Circuitos RLC Con E.D

October 10, 2022 | Author: Anonymous | Category: N/A
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Wk b`rbu`tl b`rbu`tl gs  gs uka rgj ghàbtr`ba (`ktgrblkgx`òk jg jls l más blmplkgktgs, tahgs blml rgs`stgkb`as,  rgs`stgkb`as,  `kjubtlrgs, `kjubtlrgs, bapab`tlrgs,, nugktgs, bapab`tlrgs nugktgs, `ktgrruptlrgs  `ktgrruptlrgs  y sgm`blkjubtlrgs) sgm`blkjubtlrgs) qug blkt`gkg ah mgkls uka traygbtlr`a bgrraja. Hls b`rbu`tls qug blkt`g blk t`gkgk kgk slhl slhl nugktg nugktgs, s, blm blmplk plkgkt gktgs gs h`k h`kgah gahgs gs (rgs`s (rgs`stlr tlrgs, gs, bapab`tlrgs, `kjubtlrgs), y ghgmgktls jg j`str`fub`òk h`kgahgs (hík (h íkga gas s jg trak traksm sm`s `s`ò `òk k l bafh bafhgs gs)) pugj pugjgk gk ak akah ah`z `zar arsg sg plr  plr  màtljl màt ljls s ahigfra`bls ahigfra`bls para  para jgtgrm`kar su blmplrtam`gktl gk j`rgbta l  l gk blrr`gktg ahtgrka. ahtgrka. blrr`gktg j`rgbta

Hls b`rbu`tls fás`bls, nlrmajls plr rgs`stgkb`as (V), blkjgksaj blkjg ksajlrgs lrgs (B) (B)   y flf flf`k `kas as (H) (H),, buakjl sg ah`mgktak plr  uka nugktg jg tgks`òk. Gstls b`rbu`tls sg jgklm`kak VHB VHB.. Wk b`rbu`tl VH VH slhamgktg  slhamgktg plsgg Ha nugktg ha rgs`stgkb`a (V) (V) y  y ha Flf`ka (H)

 

Gk gstg b`rbu`tl b`rbu`tl s` sg aph`ba aph`ba ha sgiukja sgiukja hgy  hgy  jg E`rbddln E`rbddlnn, n, sg tgkjrá qug gh vahlr  `kstaktákgl jgh vlhtacg gs3 v =` V   +   H

 

  j` jt 

v = H  H`` (t ) + V` ' 

Gsta óht`ma gxprgs` gxprgs`òk, òk, gs uka gxprgs`ò gxprgs`òk k j`ngrgk j`ngrgkb`ah b`ah kl dlmliàkg dlmliàkga, a, h`kgah h`kgah jg pr`mgr lrjgk. Gh s`iu`gktg b`rbu`tl gs VHB

 

Jg abugrjl blk ha hgy jg E`rbddlnn ha gbuab`òk j`ngrgkb`ah jg ha blrr`gktg jgh b`rbu`tl jg ha n`iura gs3

 Ah jgsarrlhharsg jgsarrlhharsg sg t`gkg qug gs gqu`vahg gqu`vahgktg ktg a3 ' ' 



 1

 HQ  H Q ( t )+ V Q ( t )+  Q ( t )= ^  (  ( t ) B  ' ' 



 Jlkjg

1

 H q ( t ) + V q (t ) +  q ( t ) =^ ( t ) B  q ( t )= baria

jQ ( t ) (Nhucl ucl jg ghgbt ghgbtrlk rlkgs, gs, mlv`m` mlv`m`gkt gktl l jg ghgbt ghgbtrlk rlkgs gs a trav travàs às jgh jgh   =q'  ( t )(Nh jt  t`gmpl).  ` ( t )=

Rg jgfg rgblrjar qug3

v =`V

1. Ha baíja jg vlhtacg a travàs jg ha rgs`stgkb`a gs

1

6. Ha baíja jg jg vlhtacg a travàs jgh bapab`tlr gs

v= Q B  v = H

2. Ha baíja jg vlhtacg a travàs jg ha `kjubtakb`a gs

j` jt 

 

Blml sg lfsgrva ha slhub`òk jg gsta bhasg jg b`rbu`tls sg hlira a travàs jg uka gbuab`òk j`ngrgkb`ah jg blgn`b`gktgs blkstaktgs jg sgiukjl lrjgk kl dlmliàkgl Wk b`rbu`tl VB plsgg rgs`stgkb`a y bapab`takb`a.

' ' 

 HQ ( t )+

 1



Q ( t )=^ ( t )

Ha gbuab` b`ò òk j`ng `ngrg rgk kb`a `ahh sg rg rgj jubg a3 blkj`b`lkgs jg uka GJ. Jg lrjgk 6 Blgn`b`gktgs blkstaktgs.

bumph bum ph`gk `gkjl jl

has

Wka Flf`ka Flf`ka Ahmabgka  Ahmabgka gkgriía. Wk blkjg blkjgksaj ksajlr lr ghàbtr`bl ghàbtr`bl  blk blklb` lb`jl jl nrg nrgbug bugktg ktgmgk mgktg tg blm blml l bapab`tlr , gs uk j`spls`t`vl, bapaz jg ahmabgkar gkgriía  gkgriía sustgktak sustgktakjl jl uk bampl ghàbtr`bl ghàbtr`bl.. Auk Aukqu qug g jgsjg gh puktl jg v`sta nís`bl uk blkjgksajlr kl ahmabgka baria k` blrr blrr`g `gkt ktg g ghàb ghàbtr tr`b `ba a, s`kl s`mphgmgktg gkgriía mgbák`ba  hatgktg5 ah sgr `ktrljub`jl gk uk b`rbu`tl sg mgbák`ba b`rbu`tl sg blmplrta gk ha prábt`ba blml uk ghgmgktl bapaz jg ahmabgkar ha gkgriía ghàbtr`ba ghàbtr`ba qug  qug rgb`fg juraktg gh pgr`ljl jg baria, ha m`sma gkgriía qug bgjg jgspuàs juraktg gh pgr`ljl jg jgsbaria. Ha rgs`stgkb`a V sg m`jg gk ldm`ls  ldm`ls ( Π ) Ha `kjubtakb`a H sg m`jg gk dgkr`ls gk dgkr`ls ( D   ¼¼

 

Ha bapab`takb`a B sg m`jg gk naraj`ls ( n   ¼¼

dtps3//www.yluufg.blm/wabd? t ^  Gkbugktrg ha baria gk gh bapab`tlr y ha `ktgks`jaj jg blrr`gktg jgh b`rbu`tl para gh t`gmpl t   q ( ? )=? B   ` ( ? )=? A    V 6? Π G ( t )= 1?? sgk >? t ^ 

Rg rgprgsgkta plr uka gbuab`òk j`ngrgkb`ah3 ' ' 

1



 H q ( t ) + V q (t ) +  q ( t ) =^ ( t ) B 

Vggmphazl3

1

' ' 



q (t ) + 6? q ( t )+

6

  1

q ( t )=1?? sgk >? t 

?.??1

G.J. jg lrjgk 6, Kl dlmliàkga, jg blgn`b`gktgs blkstaktgs y blk blkj`b`lkgs jg `k`b`l. Rg rgsughvg plr traksnlrmaja jg Haphabg  H

{

1 6

'' 



q ( t ) + 6? q ( t )+

H`kgah`jaj  H

{

1 6

  1 ?.??1

}

}

q ( t ) = H { 1?? sgk >? t }

q ( t ) + H { 6? q ( t ) } + H '' 



{

  1 ?.??1

}

q ( t ) =1?? H { sgk >? t }

 

1 6 1 6

{

' ' 

{

' ' 

 H q ( t )

 H q ( t )

  1  H { q ( t ) }=1?? H { sgk >? t }  }+ 6? H { q ( t ) }+ ?.??1 ' 

 }+ 6? H { q ( t ) }+ 1??? H { q ( t ) }=1?? H { sgk >? t } ' 

Rg aph`ba tglrgma jg ha traksnlrmaja jg uka jgr`vaja 1

'  s Q ( s ) ∖sq ( ? )∖ q ( ? ) ) + 6? ( sQ ( s ) ∖q ( ? ) ) + 1??? ( Q ( s ) )=1?? ( 6 6

(

  >? 6

s + 2>??

)

Vggmphazl blkj`b`lkgs jg `k`b`l3 1

( s Q ( s) ∖s (? )∖( ? ) )+ 6? ( sQ ( s ) ∖(? )) +1??? ( Q ( s ) )=1?? 6 6

1

( s Q ( s) ) + 6?( sQ ( s ) ) +1??? ( Q ( s ) )=1?? 6 6

(

  >? 6

s + 2>??

(

  >?

s

6

+ 2>??

)

)

Vgsughvl hls paràktgs`s plr fás`bas3 1 6

6

s Q ( s ) + 6? sQ ( s )+ 1??? Q ( s )=

(

  >???

s

6

+ 2>??

)

Rg jgfg rgslhvgr Q ( s ) Nabtlr blmók gv`jgktg3 Q ( s )

Q ( s )=

 

(

1 6

)(

6

s + 6? s + 1? 1?? ?? =

  >??? 6

s + 2>??

)

>???

( s ¼¼ 6 + 2>?? )

(

1 6

6

)

s + 6? s + 1? 1?? ?? ¼

@kvgrsa jg Haphabg ∖1

 H

{ Q ( s ) }= H∖ ¼ 1

Rg jgfgk aph`bar nrabb`lkgs parb`ahgs3 Jgfg gstar tljl gh jgklm`kajlr tltahmgktg nabtlr`zajl 1

(

6

6s

)

+ 6? s + 1??? =?

 

1

_lr buajrát`ba3 a = f =6? b =1??? 6

6

J`sbr`m`kaktg ( 6? ) ∖ :

( )( 1

1???

6

)= :??∖6??? =∖1>?? 8 ?

Rg blmphgtak buajrajls a s + fs + b =? 6

GH BLGN@B@GKZG _V@KB@_AH JGFG RGV 1. Gktlkbgs sg j`v`jg plr 1s

f a

6

b a

+  s + =?

Rg suma bgrl 6

 f

 f

6

6

(  ) (  ) ( (  ) ) ( (  ) ) ( (  ) ( (  ) )

1s

+ fa s + ba + a6 ∖ a6 =?

 Airupl

 f a

s+

6

1s

6

f a

+  s +

6

+

 f a

 b + a

 f a

6

6

6

=?

Gk gh gcgrb`b`l3

(

(

1 6

6

6

s

s+

)

+ 6? s + 1??? =? 6? 1 6

s+

 )

1??? 1 6

=?

( s + :? s + 6??? )=? 6

 Airgil bgrl3

6

+

b + a

 f a

6

6

=?

a

 

(

6

s + :? s + 6???+

(  ) ∖(  ) )= :?

6

 :?

6

?

6

6

( s + :? s + 6??? +( 6? ) ∖( 6? ) ) =? 6

6

6

 Airupa3 ( s + :? s + ( 6? ) ) + ( 6??? ∖( 6? ) )= ? 6

6

6

6

( s +6? ) + 1>?? =? Hugil  H∖ { Q ( s ) }= H∖ ¼ 1

1

Nrabb`lkgs parb`ahgs3 ∖1

 H

{ Q ( s ) }= H∖ ¼ 1

_lr h`kgah`jaj ∖1

 H ∖1

 H

∖1

 H

∖1

{ Q ( s ) }= H ¼ { Q ( s ) }= H∖ ¼. 1

{ Q ( s ) }= A H∖ ¼. 1

 A qu`gk traksnlrmò para<

q ( t )= Abls >? t +

 J :?

∖6? t 

g

:?

∖6? t 

g

>?

sgk >? t + b H

∖1

sgk >? t + b H

∖1

{(

 

s

( s +6? ) +1>?? ) 6

}



:?

sgk



q ( t )= Abls >? t +

 J

 F

 F >?

{(

  s + 6?∖6? 6

( s + 6? ) + 1>??

)}



sgk : ? t 

_lr h`kgah`jaj q ( t )= Abls >? t +

 F >?

sgk >? t + b H

 

∖1

s + 6? 6

{

( ( s+6? ) +1>?? )

∖ b H∖

1

} {

 

6?

+

6

 }

( ( s+ 6? ) + 1>?? )

 J :?

∖6? t 

g

sgk : ? t 

 

q ( t )= Abls >? t +

 F >?

∖6? t 

sgk >? t + b g



bls bls :? t 

6? :?

∖6? t 

bg

sgk :? t +

 J :?

∖6? t 

g

sgk :? t 

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