */ 2*/+' 1 "0 */ 2*/+' Z /'/ 0.2%/0% 0"& 2"#+.$'&"#% 2%#$'#=' =$%&+' ?"

    ='&' 0"&&" 2'=.>.'/% #%$.2#'$" 0%. 2*/+. 1 % Z; .'/. 0. $"#"++%#% :%/%#"&% .?2'#+"/+.;

    KT"22&.$">.'/% 0%&&" kYK "0 */ $.#$*.+' 0. 1 &"+. %0 7/'0. $'/=%/+% &" =$#.++*#" 0. /*?%#'=%%E*">.'/. $A% 2%#U /'/ ='/' +*++% ./0.2%/0%/+. +#" 0. &'#'; .'/% 0%&&" kYK $'/=%/+% &" =$#.++*#" 0. 1>,7>/. V 1>7D/%E*">.'/. &./%"#?%/+%

    ./0.2%/0%/+.; n/ ?'0' =%?2&.$% 2%# =$#.B%#% 1>7D/ %E*">.'/. ./0.2%/0%/+. $'/=.=+%/%&&T*+.&.>>"#% 1. $*5%1. &*1 -.51"%;

    N%$'/0' E*%=+" #%:'&"C 2%# +#'B"#% 1>7D/%E*">.'/. &./%"#?%/+% ./0.2%/0%/+. ./ */ $.#$*.+' =.

    2#'$%0% /%& =%:*%/+% ?'0'H

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    8/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; o

    N. =$%:&.% */ $"??./' $A.*=' % =. =$#.B% &" $'##.=2'/0%/+% %E*">.'/%; N. $"/$%&&" P.0%"&?%/+%R */' 0%. &"+. 0%& 2#.?' $"??./' $A.*='; N. =$%:&.% */ =%$'/0' $"??./' $A.*=' P=+"/0' ?'&+' "++%/+. " /'/ ./$&*0%#% .& &"+'

    %&.?./"+'R % =. =$#.B% &" $'##.=2'/0%/%+% %E*">.'/%;

    N. 2#'$%0% ./ ?'0' .+%#"+.B' 2#%=+"/0' "++%/>.'/% " /'/ ./$&*0%#% ?". . &"+. %&.?./"+./%. 2#%$%0%/+. 2"=="::.;

    N. "##.B"C ./ E*%=+' ?'0'C " =$#.B%#% 1>7D/ %E*">.'/. $A% ='/' &./%"#?%/+%./0.2%/0%/+.;

    N%$'/0" $'/=.0%#">.'/% :%/%#"&% P"/"&':" "& $"=' B.=+' 2%# &" kLKR; K% %E*">.'/. #%&"+.B%

    "&&T"22&.$">.'/% 0%&&" kYK /'/ 0.2%/0'/' 0"&&" /"+*#" 2"#+.$'&"#% 0%. $'?2'/%/+. ?" ='&'

    0"&&" +'2'&':." 0%& $.#$*.+' P'BB%#' 0"& ?'0' ./ $*. . $'?2'/%/+. ='/' $'&&%:"+. +#" 0. &'#'R;

    .'/% 0%&&" kYK ='/'H%E*">.'/. "&:%O#.$A%g &./%"#.g $'/ $'%@@.$.%/+. 2"#. " 8C 98 '22*#% 7;

    J==%#B">.'/%H $'?% =$#.++' "&&T./.>.'C 2%# ./0.B.0*"#% E1 ./$':/.+% 0'OO."?' =$#.B%#% E1%E*">.'/. 0%&&% E*"&. 1B%/:'/' @'#/.+% 0"&&% &%::. 0.k.$AA'@@; N% &" kLK @'#/.=$% 7>/0. E*%=+%

    %E*">.'/.C &" kYK /'/ 2*U $A% @'#/.#% &% #%=+"/+. 1>,7>/.%E*">.'/.;

    J&+#% "&&% +%/=.'/. 0. &"+' PE*%&&% ?.=*#"+% +#" . ?'#=%++. 0%. 0.=2'=.+.B.R F =2%==' *+.&%

    B%#.@.$"#% "/$A% &% +%/=.'/. 0. /'0' P'BB%#' &" +%/=.'/% 2#%=%/+% +#" */ /'0' 0. #.@%#.?%/+' ,0%++' ?"==" , " +%/=.'/% 7 % */ :%/%#.$' /'0' 0%& $.#$*.+'R;

    M%&&" @.:*#" 0. %=%?2.' #.2'#+"+" " &"+' 2'==."?'

    ./0.B.0*"#%H

    d 1% c 7 K% +%/=.'/. 0. &"+'H Y1ZC Y14C YZ4C YZL% YL4; K% +%/=.'/. 0. /'0' P"==*?%/0' .& /'0' 4 $'?%

    /'0' 0. #.@%#.?%/+' , E*./0. %4V7R;

    -%# 2'+%# 0%+%#?./"#% &% +%/=.'/. ". /'0. F /%$%=="#.' 0%@./.#% &" +%/=.'/% 0. */ /'0' % .& =*'

    &%:"?% $'/ &" +%/=.'/% 0. &"+'; 1 +"&% 2#'2'=.+' =. #.$'##% "& =%$'/0' %/*/$."+' 0%&&" kYK 0%++'

    ?:6 &*11* -*)4"%)" .1 )%&%;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    9/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; p

    75(#A5 F 1 0A %6596E8 (& +6AA6B6$

    .'/. 0%&&" kLK "&&% $'##%/+. ". /'0. 2%# +*++.

    % +#% . /'0. "0'++"/0'C $'?% $'/B%/>.'/%C .& =%:/' 2'=.+.B' 2%# &%

    $'##%/+. *=$%/+. 0"& /'0' P%0 "==*?%/0' &" $'/B%/>.'/%0%&&T*+.&.>>"+'#%R; J++%/."?' 0*/E*%H

    A"#i1+ i

    2+ i

    3= 0

    B"#

    i2#

    i3+ i

    4+ i

    5= 0

    C" i1# i

    4# i

    5= 0

    $

    %

    &

    '&

    N"22."?' $A% &% +#% %E*">.'/. /'/ ='/' &./%"#?%/+% ./0.2%/0%/+. P./@"++. &" +%#>" %E*">.'/% F

    &" ='??"C $"?O."+" 0. =%:/'C 0%&&% 2#.?% 0*%R; K% +#% %E*">.'/. 2'=='/' "/$A% %==%#% =$#.++%

    ./ @'#?" ?"+#.$."&% '++%/0%/0' $'=q */" ?"+#$.% 0. 7 5!;86 ,74%!.% 1 3414776 ,12-!.;

    "1 1 1 0 0

    0 "1 "1 1 1

    1 0 0 "1 "1

    #

    $

    %

    %%

    &

    '

    (

    ((

    i1

    i2

    i3

    i4

    i5

    #

    $

    %%

    %%%%

    &

    '

    ((

    ((((

    =

    0

    0

    0

    #

    $

    %

    %%

    &

    '

    (

    ((

    N. '==%#B" $A% 2%# $."=$*/" $'&'//" . $'%@@.$.%/+. 8 % 98 "22".'/' ='&' */" B'&+" $."=$*/';

    \*%=+' F 0'B*+' "& @"++' $A% */ 0.=2'=.+.B' $'/ 0*% ?'#=%++. F "++"$$"+' " ='&' 0*% /'0. % $A%

    &" $'##%/+% ="#S 2'=.+.B" %/+#"/+% ./ */ /'0' % 2'=.+.B" *=$%/+% 0"&&T"&+#'; K" ?"+#.$% $'=q'++%/*+" F 0%++" 2.-$"0* ")0"&*)(. 0%& $.#$*.+' P% =. ./0.$" $'/ &" &%++%#" 1R; 4" %==" F2'==.O.&% #.$'=+#*.#% &" +'2'&':." 0%& $.#$*.+' P"==*?%/0' &% $'/B%/>.'/. ='2#" 0%=$#.++% ,$'/B%/>.'/% 0%&&T*+.&.>>"+'#% % $'##%/+. 2'=.+.B% *=$%/+. /%& /'0'R; N% .& B%++'#% !F &T./=.%?%

    '#0./"+' 0%&&% $'##%/+. 0. &"+'C 2'==."?' =$#.B%#%C ./ @'#?" =./+%+.$"C &% / %E*">.'/. ". /'0.

    $'?%)! $ B;

    -%# &' =+%==' $.#$*.+' P*+.&.>>"/0' &" $'/B%/>.'/% 0%&&T*+.&.>>"+'#%R

    2'==."?' =$#.B%#% &% %E*">.'/. #%&"+.B% "&&% &%::. 0. k.#$AA'@@ 0%&&%+%/=.'/. 0. /'0';

    v1= e

    C" e

    A

    v2= e

    A" e

    B

    v3= e

    A" e

    B

    v4= e

    B" e

    C

    v5= e

    B" e

    C

    #

    $

    %%%

    &

    %%%

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    10/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; 87

    1/$A% E*%=+% %E*">.'/. 2'=='/' %==%#% =$#.++% ./ @'#?" ?"+#.$."&%C $'?% #.2'#+"+' 0. =%:*.+'Hv

    1

    v2

    v3

    v4

    v5

    "

    #

    $$

    $

    $$$

    %

    &

    ''

    '

    '''

    (1 0 1

    1 (1 0

    1

    (1 0

    0 1 (1

    0 1 (1

    "

    #

    $$

    $

    $$$

    %

    &

    ''

    '

    '''

    =

    eA

    eB

    eC

    "

    #

    $

    $$

    %

    &

    '

    ''

    3T .?2'#+"/+% '==%#B"#% $A% &" ?"+#.$% $A% 0%@./.=$% &% #%&">.'/. +#" &% +%/=.'/. 0. &"+' % &%

    +%/=.'/. 0. /'0' F *:*"&% "&&" B%#=.'/% +#"=2'=+" 0%&&" ?"+#.$% ./$.0%/>"; 4" $.UC =% 2'/."?'$'/ " V r"/0 "E0 "G0 "L0 "?s % 6 $ M6)0 6*0 6KNC 2'==."?' =./+%+.$"?%/+% =$#.B%#% " $ )O6; \*"/+'B.=+'

    ./ E*%=+' %=%?2.' 2*U %==%#% %=+%=' " +*++. . $.#$*.+. 2%# $*. B"&:'/' &% &%::. 0. k.#$AA'@@;

    t"$$."?' '#" */T'==%#B">.'/% $'/=.0%#"/0' &% 0*% =%:*%/+. $'22.% 0. $.#$*.+.;

    >' &% +%/=.'/.C "B#U

    +%/=.'/. 0. &"+' 0.B%#=%; .'/% +'2'&':.$" $.#$*.+"&%C %=.=+'/' ./@./.+. ./=.%?.

    0. B"&'#. 0. $'##%/+% $A% ='00.=@"/' &% kLK % ./@./.+. ./=.%?. 0. B"&'#. 0. +%/=.'/% $A%='00.=@"/' &% kYK "&&% ?":&.% % ./@./.+. ./=.%?. 0. B"&'#. 0. +%/=.'/. 0. /'0' $A% ='00.=@"/' &%

    kYK 0. /'0';

    ^.*/:."?' E*./0. "&&T%/*/$.">.'/% 0%& G*%$*2. &" G*11*5*); N." 0"+' */ :%/%#.$' $.#$*.+' 0. 1

    12-!% 7 74%!g =." ! $ M!/0 !E0 A0 !1N*/ ./=.%?% 0. B"&'#. 0. $'##%/+% 0. &"+' $A% ='00.=@./' &% kLKg =."" $ M"/0 "E0 A0 "1N */ ./=.%?% 0. B"&'#. 0. +%/=.'/% 0. &"+' $A% ='00.=@./' &% kYK 2%# E*%=+'

    $.#$*.+'; 1&&'#" "B#%?' $A%H

    vkik

    k=1

    l

    " = 0 K" 0.?'=+#">.'/% F .??%0."+"; N% ./@"++. =. %@@%++*" .& 2#'0'++' =$"&"#% 0%. 0*% B%++'#. " % !

    '++%/."?'H "O! $ ,)O6.O! $ 6O,)O.O! $ 6O)! $ B P2'.$Aa)!$BR

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    11/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; 88

    3T .?2'#+"/+% '==%#B"#% $A% /%&&% .2'+%=. /'/ F =+"+' #.$A.%=+' $A% . 0*% B%++'#. " % !

    ='00.=@"$%==%#' $'/+%?2'#"/%"?%/+% &% &%::. 0. k.#$AA'@@ % $A% E*./0.C /%& &'#' ./=.%?%C#"22#%=%/+"==%#' &" ='&*>.'/% 0. */ $.#$*.+' 2"#+.$'&"#%; 1OO."?' ='&' =*22'=+' $A%C

    =./:'&"#?%/+%C &% $'##%/+. ='00.=@"$%==%#' &% kLK % &% +%/=.'/. ='00.=@"$%==%#' &% kYK;

    M%& $"=' ./ $*. . B%++'#. " % ! 2#%=. ./=.%?% =."/' %@@%++.B"?%/+% &" ='&*>.'/% 0. */ $.#$*.+'2"#+.$'&"#%C .& +%'#%?" 0. D%&&%:%/ "@@%#?" $A% &" ='??" "&:%O#.$" 0%&&% 2'+%/>% =$"?O."+% ./

    ':/. .=+"/+% 0" +*++. . 0.=2'=.+.B. 0%& $.#$*.+' P./ $*. +*++. . &"+. =."/' $"#"++%#.>>"+. 0"&&" =+%=="$'/B%/>.'/%R F *:*"&% " >%#' %0 %=2#.?%C 2%#+"/+'C .& 2#./$.2.' 0. $'/=%#B">.'/% 0%&&T%/%#:."

    %&%++#.$";

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    12/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; 85

    *64&5$6 : 1 J&H"5H&%&K& 6A6%%9&@&

    75(#A5 3 1 J&H"5H&%&K& 6A6%%9&@&

    J:/. 0.=2'=.+.B' 0%B% %==%#% 0'+"+' 0. ?'#=%++. P' +%#?./"&.R *+.&. =." 2%#$'&&%:"#% +#" &'#' . $'?2'/%/+. $A% 2%# 2'+%# $'//%++%#% :&. =+#*?%/+. 0.

    ?.=*#"; < 0.=2'=.+.B. +#"++"+. ./ E*%=+' $'#=' ='/' 2%# &' 2.b 0'+"+. 0. 0*%?'#=%++. % 2%#$.U =. 0.$'/' 7"#%1";

    J:/. 0.=2'=.+.B' #%"&% F $"#"++%#.>>"+' 0" */ 0.B%#='$'?2'#+"?%/+' %&%++#.$' P=. 2%/=. "& O"/"&% %=%?2.' 0%&&"

    &"?2"0./" @"++' "&&T./.>.'R; K" /"+*#" %&%++#.$" F E*./0. &" 2.b

    /"+*#"&% $&"==.@.$">.'/% "0'++"O.&% 2%# . $'?2'/%/+.; -#%='*/ :%/%#.$' 0.=2'=.+.B'C */" B'&+" $'&&%:"+' "0 */ $.#$*.+'

    %&%++#.$' . B"&'#. 2"#+.$'&"#. 0. +%/=.'/% ". ?'#=%++. % 0.$'##%/+% "++#"B%#=' */" =%>.'/% 0.2%/0%#"//' 0"&

    2"#+.$'&"#% $.#$*.+' "& E*"&% .& 0.=2'=.+.B' F =+"+' $'&&%:"+';

    K% +%/=.'/. % &% $'##%/+. 0. &"+' 0%& 0.=2'=.+.B' ='/' =%?2#% $'##%&"+% +#" 0. &'#' 0" */"

    @*/>.'/% $"#"++%#.=+.$" 0%++" "/$A% $*1.("%)* 0%4-"-'-",.0%& $'?2'/%/+% PXP"0!0-R V 7R; 3=="/'/ 0.2%/0% 0"& 2"#+.$'&"#% $.#$*.+' " $*. .& 0.=2'=.+.B' F $'&&%:"+' O%/=q ='&' 0"&&" /"+*#"2"#+.$'&"#% 0%& 0.=2'=.+.B' P'==." &% $"#"++%#.=+.$A% @.=.$A% $A% /% 0%+%#?./"/' .&

    $'?2'#+"?%/+' %&%++#.$'R; H"4#%4"-"," 4"2"1" ="#"//' $"#"++%#.>>"+. 0" #%&">.'/. $'=+.+*+.B%

    =.?.&.C $A% A"//' &" =+%==" @'#?*&" ?"+%?"+.$" % ='/' "=='$."O.&. "0 */ .0%/+.$' ?'0%&&'; N%/%&&" #%&">.'/% $'=+.+*+.B" /'/ $'?2"#% &" B"#."O.&% +%?2' P./=.%?% "&&" +%/=.'/% % "&&"

    $'##%/+% 0. &"+'R 0.#%?' $A% .& 0.=2'=.+.B' F -*2#% "),.$".)-*;

    .'/%$'=+.+*+.B" F 0. +.2' ./+%:#'90.@@%#%/>."&%;

    N. 2"#&" 0. &"4#%4"-"," $*4"4-","E*"/0' =. A" " $A% @"#% $'/ 0.=2'=.+.B. &" $*. #%&">.'/%$'=+.+*+.B" F 0. +.2' "&:%O#.$'9+#"=$%/0%/+%;

    L'/=%:*%/+%?%/+% =. 2"#&%#S 0. 0"$0'"-" &").2"0" E*"/0' .& $.#$*.+' $'/+.%/% "&?%/' */$'?2'/%/+% 0./"?.$' % 0. 0"$0'"-" $*4"4-","/%:&. "&+#. $"=.;

    75(#A5 : 6 F 1 )H6E"& (& (&H"5H&%&K& L3 6 :M

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    13/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; 8]

    n="/0' &" $'/B%/>.'/% 0%:&. *+.&.>>"+'#.C &" #%&">.'/% $'=+.+*+.B" 0%&

    #%=.=+'#% F #"&$ PB.%/% $A."?"+" "/$A:% &%::% 0. JA? , &" @'#?*&"

    ./0.$" $A% ./ */ #%=.=+'#%C +%/=.'/% % $'##%/+% ='/' =%?2#%

    2#'2'#>.'/"&. +#" &'#'R; M%&&" $'/B%/>.'/% 0%& :%/%#"+'#% P&"

    $'##%/+% ! %=$% 0"& ?'#=%++' f 0%& O.2'&'R &" &%::% 0. JA? 0.B%/+"

    #"'&$ P.& =%:/' , F 0'B*+' "& B%#=' 0%&&" $'##%/+%R; \*%=+"0.=+./>.'/% F .?2'#+"/+% /%&&" ='&*>.'/% 0%. $.#$*.+.; K" $'/0*++"/>"

    P^R F &T./B%#=' 0%&&" #%.=+%/>" P)R % &" &%::% 0. JA?C ./ E*%=+' $"='C F

    $"(# PB"&:'/' &% =+%==% $'/=.0%#">.'/. @"++% 2%# &" #%=.=+%/>" ./

    ?%#.+' "&&" $'/B%/>.'/%R;

    )%=.=+'#. 0.B%#=. A"//' $A."#"?%/+% 0.B%#=" #%=.=+%/>"; M%& :#"@.$' F

    B.=*"&.>>"+" &" #"22#%=%/+">.'/% 0%&&" #%&">.'/% +%/=.'/.W$'##%/+. 0.

    0*% 0.B%#=. #%=.=+'#.; K" 0.B%#=" 2%/0%/>" %=2#.?% .& 0.B%#=' B"&'#%

    0%& 2"#"?%+#' );

    4.?%/=.'/"&?%/+%C &" #%=.=+%/>" =. ?.=*#" ./ 'A? P=.?O'&' uR

    ?%/+#% &" $'/0*++"/>" =. ?.=*#" ./ N.%?%/= P=.?O'&' N V u 98R;

    1/"&.>>"/0' &" $"#"++%#.=+.$" +%/=.'/%9$'##%/+% 0. */ #%=.=+'#%

    %?%#:% $A% &" 2'+%/>" .=+"/+"/%" P+,-.$",-.!,-.R F =%?2#% ?"::.'#%

    P' *:*"&%R 0. >%#' ./ E*"&=."=. $'/0.>.'/% 0. @*/>.'/"?%/+' P'BB%#'

    2%# E*"&=."=. +%/=.'/% % $'##%/+% 0. &"+'R; \*%=+' =.:/.@.$" $A% .&

    #%=.=+'#% "=='#O% =%?2#% 2'+%/>" 0"& $.#$*.+' " $*. F $'&&%:"+';

    .'/%H

    &"4#%4"-"," #.44"," * &"4#%4"-"," .--","; K" 0%@./.>.'/% =. "22&.$" "&&"

    $'/B%>.'/% 0%:&. *+.&.>>"+'#.;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    14/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; 8c

    .'/% $'=+.+*+.B" /'/ $'/+.%/%

    %=2&.$.+"?%/+% "&&" $'##%/+%C '==." */ 0.=2'=.+.B' 2%# $*. .& B"&'#% 0.

    +%/=.'/% ". ?'#=%++. F ./0.2%/0%/+% 0"& 2"#+.$'&"#% B"&'#% 0.

    $'##%/+% 0. &"+';

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    15/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; 8h

    .'/% $'=+.+*+.B" /'/ $'/+.%/%

    %=2&.$.+"?%/+% &" +%/=.'/%C '==." */ 0.=2'=.+.B' 2%# $*. .& B"&'#% 0.

    $'##%/+% ". ?'#=%++. F ./0.2%/0%/+% 0"& 2"#+.$'&"#% B"&'#% 0.

    +%/=.'/% 0. &"+';

    1/$A% ./ E*%=+' $"=' . :%/%#"+'#. B%/:'/' =*00.B.=. ./ 0*% +.2.

    0.@@%#%/+.H 5*)*$.-%$" &" 0%$$*)-* 0%4-.)-* % ") 0%)-")'. P! F$'=+"/+% /%& +%?2'R % 5*)*$.-%$" &" 0%$$*)-* ,.$".7"1* P! F */"XP+RR;

    D#" . :%/%#"+'#. 0. $'##%/+% B"#."O.&.C 2"#+.$'&"#% #.&%B"/>" A"//'E*%&&. &" $*. #%&">.'/% $'=+.+*+.B" F 0"+" 0"&&" @'#?" !,-.$) 9!7,!-.

    P'BB%#' . :%/%#"+'#. 0. $'##%/+% B"#."O.&. $'/ @'#?" 0T'/0"

    =./*.='0"&%R;

    4"&&T%="?% 0%&&% $*#B% $"#"++%#.=+.$A% 0%& :%/%#"+'#% 0. $'##%/+% P=."

    /%& $"=' $'=+"/+% $A% /%& $"=' B"#."O.&%R =. '==%#B" $A%C 0" */ 2*/+'

    0. B.=+" %/%#:%+.$'C */ :%/%#"+'#% 0. $'##%/+% 2*U =." "=='#O.#% $A%

    %#':"#% 2'+%/>"; >"+'#.;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    16/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; 8d

    " /*&&"; K" $'##%/+%

    F E*./0. !% &" +%/=.'/% F /*&&";

    " /*&&" P' #%=.=+%/>" ./@./.+"R; K" +%/=.'/% ". $"2. F "

    ?%/+#% &" $'##%/+% F /*&&";

    KT./+%##*++'#% F 2#%=%/+"+' $'?% O.2'&' 2"#+.$'&"#% $A% 2*U %==%#%

    */ $.#$*.+' "2%#+' '22*#% */ $'#+' $.#$*.+'; M%&&" @.:*#" 0. =./.=+#"

    &T./+%##*++'#% F "2%#+' F /%&&T.=+"/+% -$-/ =. $A.*0%; M%&&" @.:*#" 0.

    0%=+#" &T./+%##*++'#% F $A.*=' % /%&&T.=+"/+% -$-E=. "2#%;

    Y'&+?%+#' % "?2%#'?%+#' .0%"&. ='/' 0*% =+#*?%/+. 0. ?.=*#"

    #.=2%++.B"?%/+% 0%&&" +%/=.'/% % 0%&&" $'##%/+%;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    17/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; 86

    *64&5$6 N 1 >5A#4&5$6 (6& @&9@#&%& 96H&H%&K&

    75(#A5 3 1 76%5(5 (6AA8 E8%9&@6 H"89H8Y%/:'/' O#%B%?%/+% #.$A."?"+. "&$*/. $'/$%++. B.=+. /%&&%

    &%::. 0. k.#$AA'@@ ./ ?%#.+' "&&" 0%+%#?./">.'/% 0%&&%%E*">.'/. 2%# &" ='&*>.'/% 0. */ $.#$*.+'; .'/% 0. E*%=+' ?%+'0'; -"#+%/0' 0"& $.#$*.+' %&%++#.$' ./0.$"+' ./ @.:*#" P$A% A" c

    /'0. % d &"+.RC B.%/% $'=+#*.+" &" ?"+#.$% #.2'#+"+" ='++';

    3T .?2'#+"/+% '==%#B"#% $'?% &" ?"+#.$% =." =+"+" $'=+#*.+" .?2.%:"/0' 7>/PV1'ER %E*">.'/.

    0"+% 0"&&" kLKC "&+#% 1>7D/ PV1'E 2%# */ +'+"&% 0. 1R %E*">.'/. 0"+% 0"&&" kYK % 1 %E*">.'/.0%+%#?./"+% 0"&&% #%&">.'/. $'=+.+*+.B% P./ :%/%#% #.$"B"+% 0"&&T"22&.$">.'/% 0%&&" &%::% 0. JA?

    ". =./:'&. &"+.WO.2'&. , /%&&T%=%?2.'C %==%/0' d . &"+.C #.$"B' d %E*">.'/.R 2%# */ +'+"&% 0. E1

    %E*">.'/.; .'/% 0%&&T*+.&.>>"+'#%C

    '++%/:'H

    3E*">.'/. 0'B*+% "&&" kLK 3E*">.'/. 0'B*+% "&&" kYK3E*">.'/. 0%#.B"/+. 0"&&% #%&">.'/.

    $'=+.+*+.B%;

    3))1D1 LJ))

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    18/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; 8o

    -*#+#'22'C $'?% =. 2*U '==%#B"#% 0"&&" ?"+#.$%C E*%=+" ='&*>.'/% $. 2'#+" "0 "B%#% */ =.=+%?"

    2"#+.$'&"#?%/+% :#"/0% :.S 2"#+%/0' 0" */ $.#$*.+' =%?2&.$% ./'&+#% %=.=+'/' ?'&+.$'%@@.$.%/+. 0%&&" ?"+#.$% 2"#. " >%#' P0" $.U .& /'?% 0. ?"+#.$% =2"#="R; \*./0.

    $'/$%++*"&?%/+%C E*%=+' ?%+'0'C F ?'&+' =%?2&.$% ?" .& =*' *+.&.>>' F ?'&+' &.?.+"+' 2%#$Aa

    $'?2'#+" */ /*?%#' %&%B"+' 0. $"&$'&.;

    n/ ?%+'0' .0%"&% ="#%OO% E*./0. $"#"++%#.>>"+' 0" */" O"==" 34H+1699!-P% 0" */ O"==' 349-4

    34H+% $A% $'=+.+*.=$'/' .& 0.=2'=.+.B' 4 % .&

    ='++'$.#$*.+' Z $A% ='/' E*"=. =%?2#% 0.B%#=%R;

    >% 0. &"+' 0%& $.#$*.+' 1

    /'/ $"?O."/' =% /%&&" #%+% $'?2&%==.B" .& ='++'$.#$*.+' Z B.%/% ='=+.+*.+' $'/ .& 0.=2'=.+.B' 4C"??%==' $A% =." $'//%==' ./ ?'0' '22'#+*/';

    3T $A."#' $A% +#"?.+% E*%=+' 2#./$.2.' F 2'==.O.&% 2#':%++"#% % $"#"++%#.>>"#% #%+. 0. $.#$*.+."/$A% 0. :#"/0% $'?2&%==.+S #.0*$%/0' &" ='&*>.'/% 0. 2#'O&%?. :#"/0. " $.#$*.+. B." B." 2.b

    =%?2&.$.;

    M%& =%:*.+' 0%& ?'0*&' B%/:'/' .&&*=+#"+. 0.B%#=. $"=. +*++. ?'&+' .?2'#+"/+. ?" "/$A%

    =%?2&.$%; 1/$A% ./ E*%=+' $"=' ?. &.?.+' " #.2'#+"#% &% @.:*#% 2#./$.2"&. $'/ . $'??%/+.%==%/>."&.;

    L'//%==.'/% ") 4*$"*; < 0*% 0.=2'=.+.B.='/' $'//%==. +#"?.+% */ /'0' "& E*"&%

    /'/ F $'//%==' /%==*/ "&+#' 0.=2'=.+.B';

    K" $'##%/+% 0. &"+' F ./ E*%=+' =%?2#%

    .0%/+.$" PO"=+" $"&$'&"#% &" kLK "& /'0'

    0. $'//%==.'/%R;

    M%& $"=' 0. 7 #%=.=+'#. $'//%==. ./ =%#.% F @"$.&% 0%+%#?./"#% &"

    #%=.=+%/>" %E*.B"&%/+% R)*0"+" =%?2&.$%?%/+% 0"&&" ='??" 0. +*++%&% #%=.=+%/>%; N. '==%#B. $A% R)* F 2.b :#"/0% 0. E*"&*/E*% 0%.

    #%=.=+'#. R/0 A0 R7;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    19/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; 8p

    L'//%==.'/% ") #.$.11*1%; .'/% ?"/*"&% 0%. $.#$*.+. #%=.=+.B. &./%"#.; < +%'#%?. 0.DAaB%/./ % M'#+'/ ='/' +#" &'#' 0*"&.;

    G*%$*2. &" G@J,*)")n/ $.#$*.+' #%=.=+.B' &./%"#%C 0'+"+' 0. 0*% ?'#=%++.C

    2*U %==%#% ='=+.+*.+'C ". @./. %=+%#/.C $'/ */ $.#$*.+'

    #%"&.>>"+' 0" */ :%/%#"+'#% ./0.2%/0%/+% 0. +%/=.'/% %0" */" #%=.=+%/>"C $'//%==. ./ =%#.% % =$%&+. ./ ?'0'

    +"&% $A% &" $"#"++%#.=+.$" ". ?'#=%++. =." *:*"&% " E*%&&"

    0%& $.#$*.+' $A% =. ./+%/0% ='=+.+*.#%;

    >"+' 0" */ :%/%#"+'#% ./0.2%/0%/+% 0. $'##%/+% %0" */" #%=.=+%/>"C $'//%==. ./ 2"#"&&%&' % =$%&+. ./

    ?'0' +"&% $A% &" $"#"++%#.=+.$" ". ?'#=%++. =." *:*"&% "

    E*%&&" 0%& $.#$*.+' $A% =. ./+%/0% ='=+.+*.#%;

    ";

    -%# 1. $*4"4-*)(. &*1 1.-% *I'",.1*)-* =. 2#'$%0%#%

    /%& =%:*%/+% ?'0'H

    L#*5)*$* -'--" " 5*)*$.-%$"./0.2%/0%/+. /%&$.#$*.+' P'==." 4%4-"-'*)&% " 5*)*$.-%$" &"

    -*)4"%)* 0%) ') 0%$-% 0"$0'"-% * I'*11" &"

    0%$$*)-* 0%) ') 0"$0'"-% .#*$-%Rg

    L"&$'&"#% &" #%=.=+%/>" B.=+" ". ?'#=%++. 1 % Z0%& $.#$*.+' $A% =. '++.%/% P$A% $'/+%##S ='&'

    $'?2'/%/+. 2"==.B.R;

    K" -*)4"%)* &*118*I'",.1*)-* G@J,*)")C =. $"&$'&"./B%$% /%& =%:*%/+% ?'0'H

    N. 0%+%#?./" &" +%/=.'/% +#" . ?'#=%++. 1 % Z/%& $.#$*.+' $A% =. ./+%/0% ='=+.+*.#%C E*"/0'

    E*%=+. ?'#=%++. ='/' &"=$."+. "2%#+. P+%/=.'/%

    " B*'+'R;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    24/61

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    25/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; 5h

    \*%=+' =.:/.@.$"C ./ =./+%=.C $A% 2%# */ $.#$*.+'

    #%=.=+.B' &./%"#% 0'+"+' 0. 0*% ?'#=%++. $A% ". @./.

    %=+%#/. =. $'?2'#+. $'?% */ :%/%#"+'#% ./0.2%/0%/+%

    0. $'##%/+% /'/ F 2'==.O.&% $"&$'&"#% */ %E*.B"&%/+%

    DAaB%/./;

    \*%=+' =.:/.@.$"C ./ =./+%=.C $A% 2%# */ $.#$*.+'

    #%=.=+.B' &./%"#% 0'+"+' 0. 0*% ?'#=%++. $A% ". @./.

    %=+%#/. =. $'?2'#+. $'?% */ :%/%#"+'#% ./0.2%/0%/+%

    0. +%/=.'/% /'/ F 2'==.O.&% $"&$'&"#% */ %E*.B"&%/+%

    M'#+'/;

    .'/% 0%. 0*% +%'#%?. "& $.#$*.+' 0"+'; L'/

    #.@%#.?%/+' "&&" @.:*#" #.2'#+"+"C 2%# $"&$'&"#% &" #%=.=+%/>" %E*.B"&%/+% 2'==."?'H

    M%& $.#$*.+' 0. =./.=+#"H $'#+'$.#$*.+"#% .& :%/%#"+'#% 0. +%/=.'/% '++%/%/0' $A% RU$ RO; M%& $.#$*.+' 0. 0%=+#"H ='=+.+*.#% .& :%/%#"+'#% 0. $'##%/+% $'/ */ $.#$*.+' "22%#+' '++%/%/0' $A% RO$ RU;

    )":.'/"/0' "&&' =+%==' ?'0' 2'==' 0%+%#?./"#% .& :%/%#"+'#% 0. $'##%/+% %E*.B"&%/+% PM'#+'/R ' E*%&&' 0.

    +%/=.'/% %E*.B"&%/+% PDAaB%/./R; 1&&" @./% =. '++%/:'/' . =%:*%/+. #.=*&+"+.H&-" &)3 .)" &-/ 0-3 0-" .),&)

    N%:*%C ./@./%C */ =%?2&.$% %=%?2.' 0. $"&$'&' 2%# .&

    E*"&% #.2'#+' . 2"==. %==%/>."&. 2%# #.='&B%#%

    &T%=%#$.>.'H

    " %E; 1Z PROR; N. =2%:/% &T*/.$'

    :%/%#"+'#% 0. $'##%/+% P='=+.+*%/0'&' $'/ */ $.#$*.+'

    "2%#+'R; 1B#%?' E*./0.H

    ROV P]u =%#.% cuR WW 5u V 8cWp u

    -%# &" +%/=.'/% 1Z P6OR; K% #%=.=+%/>% cu % 5u ='/' ./

    =%#.% PV duR E*./0. A' */ =%?2&.$% 2"#+.+'#% 0.

    $'##%/+%; L"&$'&' "&&'#" &" $'##%/+% !EH

    !EV P81 v ]uRWP ]ufduR V ]Wp 1 V 8W] 1

    ."&. 2%# #.='&B%#%

    &T%=%#$.>.'H

    " %E; 1Z PRUR; N. =2%:/% &T*/.$'

    :%/%#"+'#% 0. +%/=.'/% P='=+.+*%/0'&' $'/ */ $'#+'

    $.#$*.+'R; 1B#%?' E*./0.H

    RUV hu WW 6u V ]hW85 u

    -%# &" $'##%/+% /%& $'#+' $.#$*.+' 1Z P!3V3VR; K"

    #%=.=+%/>" 0" 6u =. +#'B" $'#+'$.#$*.+"+" PE*./0. &" =*"

    $'##%/+% F /*&&"R % &" $'##%/+% $A% 2"==" "++#"B%#=' .&

    $'#+' $.#$*.+' 1Z F &" =+%==" $A% "++#"B%#=" .& #%=+' 0%&

    $.#$*.+'; L"&$'&' "&&'#" &" $'##%/+% !3V3VH

    !3V3VV P5YRWPhuR V 5Wh 1 V 7;c 1

    \*./0.H

    .

    .

    .

    ##

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    26/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; 5d

    75(#A5 F 1 +98HD59E84&5$6 %9&8$B5A5 H%6AA8

    N. =*22'/:" 0. B'&%# $"&$'&"#% &" 2'+%/>" %#':"+" 0"& :%/%#"+'#% 0.

    +%/=.'/% /%& $.#$*.+' #.2'#+"+' E*. " @."/$'; N"#%OO% 0. ./0*OO."$'?'0.+S 2'+%# $"&$'&"#% &" #%=.=+%/>" %E*.B"&%/+% B.=+" 0"&

    :%/%#"+'#% 0. +%/=.'/% PR)*R 2%# 2'. $"&$'&"#% &" 2'+%/>"H

    +,-. $ 6E,-. ' R)*

    N. /'+" =*O.+'C 2%#UC $A% &% $./E*% #%=.=+%/>% /'/ ='/' $'&&%:"+% /a ./ =%#.% /a ./ 2"#"&&%&' % .&

    $"&$'&' 0%&&" #%=.=+%/>" %E*.B"&%/+% /'/ =%?O#" "@@"++' O"/"&%; K" ='&*>.'/% $'/=.=+% /%&

    #.$'/'=$#%C /%& $.#$*.+'C */ 2"#+.$'&"#% +.2' 0. $'&&%:"?%/+' %C *+.&.>>"/0' "22'=.+% @'#?*&%C+#"=@'#?"#&' ./ */ "&+#' +.2' 0. $'&&%:"?%/+'; N. 2"#&" "&&'#" 0. +#"=@'#?">.'/% -$".)5%1%.'/% =+%&&"9+#."/:'&' 0%@./.=$'/' 2#'2#.' $'?% =$%:&.%#% . B"&'#. 0%&&% #%=.=+%/>% 0%.#%=.=+'#. "@@./$Aa . $.#$*.+.C 0"& 2*/+' 0. B.=+" %=+%#/'C =."/' %E*.B"&%/+.;

    4. =%:*.+' B%/:'/' #.2'#+"+% &% @'#?*&% #%&"+.B% "&&% +#"=@'#?">.'/. +#."/:'&' =+%&&"; N. '==%#B.C2#.?" 0. +*++'C $A% &% #%=.=+%/>% 0%& +#."/:'&' ='/' ./0.$"+% $'/ &% &%++%#% ?".*=$'&% PR)0 R*0 RKR

    ?%/+#% E*%&&% 0%&&" =+%&&" ='/' ./0.$"+% $'/ &% &%++%#% ?./*=$'&% P5)0 5*0 5KR;

    N. /'+.C 2'.C $A% ?%/+#% /%& +#."/:'&' &" #%=.=+%/>" R)F E*%&&" '22'=+" "& /'0' 1C /%&&" =+%&&" 5)

    F &" #%=.=+%/>" $'&&%:"+" "& /'0' 1 P$'=q B"&% 2%# :&. "&+#. 0*% &"+. ' /'0.R;

    K% @'#?*&%C 2'.C ='/' @"$.&. 0" $"&$'&"#% 2%#$Aa ./ %/+#"?O. . $"=. &" #%=.=+%/>" $%#$"+" P"0

    %=%?2.' &" #%=.=+%/>" $'/ 2%0.$% 1R F *:*"&% "& 2#'0'++' 0%&&% #%=+"/+. #%=.=+%/>% P2%# #%=+"/+.?. #.@%#.=$' "&&" /'>.'/% /%& 2%0.$% , E*./0. Z % LR 0.B.=' &" #%=.=+%/>" %E*.B"&%/+% $A% ./B%$%

    B"#." " =%$'/0" 0%& +.2' 0. $'&&%:"?%/+';

    D$**(55&$*( - 5'(%%-D$**(55&$*( - 5'(%%-

    D$**(55&$*( - '4&-*E$%$D$**(55&$*( - '4&-*E$%$

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    27/61

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    28/61

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    29/61

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    30/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; ]7

    -'.$Aa ")* $ 6S C RS!S PS F .& :%/%#.$' y9%=.?' &"+'R

    "B#%?'H

    ik=

    ek" v

    ab

    Rk

    #k:1$ k$n

    \*"/0' . ?'#=%++. 1Z ='/' &"=$."+. "2%#+.C &" $'##%/+%%/+#"/+% ". ?'#=%++. F 2"#. " >%#'; \*./0. 2'==."?'

    =$#.B%#%H

    ik

    k=1

    n

    " =ek

    Rkk=1

    n

    " # v

    ab

    Rkk=1

    n

    " =0 $ vab =

    ek

    Rkk=1

    n

    "

    1

    Rkk=1

    n

    "

    KT*&+.?" @'#?*&" F "22*/+' $A."?"+" A%$2'1. &"

    N"112.);

    -'.$Aa &" $'##%/+% ! F &" ?%0%=.?"C 2'==."?'

    '==%#B"#% $A%C 2%# ':/. SH

    i =ik=a

    k"

    vk

    Rk

    #k :1$ k$ n

    LA%C ./ +%#?./. 0. $'/0*++"/>"C 0.B%/+"H1

    Rk

    =Gk" i =a

    k# v

    kG

    k" v

    k=

    ak# i

    Gk

    \*"/0' . ?'#=%++. 1Z ='/' ./ $'#+' $.#$*.+'C &"+%/=.'/% ". ?'#=%++. F 2"#. " >%#' E*./0. 0%B% %==%#%

    >%#' &" ='??" 0%&&% +%/=.'/. &*/:' &" ?":&.";

    -'==."?' "&&'#" =$#.B%#%H

    vk

    k=1

    n

    " =a

    k

    Gkk=1

    n

    " # i

    Gkk=1

    n

    " =0 $ i =

    ak

    Gkk=1

    n

    "

    1

    Gkk=1

    n

    "

    K" @'#?*&" $'=q +#'B"+" F &T%E*.B"&%?/+% 0%&&" A%$2'1.

    &" N"112.) /%& $"=' 0. :%/%#"+'#. 0. $'##%/+%

    "$$'?2":/"+.;

    75(#A5 F 1 +6596E8 (6A E8HH&E5 %98HD69&E6$%5 (& "5%6$48

    \*%=+' +%'#%?"C 0. :#"/0% #.&%B"/>" 2#"+.$"C 2*U %==%#% "22&.$"+'C ./ :%/%#"&%C " 0.B%#=.$.#$*.+.; " "=='#O.+" 0"&

    $"#.$' 0%& :%/%#"+'#% "$$'?2":/"+'; L. =. 2#'2'/% 0. $"&$'&"#%C E*./0.CE*"&% =." &" ?"==.?" 2'+%/>" '++%/.O.&% 0" */ :%/%#"+'#% 0. #%=.=+%/>"

    ./+%#/" R;"& B"#."#% 0%& $"#.$' R[;

    "C &" 2'+%/>" =*& $"#.$'H

    PL= iv

    L= i

    2R

    L=

    e(t)

    Rg+R

    L

    "

    #$$

    %

    &''

    2

    RL

    -%# 0%+%#?./"#% .& B"&'#% 0. R[ +"&% $A% &" 2'+%/>" \[ =." ?"==.?"C 2'==."?' 0%#.B"#% &"2'+%/>" =+%==" ./ @*/>.'/% 0%&&" #%=.=+%/>" 0. $"#.$' %0 *:*":&."#% &" 0%#.B"+" " >%#'H

    "PL

    "RL=e

    2(t)

    1

    Rg+R

    L( )2# 2

    RL

    Rg+R

    L( )3

    $

    %

    &&

    '

    (

    ))=e

    2(t)

    Rg +RL# 2RL

    Rg+R

    L( )3

    $

    %

    &&

    '

    (

    ))=0

    -%# "//*&&"#% &" 0%#.B"+" F =*@@.$.%/+% "//*&&"#% .& /*?%#"+'#% "&&T./+%#/' 0%&&% 2"#%/+%=.E*"0#% % +"&% $'/0.>.'/% =. B%#.@.$" =% % ='&' =% R[V R;; -'==."?' "&&'#" 0.#% $A% \[F ?"==.?"=% R[V R;;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    31/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; ]8

    " ./+%#/" 2"#. " R;C &" ?"==.?"

    2'+%/>" +#"=@%#.O.&% "0 */ $"#.$' #%=.=+.B' P0%++" #%-*)(. &"4#%)"7"1*R B"&%H

    PLMAX =e2(t)

    4Rg

    K" $'/0.>.'/% "@@./$Aa B. =." ?"==.?' +#"=@%#.?%/+' 0. 2'+%/>" 0" */ :%/%#"+'#% "0 */ $"#.$'

    F $A% &" #%=.=+%/>" 0%& $"#.$' =." *:*"&% "&&" #%=.=+%/>" 0%& #%=.=+'#% ./+%#/' "& :%/%#"+'#%; " ./+%#/";

    " ./+%#/" ". :%/%#"+'#. $A% /'/ F ?". /*&&" % /'/ 2*U %==%#% ?'0.@.$"+" " 2'=+%#.'#.H

    "& 2.b 2*U %==%#% '++.?.>>"+" ./ @"=% 0. 2#':%++">.'/% % $'=+#*>.'/% 0%&&' =+#*?%/+' P0%&:%/%#"+'#%R;

    " +#"=@%#.O.&% 0" */ :%/%#"+'#% .0%"&% /'/ F .&&.?.+"+" 2%#':/. B"&'#% 0. +%/=.'/% "/>. F "& 2.b *:*"&% " E*%&&" 0.==.2"+" ./+%#/"?%/+%;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    32/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; ]5

    *64&5$6 S 1 T6$698%59& "&A5%8%& 6 %98HD59E8%596 &(68A6

    75(#A5 3 1 J&H"5H&%&K& 8 "&U E59H6%%&

    ."C $'/ E*%=+" &%>.'/%C &" 0.=$*==.'/% 0. 0.=2'=+.B. " 2.b ?'#=%++.; Y%/:'/' @'#/.+% "&$*/%/'>.'/. 0. O"=% % /'?%/$&"+*#% B"#.%;

    n/ 0.=2'=.+.B' " 7 +%#?./"&. F 0%++' 1'!232; >"+. 0" #%&">.'/. $'=+.+*+.B%;

    .'/% #%&"+.B" "&&" kLK "0 */"

    =*2%#@.$.% $A% $'/+%/:" .& ='&' 0.=2'=.+.B' P$'?% ./

    @.:*#"R =. #.$"B" $A% &" ='??" 0%&&% $'##%/+. 0%B%

    %==%#% /*&&";

    4T"&+#" 2"#+% $"&$'&"/0' &% +%/=.'/. 0. $."=$*/

    ?'#=%++' #.=2%++' "0 */' 0. %==. "==*/+' $'?%

    #.@%#.?%/+' P?'#=%++' 0. ?"==" $'/ 2'+%/>."&% /*&&'R

    =. 2*U '==%#B"#% $'?%C /%& 0.=2'=.+.B' "0 7 +%#?./"&.C

    $. =."/' ./ #%"&+S 7>/ +%/=.'/. 0. /'0' ./0.2%/0%/+. 0"

    E*. F 2'==.O.&% #.$"B"#% +*++% &% +%/=.'/. +#" $'22.% 0.

    ?'#=%++.;

    /.%E*">.'/.$A% /%& &'#' ./=.%?% .0%/+.@.$"/' .& $'?2'#+"?%/+' %&%++#.$' 0%& 0.=2'=.+.B'; 1/$A% ./ E*%=+'

    $"='C &" /"+*#" ?"+%?"+.$" 0%&&" #%&">.'/% $'=+.+*+.B" $'/=%/+% */" $&"==.@.$">.'/% 0%.$'?2'/%/+.; %/%#"&.>>"/0' E*"/+' :.S 0%++' 2%# . O.2'&.C "OO."?'H

    C%2#%)*)-* $*4"4-",%H E*"/0' &" #%&">.'/% $'=+.+*+.B" F 0. +.2' "&:%O#.$' '+#"=$%/0%/+%;

    o 6")*.$*H &" #%&; $'=+; F 0. +.2' &./%"#% P%E*">.'/% 0. 2#.?' :#"0'Ro K%) 1")*.$*H &" #%&; $'=+; F 0. +.2' /'/ &./%"#%

    C%2#%)*)-* &").2"0%H E*"/0' &" #%&">.'/% $'=+.+*+.B" F 0. +.2' ./+%:#'W0.@@%#%/>."&%; H"4#%4"-"," -*2#%,.$".)-"H &" #%&; $'=+; F @*/>.'/% %=2&.$.+" "/$A% 0%& +%?2'; H"4#%4"-"," -*2#%"),.$".)-"H &" #%&; $'=+; /'/ 0.2%/0% %=2&.$.+"?%/+% 0"& +%?2';

    M%& =%:*.+' 0%& $'#=' $. =. '$$*2" ='&' 0. 0.=2'=.+.B. "0 /92'&. &./%"#. % +%?2' ./B"#."/+.;

    M%&&" ?"::.'# 2"#+% 0%. $"=.C . 0.=2'=.+.B. "0 /9+%#?./"&. ='/'#%"&.>>"+. %0 *+.&.>>"+. ./ ?'0' +"&% $A% &% $'##%/+. ". +%#?./"&. /'/

    =."/' +#" &'#' ./0.2%/0%/+.;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    33/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; ]]

    3T @"$.&% '==%#B"#% $A% ./ E*%=+. 0.=2'=+.B. "0 /92'#+%C .& /*?%#' 0. $'##%/+. &./%"#?%/+%

    ./0.2%/0%/+. F 2"#. "0 ./7'BB%#' "&&" ?%+S 0%& /*?%#' 0. ?'#=%++. 0%& 0.=2'=.+.B';

    K% +%/=.'/. ./+%#%=="/+.C ./B%$%C ='/' E*%&&% +#" . +%#?./"&. 0.

    $."=$*/" 2'#+" P./ @.:*#"C "0 %=%?2.'C "/$"))WR E*./0. ='/' "/$'#"

    */" B'&+" 7PV ?%+S 0%& /*?%#' 0. +%#?./"&.R;

    .'/. /%&&% E7 :#"/0%>>%

    $"#"++%#.=+.$A% P'==." /%&&% 7$'##%/+. 0. 2'#+" % /%&&% 7+%/=.'/. 0.2'#+"R;

    .'/. $'=+.+*+.B% =."/' ./+%#0.2%/0%/+. % ./+#%$$."+%; M%& $"=' 2"#+.$'&"#% 0%& $"&$'&' 0%&&"

    2'+%/>" =$"?O."+" 0" */ 0.=2'=+.B' "0 792'#+% $'/ .& #%=+' 0%& $.#$*.+' ./ $*. F ./=%#.+'C $. =.$'?2'#+" $"&$'&"/0' &" 2'+%/>" +'+"&% =$"?O."+" 0"& 0.=2'=+.B' $'?% ='??" 0%&&% 2'+%/>%

    =$"?O."+% 0" $."=$*/" 2'#+";

    3T .?2'#+"/+% '==%#B"#% $A% &% +%$/.$A% 2%# &" #.='&*>.'/% 0. #%+. B.=+% @./' "0 '#" 2'=='/'

    %==%#% "22&.$"+% "/$A% $'/ 0.=2'=.+.B. "0 7+%#?./"&.; .'/%C +%'#%?. 0. DAaB%/./ % M'#+'/C 2#./$.2.' 0. ='B#"22'=.>.'/% 0%:&.

    %@@%++. 2'=='/' %==%#% %=+%=. "/$A% " #%+. $'/+%/%/+. 0.=2'=.+.B. " 2.b ?'#=%++. " 2"++'

    $A% E*%=+. "OO."/' */" $"#"++%#.=+.$" &./%"#%;

    75(#A5 : 1 T6$698%59& "&A5%8%&

    N. +#"++" 0%. 2#.?. 0.=2'=.+.B. " 0*% 2'#+% +#"++"+. ./ E*%=+' $'#=' %0 A"//' $"#"++%#.=+.$A%

    $'?*/. P% 0*"&.R; Y%/:'/' =2%==' $A."?"+. 5*)*$.-%$" #"1%-.-"C ?" "/$A% 5*)*$.-%$"0%2.)&.-"'22*#% 5*)*$.-%$" &"#*)&*)-"; K" =.?O'&':." 2%# #"22#%=%/+"#&. F B"#." % /%&&%2#'==.?% @.:*#% B%/:'/' #.2'#+"+. . =.?O'&. *="+. /%& $'/+%=+' 0%& $'#=';

    #$% #&' #(' )))) ' #! #*% * +*

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    34/61

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    35/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; ]h

    E*./0. %=+%/0%#%C " +*++. . $*.#$*.+. $A% $'/+%/:"/' +"&. 0.=2'=.+.B.C +*++% &% +%$/.$A% % . ?%+'0.

    B.=+. @./' "0 '::. P?"+#.$% =2"#="C ?%+'0. #.0*>.'/%C DAaB%/./ % M'#+'/C ='B#"22'=.>.'/% 0%:&.%@@%++.R; 3T "&+#%=q .?2'#+"/+% ='++'&./%"#% $A% . :%/%#"+'#. 2.&'+"+.C " 0.=$"2.+' 0%& /'?%C /'/

    ='/' 0%. ;67652-45! 'BB%#' /'/ ='/' 0%. 0.=2'=.+.B. "++.B.; n/ $.#$*.+' %&%++#.$' $'/+%/%/+%

    ='&' 0%. :%/%#"+'#. 2.&'+"+. % 0%. #%=.=+'#.C =%/>" :%/%#"+'#. ./0.2%/0%/+.C F */ $.#$*.+' =2%/+'

    ./ $*. /'/ $.#$'&" $'##%/+%;

    .'/%

    $'=+.+*+.B" 0%& +#"=@'#?"+'#% .0%"&%C "==*?%/0' 2%# %/+#"?O%

    &% 2'#+% &" $'/B%/>.'/% 0%&&T*+.&.>>"+'#%C F &" =%:*%/+%H

    v1=kv

    2

    i1="

    1

    ki2

    #

    $%

    &%

    K" +%/=.'/% ?.=*#"+" /%&&" 2#.?" 2'#+" FC ./ ':/. .=+"/+%C 2#'2'#>.'/"&% "&&" +%/=.'/% 0%&&"

    =%$'/0" 2'#+"g "/$A% &% $'##%/+. ='/' $'##%&"+% ?" ./ ?'0' ./B%#='; K" $'=+"/+% P 0.

    $'##%&">.'/% F 0%++" 0%4-.)-* % $.##%$-% &" -$.4A%$2.("%)*%0 F $A."#"?%/+% */ /*?%#'

    "0.?%/=.'/"&% $'##%&"/0' :#"/0%>>% '?':%/%%;

    4"& 2*/+' 0. B.=+" %/%#:%+.$'C .& +#"=@'#?"+'#% .0%"&%C */" B'&+" ./=%#.+' ./ */ $.#$*.+'C =.

    $'?2'#+" $'?% 0. =%:*.+' .&&*=+#"+'; N"2%/0' ./@"++. $A% &" 2'+%/>" /%& 2#.?' +%#?./"&% P\/R F

    2"#. "& 2#'0'++' 0%&&" +%/=.'/% P8R 2%# &" $'##%/+% P=%?2#% 8RC "B#%?'H

    P1=v

    1i1= kv

    2( ) "

    1

    ki2

    #

    $%

    &

    '(="v

    2i2="P

    2

    " %/+#"/+% /%&&" 2#.?" 2'#+" FC ./ E*"&=."=. $'/0.>.'/% 0.

    @*/>.'/"?%/+'C *:*"&% "&&" 2'+%/>" *=$%/+% 0"&&" =%$'/0" 2'#+"; ";

    1/$A% . +#"=@'#?"+'#. .0%"&.C $'=q $'?% B.=+' 2%# . :%/%#"+'#. 2.&'+"+.C ='/' 0%. ?'0%&&. .0%"&.

    $A% /'/ A"//' */" $'##.=2'/0%/>" $'/ /%==*/ 0.=2'=.+.B' @.=.$' #%"&%; D*++"B." $'=+.+*.=$% */

    *+.&% =+#*?%/+' /%&&" 2#':%++">.'/% 0. #%+. %&%++#.$A% % $.#$*.+. 2%#$AaC =% '22'#+*/"?%/+%$'?O./"+' $'/ "&+#. 0.=2'=.+.B.C $'/=%/+% 0. $#%"#% ?'0%&&. "$$*#"+. 0. +#"=@'#?"+'#. $A% ='/'

    $'?2'/%/+. %&%++#.$. ?'&+' 0.@@*=.;

    L'/=.0%#"+" &" /"+*#" #%=.=+.B' &./%"#% 0%&&" #%&">.'/%

    $'=+.+*+.B" 0%& +#"=@'#?"+'#% .0%"&%C F 2'==.O.&% "22&.$"#%

    +*++. . ?%+'0. :.S =+*0."+.; 3$$' */ =%?2&.$% %=%?2.' /%&E*"&%C 0"+' .& $.#$*.+' #%=.=+.B' ./ @.:*#"C =. 0%=.0%#"

    $"&$'&"#% &T%E*.B"&%/+% DAaB%/./ ". ?'#=%++. 1 % Z;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    36/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; ]d

    -%# $"&$'&"#% &T%E*.B"&%/+%C 0'OO."?' +#'B"#% &" #%&">.'/% $A% $TF +#" &"

    $'##%/+% %/+#"/+% "& ?'#=%++' 1 % &" +%/=.'/% ?.=*#"+" +#" 1 % Z P'BB%#' &"#%&">.'/% +#" !/ % "/R; D%/%/0' 2#%=%/+% &" #%&">.'/% $'=+.+*+.B" 0%&

    +#"=@'#?"+'#% .0%"&%C 2'==."?' 2#'$%0%#% /%& =%:*%/+% ?'0'C 2"#+%/0' 0"&&"

    $'/=+"+">.'/% $A% "E$ >R!EH

    v2 = "Ri2

    dalla r.c. abbiamo che :

    v1 = kv2 = k "Ri2( ) = ...

    ancora dalla r.c. determiniamo i1 :

    ...= k -R -ki1( )[ ]= k2Ri1infine, applicando la legge di Ohm :

    RAB=

    v1

    i1

    = k2R

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    37/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; ]6

    *64&5$6 3S 1 (#6V"59%6 96H&H%&K&

    75(#A5 3 1 ,6A84&5$6 @5H%&%#%&K8 (& (#6V"59%6 96H&H%&K& L3M

    4'2' */" O#%B% ./+#'0*>.'/% $A% #.$A."?" E*"/+' B.=+' /%&&" &%>.'/% 6 P0.=2'=.+.B. " 2.b+%#?./"&. %C ./ 2"#+.$'&"#%C " 0*% 2'#+% 0%++. "/$A% %4++! ]!+41!RC B%/:'/' E*. ./+#'0'++. "&$*/.

    /*'B. 0.=2'=.+.B. " 0*% 2'#+% /'+. $'?% &'*.'/% $'=+.+*+.B" F 0%& +.2' "&:%O#.$' '+#"=$%/0%/+% P^$:,_.Rg =. 0%@./.=$% &%##"% 7"#%1% &").2"0%

    */ 0'22.' O.2'&' &" $*. #%&">.'/% $'=+.+*+.B" F 0%& +.2'./+%:#' 0.@@%#%/>."&%; .'/% .?2&.$.+"R; 4"&&" @'#?"

    .?2&.$.+" F 2'==.O.&% =$#.B%#% &" A%$2. 2.-$"0".1*0%&&" #%&">.'/% $'=+.+*+.B"H

    posto : i =i1

    i2

    "

    #

    $%

    &

    ', v =v1

    v2

    "

    #

    $%

    &

    ', A =(

    11 (

    12

    (21 (22

    "

    #

    $%

    &

    ', B =)11

    )12

    )21 )22

    "

    #

    $%

    &

    'e *=*1

    *2

    "

    #

    $%

    &

    'avremo: Av+ Bi+*= 0

    PMJD1H &% ?"+#.$. 0%. $'%@@.$.%/+. ='/' @"$.&. 0" #.$'#0"#% 2%#$Aa ='/' /%&&' =+%==' '#0./% 0%&&" #%&">.'/% $'=+.+*+.B"R

    K" #%&">.'/% $'=+.+*+.B" '#" .&&*=+#"+" =2%==' /'/ F &" 2.b 2#"+.$"; M%&&% "22&.$">.'/. F

    @#%E*%/+% *+.&.>>"#% "&+#% #"22#%=%/+">.'/. $A."?"+% *4#1"0"-*; K" &%>.'/% 2#'=%:*%.&&*=+#"/0' &% 2#./$.2"&. #"22#%=%/+">.'/. %=2&.$.+%; 1/$'#" */" B'&+" %=.=+% */ 0*"&.=?' +#" .

    0.=2'=.+.B. .&&*=+#"+. % 2%# +"&% #":.'/% #.2'#+' &" =2.%:">.'/% =*00.B.0%/0'&" ./ 0*% $'&'//%;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    38/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; ]o

    !QRR!SLSKGQTMUKS LS!MS

    B%3 .)0@*3 $.##; 0%)-$%11.-. ") 0%$$*)-*E

    !QRR!SLSKGQTMUKS RQ!Q66S6U

    B%3 .)0@*3 $.##; 0%)-$%11.-. ") -*)4"%)*E

    K" #%&">.'/% $'=+.+*+.B" 0%B% %==%#% @'#?*&"+" /%&?'0' =%:*%/+%H

    v1 = R11i1 + R12i2 + c1

    v2= R

    21i1+ R

    22i2+ c

    2

    "#$

    o, in forma matriciale:

    v = Ri + c

    con:

    v =v

    1

    v2

    %

    &'

    (

    )*, i =

    i1

    i2

    %

    &'

    (

    )*, c =

    c1

    c2

    %

    &'

    (

    )*, R =

    R11

    R12

    R21

    R22

    %

    &'

    (

    )*

    K" #%&">.'/% $'=+.+*+.B" 0%B% %==%#% @'#?*&"+" /%&?'0' =%:*%/+%H

    i1 =G11v1 +G12v2 + a1

    i2=G

    21v

    1+G

    22v

    2+ a

    2

    "#$

    o, in forma matriciale:

    i =Gv+ a

    con:

    v =v

    1

    v2

    %

    &'

    (

    )*, i =

    i1

    i2

    %

    &'

    (

    )*, a =

    a1

    a2

    %

    &'

    (

    )*, G =

    G11

    G12

    G21

    G22

    %

    &'

    (

    )*

    K" ?"+#.$% RF 0%++" 2.-$"0* $*4"4-*)(.0%& 0*% 2'#+%

    % . =*'. $'%@@.$.%/+. ='/' %=2#%==. ./ JA?; 1/"&.>>"/0'

    /%& 0%++":&.' &% 0*% $'=+"/+. 3C F .??%0."+' B%#.@.$"#%$A%H

    3/$ "/ =%H !/$ !E$ B

    3E$ "E =%H !/$ !E$ B

    \*%=+' =.:/.@.$" $A% . $'%@@.$./%+. 3/% 3E='/' 0.B%#=. 0"

    >%#'C =% % ='&' =% .& 0*% 2'#+% $'/+.%/% 0%. :%/%#"+'#.

    ./0.2%/0%/+.;

    K" ?"+#.$% ` F 0%++" 2.-$"0* 0%)&'--.)(. 0%& 0*%

    2'#+% % . =*'. $'%@@.$.%/+. ='/' %=2#%==. ./ N.%?%/= '

    JA?98; 1/"&.>>"/0' /%& 0%++":&.' &% 0*% $'=+"/+. 2C F.??%0."+' B%#.@.$"#% $A%H

    2/$ !/ =%H "/$ "E$ B

    2E$ !E =%H "/$ "E$ B

    \*%=+' =.:/.@.$" $A% . $'%@@.$./%+. 2/ % 2E ='/' 0.B%#=.

    0" >%#'C =% % ='&' =% .& 0*% 2'#+% $'/+.%/% 0%.

    :%/%#"+'#. ./0.2%/0%/+.;

    L'?% ="#S $A."#' /%&&T%=%?2.' #.2'#+"+' 2.b "B"/+.C =%

    0. */ 0.=2'=.+.B' " 0*% 2'#+% F /'+" &" =+#*++*#"

    P'BB%#' &" #%&">.'/% $'=+.+*+.B" 0%. $'?2'/%/+. % &"

    +'2'&':." ./ $*. . $'?2'/%/+. ='/' '#:"/.>>"+.R2'==."?' $"&$'&"#% . B"&'#. 0%. 2"#"?%+#. 0%&&"

    #"22#%=%/+">.'/% =%#.% P"??%==' $A% %=.=+"R

    2#'$%0%/0' /%& ?'0' 0. =%:*.+' =2.%:"+';

    1/$A% ./ E*%=+' $"=' 2'==."?' $"&$'&"#% . B"&'#. 0%.

    2"#"?%+#. 0%&&" #"22#%=%/+">.'/% 2"#"&&%&' P"??%=='

    $A% %=.=+"R 2#'$%0%/0' /%& ?'0' 0. =%:*.+' =2.%:"+';

    N. $"&$'&"/' . $'%@@.$.%/+. $'=+"/+. 3/ % 3E &"=$."/0'

    "2%#+% %/+#"?O% &% 2'#+% P.& $A% %E*.B"&% "&&"

    #%&">.'/%H !/$ !E$ BR % 0%+%#?./"/0' &% +%/=.'/. "/% "E

    ./ E*%=+" =.+*">.'/%; .'/.RC .& $'%@@.$.%/+% R// 2*U %==%#%

    $"&$'&"+' @"$%/0' .& #"22'#+' +#" "/% !/E*"/0' !EF >%#'

    P"/"&':"&?%/+% RE/ 2*U %==%#% $"&$'&"+' $'?%

    #"22'#+' +#" "E% !/=%?2#% $'/ !E$ BR 'BB%#' &"=$."/0'"2%#+" &" =%$'/0" 2'#+" P"22*/+' !E$ BR% $"&$'&"/0' "/

    % "E./ @*/>.'/% 0. !/;

    4'2' "B%# $"&$'&"+' . $'%@@.$.%/+. 2/ % 2EC =. 2'=='/'=2%:/%#% +*++. . :%/%#"+'#. ./0.2%/0%/+. /%&&" #%+% P.&

    $A% %E*.B"&% " 2'##% 2/ $ 2E $ BR % $"&$'&"#% .

    $'%@@.$.%/+. 0%&&" ?"+#.$% `; %#' P"/"&':"&?%/+% E/ 2*U %==%#% $"&$'&"+' $'?%

    #"22'#+' +#" !E % "/ =%?2#% $'/ "E $ BR 'BB%#'?%++%/0' ./ $'#+' $.#$*.+' &" =%$'/0" 2'#+" P"22*/+'

    "E$ BR% $"&$'&"/0' !/% !E./ @*/>.'/% 0. "/;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    39/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; ]p

    Y%0."?' '#" "&$*/. %=%?2. =.:/.@.$"+.B. #.@%#.+. " E*"/+' "22%/" B.=+' 2"#+%/0' 0"& 2#.?' $"='

    P$.##$*4*)-.("%)* ") 4*$"*R;

    45.6!$2 78 90!!9.5.1:0;$21. 5.9$. < =$9=>$:2 0 ? =21 @.1.90:29. $1A$!B A$ :.15$21.

    N*22'/."?' 0T"B%# #%"&.>>"+' */ $.#$*.+' $'?% E*%&&' ./0.$"+' ./ @.:*#" % 0. "B%#&' $'&&%:"+' "

    0*% #%+. %=+%#/% +#"?.+% . ?'#=%++. 1C ZC L % 4; K" #%&">.'/% $'=+.+*+.B" =. 2*U $"&$'&"#%2#'$%0%/0' /%& =%:*%/+% ?'0'; -'=+% !/ % !E $ B P?'#=%++. 1CZ % LC4 "2%#+.R 0%+%#?./' &%

    +%/=.'/. "/$ 3/6 "E$ 3E; /B@PA' h7Y =**/" #%=.=+%/>" +'+"&% ./ =%#.% 0. h7 u $A% ?. 0"//' */" $'##%/+% 0. 8z 9 0" E*. 81 v 87 u V 87Y

    , 2%# .& =%:/' O"=+" $'/=.0%#"#% $A% &" $'##%/+% =*& #%=.=+'#% 0" 87u B" 0" Z B%#=' 1R % "E$ 3E

    $ /B@;

    M'+. . B"&'#. 0%&&% $'=+"/+. 3/ % 3EC 2'==' =2%:/%#% .& :%/%#"+'#% ./0.2%/0%/+% P%==%/0' 0.

    +%/=.'/% B" ='=+.+*.+' $'/ */ $'#+' $.#$*.+'R % $"&$'&"#% . B"&'#. 0%. $'%@@.$.%/+. 0%&&" ?"+#.$% R;).$'#0"/0' $A%H

    R11

    =

    v1

    i1

    R21

    =

    v2

    i1

    "

    #$$

    %$$

    se i2= 0 e

    R12

    =

    v1

    i2

    R22

    =

    v2

    i2

    "

    #$$

    %$$

    se i1= 0

    2'==' 0%+%#?./"#% R// $'?% #"22'#+' +#" "/ % !/E*"/0' !E $ B 'BB%#' E*"/0' &" 2'#+" 5 F"2%#+"; -'=+' !E$ B"B#%?'H

    v1 =10 " i1 "40

    50e, analogalmente, v2 =10 " i1 "

    10

    50da cui # R11 = 8 e R21 = 2

    M'+" 2%# $"&$'&'H "/F &" +%/=.'/% ". $"2. 0%& #%=.=+'#% 0" 87u; N'/' ./ 2#%=%/>" 0. */ 2"#+.+'#%

    0. $'##%/+% P. 0*% #%=.=+'#. 0" ]7u % 87u ='/' ./ =%#.% % @"//' c7uR; K" $'##%/+% $A%

    "++#"B%#=" .& #%=.=+'#% 0" 87u F 0*/E*% ,!/XLB.'?B$A%C ?'&+.2&.$"+' 2%# .& #%=.=+'#% 0" 87uC ?.0" 2#'2#.' &" +%/=.'/% "/$ a!/; 1 E*%=+' 2*/+' R//$ "/'!/ $ aY; K' =+%==' B"&% 2%# .& $"&$'&' 0.RE/;

    .'/% $'=+.+*+.B"C /%&&" =*"

    @'#?*&">.'/% =%#.%C 0%& 0'22.' O.2'&' $"#"++%#.>>"+'; 1B#%?' 0*/E*%H

    v =8 2

    2 8

    "

    #$

    %

    &'i+

    (10

    10

    "

    #$

    %

    &'

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    40/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; c7

    45.6!$2 C8 90!!9.5.1:0;$21. 5.9$. < =$9=>$:2 0 )

    $'%@@.$.%/+. 3/ % 3E B"&:'/' %/+#"?O. >%#' % =. 2*U 2"=="#% 0.#%++"?%/+% "& $"&$'&' 0%.$'%@@.$.%/+. 0%&&" ?"+#.$% R; -'=+' !E $ B P2'#+" 5 "2%#+"RC =. 0%+%#?./"/' R// % RE/ ./ ?'0'

    %=+#%?"?%/+% =%?2&.$% P"&&' =+%==' ?'0'C $'/ !/$ BC =. 0%+%#?./"/' R/E% REERH

    R11=

    v1

    i1 i2=0

    = Ra+ R

    b, R

    21=

    v2

    i1 i2=0

    = Rb

    R12=

    v1

    i2 i1=0

    = Rb, R

    22=

    v2

    i2 i1=0

    = Rc+R

    b

    M'+" 2%# $"&$'&'H .& $"&$'&' F 0"BB%#' O"/"&%; M%& $"=' 0. !E$ BP&T"&+#' $"=' F 0%& +*++' "/"&':'RC&T*/.$" $'##%/+% " $.#$'&"#% F !/; \*./0. "/F 2"#. "&&" $'##%/+% !/?'&+.2&.$"+" 2%# PR2D R]R $A%

    ='/' ./=%#.% P% .& #"22'#+' +#" "/ % !/ 0"#S 2#'2#.' &" ='??" R2 D R]Rg ?%/+#% "E P$A% F &"+%/=.'/% ". $"2. 0. R]R F 2"#. =%?2#% "&&" $'##%/+% !/E*%=+" B'&+" ?'&+.2&.$"+" 2%# R];

    K" ?"+#.$% 0%&&% #%=.=+%/$% /%& $"=' 0. #"22#%=%/+">.'/% ./ =%#.% 0. */ $.#$*.+' #%=.=+.B' " D F

    0*/E*% &" =%:*%/+% P@'#?" 0. *=' @#%E*%/+%C E*./0. 0" #.$'#0"#%RH

    R =R

    a+ R

    b R

    b

    Rb

    Rc+ R

    b

    "

    #$

    %

    &'

    PK" ?"+#.$% F @"$.&% 0" #.$'#0"#% =% =. @" #.@%#.?%/+' "&&' =$A%?" %&%++#.$' 0%& #.$#$*.+'; $:2 0 ?

    %#' %0 F 2'==.O.&% 2"=="#% "&&" 0%+%#?./">.'/% 0%&&" ?"+#.$% 0%&&% $'/0*++"/>%;

    -#%=+"/0' ?'&+" "++%/>.'/% "& @"++' $A% =+."?' +#"++"/0' $'/0*++"/>% P% /'/ 0.#%++"?%/+% .#%=.=+'#.RC F @"$.&% 0%+%#?./"#% . =./:'&. $'%@@.$.%/+. $'?% 0. =%:*.+' #"22#%=%/+"+'H

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    41/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; c8

    G11=

    i1

    v1 v2=0

    =Ga+G

    c, G

    21=

    i2

    v1 v2=0

    = "Gc

    G12=

    i1

    v2 v1=0

    = "Gc, G

    22=

    i2

    v2 v1=0

    =Gb+G

    c

    K" ?"+#.$% 0%&&% #%=.=+%/$% /%& $"=' 0. #"22#%=%/+">.'/% ./ 2"#"&&%&' 0. */ $.#$*.+' #%=.=+.B' "{ F 0*/E*% &" =%:*%/+% P@'#?" 0. *=' @#%E*%/+%C E*./0. 0" #.$'#0"#%RH

    G =G

    a+G

    c "G

    c

    "Gc

    Gb+G

    c

    #

    $%

    &

    '(

    P1/$A% ./ E*%=+' $"=' &" ?"+#.$% F @"$.&% 0" #.$'#0"#% =% =. @" #.@%#.?%/+' "&&' =$A%?" %&%++#.$'

    0%& #.$#$*.+'; K" $'/0*++"/>" ./ $'?*/% F `3, 2#%=" $'/ =%:/' /%:"+.B' @*'#. 0"&&" 0.":'/"&%2#./$.2"&% , % $'?2"#% ./ +*++% &% 2'=.>.'/% % 2'.C /%&&" 0.":'/"&% 2#./$.2"&%C "::.*/:' `2=*&

    2#.?' +%#?./% % `]=*& =%$'/0'R;

    75(#A5 : 1 ,6A84&5$6 @5H%&%#%&K8 (& (#6V"59%6 96H&H%&K& L:M

    .'/% =. +#"++%#"//' 0.=2'=.+.B. " 0*% 2'#+% #%"&.>>"+. $'//%++%/0' "#O.+#"#."?%/+%

    $'?2'/%/+. 2"==.B. 'BB%#' 0.=2'=.+.B. ./ $*. . $'%@@.$.%/+. "/% "E/%&&" @'#?*&">.'/% .?2&.$.+"

    0%&&" #%&">.'/% $'=+.+*+.B" ='/' %/+#"?O. /*&&.;

    !QRR!SLSKGQTMUKS MV!MHQ = !QRR!SLSKGQTMUKS MV!MHQ F

    4.#%?' $A% */ 0.=2'=.+.B' " 0*%92'#+% #%=.=+.B'

    &./%"#% "??%++% */" $.##$*4*)-.("%)* "7$"&. &*1#$"2% -"#%P' =%?2&.$%?%/+% "7$"&. =R =% F 2'==.O.&%

    =$#.B%#% &" #%&">.'/% $'=+.+*+.B" /%&&" =%:*%/+% @'#?"H

    v1= h

    11i1+ h

    12v

    2

    i2= h

    21i1+ h

    22v

    2

    "#$

    in forma matriciale :

    v1

    i2

    %

    &'

    (

    )*= H

    i1

    v2

    %

    &'

    (

    )*

    con :

    H =h

    11 h

    12

    h21

    h22

    %

    &'

    (

    )*

    K" ?"+#.$% x F 0%++" 2.-$"0* "7$"&. = P=. ./0.$"

    :%/%#"&?%/+% $'/ W=R % . =*'. $'%@@.$.%/+.C 0" */ 2*/+'

    0. B.=+" 0.?%/=.'/"&%C /'/ ='/' '?':%/%. P./@"++.

    $'##%&"/'C 0. B'&+" ./ B'&+"C :#"/0%>>% '?':%/%% %

    0.='?':%/%%R;

    4.#%?' $A% */ 0.=2'=.+.B' " 0*%92'#+% #%=.=+.B'

    &./%"#% "??%++% */" $.##$*4*)-.("%)* "7$"&. &*14*0%)&% -"#% P' =%?2&.$%?%/+% "7$"&. FR =% F

    2'==.O.&% =$#.B%#% &" #%&">.'/% $'=+.+*+.B" /%&&"

    =%:*%/+% @'#?"H

    i1= h

    11

    'v

    1+ h

    12

    'i2

    v2= h

    21

    'v

    1+ h

    22

    'i2

    "#$

    in forma matriciale :

    i1

    v2

    %

    &'

    (

    )*= H

    ' v

    1

    i2

    %

    &'

    (

    )*

    con :

    H'=

    h11

    'h

    12

    '

    h21

    'h

    22

    '

    %

    &'

    (

    )*

    K" ?"+#.$% xw F 0%++" 2.-$"0* "7$"&. F % B"&:'/' &%

    ?%0%=.?% $'/=.0%#">.'/. :.S B.=+% 2%# &" ?"+#.$%

    .O#.0" 8;

    .'/% .O#.0" 5 &% #%&">.'/.

    $'=+.+*+.B% ='/' /%&&" =%:*%/+% @'#?"H

    i1=i

    1(v

    1,i

    2)

    v2 =

    v2(v

    1,i

    2)

    "#$

    'BB%#' &% 0*% :#"/0%>>% !/%"E='/' =$#.++% ./ @*/>.'/%

    0%&&% 0*% :#"/0%>>% "/% !E;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    42/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; c5

    3=+%/0%/0' E*"/+' :.S B.=+' /%& ?'0*&' 2#%$%0%/+%C

    0"+' */ 0.=2'=.+.B' " 0*%92'#+% #%=.=+.B' &./%"#%C F

    2'==.O.&% 0%+%#?./"#% . $'%@@.$.%/+. 0%&&" ?"+#.$%

    .O#.0" 8 P"??%==' $A% E*%=+" #"22#%=%/+">.'/%

    %=.=+"R '==%#B"/0' E*"/+' =%:*%H

    h11 =v1

    i1 v

    2=0

    h12 =v1

    v2 i

    1=0

    h21=

    i2

    i1 v

    2=0

    h22=

    i2

    v2 i

    1=0

    M% $'/=%:*% $A% 2%# $"&$'&"#% 8// % 8E/ 0'B#%?'

    $A.*0%#% ./ $'#+' $.#$*.+' &" =%$'/0" 2'#+" P"E $ BR %

    $"&$'&"#% $'?% B"#."/' "/ % !E ./ @*/>.'/% 0. !/g 2%#

    $"&$'&"#% 8/E % 8EE 0'B#%?' &"=$."#% "2%#+" &" 2#.?"

    2'#+" P!/ $ BR % $"&$'&"#% $'?% B"#."/' "/ % !E ./

    @*/>.'/% 0. "E;

    .'/% $'=+.+*+.B"C 0*% B"#."O.&.C */" 2%# $."=$*/" 2'#+"C

    ='/' #"22#%=%/+"+% ./ @*/>.'/% 0%&&% "&+#% 0*%;

    Y%/:'/' ./@./% .&&*=+#"+% &% 0*% #"22#%=%/+">.'/. 0. +#"=?.==.'/% $A% ='/' ?'&+' *+.&.

    /%&&T%&%++#'/.$" 0%&&% +%&%$'?*/.$">.'/.;

    !QRR!SLSKGQTMUKS G!QLNMLLMUKS =X GMRU !QRR!SLSKGQTMUKS G!QLNMLLMUKS FX GMRU

    4.#%?' $A% */ 0.=2'=.+.B' " 0*%92'#+% #%=.=+.B'

    &./%"#% "??%++% */" $.##$*4*)-.("%)* &"

    -$.42"44"%)* &*1 #$"2% -"#%=% F 2'==.O.&% =$#.B%#% &"

    #%&">.'/% $'=+.+*+.B" /%&&" =%:*%/+% @'#?"H

    v1= t

    11v

    2" t

    12i2

    i1=t

    21v

    2" t

    22i2

    #$%

    in forma matriciale :

    v1

    i1

    &

    '(

    )

    *+=T

    v1

    i2

    &

    '(

    )

    *+

    con :

    T =t11

    t12

    t21

    t22

    &

    '(

    )

    *+

    .'/. 2#"+.$A%C ='B%/+%C &" $'##%/+%

    0%&&" =%$'/0" 2'#+" B.%/% 2#%=" 2'=.+.B" *=$%/+% 0"&

    ?'#=%++'; N. '==%#B"C ./'&+#%C $A% &" #"22#%=%/+">.'/%

    0. +#"=?.==.'/% /'/ F */" #"22#%=%/+">.'/% $"/'/.$"

    2%#$AaC ./ E*%=+' +.2' 0. #"22#%=%/+">.'/%C &% 0*%

    :#"/0%>>% 0. */" ='&" 2'#+" ='/' %=2#%==% ./ @*/>.'/%0%&&% 0*% :#"/0%>>% 0%&&T"&+#" 2'#+";

    4.#%?' $A% */ 0.=2'=.+.B' " 0*%92'#+% #%=.=+.B'

    &./%"#% "??%++% */" $.##$*4*)-.("%)* &"

    -$.42"44"%)* &*1 4*0%)&% -"#%=% F 2'==.O.&% =$#.B%#%

    &" #%&">.'/% $'=+.+*+.B" /%&&" =%:*%/+% @'#?"H

    v2= t

    11

    'v

    1+ t

    12

    'i1

    "i2= t

    21

    'v

    1+ t

    22

    'i1

    #$%

    in forma matriciale :

    v2

    "i2

    &

    '(

    )

    *+= T

    ' v

    1

    i1

    &

    '(

    )

    *+

    con :

    T'=

    t11

    't12

    '

    t21

    't22

    '

    &

    '(

    )

    *+

    -#%/0."?' '#" */ 0.=2'=.+.B' 0*%92'#+% #%=.=+.B' &./%"#% $A% /'/ $'/+%/:" "& =*' ./+%#/'

    "&$*/ :%/%#"+'#% ./0.2%/0%/+%H .& B%++'#% "0. $'%@@.$.%/+. "/% "E/%&&" @'#?*&">.'/% .?2&.$.+"

    0%&&" #%&">.'/% $'=+.+*+.B" ="#S .0%/+.$"?%/+% /*&&'; -%# E*%=+' +.2' 0. 0'22.' O.2'&'C 2%#

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    43/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; c]

    0%@./.>.'/%C F =%?2#% 2'==.O.&% =$#.B%#% &" #%&">.'/% $'=+.+*+.B" /%&&" @'#?" .?2&.$.+"H

    *# E +$ " F; 3T .?2'#+"/+% 2%#U '==%#B"#% $A% 2%# */ 0'22.' O.2'&' #%=.=+.B' &./%"#% :%/%#.$'C/'/ F 0%++' $A% %=.=+"/+' +*++% &% #"22#%=%/+">.'/. $A% ='/' =+"+% "22%/" 0%@./.+% $'?%

    ./0.$"+' /%. 2#'==.?. %=%?2.;

    ."?' $'/ .& $'/=.0%#"#% .& +#"=@'#?"+'#% .0%"&%;).$'#0."?' $A% /%&&" @'#?" +#"=?.==.'/%C &" #%&">.'/%

    $'=+.+*+.B" 0%& +#"=@'#?"+'#% FH

    v1=kv

    2

    i1="

    1

    ki2

    #

    $%

    &%

    3="?./"/0' 0*/E*% &" #%&">.'/% $'=+.+*.B" "22"#% %B.0%/+% $A% E*%=+' 0'22.' O.2'&'

    "??%++%C '&+#% &" @'#?" +#"=?.==.B" 0%& 2#.?' '#0./%C "/$A% &" @'#?" /%& =%$'/0' '#0./%H

    T=k 0

    01

    k

    "

    #

    $$

    %

    &

    ''e T

    '=

    1

    k0

    0 k

    "

    #

    $$

    %

    &

    ''

    122"#% 2%#U %B.0%/+% $A% /'/ F 2'==.O.&% +#'B"#% */" ?"+#.$% R'22*#% */" ?"+#.$% `; >"+' 0"&

    =%?2&.$% O.2'&' .&&*=+#"+' ./ @.:*#"; 3T 0%& +*++' %B.0%/+% $A%

    "/ $ R,!/ D !E. $ "E; N$#.B."?' '#" &" #%&">.'/% $'=+.+*+.B" /%&&"=*" @'#?" .?2&.$.+"H

    v1= v

    2

    v1 = R(i1 + i2 )

    "#$

    % Av+ Bi =0%1 &1

    1 0

    '

    ()

    *

    +,v

    1

    v2

    '

    ()

    *

    +,+

    0 0

    &R &R

    '

    ()

    *

    +,i

    1

    i2

    '

    ()

    *

    +,=

    0

    0

    '

    ()

    *

    +,

    J==%#B."?' $A% .& 0%+%#?./"/+% 0%&&" ?"+#.$% ) F 0.B%#=' 0" >%#'; -'==."?' E*./0.

    ?'&+.2&.$"#% %/+#"?O. . ?%?O#. 0%&&" #%&">.'/% $'=+.+*+.B" /%&&" @'#?" .?2&.$+"C 2%# &T./B%#='

    0%&&" ?"+#$.% ) % #.$"B"#% .??%0."+"?%/+% &" #"22#%=%/+">.'/% =%#.% 0%& /'=+#' 0'22.'O.2'&'; K" #"22#%=%/+">.'/% =%#.% ="#%OO% 0*/E*%H

    v1= Ri

    1+ Ri

    2

    v2 = Ri1 + Ri2

    "#

    $% R =

    R R

    R R

    &

    '(

    )

    *+

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    44/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; cc

    M%&&T*&+.?' %=%?2.' 2#%/0."?' ./ $'/=.0%#">.'/% .& :%/%#"+'#%

    0. +%/=.'/% 2.&'+"+' ./ $'##%/+% &" $*. #%&">.'/% $'=+.+*+.B" F &"

    =%:*%/+%H

    v1 =0

    v2="i

    1

    #$%

    1/$'#" */" B'&+" =$#.B."?' &" #%&">.'/% $'=+.+*+.B" ./ @'#?" .?2&.$.+"H

    Av+ Bi = 0"1 0

    0 1

    #

    $%

    &

    '(v

    1

    v2

    #

    $%

    &

    '(+

    0 0

    )* 0

    #

    $%

    &

    '(i

    1

    i2

    #

    $%

    &

    '(=

    0

    0

    #

    $%

    &

    '(

    -'.$Aa .& 0%+%#?./"/+% 0%&&" ?"+#.$% )F *:*"&% " 8 P0.B%#=' 0" >%#'RC "/$A% ./ E*%=+' $"='

    2'==."?' =*O.+' $"&$'&"#% &" #"22#%=%/+">.'/% =%#.% 0%& 0'22.' O.2'&'; K" ?"+#.$% R $'=q

    '++%/*+" ="#SH

    R =0 0

    " 0

    #

    $%

    &

    '(

    L'?% B.=+' /%& 2#%$%0%/+% $"='C "/$A% E*%=+" B'&+" .& @"++' $A% .& 0%+%#?./"/+% 0%&&" ?"+#.$% *

    =." /*&&' =.:/.@.$" $A% 2%# */ :%/%#"+'#% 0. +%/=.'/% 2.&'+"+' ./ $'##%/+% /'/ %=.=+% */"#"22#%=%/+">.'/% 2"#"&&%&'; )":.'/"?%/+. "/"&':A. ='/' %=+%/0.O.&. "0 "&+#. :%/%#"+'#.

    2.&'+"+.;

    -.b ./ :%/%#"&% F 2'==.O.&% '==%#B"#% $A% :%/%#"+'#. 2.&'+"+. "??%++'/' % ='&' */"

    #"22#%=%/+">.'/% $"#0./"&% 2.b */" #"22#%=%/+">.'/% 0%& +.2' +#"=?.==.'/%;

    M'+"H ./ E*%=+. +#% %=%?2. F ./+%#%=="/+% '==%#B"#% $A%C *="/0' &% ?"+#.$. % &% &'#' ./B%#=%C =.

    2'==" 2"=="#% 0" */" @'#?" $"#0./"&% "&&" @'#?" 0*"&%;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    45/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; ch

    75(#A5 F 1 295"9&6%W (6& (#6V"59%6

    t./' "0 '#" $. =."?' '$$*2"+. 0. 0%+%#?./"#% . 2"#"?%+#. 0. */" #%&">.'/% $'=+.+*+.B" 0. */

    0'22.' O.2'&' 0. $*. =." /'+" &" =+#*++*#"; >"+' 0"

    */" #"22#%=%/+">.'/% =%#.% 0%& =%:*%/+% +.2'H

    v = Ri" R =R

    11 R

    12

    R21

    R22

    #

    $%

    &

    '(

    \*%=+' " 2"++' $A%H

    -'#+" 8H &" #%=.=+%/>" 0%B% %==%#% R//; -'#+" 8H .& :%/%#"+'#% 2.&'+"+' ./ $'##%/+%

    0%B% .?2#.?%#% */" +%/=.'/% 2"#. " R/E#!E;

    -'#+" 5H &" #%=.=+%/>" 0%B% %==%#% REE; -'#+" 5H .& :%/%#"+'#% 2.&'+"+' ./ $'##%/+%

    0%B% .?2#.?%#% */" +%/=.'/% 2"#. " RE/#!/;

    122&.$"/0' &% +%$/.$A% 0. $"&$'&' 0%. $'%@@.$.%/+. 0. */"#"22#%=%/+">.'/% B.=+% @./' "0 '#"C F 2'==.O.&%

    B%#.@.$"#% $A% .& $.#$*.+' ./ @.:*#" F $"#"++%#.>>"+' 0"

    */" #"22#%=%/+">.'/% 2"#"&&%&' 0%& =%:*%/+% +.2'H

    i = Gv"G =G

    11 G

    12

    G21

    G22

    #

    $%

    &

    '(

    \*%=+' " 2"++' $A%H

    -'#+" 8H &" #%=.=+%/>" 0%B% "B%#% $'/0*++"/>"2"#. " `//;

    -'#+" 8H .& :%/%#"+'#% 2.&'+"+' ./ +%/=.'/%0%B% .?2#.?%#% */" $'##%/+% 2"#. " `/E#"E;

    -'#+" 5H &" #%=.=+%/>" 0%B% "B%#% $'/0*++"/>"2"#. " EE;

    -'#+" 5H .& :%/%#"+'#% 2.&'+"+' ./ +%/=.'/%0%B% .?2#.?%#% */" $'##%/+% 2"#. " E/#"/;

    MJD1H E*"/+' E*. #.2'#+"+' 2*U %==%#% ./+%#2#%+"+' "/$A% /%& =%:*%/+% ?'0'H /'+" &" ?"+#.$% 0%. $'%@@.$.%/+. %

    B%#.@.$"+% &% $'/0.>.'/.C 2'==' 349-5

    !QRR!SLSKGQTMUKS MV!MHQ =

    v1=h

    11i1+ h

    12v2

    i2= h

    21i1+ h

    22v2

    "#$

    N*22'/."?'C ./@./%C $A% =."/' /'+. . $'%@@.$.%/+. 0%&&" ?"+#.$% W=0%&&" #%&">.'/% $'=+.+*+.B"C 0. */ 0'22.' O.2'&'C

    ./ @'#?" .O#.0" 8; 3T 2'==.O.&% B%#.@.$"#% $A% .& $.#$*.+' %E*.B"&%/+% #.2'#+"+' ./ @.:*#" ='00.=@" &" #%&">.'/%

    $'=+.+*+.B" 0"+"C " 2"++' $A%H -'#+" 8H &" #%=.=+%/>" 0%B% %==%#% 2"#. " 8//; -'#+" 8H .& :%/%#"+'#% 2.&'+"+' ./ +%/=.'/% 0%B% .?2#.?%#% */" +%/=.'/% 2"#. " 8/E#"E; -'#+" 5H &" #%=.=+%/>" 0%B% "B%#% $'/0*++"/>" 2"#. " 8EE; -'#+" 5H .& :%/%#"+'#% 2.&'+"+' ./ $'##%/+% 0%B% .?2#.?%#% */" $'##%/+% 2"#. " 8E/#!/;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    46/61

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    47/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; c6

    L'&&%:"?%/+' ./ $"=$"+" 0. 0*% 0'22. O.2'&.

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    48/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; co

    *64&5$6 X 1 !$8A&H& $5(8A6

    75(#A5 3 1 >&E#A84&5$6 @&9@#&%8A6

    .'/"&% $"&$'&' H27.'/% 0. #%+.

    % "&&T"/"&.=. 0%& $'?2'#+"?%/+' %&%++#.$' 0%. $.#$*.+. P=.?*&"+'#. $.#$*.+"&.R; D#" . =.?*&"+'#.$.#$*.+"&. 0. $.#$*.+. "/"&':.$.C */' 0%. 2.b /'+. F N-."&?%/+% 0" h 2"#+.

    0.=+./+% .&&*=+#"+% ./ @.:*#";

    K% 2"#+. ='/'H

    8; 4"+" %/+#GH ./2*+ 0%. 0"+. V 0%=$#.>.'/% 0%& $.#$*.+' ./ */ &./:*"::.' &%::.O.&% 0"&$"&$'&"+'#%;

    5; K.O#%#."H =. +#"++" 0. */" &.O#%#." 0. 0.=2'=+.B. %&%++#.$. W $'?2'/%/+.;]; !%+'0' =$#.++*#" %E*">.'/.c; !'+'#% 0%&&% %E*">.'/.; >">.'/% % .& $'/@#'/+' 0%.#.=*&+"+. 0%&&" =.?*&">.'/%;

    4. /'#?" . $'?2'/%/+. 0%@./.+. 2%# ?%>>' 0%&&" &.O#%#."='/' $"#"++%#.>>"+. 0" "&$*/% 2#'2#.%+SH .& /*?%#' 0.

    ?'#=%++.C &T%E*">.'/% ?"+%?"+.$" $A% 0%=$#.B% &" #%&">.'/%0%& $'?2'/%/+% % */" &.=+" 0. 2"#"?%+#. .?2'=+"O.&.

    0"&&T*+%/+%;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    49/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; cp

    < @'#?"+. ./ $*. F 2'==.O.&%

    0%=$#.B%#% */ $.#$*.+' 2%# 2'.%@@%++*"#/% &" =.?*&">.'/% ='/'

    0*%H &' =$A%?"+.$' % &" /%+&.=+

    P0. $*. =. B%0% */ %=%?2.' ./

    @.:*#"R;

    -.b $A% =*& 2#':#"??" ./ E*"/+' +"&%C ./ E*%=+" 2"#+% 0%& $'#=' $. =. ='@@%#?" =*& ?%+'0'"*+'?"+.$' 0. =$#.++*#" 0%& =.=+%?" 0. %E*">.'/. #%&"+.B' "&&" ='&*>.'/% 0%. $.#$*.+. +#"++"O.&.

    $'/ */ =.?*&"+'#%; -*# %=.=+%/0' 0.B%#=. ?%+'0.C ./ &./%" :%/%#"&%C 2%# %==%#% %@@.$.%/+%?%/+%*+.&.>>"O.&% ./ */ NLC */ ?%+'0' 0. "/"&.=. 0'B#%OO% %==%#%H

    $'?2&%+"?%/+% "*+'?"+.>>"O.&% 'BB%#' +#"0*$.O.&% ./ =%E*%/>% 0. '2%#">.'/.%=%:*.O.&. 0" */ $"&$'&"+'#% 0.#%++"?%/+% " 2"#+.#% 0"&&" /%+&.=+ 0. 0.=$#%>.'/% 0%&&" #%+%

    PE*./0. =%/>" #.$A.%0%#% "&$*/ +#"++"?%/+' 0. =%?2&.@.$">.'/% % #.0*>.'/% ?"/*"&%R;

    "22&.$"O.&% " $.#$*.+. 0. E*"&=."=. +.2' $A% $'/+%/:'/'C E*./0.C $'?2'/%/+. &./%"#. % /'/&./%"#.C #%=.=+.B. % 0./"?.$.C $'/ :%/%#"+'#. $'=+"/+. % B"#."O.&. /%& +%?2';

    %$'/'?.$' 0"& 2*/+' 0. B.=+" ?"+%?"+.$' PO"==" $'?2&%==.+S % 2%=' $'?2*+">.'/"&%R;\*%=+' 2%# $'/=%/+.#% &T%&"O'#">.'/% 0. $.#$*.+. 2"#+.$'&"#?%/+% $'?2&%==.;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    50/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; h7

    75(#A5 : 1 !$8A&H& $5(8A6

    -#.?" 0. %/+#"#% /%& B.B' 0%&&T"#:'?%/+'C =.

    #%/0'/' /%$%=="#.% "&$*/% 0%@./.>.'/. 0. O"=%PB%0. @.:*#" " &"+'R;

    H"4#%4"-",% 0%)-$%11.-% ") -*)4"%)*Y &"

    #%&">.'/% $'=+.+*+.B" F */" @*/>.'/% 0%&&"

    +%/=.'/% PE*./0. "0 ':/. B"&'#% 0. +%/=.'/% 0.&"+'C $'##.=2'/0% */ ='&' B"&'#% 0. $'##%/+% 0.

    &"+'R; .'/% ./.%++.B" % "V -679!476 2! H4596--! %61 34H+4767-6R;

    n/ %=%?2.' 0. 0.=2'=+.B' $'/+#'&&"+' =." ./

    +%/=.'/% $A% ./ $'##%/+% F 2#'2#.' .& #%=.=+'#%

    .0%"&%;

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    51/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; h8

    Y.%/% '#" %/*/$."+' .& 2*-%&% &*118.).1"4" )%&.1* #*$ " 0"$0'"-" 0%)-$%11.-" ") -*)4"%)*

    P=*$$%==.B"?%/+% B%##S %=+%=' " +*++. . $.#$*.+. 2%# $*. B"&:'/' &% &%::. 0. k.#$AA'@@ %/*/$."/0'.& ?%+'0' 0%&&T"/"&.=. /'0"&% ?'0.@.$"+"R; D"&% ?%+'0' =@#*++" .& @"++' $A% ./ */" #%+% ./ $*. +*++.

    . 0.=2'=.+.B. =."/' $'/+#'&&"+. ./ +%/=.'/%C ':/. :#"/0%>>" 0. &"+' F %=2#.?.O.&% $'?% @*/>.'/%

    0%&&% +%/=.'/. 0. /'0';

    KT.0%" 0. O"=% F E*%&&" 0. #.='&B%#% .& $.#$*.+' $"&$'&"/0'/% 7 C /+%/=.'/. 0. /'0' ./0.2%/0%/+.

    % 0. #.$"B"#%C 0" E*%=+%C +*++% % ='&% &% :#"/0%>>% 0. &"+' $A% ./+%#%=="/' 2%# .& 2"#+.$'&"#%$.#$*.+' ./ %="?% *+.&.>>"/0' &% #%&">.'/. $'=+.+*+.B% 0%. &"+. 2.b #.&%B"/+.;

    .'/"&%;

    M%&&T"/"&.=. /'0"&%C &" ='&*>.'/% 0. */ $.#$*.+'$'/+#'&&"+' ./ +%/=.'/%C "BB.%/% "++#"B%#=' .

    =%:*%/+. 2"==.H

    N$#.++*#" 0. +*++% &% $'##%/+. 0. &"+' ./@*/>.'/% 0%&&% +%/=.'/. 0. /'0' *="/0'

    &% #%&">.'/. $'=+.+*+.B% 0. +*++. .0.=2'=.+.B.;

    N$#.++*#" 0. P7 > /R %E; ./0.2;"22&.$"/0' &% KkL "0 P7 > /R /'0. 0%&

    $.#$*.+';

    /R %E;./0.2; ./ @*/>.'/% 0%&&% P7 > /R +%/=.'/.

    0. /'0' ./0.2%/0%/+.;

    N. 2#'$%0% #.='&B%/0' .& =.=+%?" $'=q =$#.++'; .'/. $'=+.+*+.B%R;

    Y%0."?' '#" */ %=%?2.' 2#"+.$' #%&"+.B' "& $.#$*.+'

    .&&*=+#"+' ./ @.:*#" $A% $'/+.%/% ='&' 0.=2'=.+.B.$'/+#'&&"+. ./ +%/=.'/% P=. 2*U 0*/E*% "22&.$"#% .&

    ?%+'0' "22%/" %/*/$."+'R; K" $'##%/+% ./ $."=$*/ &"+' F%=2#.?.O.&% ./ @*/>.'/% 0%&&% +%/=.'/. 0. /'0'; ).=*&+"

    ./@"++.H

    i1 =

    (e1" e

    0)

    R1

    i3 =

    (e2 " e3)

    R3

    i2 =

    (e2" e

    1)

    R2

    i4 =

    (e2 " e3)

    R4

    i5 =

    (e3 " e0 )

    R5

    #v*=#(e2 " e3)

    4'2' "B%# %=2#%==' +*++% &% $'##%/+. 0. &"+' ./ @*/>.'/% 0%&&% +%/=.'/. 0. /'0' 2#'$%0."?'

    =$#.B%/0' ] %E*">.'/. #%&"+.B% "&&% KkL 0%&&% $'##%/+. 0. /'0' 2%# . /'0. 8C 5 % ]; -%# $'?'0.+SC=. 2#%/0'/' $'?% 0.#%>.'/. 2'=.+.B% 0%&&% $'##%/+. E*%&&% *=$%/+. 0". /'0.; 1B#%?' 0*/E*%H

    +,-%../-# )% ./..*

    $* ,(--*".% )% $#.(%" 0/"1%("* )*$$*

    .*"&%("% )% "()(

    +,-%../-# )% !!"#"*2/#1%("%

    %")%3*")*".% -*$#.%4* #$$##33$%,#1%("* )*$$# 567 #)

    !!"#""()% )% ,%-,/%.(

    !!"#"*2/#1%("% %")%3*")*".%"*$$* !!"#".*"&%("% )% "()(

    %")%3*")*".% )*$ ,%-,/%.(

    +($/1%("* )*$ &%&.*8#

    7#$,($( )*$$* 9-#")*11* )% $#.( %",(9"%.*

    %" 0/"1%("* )*$$* .*"&%("% )% "()(

  • 5/26/2018 Appunti di ELETTROTECNICA PARTE 1 - Marcello Rutter

    52/61

    !"#$%&&' )*++%# , -'&.+%$/.$' 0. !.&"/' , 122*/+. 0. 3&%++#'+%$/.$" 4! 567 , !"#$%&'("%)* ,"*-.-. -"#+% 8 9 -":; h5

    1" i1# i

    2# a(t) =0"

    e1

    R1

    #(e