Diseño de Filtros Activos 2015

8/19/2019 Diseño de Filtros Activos 2015

1/41

DISEÑO DE FILTROS ACTIVOS

Métodos:

1.- Clásico

2.- Prst!"lcido

#.- T!"l!s

#.1 $%ttr&ort'

#.2 C'"(s')

1.- M*TODO CL+SICO

El ,étodo clásico %tili! l! !ro/i,!ci0 dl iltro co l! !,lit%d ! -# d" 34.545 A,á/6 !l! rc%ci! d cort c.

1.1.- FILTRO PASA $A7O

El ,odlo dl circ%ito iltro d s8%do ord s l ,ostr!do.


2/41

P!r! todo sist,! d s8%do ord !s! "!9! l! %ci0 d tr!srci! s ri8 ! %!or,! c!0ic!:

Co,!r!do co l! or,! or,!li!d! dl iltro:

s o"ti l!s c%!cios:

; 1 !r! l iltro !s! "!9!

P!r! dtr,i!r &o %ci0 d &c ; 2< c s )!l=! l ,0d%lo d Vo>Vi d l! or,!

c!0ic! s ; 9& 3dod & ; &c6 ( dic'o ,0d%lo s i8%!l! ! 4.545 sto s

Ds9!do &o

&o ; 1.??# &c

R,l!!do &o 326 ( 3#6:

Dic'!s c%!cios s %s! !r! di,sio!r )!lors rsistci!s ( c!!cit!ci!s.


3/41

Ejemplo:

Dis@!r % iltro !s! "!9! d s8%do ord % c%,l! co %! rc%ci! d cort c; 2? B.

Sol%ci0:

&c ; 2< c ; 2< 32? / 14#6 ; ?4< / 14# r!d>s

r,l!!do &c 3#6 ( l%8o s%stit%(do 316 326:

Co,o /ist ic08it!s ( solo dos c%!cios s li8 %! c!!cit!ci! co,rci!l:

C2 ; 1 F

s ds9! d 326 R1 R2 ; G.1H B o',

!6 Es )álido %s!r l critrio R1 ; R2 tocs R1 ; R2 ; G.1H B > 2 ; .4H5 B o',

R1 ( R2 316 %d!:

C1 ; 4.HHG F s r0/i,o ! 1 F.

El circ%ito %d!:


4/41

Co,ro"!do l Circ%itM!Jr:

"6 Co R1 ; 2 R2 tocs R1 ; ?.# B o', R2 ; 2.5#1 B o',

R1 ( R2 316 %d!:

C1 ; 1.12? F.

El circ%ito %d!:


5/41


1.2.- FILTRO PASA ALTA



6/41

P!r! todo sist,! d s8%do ord !s! !lt! l! %ci0 d tr!srci! s ri8 ! %!or,! c!0ic!:


s o"ti l!s c%!cios:

; 1 !r! l iltro !s! !lt!

P!r! dtr,i!r &o %ci0 d &c ; 2< c s )!l=! l ,0d%lo d Vo>Vi d l! or,!c!0ic! s ; 9& 3dod & ; &c6 ( dic'o ,0d%lo s i8%!l! ! 4.545 sto s


7/41

Ds9!do &o

&o ; 4.# &c

R,l!!do &o 326 ( 3#6:

Dic'!s c%!cios s %s! !r! di,sio!r )!lors rsistci!s ( c!!cit!ci!s.

Ejemplo:

Dis@!r % iltro !s! !lt! d s8%do ord % c%,l! co %! rc%ci! d cort c; 14 B.

Sol%ci0:

&c ; 2< c ; 2< 314 / 14#6 ; 24< / 14# r!d>s

r,l!!do &c 326 ( 3#6:

Co,o /ist ic08it!s ( solo dos c%!cios s li8 %! c!!cit!ci! co,rci!l:!r! C1 ( C2 o s! C1 ; C2 ; 1 F

s ds9! R2 d 316 R2 ; 2.5# B o',

( l%8o s ds9! R1 d 326 R1 ; 2.5# B o',

El circ%ito %d!:


8/41


1.#.- FILTRO PASA $AKDA



9/41

P!r! todo sist,! d s8%do ord !s! "!d! l! %ci0 d tr!srci! s ri8 !%! or,! c!0ic!:


s o"ti l!s c%!cios:

; 1 > 326 !r! l iltro !s! "!d! dod s l !ctor d c!lid!d dl iltro.

P!r! iltros:

!6 !s! "!d! !c'!: 4.? ; 1"6 !s! "!d! !8ost!: N1

El !ctor d c!lid!d s i8%!l !:

; &o > dod s l !c'o d "!d! r!di!s or s8%do.

; &c2 &c1o

; o > $ dod $ s l !c'o d "!d! rt.

$ ; c2 c1

L!s c%!cios 316 326 ( 3#6 s %s! !r! di,sio!r )!lors rsistci!s (c!!cit!ci!s.


10/41

Ejemplo 1:

Dis@!r % iltro !s! "!d! !c'! d s8%do ord % c%,l! co %! rc%ci! o

; 1 B ( % !c'o d "!d! $ ; 1 B.

Sol%ci0:

; o > $ ; 1

&o ; 2< o ; 2< / 14# r!d>s

; 1 > 326 ; 1>2

r,l!!do ( &o 326:

Co,o /ist ? ic08it!s ( solo trs c%!cios s li8 %! c!!cit!ci! co,rci!l:!r! C1 ( C2 o s! C1 ; C2 ; 1 %F ( s ds9! R#:

R# ; #1G.#1 o',

R,l!!do B ; 1 &o ( C1 316 s ds9! R1:

R1 ; 1?H.1? o',

R,l!!do R1 R# C1 ( C2 3#6 s ds9! R2:

R2 ; 1?H.1?H o',

El circ%ito %d!:


11/41

Co,ro"!do l Circ%itM!Jr

Ejemplo 2:

Dis@!r % iltro !s! "!d! !8ost! d s8%do ord % c%,l! co %! rc%ci!o ; 1 B ( % !c'o d "!d! $ ; 244 .

Sol%ci0:

; o > $ ; ?

&o ; 2< o ; 2< / 14#

r!d>s

; 1 > 326 ; 1 > 14 ; 4.1

r,l!!do ( &o 326:


12/41

Co,o /ist ? ic08it!s ( solo trs c%!cios s li8 %! c!!cit!ci! co,rci!l:!r! C1 ( C2 o s! C1 ; C2 ; 1 %F ( s ds9! R#:

R# ; 1.?H2 B o',

R,l!!do B ; 1 &o ( C1 316 s ds9! R1:

R1 ; 5H?.5 o',

R,l!!do R1 R# C1 ( C2 3#6 s ds9! R2:

R2 ; 1.2# o',

El circ%ito %d!:



13/41

2.- M*TODO PREESTA$LECIDO

El ,étodo rst!"lcido %tili! l! !ro/i,!ci0 dl iltro co l! !,lit%d ! -# d" 34.545A,á/6 ! l! rc%ci! d cort c. Dic'o ,étodo s 8%Q! r%"!s r!li!d!s ( l!t!

0r,%l!s codicio!d!s ! dtr,i!dos r!8os d c!!cit!ci!s ( !ctor d c!lid!d. Los,odlos so d s8%do ord.

2.1.- FILTRO PASA $A7A

El circ%ito iltro !s! "!9! d s8%do ord %tili! l! str%ct%r! S!ll-B(

Los )!lors d R C1 ( C2 s o"ti ,di!t l!s c%!cios st!"lcid!s si8%its:


14/41

Ejemplo:

Dis@!r % iltro !s! "!9! d s8%do ord % c%,l! co %! rc%ci! d cort c

; 1 B.

Sol%ci0:

R,l!!do c l! c%!ci0 d C1:

C1 ; 4.41 %F

r,l!!do C1 l! c%!ci0 d C2 ( c l! c%!ci0 d R:

C2 ; 4.42 %F

R ; 11.2? Bo',

2R ; 22.? Bo',

El circ%ito %d!:



15/41

2.2.- FILTRO PASA ALTA

El circ%ito iltro !s! !lt! d s8%do ord %tili! l! str%ct%r! S!ll-B(

Los )!lors d R ( C s o"ti ,di!t l!s c%!cios st!"lcid!s si8%its:

Ejemplo:

Dis@!r % iltro !s! !lt! d s8%do ord % c%,l! co %! rc%ci! d cort c

; 1 B.

Sol%ci0:

R,l!!do c l! c%!ci0 d C:

C ; 4.41 %F

r,l!!do C ( c l! c%!ci0 d R:

R ; 22.? Bo',

R>2 ; 11.2? Bo',


16/41

El circ%ito %d!:



17/41

2.#.- FILTRO PASA $AKDA

El circ%ito iltro !s! "!d! d s8%do ord %tili! l! str%ct%r! d R!%c' o dM=ltil Fd"!cJ 3MF$6

Los )!lors d R1 R2 R# ( C s o"ti ,di!t l!s c%!cios st!"lcid!ssi8%its:

Ejemplo 1:

Dis@!r % iltro !s! "!d! !c'! d s8%do ord % c%,l! co %! rc%ci! o; 1 B ( % !c'o d "!d! $ ; 1 B.

Sol%ci0:

; o > $ ; 1

r,l!!do o C:

C ; 4.41 %F

S li8 J ;1 ( s ,or % 22

r,l!!do C c J ( l! c%!ci0 d R1 R2 ( d R#:

R1 ; 1?.H1 Bo',

R2 ; 1?.H1 Bo',

R# ; #1.G Bo',


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El circ%ito %d!:



19/41

Ejemplo 2:

Dis@!r % iltro !s! "!d! !8ost! d s8%do ord % c%,l! co %! rc%ci!o ; 1 B ( % !c'o d "!d! $ ; 244 .

Sol%ci0:

; o > $ ; ?

r,l!!do o C:

C ; 4.41 %F

S li8 J ;1 ( s ,or % 22

r,l!!do C c J ( l! c%!ci0 d R1 R2 ( d R#:

R1 ; 5H.?5 Bo',

R2 ; 1.2 Bo',

R# ; 1?H.1? Bo',

El circ%ito %d!:



20/41

#.- M*TODO POR TA$LAS

El ,étodo or t!"l!s %tili! d!tos ro)its d t!"l!s rrci!ls d !ro/i,!ci0dl iltro co l! !,lit%d A,á/ d" ! l! rc%ci! d cort c.

D los dirts ,étodos or t!"l!s s !"ord! dos:

#.1.- Método d $%ttr&ort'

#.2.- Método d C'"(s')

#.1.- M*TODO DE $TTERORT

#.1.1.- FILTRO PASA $A7A

E % iltro !s! "!9! "%ttr&ort' l! rc%ci! d cort stá rl!cio!d! co l i)l d

!,lit%d

E dis@o s sciic! d" l! !,lit%d A,á/ ; % %i)!l !:

A,á/3d"6 ; 24 lo814 3 6

ds9!do :


21/41

D !c%rdo !l ord dl iltro !s! "!9! s li8 % olio,io d "%ttr&ort' s8= l!

t!"l! si8%it:

Dod S! s %ci0 d l! rc%ci! d cort &c ( d :

L! %ci0 d tr!srci! dl iltro s:

Dic'! %ci0 s co,!r! co l! or,! c!0ic! dl sist,! iltro d ord ( orco,!r!ci0 s /tr! l!s c%!cios d dis@o.

Ejemplo:

Dis@!r % iltro !s! "!9! $%ttr&ort' d s8%do ord % c%,l! co %!rc%ci! d cort c ; 4 ( A,á/ ; 1 d".

Sol%ci0:

&c ; 2< c ; 2< 346 ; 124< r!d>s

co A,á/3d"6 ; 1d" s c!lc%l! :

; 4.?4GG


22/41

R,l!!do ; 4.?4GG l! c%!ci0 d A ,á/

A ,á/ ; 4.GH1

S! ; 3s > ?2G.?6

d l! t!"l! d "%ttr&ort' !s! "!9! s li8 ; 2:

Vo 1----- ; ------------

Vi $23S!6

s r,l!! Vo > Vi ( s o"ti:

S !dot! l ,odlo si8%it d "%ttr&ort' d s8%do ord:


23/41

Co,!r!do l! %ci0 dl iltro co l! o"tid! d l! t!"l! s or,! l!s c%!cios ddis@o:

Co,o /ist ic08it!s ( solo dos c%!cios s li8 %! rsistci! !r! R1 ( R2:R1 ; R2 ; 14 Bo', s r,l!! R1 ( R2 326 ( s ds9! C1

C1 ; 2G F

Co R1 R2 ( C1 s s%stit%( 316 ( s ds9! C2:

C2 ; 1# F

El circ%ito %d!:



24/41

#.1.2.- FILTRO PASA ALTA

E % iltro !s! !lt! "%ttr&ort' l! rc%ci! d cort stá rl!cio!d! co l i)l d

!,lit%d


A,á/3d"6 ; 24 lo814 3 6

ds9!do :


25/41

D !c%rdo !l ord dl iltro !s! "!9! s li8 % olio,io d "%ttr&ort' s8= l!t!"l! si8%it:




Ejemplo:

Dis@!r % iltro !s! !lt! $%ttr&ort' d s8%do ord % c%,l! co %!rc%ci! d cort c ; 14 B ( A,á/ ; 4.? d".

Sol%ci0:

&c ; 2< c ; 2< 314B6 ; 24< / 14# r!d>s

co A,á/3d"6 ; 4.?d" s c!lc%l! :

; 4.#H#


26/41

R,l!!do ; 4.#H# l! c%!ci0 d A ,á/

A ,á/ ; 4.H

S! ; 3#51#. > s6

d l! t!"l! d "%ttr&ort' !s! "!9! s li8 ; 2:

Vo 1----- ; ------------ Vi $23S!6

s r,l!! Vo > Vi ( s o"ti:

S !dot! l ,odlo si8%it d "%ttr&ort' d s8%do ord:


27/41


Co,o /ist ic08it!s ( solo dos c%!cios s li8 %! c!!cit!ci! co,rci!l!r! C1 ( C2: C1 ; C2 ; 1F s r,l!! C1 ( C2 326 ( s ds9! R2

R2 ; #G.1 Bo',

Co C1 C2 ( R2 s s%stit%( 316 ( s ds9! R1:

R1 ; 1H.4# Bo',

El circ%ito %d!:



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#.1.#.- FILTRO PASA $AKDA

E % iltro !s! "!d! "%ttr&ort' l! str%ct%r! dl circ%ito iltro s d S!ll B(

Est ,étodo s 8%Q! or t!"l!s ( d !c%rdo ! r%"!s s l!t! l!s si8%itsc%!cios.

El ,étodo icl%( l cálc%lo d


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Ejemplo 1:

Dis@!r % iltro !s! "!d! !c'! $%ttr&ort' d s8%do ord % c%,l! co %!rc%ci! o ; 14 B % !c'o d "!d! $ ; 1B ( A,á/ ; 4.? d".

Sol%ci0:

&o ; 2< c ; 2< 314B6 ; 2< / 14 r!d>s

; 2< $ ; 2< 31B6 ; 2< / 14 # r!d>s

co A,á/3d"6 ; 4.?d" s c!lc%l! :

; 4.#H#

R,l!!do ; 4.#H# l! c%!ci0 d A ,á/

A ,á/ ; 4.H

El circ%ito %d!:


30/41


KOTA:

S '!c ot!r % l! rc%ci! idic!d! l dis@o o ; 14 B o coicid co o dl8ráico sto s or,!l or% !l !ro/i,!r l co,ort!,ito dl iltro ! rc%ci!s!lt!s 314 B o ,!(or6 % iltro d s8%do ord /ist %! ds)i!ci0 rc%ci! ro l !c'o d "!d! s ,%( r0/i,o ! lo /i8ido. Asi,is,o sicr,t! l! 8!!ci! dl iltro % )!lor s%rior ! 5 si ,"!r8o s %d !t%!r! 1 ,di!t %! t!! !dicio!l.


31/41

Ejemplo 2:

Dis@!r % iltro !s! "!d! !8ost! $%ttr&ort' d s8%do ord % c%,l! co%! rc%ci! o ; 1 B % !c'o d "!d! $ ; 244 ( A,á/ ; 4.? d".

Sol%ci0:

&o ; 2< c ; 2< 31B6 ; 2< / 14 # r!d>s

; 2< $ ; 2< 32446 ; < / 14 2 r!d>s

co A,á/3d"6 ; 4.?d" s c!lc%l! :

; 4.#H#R,l!!do ; 4.#H# l! c%!ci0 d A ,á/

A ,á/ ; 4.H


32/41

El circ%ito %d!:


KOTA:

S '!c ot!r % l! rc%ci! idic!d! l dis@o o ; 1 B coicid co o dl8ráico or% !l !ro/i,!r l co,ort!,ito dl iltro ! rc%ci!s "!9!s 314 ! ?B6 % iltro d s8%do ord o /ist %! ds)i!ci0 rc%ci! ( l !c'o d"!d! s ,%( r0/i,o ! lo /i8ido. Asi,is,o s icr,t! l! 8!!ci! dl iltro %)!lor s%rior ! # si ,"!r8o s %d !t%!r ! 1 ,di!t %! t!! !dicio!l.


33/41

#.2.- M*TODO DE CE$SEV

#.2.1.- FILTRO PASA $A7A

E % iltro !s! "!9! c'"(s') l! rc%ci! d cort t!,"ié stá rl!cio!d! co l

i)l d !,lit%d !l i8%!l % or l ,étodo d "%ttr&ort' L! tr!sici0 d l!s@!l s !"r%t! crc! d l! rc%ci! d cort si ,"!r8o l! c!r!ctrQstic! s % s%rs%st! rc%ci! dl iltro s oscil!tori! 3rios6 los i)ls !lto ( "!9o.


A,á/3d"6 ; 24 lo814 3 6

ds9!do :

A dirci! d l! t!"l! d $%ttr&ort' l! d C'"(s') rl!cio! !r! c!d! A,!/3d"6 (l ord dl iltro s%s olio,ios. Por 9,lo !r! % iltro !s! "!9! d ord 2.


34/41




Ejemplo:

Dis@!r % iltro !s! "!9! C'"(s') d s8%do ord % c%,l! co %!rc%ci! d cort c ; 4 ( A,á/ ; 1 d".

Sol%ci0:

&c ; 2< c ; 2< 346 ; 124< r!d>s

co A,á/3d"6 ; 1d" s c!lc%l! :

; 4.?4GGR,l!!do ; 4.?4GG l! c%!ci0 d A ,á/

A ,á/ ; 4.GH1

S! ; 3s >124


35/41

d l! t!"l! d C'"(s') !s! "!9! A,á/d" ; 1d" ; 2:

Vo 1----- ; ------------ Vi $23S!6

$23S!6 s r,l!! Vo > Vi ( s o"ti:

Co,!r!do st! %ci0 Vo>Vi co l! or,! c!0ic! d s8%do ord.

S ot! % B s distit! d %o or c%!to l trcr tér,io dl do,i!dor d"coicidir co l tér,io dl %,r!dor.

Por st! r!0 s !9%st! B % !ctor d !t%!ci0 B ; 4.HG2 > 1.142? ( %d!

S !dot! l ,odlo d "%ttr&ort' !s! "!9! !r! C'"(s') d s8%do ord:



36/41

Co,o /ist ic08it!s ( solo dos c%!cios s li8 %! rsistci! !r! R1 ( R2:R1 ; R2 ; 14 Bo', s r,l!! R1 ( R2 326 ( s ds9! C1

C1 ; G F

Co R1 R2 ( C1 s s%stit%( 316 ( s ds9! C2:

C2 ; 1#2 F

Co,o l !ctor B 3 B ; 4.GH16 s distito d %o s coct! l circ%ito d !t%!ci0 ! l!s!lid! dl iltro ( %d!:



37/41

#.2.2.- FILTRO PASA ALTA

E % iltro !s! !lt! c'"(s') l! rc%ci! d cort t!,"ié stá rl!cio!d! co l

i)l d !,lit%d !l i8%!l % or l ,étodo d "%ttr&ort' L! tr!sici0 d l!s@!l s !"r%t! crc! d l! rc%ci! d cort si ,"!r8o l! c!r!ctrQstic! s % s%rs%st! rc%ci! dl iltro s oscil!tori! 3rios6 los i)ls !lto ( "!9o.


A,á/3d"6 ; 24 lo814 3 6

ds9!do :

L! t!"l! d C'"(s') !r! l iltro !s! !lt! s l! ,is,! % !r! l iltro !s! "!9!. Por 9,lo !r! % iltro !s! "!9! d ord 2.


38/41

Dod S! s %ci0 d l! rc%ci! d cort &c ( d . P!r! l iltro !s! !lt! s



Ejemplo:

Dis@!r % iltro !s! !lt! C'"(s') d s8%do ord % c%,l! co %! rc%ci!d cort c ; 14 B ( A,á/ ; 4.? d".

Sol%ci0:

&c ; 2< c ; 2< 314B6 ; 24< / 14 # r!d>s

co A,á/3d"6 ; 4.?d" s c!lc%l! :

; 4.#H#

R,l!!do ; 4.#H# l! c%!ci0 d A ,á/

A ,á/ ; 4.H

S! ; 324< / 14#

> s6


39/41

d l! t!"l! d C'"(s') !s! "!9! A,á/6d"6 ; 4.?d" ; 2:

Vo 1----- ; ------------ Vi $23S!6

$23S!6 s r,l!! Vo > Vi ( s o"ti:

Co,!r!do st! %ci0 Vo>Vi co l! or,! c!0ic! d s8%do ord.

S ot! % B s distit! ( s !9%st! B % !ctor d !t%!ci0 B ; 4.HH?

S !dot! l ,odlo d "%ttr&ort' !s! !lt! !r! C'"(s') d s8%do ord:


Co,o /ist ic08it!s ( solo dos c%!cios s li8 %! c!!cit!ci! !r! C1 (C2: C1 ; C2 ; 1 F s r,l!! C1 ( C2 326 ( s ds9! R2

R2 ; ##.G# Bo',


40/41

Co C1 R2 ( C2 s s%stit%( 316 ( s ds9! R1:

R1 ; 11.# Bo',

Co,o l !ctor B 3 B ; 4.H?6 s distito d %o s coct! l circ%ito d !t%!ci0 ! l!

s!lid! dl iltro ( %d!:



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#.2.#.- FILTROS PASA $AKDA CE$SEV COK K PAR DE FILTROS PASA $A7A PASA ALTA.

Los iltros !s! "!9! ( !s! !lt! s %d dis@!r coct!do dos iltros c!sc!d!

%o !s! "!9! ( otro !s! !lt!. Lo ,ás i,ort!t s !9%st!r l!s rc%ci!s d cortco,o !rá,tro dl !c'o d "!d!.

E9,lo

El circ%ito %d!:

Diseño de Filtros Activos 2015

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