2 nd Order Transfer Functions

Transcription

1 nd Order Trnfer Function Imgry xi zeroe Tow-Thom Biqud Exmple EECS 47 Lecture 3: Second Order Trnfer Function B. Boer Imgry Axi Zero Shrpen trnition nd notch out terference High-p filter (HF) Bnd-reject filter H( jω) ( ) ωz H K ωq ω ω ω K ω Z Note: Alwy repreent trnfer function product of g term, pole, nd zero (pir if complex). Then ll coefficient hve phyicl meng, reonle mgnitude, nd eily checle unit. EECS 47 Lecture 3: Second Order Trnfer Function B. Boer

2 Imgry Axi Zero No fite zero With fite zero Mgnitude epone (-plne) Mgnitude epone (-plne).5 Mgnitude [ler].5.5 Mgnitude [ler] x x 5 x Frequency [Hz] Sigm [Hz] x Frequency [Hz] Sigm [Hz] EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 3 Imgry Zero f Q f Z Hz 3 f Zero utntilly hrpen trnition nd At the expene of reduced topnd ttenution t high frequency x 6 ole-zero Mp With zero No zero Mgnitude [db] - Img Axi Frequency [Hz] el Axi x 6 EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 4

3 Movg the Zero f Q Hz f Z f x 5 ole-zero Mp 6 4 Mgnitude [db] - - Img Axi Frequency [Hz] el Axi x 5 EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 5 Tow-Thom Biqud ritic enitive Multiple output ef:. E. Fleicher nd J. Tow, Deign Formul for iqud ctive filter ug three opertionl mplifier, roc. IEEE, vol. 6, pp. 66-3, My 973. EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 6

4 EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 7 Frequency epone ( ) ( ) ( ) ( ) 3 o o o o implement generl iqud ection with ritrry pole nd zero o nd o3 relize the me pole ut re limited to t mot one fite zero EECS 47 Lecture 3: Second Order Trnfer Function B. Boer Component lue C C C C C C C C C C C C C nd,,,, given C C i i i tht it follow 7 3 C Q C C ω ω

5 Filter Deign Exmple Appliction: tetg of ultr-ler ADC rolem: uoidl ource h higher ditortion thn the ADC! Solution Filter ource with ndp efore convertg Chec reultg ource with pectrl nlyzer Twit: the nlyzer i not ufficiently ler either notch out uoid nd loo jut t hrmonic Implementtion Bndp & Notch t Hz Ue o for ndp (only poiility), o for notch EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 9 Filter Deign Exmple Hz Genertor Hz BF Hz Notch pectrum nlyzer Our filter ADC under tet rciple: IC tet circuit re uele if you cn t verify their performnce! EECS 47 Lecture 3: Second Order Trnfer Function B. Boer

6 o o o3 Filter Coefficient ( ) ( ) ( ) ( ) Deign Notch : Get Bndp for "free": Chooe reonle ignl level : ω π.5 ( Hz) (jut we wnt ndp) (to eep unued o3 elow other output) lightly EECS 47 Lecture 3: Second Order Trnfer Function B. Boer Fl Filter o o o3.5 Chooe: CCnF (lrge to mimize noie) Ω f Hz, Q 3 (chec enitivity!) Solve eqution 4.63Ω.49Ω Ω 44.63Ω 5.49Ω 67 Let order the prt EECS 47 Lecture 3: Second Order Trnfer Function B. Boer

7 Cpcitor CG cpcitor ihy itrmon, CG Dielectric Cpcitor dtheet,. Negligile voltge coefficient (for lerity) Excellent tempco (3ppm/ C) % itil ccurcy i ey to get No high-vlue cpcitor re trimmle eitor will e trimmed to compente for cpcitor vrition EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 3 eitor Trimmed reitor come fixed metl film reitor nd preciion trim potentiometer erie %-ccurte, 5ppm/ C, l grde metl film reitor provide 9% of the noml reitnce ef: Cddoc Electronic, Type TN L Grde Low TC reciion Film eitor dtheet, ppm/ C trim pot provide etween % nd % of the noml reitnce ef: ihy Foil eitor, Model 6 reciion Trimmg otentiometer dtheet Ue two fixed reitor erie with the trimpot to mimize trimpot vlue nd optimize overll tempco 6- re.%-ccurte, 5ppm/ C metl film EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 4

8 Opmp For opmp, we ll ue the Burr-Brown OA67 ef: Tex Intrument / Burr-Brown, OA67 nd OA64 dtheet, 99. The fet udio opmp the world, nd, t $5/ech, priced ccordgly! But money i no oject when deigng IC tet fixture (only few re ever uilt) Adequte peed for thi ppliction EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 5 Bndp/Bndtop epone EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 6

9 Filter Deign Exmple (cont.) Note tht the ndp output H provide >3dB ttenution to ll hrmonic preent the Hz genertor output Opmp output hve.±.5db pe g Thi mximize ech opmp output wg for et dynmic rnge Let mgnify the frequency xi for the two repone of teret EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 7 Bndp/Bndtop epone EECS 47 Lecture 3: Second Order Trnfer Function B. Boer

10 Filter Deign Exmple Temperture chnge won t chnge thee repone too much L temperture re tle to 5±3 C Our l-grde C product move <ppm/ C Initil component vlue re nother tory Wht if C4nF nd C3nF? Tht with their ±% ccurcy pecifiction S ω C Wht? EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 9 Bndp/Bndtop epone H G (db) H C.4mF C.3mF noml Frequency (Hz) EECS 47 Lecture 3: Second Order Trnfer Function B. Boer

11 Filter Deign Exmple Oviouly, we ve got to tune the filter c to it origl pecifiction How i tht tung done? Do you tell your technic to twiddle pot rndomly until it wor? Or do you document rout tung procedure? EECS 47 Lecture 3: Second Order Trnfer Function B. Boer C Filter Tung Strtegy Fmou iqud lie the Tow-Thom come complete with their own tung trtegie The circuit topologie llow trim opertion to djut deign prmeter (uch f, f Z, Q, Q Z, g) without chngg the other tionle for iqud tung trtegy ecome pprent when tudyg deign eqution uch the Tow-Thom eqution on lide 6 EECS 47 Lecture 3: Second Order Trnfer Function B. Boer

12 Tow-Thom Tung Strtegy 3 will e et to fixed vlue to eep the unued OAM3 output elow db Tung volve the followg tep performed the pecified equence: Adjut to center the ndp t Hz Adjut 5 to center the notch t Hz Adjut to et the ndp Q to 3 Adjut 4 to deepen the notch EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 3 Tow-Thom Tung Strtegy The deign eqution lo provide the rnge of djutment required for given reitor ememer tht n exceively lrge djutment rnge trnlte to exceively lrge tempco tung rnge (from lide 7): < < C C MAX C MIN nown et y cpcitor tolernce EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 4

13 Tow-Thom Tung Strtegy An even impler wy to determe reitor rnge i to: Set ll cpcitor to their high tolernce limit (noml% thi ce) Clculte for thee cpcitnce (thee will e the mimum reitnce vlue) Set cpcitor to their low tolernce limit Clculte mximum EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 5 Tow-Thom Biqud C (.m) 3 (.35K) (4K5K) (K) C (.m) 7 (K) (.4K) OAM OAM OAM3 4 (4K5K) 6 (K) 5 (.4K) v IN reitor: metl film trimpot EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 6

14 Tow-Thom Tung Strtegy If you ve left your filter unttended for while, ume tht it trim potentiometer re completely midjuted Adjut ll trimpot to Ω nd trt over Let return to our C4nF, C3nF exmple EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 7 Bndp/Bndtop epone H G (db) H C4nF C3nF noml Frequency (Hz) EECS 47 Lecture 3: Second Order Trnfer Function B. Boer

15 Bndp/Bndtop epone H G (db) H C4nF C3nF trimpotw Frequency (Hz) EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 9 Tow-Thom Tung Strtegy For mot nd C thi iqud Hence, f S x f ~ Thi men % chnge will cue % chnge f Note tht f Z enitivitie re lo / A 4% cree 5 will hift our notch (currently t.hz) c to the right plce x EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 3

16 Bndp/Bndtop epone G (db) H H C4nF C3nF 4W 456W 335W 44W 5456W 67W Frequency (Hz) EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 3 Summry Generl nd order trnfer function Imgry xi zero Generl purpoe iqud Lrge election literture Tow-Thom iqud: 3 opmp ritic enitive Multiple output Tung trtegy EECS 47 Lecture 3: Second Order Trnfer Function B. Boer 3