Special Notes: Filter Design Methods

Transcription

1 Page Special Note: Filter Deig Method Spectral Poer epoe For j j j exp What i j Magitude (ut be the ae!): N M Q i i p z K j Phae: N M Q i i a p a z a j ta ta ta N M Q i i a p a z a j ta ta ta herefore j j ad j j he, hat i j j j j j j exp exp or j j j hi i a poer ter (otice the quare), o e ue *log to create decibel. It i the ae reult!! Note, thi ork for (,-) too!! hi i the geeric for for defiig the agitude repoe of a filter! Why he pole ad zero are yetric about the j axi of the -plae! herefore, the HP ad HP eleet ca be eparated ito () ad () ad guaratee argial tability!!

2 Page he Butterorth opa Filter j j j j haracteritic Eq. Frequecy oralized eferece: M.E. a alkeburg, Aalog Filter Deig, Oxford Uiv. Pre, 98 ISBN:

3 Page Solvig for the Butterorth Filter pole: Filter i j j j aplace j j haracteritic Eq. Noralize For odd: oot at j exp j exp et be the HP pole ad be the HP pole For eve: j j oot at j j exp j j exp et be the HP pole ad be the HP pole

4 Matlab ode (BW_Filter_Exaple.) % BW Filter geeratio deotratio % cloe all clear all i=; load=; atch=; PBfreq=; PiW=logpace(log(PBfreq)-,log(PBfreq)+,); coloreq=['b' 'g' 'r' 'y' '' 'c']; ii=; Poleage=6:-: for BW=Poleage ii=od(ii,6)+; dep=root([((-/(pbfreq^))^(bw)) zero(,*bw-) ]) [Y,I] = ort(real(dep)); deport=dep(i) de=poly(deport(:bw)); figure() plot(real(dep),iag(dep),pritf('%cx',coloreq(ii)) ); title('poer Magitude Pole') grid o; hold o; u = [PBfreq^(BW)]; zpi=ab(root(u)); ppi=ab(root(de)); BWy=tf(u,de) [PiMAG, PiPHASE]=bode(BWy,PiW); figure() eilogx(piw, dbv(queeze(pimag)),coloreq(ii) ); grid o; hold o; title('poer v. Frequecy') xlabel('freq (rad/ec)'); ylabel('magitude db'); plotv=axi; axi([plotv() plotv() - ]) figure() eilogx(piw, (queeze(piphase)),coloreq(ii) ); grid o; hold o; title('phae v. Frequecy') xlabel('freq (rad/ec)'); ylabel('phae'); axi([plotv() plotv() -ax(poleage)*9 5]) paue ed Page

5 eult Poer Magitude Pole Poer v. Frequecy - Magitude db Freq (rad/ec) Phae v. Frequecy Phae Freq (rad/ec) Page 5

6 What if e at to chage the frequecy j Jut chage the atural frequecy, f ; the ceter frequecy i iply caled! he circle radiu of the pole defie the cut-off frequecy. Deig approach:. Deterie the order of the filter you at. What atteuatio do you eed at the poit? (here are plety of curve, like thoe above, if the value you eed coe before t x the cutoff frequecy.). Geerate the Butterorth oefficiet o the uit circle for =. Scale the pole by the deired frequecy (reeber that = i i radia/ec, therefore ultiply by f. Page 6

7 Active Audio Frequecy Filter A active lopa filter ipleetatio of a t order Butterorth filter i - + OP- Ap he trafer fuctio for thi circuit i i MaxGai G o tue the circuit. Page 7

8 A alterate approach: +dc + OP- Ap - -dc a b i a b b MaxGai G a b b o tue the circuit. Page 8

9 Page 9 A Secod Order Butterorth opa Filter et do the ath for the ecod order yte, for = ad. j ad For A ecod order uderdaped yte ith or 77., j After frequecy calig, j Ho to ake a ecod order PF for audio.

10 Page Salle-Key ircuit opa Filter A active lopa filter ipleetatio of a uity gai Fried ircuit, alo referred to a a Salle-Key circuit a decribed i: Walter G. Jug, I OP-Ap ookbook, Hoard W. Sa o. Ic, Idiaapoli, IN, dc -dc OP- Ap he trafer fuctio for thi circuit i (a geeric ecod order filter equatio i alo ho) K ettig ad ad K K MaxGai K

11 Page Fuctio Derivatio he circuit derivatio aue a perfect op-ap, ith ifiite gai, ifiite iput ipedace, ad zero output ipedace, o-liitig poer upplie ad voltage drop, ad o frequecy repoe coideratio. he circuit derivatio follo: o p p o ettig p o o o o o o o o o

12 Page o o ettig ad ad G G G o eultig i G MaxGai Ad G Note that for a table yte G Iplyig that

13 Page Multiple Feedback (MFB) ircuit opa Filter A active lopa filter ipleetatio of a ultiple feedback circuit (MFB), that i ay alo be referred to a a derivative of the Salle-Key Filter dc -dc OP- Ap Figure. MFB opa Filter he trafer fuctio for thi circuit i o o eultig i K MaxGai ettig,,,, ad G K o K MaxGai

14 Page Fuctio Derivatio he circuit derivatio aue a perfect op-ap, ith ifiite gai, ifiite iput ipedace, ad zero output ipedace, o-liitig poer upplie ad voltage drop, ad o frequecy repoe coideratio. he circuit derivatio follo: o o obiig o o o o o o o eultig i G MaxGai Ad

15 Higher Order Butterorth opa Filter ake ultiple tage ad cacade the! eeber to deterie the pole locatio that each tage of the filter require. A a rule-of-thub, you hould elect the order for the tage of your filter. If you look at the output of each tage, it ill be the product of the trafer fuctio to that locatio! So, poible ue thoe ith dapig factor cloet to oe before the aller oe. Ji Karki, exa Itruet, Active o-pa Filter Deig, Applicatio eport, SOA9B, Septeber. Note:. eal eleet ay ot exactly atch the value you elect.. opoet have a tolerace, they are ithi +/- oe %!. If poible ue cheaper copoet ad oe (or to) that are adjutable (potetioeter). What do F deiger do? Why ight it be differet? Page 5

16 o Pa Filter, rd Order he claic rd order adder o Pa Filter. i Figure. adder rd Order o Pa Filter he circuit derivatio aue a ource ad load reitace. he ource reitace i placed prior to the iput voltage ad the load i placed o the output. For ad : i Page 6

17 Page 7 heoretical Derivatio he circuit derivatio aue a ource ad load reitace. he ource reitace i placed prior to the iput voltage ad the load i placed o the output. he circuit ode equatio follo: i Solvig for ad ubtitutig: i i i i i i i

18 Page 8 i For : i or i For : i i For ad : i

19 heoretical Derivatio Pi-Filter i Figure. adder rd Order o Pa Filter he circuit derivatio aue a ource ad load reitace. he ource reitace i placed prior to the iput voltage ad the load i placed o the output. For ad : i Page 9

20 Page heoretical Derivatio Pi-Filter he circuit derivatio aue a ource ad load reitace. he ource reitace i placed prior to the iput voltage ad the load i placed o the output. he circuit ode equatio follo: i Solvig for ad ubtitutig: i i i i i

21 Page i For : i For : i For ad : i i

22 .5 MHz o Pa Filter, 7 th Order, oilcraft P7P55 he 7th order elliptical adder o Pa Filter. Maufacturer frequecy repoe Figure. oilcraft adder o Pa Filter oilcraft adder o Pa Filter Page

23 et Aalyi A tet circuit a built ad teted uig the etork aalyzer. i aued to be 5 oh, ad ere variable iductor i the rage of.578 to.95 uh ad a parallel pf (K) capacitor or pf. Netork Aalyzer Meaureet Page

24 eferece [] Walter G. Jug, I OP-Ap ookbook, Hoard W. Sa o. Ic, Idiaapoli, IN, 97. [] M.E. a alkeburg, Aalog Filter Deig, Oxford, 98. ISBN: [] [] I Applicatio Note: Slod6b Sloa9 I Applicatio Note o Filterig Active Filter Deig echique SOA88 Aalyi of the Salle-Key Architecture (ev. B) SOA FilterPro MFB ad Salle-Key o-pa Filter Deig Progra SBFAA Active o-pa Filter Deig (ev. A) SOA9 Uig the exa Itruet Filter Deig Databae SOA6 Filter Deig i hirty Secod SOA9 Filter Deig o a Budget SOA65 More Filter Deig o a Budget SOA96 Page