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Electrónica IIIClase 08

I Término 2013



Agenda:

Lección #1

Filtros de 2do Orden

Filtros Sallen-Key Filtro Pasa Baas

Filtro Pasa !ltas



Lección

1" mins



Filtros de 2do Orden

T$ere are t%o to&olo'ies (or a second-order (ilter)

t$e Sallen-Key and t$e *+lti&le Feed,ac .*FB/

to&olo'y



Low-Pass Filter

( )

( ) 222

2

0

1 ω α ω

ω

+−

= A

G

2

00

0

1

)(

+

+

=

ω ω α

s s

A sG

0

0

:

:

:

:

A Band pass gain

Critical frequency

Damping coefficient

Normalizad frequency

ω

α

ω

( )21tan

ω

αω φ

−−= Arc



Daming (Amortig!amiento)



E""ects o" t#e Daming $oe""icient



E""ects o" t#e Daming $oe""icient

!o may ,e di((erent

F-3d, does not e+al ( o

Transient res&onse aries %idely

( o is constant



%!tterwort# Low-Pass Filters

T$e B+tter%ort$ lo%-&ass (ilter &roides maim+m&ass,and (latness T$ere(ore) a B+tter%ort$ lo%-&assis o(ten +sed as anti-aliasin' (ilter in data conertera&&lications %$ere &recise si'nal leels are re+ired

across t$e entire &ass,and



$#e&'s#e Low-Pass Filters

T$e $e,ys$e lo%-&ass (ilters &roide an een

$i'$er 'ain rollo(( a,oe ( 0 4o%eer) t$e &ass,and

'ain is not monotone) ,+t contains ri&&les o( constant

ma'nit+de instead For a 'ien (ilter order) t$e $i'$er

t$e &ass,and ri&&les) t$e $i'$er t$e (ilter5s rollo((



$#e&'s#e Low-Pass Filters

(cont) 6it$ increasin' (ilter order) t$e in(l+ence o( t$e ri&&le

ma'nit+de on t$e (ilter rollo(( diminis$es 7ac$ ri&&le

acco+nts (or one second-order (ilter sta'e Filters

%it$ een order n+m,ers 'enerate ri&&les a,oe t$e

0-dB line) %$ile (ilters %it$ odd order n+m,ers createri&&les ,elo% 0 dB $e,ys$e (ilters are o(ten +sed

in (ilter ,ans) %$ere t$e (re+ency content o( a

si'nal is o( more im&ortance t$an a constant

am&li(ication



%essel Low-Pass Filters

T$e Bessel lo%-&ass (ilters $ae a linear &$ase res&onseoer a %ide (re+ency ran'e) %$ic$ res+lts in a constant'ro+& delay in t$at (re+ency ran'e Bessel lo%-&ass (ilters)t$ere(ore) &roide an o&tim+m s+are-%ae transmission,e$aior 4o%eer) t$e &ass,and 'ain o( a Bessel lo%-&ass

(ilter is not (lat and t$e transition (rom &ass,and to sto&,andis not s$ar&



$omarison



*eneral +allen-,e' Low-Pass

Filter

( ) ( )[ ] 2

2121210211

0

11)(

sC C R R sC R A R RC

A sG

+−+++

=

.1 R R Ao +=



/nit'-*ain +allen-,e' Low-Pass

Filter To sim&li(y t$e circ+it desi'n) it is common to c$oose

+nity-'ain .!0 8 1/) and 91 8 92 8 9

212

1

C C R f o

π =

2

21

2

121

1)(

sC C R s RC sG

++=

2

12C

C =α

1=o A



/nit'-*ain



/nit'-*ain



Eamle - "rom et&oo3

:esi'n a (ilter +sin' t$e Sallen-Key +nity 'ain

lo% &ass actie (ilter to meet t$e (ollo%in'

s&eci(ications;

9ollo(( rate; <0 dB=dec ritical (re+ency; 2 4>

Pass ,and as (lat as &ossi,le

?ain o( " at :



E4!al-$omonent +allen-,e'

Low-Pass Filter

! s&ecial case o( t$e 'eneral Sallen-Key

to&olo'y is t$e a&&lication o( e+al resistor

al+es and e+al ca&acitor al+es; 91 8 92 8

9 and 1 8 2 8

( ) 2220

0

-1)(

sC R s A RC

A sG

+−+

= RC

f oπ 2

1=

o A−= -α



E4!al $omonent



E4!al $omonent



Eamle -5 "rom et&oo3

:esi'n a (ilter +sin' t$e Sallen-Key e+al

com&onent lo% &ass actie (ilter to meet t$e

(ollo%in' s&eci(ications;

9ollo(( rate; <0 dB=dec ritical (re+ency; 2 4>

Pass ,and as (lat as &ossi,le

?ain o( " at :



Fre4!enc' $orrection Factor

0- f k f lpdB =−



E6ercicio:

T$e tas is to desi'n a second order e+al

com&onent $e,ys$e lo% &ass actie (ilter

%it$ a (re+ency ( -3dB 8 3 4> and a 3dB

&ass,and ri&&le



7ig#-Pass Filter



7ig#-Pass Filter (cont)

2

0 0

( )

1

AG s

s s

ω ω α

∞= + + ÷ ÷

( )

( )

2

22 2 2

1

AG

ω ω

ω α ω

∞=

− +

( )21tan

ω

αω φ

−−= Arc

0

:

:

:

:

A Band pass gain

Critical frequency

Damping coefficient

Normalizad frequency

ω

α

ω

∞



#e general +allen-,e' toolog'

( ) ( )2 1 2 1 2

2

1 2 1 2 1 2 1 2

( )1 1 1 1

1

AG s

R C C R C A

R R C C s R R C C s

∞

∞

=+ + −

+ × + ×

.

1 R

R

Ao +=



/nit'-*ain +allen-,e' 7ig#-Pass

Filter

( )2

21

2

21

21 1111

1)(

sC C R sC RC

C C sG

⋅+⋅+

+=

1 A∞ =

2121

C C R f o

π =

1

2

2

1

C

C

C

C +=α



E4!al-$omonent +allen-,e'

7ig#-Pass Filter

C C C

R R R

====

21

21

Aα ∞= −2 2 2

( ) 1 1 1

1

AG s

A

RC s R C s

∞

∞

=−

+ × + ×

RC f o

π 2

1=



Fre4!enc' $orrection Factor

0- f k f hpdB =−

lp

hpk

k 1

=



Eamle -8 "rom et&oo3

For an e+al com&onent $i'$ &ass actie(ilter %$ose com&onents are listed ,elo%)calc+late t$e -3dB (re+ency) (ilter ty&e and&ass ,and 'ain 9 8 10@ 8 01AF 9< 8 "@

93 8 10@

?ain-Band%it$ &rod+ct (or a C<1 is 1*4>

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