EE247 Lecture 5. Frequency tuning for continuous-time filters. EECS 247 Lecture 5: Filters 2004 H.K. Page 1. Summary Last Lecture

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1 Summry lst lecture EE247 ecture 5 ontinuoustime filters Fcts bout monolithic Rs & s nd its effect on integrted filter chrcteristics Opmp MOSFET filters Opmp MOSFETR filters Gm filters Frequency tuning for continuoustime filters Trimming Automtic frequency tuning ontinuous tuning Periodic tuning EES 247 ecture 5: Filters 2004 H.K. Pge Summry st ecture High Q high order filters Trnsmission zero implementtion Exmple rious integrtor topologies utilized in monolithic filters Resistor bsed filters Trnsconductnce (gm) bsed filters Switchedcpcitor filters Effect of integrtor nonidelities on filter behvior EES 247 ecture 5: Filters 2004 H.K. Pge 2

2 Summry st ecture Trnsmission zero Implementtion for Integrtor Bsed dder Filters in I 2 3 Rs 2 I 3 I 2 I I 5 R Use K & K to derive : I I 3 2 = s( ) 4 I3 I5 4 = s( ) oltge ontrolled oltge Source! EES 247 ecture 5: Filters 2004 H.K. Pge 3 Summry st ecture Integrtor Bsed dder Filters Trnsmission zeros in I 2 3 Rs 2 I 3 I 2 4 I 5 ( ) ( 3 ) 4 I Replce shunt cpcitor with voltge controlled voltge sources: I I3 2 = s( ) 4 I3 I5 4 = s 2 ( 3 ) 3 R EES 247 ecture 5: Filters 2004 H.K. Pge 4

3 in Summry st ecture Integrtor Bsed dder Filters Trnsmission zeros I I 5 Rs 2 I 3 ( ) ( 3 ) 4 I I R in 2 s Rs ( ) s2 s( ) 3 I I 2 I 3 I 4 o R EES 247 ecture 5: Filters 2004 H.K. Pge 5 in Summry st ecture Seventh Order Differentil owpss Filter Including Trnsmission Zeros Trnsmission zeros implemented with coupling cpcitors EES 247 ecture 5: Filters 2004 H.K. Pge 6

4 Summry st ecture Effect of Integrtor NonIdelities on Filter Performnce Idel Intg. Rel Intg. R in o = ωo = in sr s ωo H(s) = H(s) s s s ( s )( )( )... ωo p2 p3 EES 247 ecture 5: Filters 2004 H.K. Pge 7 Effect of Integrtor Finite D Gin on Q log H ( s) ω0 P = ω 0 ω o ω π ArctnP 2 ωo ψ 90 o P ωo Phse led@ ωo (in rdin) Exmple: P/ ω 0 =/=/00 EES 247 ecture 5: Filters 2004 H.K. Pge 8

5 Effect of Integrtor Finite D Gin on Overll Filter Frequency Response Phse ω 0 Droop in the pssbnd Mgnitude (db) Droop in the pssbnd jω splne σ Normlized Frequency Poles pushed wy from jω xis EES 247 ecture 5: Filters 2004 H.K. Pge 9 Effect of Integrtor NonDominnt Poles log H ( s) ω 0 P2P3 ω o π 2 ω Arctn ωo p i= 2 i ψ 90 o ωo p i= 2 i Phse ωo (in rdin) Exmple: ω 0 /P2 =/00 EES 247 ecture 5: Filters 2004 H.K. Pge 0

6 Effect of Integrtor NonDominnt Poles on Overll Filter Frequency Response Mgnitude (db) Peking in the pssbnd Phse ω 0 Peking in the pssbnd In extreme cses could result in oscilltion! jω splne Normlized Frequency σ Poles pushed loser to jω xis EES 247 ecture 5: Filters 2004 H.K. Pge Effect of Integrtor NonDominnt Poles & Finite D Gin on Q log H ( s ) ω0 P = ψ ω 0 P2P3 ω o ω π 2 Arctn P ωo ω Arctn o p 90 i = 2 i 90 o Note tht the two terms cn cncel ech other s effect EES 247 ecture 5: Filters 2004 H.K. Pge 2

7 Summry Effect of Integrtor NonIdelities on Q Q intg. idel = Q intg. rel ω o p i= 2 i Phse ω 0 Phse ω 0 Amplifier D gin reduces the overll Q in the sme mnner s series/prllel resistnce ssocited with pssive elements Amplifier poles locted bove integrtor unitygin frequency enhnce the Q! If nondominnt poles close to unitygin freq. Oscilltion Depending on the loction of unityginfrequency, the two terms cn cncel ech other out! EES 247 ecture 5: Filters 2004 H.K. Pge 3 Few Fcts About Monolithic Rs & s & Gms Monolithic continuoustime filter criticl frequency set by Rx or Gmx Absolute vlue of integrted Rs & s & Gms re quite vrible Rs vry due to doping nd etching nonuniformities ould vry by s much s ~30 to 40% due to process & temperture vritions s vry becuse of oxide thickness vritions nd etching inccurcies ould vry ~ 0 to5% Gms typiclly function of mobility, oxide thickness, current, device geometry ould vry > ~ 40% or more with process & temp. & supply voltge ontinuoustime filter criticl frequency could vry by over 50% EES 247 ecture 5: Filters 2004 H.K. Pge 4

8 Few Fcts About Monolithic Rs & s While bsolute vlue of monolithic Rs & s nd gms re quite vrible, with specil ttention pid to lyout, & R & gms quite wellmtched Rtios very ccurte nd stble over time nd temperture With specil ttention to lyout (e.g. interleving, use of dummy devices, commoncentroid geometries ): pcitor mtching <<0.% Resistor mtching <0.% Gm mtching <0.5% EES 247 ecture 5: Filters 2004 H.K. Pge 5 Impct of Process ritions on Filter hrcteristics in Rs 2 3 R R Filters Fcts bout R filters ω 3dB determined by bsolute vlue s & s Shpe of filter depends on rtios of normlized s & s R Norm Norm = r = R * ω 3dB Norm R * R Norm 2 2 = r 2 = ω 3dB EES 247 ecture 5: Filters 2004 H.K. Pge 6

9 Effect of Monolithic R & ritions on Filter hrcteristics Filter shpe (whether Elliptic with 0.dB Rpss or Butterworth..etc) is function of rtio of normlized s & s in R filters riticl frequency (e.g. ω 3dB ) function of bsolute vlue of s & s Absolute vlue of integrted Rs & s & Gms re quite vrible Rtios very ccurte nd stble over time nd temperture Wht is the effect of onchip component vritions on monolithic filter frequency chrcteristics? EES 247 ecture 5: Filters 2004 H.K. Pge 7 Impct of Process ritions on Filter hrcteristics in Rs 2 3 R * R Rs in sτ 2 sτ sτ 3 * R R R Filters Integrtor Bsed Filters R * Norm τ =.R = ω 3dB R Norm τ = = R * ω 3dB τ Norm = τ Norm 2 2 EES 247 ecture 5: Filters 2004 H.K. Pge 8

10 Impct of Process ritions on Filter hrcteristics in R3 R32 R2 R22 τ2 Norm Norm 2 = Rn Rn2 I3 Norm τ i n t g = I.R = ω intg intg In τ I2 I R R2 R3 o rition in bsolute vlue of integrted 3dB Rs & s cuses chnge in criticl freq. (ω3db ) Norm τ 2i n t g = I 2.R2 = 2 ω 3dB intg τ intg τ2 = I.R I 2.R2 = Since Rtios of Rs & s very ccurte Norm Norm 2 à ontinuous time monolithic filters fully retin their shpe EES 247 ecture 5: Filters 2004 H.K. Pge 9 Exmple: PF Worst se orner Frequency ritions Nominl Bndwidth Detiled pssbnd (note shpe is wellretined) Worst cse bndwidth vrition While bsolute vlue of onchip R (gm ) timeconstnts vry by s much s 00% (process & temp.) With proper precutions, excellent mtching cn be chieved: à Wellpreserved reltive mplitude & phse vs freq. chrctersitics à Need to djust (tune) continuous time filter criticl frequencies only EES 247 ecture 5: Filters 2004 H.K. Pge 20

11 Tunble OpmpR Filters Exmple: A st order OpmpR filter is designed to hve corner frequency of.6mhz Assuming process vritions of: vries by 0% R vries by 25% Build the filter in such wy tht the corner frequency cn be djusted postmnufcturing. R=0KΩ in R=0KΩ =0pF Nominl R & vlues for.6mhz corner frequency EES 247 ecture 5: Filters 2004 H.K. Pge 2 Tunble Resistor Mke provisions for either R or to be djustble (exmple djustble R) Monolithic Rs cn only be mde djustble in discrete steps (not continuous) Assuming expected process vritions of: Mximum vritions by 0% min=9pf, mx=pf Mximum R vritions by 25% Rmin=7.5K, Rmx=2.5K orner frequency vries by 35% Assuming n=3bit (0 or ) control signl for djustment Rmx=Rnom(35%)=3.5KOHM Rmin=Rnom(35%)=6.5KOHM R=Rmin R2 =(RmxRmin)4/7=4K (2 n /(2 n )) R3 =(RmxRmin)2/7=2K (2 n2 /(2 n )) R4 =(RmxRmin)/7=K (2 n3 / (2 n )) Tuning resolution 0% (K/0K) If finer resolution needed dd more bits & Rs D2 D D0 R R2 R3 R4 rible Resister MOS xtors ct s switches EES 247 ecture 5: Filters 2004 H.K. Pge 22

12 D2 D D0 Rtotl 6.5K 0 7.5K 0 8.5K K Post mnufcturing: Set ll Dx Mesure 3dB frequency If frequency too high decrement D to D If frequency too low increment D to D If frequency within 0% of the desired corner freq. stop Tunble OpmpR Filter in D0 R R2 R3 R4 For higher order filters, ll filter integrtors tuned simultneously D2 D R R2 R3 R4 EES 247 ecture 5: Filters 2004 H.K. Pge 23 Tunble OpmpR Filters Summry Tunble Opmp R Integrtor Progrm s nd/or Rs to freq. tune the filter All filter integrtors tuned simultneously Tuning in discrete steps & not continuous Tuning resolution limited Switch prsitic & series R cn ffect the freq. response of the filter EES 247 ecture 5: Filters 2004 H.K. Pge 24

13 Exmple: Tunble owpss OpmpR Filter Adjustble pcitors EES 247 ecture 5: Filters 2004 H.K. Pge 25 EES 247 ecture 5: Filters Disdvntges Opmps hve to drive resistive lod, low output impednce is required à High power consumption ontinuous tuning not possible Tuning requires progrmmble Rs nd/or s Advntges Since resistors re quite liner, linerity only function of opmp linerity à good linerity Opmp R Filters o 2004 H.K. Pge 26

14 Integrtor Implementtion OpmpR & OpmpMOSFET & OpmpMOSFETR in R tune in tune in R Opmp R Opmp MOSFET Opmp MOSFETR o ωo = where ωo = in s Req EES 247 ecture 5: Filters 2004 H.K. Pge 27 Use of MOSFETs s Resistors in R R replced by MOSFET ontinuously vrible resistor: tune in Opmp R Opmp MOSFET I D Triode region GS MOSFET I chrcteristic: Nonliner R DS EES 247 ecture 5: Filters 2004 H.K. Pge 28

15 Use of MOSFETs s Resistors SingleEnded Integrtor W 2 ID = µ ox ds ( gs th ) ds 2 W 2 i I = µ ox ( gs D th ) i 2 I D W G = = µ ox ( gs th i) i G in I D Tunble by vrying G: Problem: Single ended MOSFET Integrtor Effective R nonliner Note tht the nonlinerity is minly 2 nd order type EES 247 ecture 5: Filters 2004 H.K. Pge 29 Use of MOSFETs s Resistors Differentil Integrtor W I ds D = µ ox gs th 2 ds W i I i D= µ ox gs th 4 2 W i I i D2= µ ox gs th 4 2 W I D I D2 = µ ox ( gs th ) i ( ) ID ID2 W G = = µ ox gs th i ( ) i/2 i/2 I D I D2 M2 G M ut Nonliner term cncelled! Admittnce independent of i Opmp MOSFET Problem: Threshold voltge dependence EES 247 ecture 5: Filters 2004 H.K. Pge 30

16 MOSFET Integrtor For the OpmpR integrtor, opmp input stys t 0 (virtul gnd.) i/2 i/2 0 0 ut For the MOSFET integrtor, opmp input stys t the voltge x which is function of 2 nd order MOSFET nonlinerities i/2 i/2 G x x ut ommonmode voltge sensitivity EES 247 ecture 5: Filters 2004 H.K. Pge 3 Use of MOSFET s Resistor Issues MOS xtor operting in triode region ross section view Distributed chnnel resistnce & gte cpcitnce Distributed nture of gte cpcitnce & chnnel resistnce results in infinite no. of highfrequency poles excess phse Filter performnce mndtes wellmtched MOSFETs long chnnel devices Excess phse increses with 2 Trdeoff between mtching nd integrtor Q This type of filter limited to low frequencies EES 247 ecture 5: Filters 2004 H.K. Pge 32

17 Exmple: Opmp MOSFET Filter Suitble for low frequency pplictions Issues with linerity inerity chieved ~4050dB Needs tuning 5 th Order Elliptic MOSFET PF with 4kHz Bndwidth Ref: Y. Tsividis, M.Bnu, nd J. Khoury, ontinuoustime MOSFET Filters in SI, IEEE Journl of Solid Stte ircuits ol. S2, No. Feb. 986, pp. 530 EES 247 ecture 5: Filters 2004 H.K. Pge 33 Improved MOSFET Integrtor W I ds D = µ ox gs th ds 2 W i I i D= µ ox gs th 4 2 W i I i D3= µ ox gs2 th 4 2 IX = ID ID3 W i = µ i ox gs gs2 2 2 W i I i X2= µ ox gs2 gs 2 2 W I X I X2 = µ ox ( gs gs2 ) i G ox i ( ID ID2 ) = = µ W ( gs gs2 ) i/2 i/2 G No threshold dependence First order ommonmode nonlinerity cncelled inerity chieved in the order of 6070dB Ref: Z. zrnul, Modifiction of the BnuTsividis ontinuoustime Integrtor Structure, IEEE Trnsctions on ircuits nd Systems, ol. AS33, No. 7, pp. 7476, July 986. I D I D2 M2 M I D3 ID4 M4 G2 M3 I X I X2 ut EES 247 ecture 5: Filters 2004 H.K. Pge 34

18 RMOSFET Integrtor G G2 i/2 i/2 R R M2 M M4 M3 ut Improvement over MOSFET by dding resistor in series with MOSFET oltge drop primrily cross resistor smll MOSFET ds improved linerity inerity in the order of 90dB possible Generlly low frequency pplictions Ref: UK Moon, nd BS Song, Design of owdistortion 22kHz Fifth Order Bessel Filter, IEEE Journl of Solid Stte ircuits, ol. 28, No. 2, pp , Dec EES 247 ecture 5: Filters 2004 H.K. Pge 35 RMOSFET ossy Integrtor R2 i/2 i/2 R2 R G M2 M M4 G2 M3 ut Negtive feedbck round the nonliner MOSFETs improves linerity Reduced frequency response ccurcy Ref: UK Moon, nd BS Song, Design of owdistortion 22kHz Fifth Order Bessel Filter, IEEE Journl of Solid Stte ircuits, ol. 28, No. 2, pp , Dec R2 EES 247 ecture 5: Filters 2004 H.K. Pge 36

19 Exmple: Opmp MOSFETR Filter 5 th Order Bessel MOSFETR PF 22kHz bndwidth THD 90dB for 4pp 2kHz input signl Suitble for low frequency pplictions Significnt improvement in linerity compred to MOSFET Needs tuning Ref: UK Moon, nd BS Song, Design of owdistortion 22kHz Fifth Order Bessel Filter, IEEE Journl of Solid Stte ircuits, ol. 28, No. 2, pp , Dec EES 247 ecture 5: Filters 2004 H.K. Pge 37 Opertionl Amplifiers (Opmps) versus Opertionl Trnsconductnce Amplifiers (OTA) Opmp oltge controlled voltge source OTA oltge controlled current source ow output impednce Output in the form of voltge n drive Rlods Good for R filters, OK for S filters Extr buffer dds complexity, power dissiption High output impednce In the context of filter design clled gmcells Output in the form of current nnot drive Rlods Good for S & gm filters Typiclly, less complex compred to opmp higher freq. potentil Typiclly lower power EES 247 ecture 5: Filters 2004 H.K. Pge 38

20 Integrtor Implementtion Gm & OpmpGm in Gm in Gm Gm Intg. GmOTA Intg. o ωo Gm = where ωo = in s EES 247 ecture 5: Filters 2004 H.K. Pge 39 Gm Filters Simplest Form of MOS Gm Integrtor MOSFET in sturtion region: µ W 2 I ox d = ( gs th ) 2 Gm is given by: Id W gm= = µ ox gs th gs I = 2 d ( gs th ) /2 W 2 = µ ox I 2 d ( ) Id vried vi control gm tunble vi control EES 247 ecture 5: Filters 2004 H.K. Pge 40

21 Gm Filters Simplest Form of MOS Gm Integrtor behvior: o = in ωo s where g M,2 m ωo = 2 intg riticl frequency continuously tunble vi control Ref: H. Khorrmbdi nd P.R. Gry, High Frequency MOS continuoustime filters, IEEE Journl of SolidStte ircuits, ol.s9, No. 6, pp , Dec EES 247 ecture 5: Filters 2004 H.K. Pge 4 Second Order Gm Filter Simple design Tunble Q function of device rtios: g Q = g M,2 m M3,4 m EES 247 ecture 5: Filters 2004 H.K. Pge 42

22 Filter Frequency Tuning Techniques omponent trimming Automtic onchip filter tuning ontinuous tuning Msterslve tuning Periodic offline tuning Systems where filter is followed by AD & DSP, existing hrdwre cn be used to periodiclly updte filter freq. response EES 247 ecture 5: Filters 2004 H.K. Pge 43 Exmple: Tunble OpmpR Filter Post mnufcturing: Usully t wfersort tuning performed D2 D D0 Mesure 3dB frequency If frequency too high decrement D to D If frequency too low increment D to D If frequency within 0% of the desired corner freq. stop in R R2 R3 R4 R R2 R3 R4 Not prcticl to require enduser to tune the filter Need to fix the djustment t the fctory EES 247 ecture 5: Filters 2004 H.K. Pge 44

23 Trimming omponent trimming Build fuses onchip, Bsed on wfersort blow fuses by pplying high current to the fuse Expensive Fuse regrowth problems! Does not ccount for temp. vritions & ging ser trimming Trim components or cut fuses by lser Even more expensive Does not ccount for temp. vritions & ging Fuse To switch D Fuse not blown D= Fuse blown D=0 EES 247 ecture 5: Filters 2004 H.K. Pge 45 Exmple:Tunble/Trimmble OpmpR Filter D2 D D0 Rtotl 6.5K 0 7.5K 0 8.5K K D0 Fuse D Fuse D2 R R2 R3 R4 Fuse in R R2 R3 R4 EES 247 ecture 5: Filters 2004 H.K. Pge 46

24 Automtic Frequency Tuning By dding dditionl circuitry to the min filter circuit Hve the filter criticl frequency utomticlly tuned Expensive trimming voided Accounts for criticl frequency vritions due to temp. nd voltge chnges EES 247 ecture 5: Filters 2004 H.K. Pge 47 MsterSlve Automtic Frequency Tuning Following fcts used in this scheme: Use replic (mster) of the min filter (clled the slve) in the tuning circuitry Plce the replic in close proximity of the min filter Use the tuning signl generted to tune the replic, to lso tune the min filter In the literture, this scheme is clled msterslve tuning! EES 247 ecture 5: Filters 2004 H.K. Pge 48

25 MsterSlve Frequency Tuning Reference Filter (F) Use biqud for mster filter (F) Utilize the fct the frequency fo the lowpss (or highpss) outputs re 90 degree out of phse wrt to input P o ω = ω 2 o φ= 90 in s s 2 ωo Qωo ωo Q s BP ωo s Apply sinusoid t the desired fo ompre the P output phse to the input Bsed on the phse difference Increse or decrese filter criticl freq. HP in P EES 247 ecture 5: Filters 2004 H.K. Pge 49 MsterSlve Frequency Tuning Reference Filter (F) rms rms tune K ref P cosφ fo Q ωo Q s ωo s Tune Amp. Filter tune P Phse omprtor f o Input Signl Frequency ref EES 247 ecture 5: Filters 2004 H.K. Pge 50

26 MsterSlve Frequency Tuning Reference Filter (F) By closing the loop, feedbck tends to drive the error voltge to zero. ocks fo, the criticl frequency of the filter to the ccurte reference frequency Typiclly the reference frequency is provided by crystl oscilltor with ccurcies in the order of few ppm ωo Q s ref ωo s P Tune Amp. Filter Phse omprtor EES 247 ecture 5: Filters 2004 H.K. Pge 5 MsterSlve Frequency Tuning Reference Filter (F) Q sτ 0 Replic Filter (Mster) sτ0 P Amp. Filter in * R Rs sτ Phse omprtor tune 2 Min Filter (Slve) sτ sτ 3 sτ 4 sτ 5 * R R ref Ref: H. Khorrmbdi nd P.R. Gry, High Frequency MOS continuoustime filters, IEEE Journl of SolidStte ircuits, ol.s9, No. 6, pp , Dec EES 247 ecture 5: Filters 2004 H.K. Pge 52

27 MsterSlve Frequency Tuning Reference Filter (F) Issues to be wre of: Input reference tuning signl needs to be sinusoid à disdvntge since clocks re usully vilble s squre wveform Reference signl feedthrough to the output of the filter cn limit filter dynmic rnge (reported levels or bout 00urms) Ref. signl feedthrough is function of: Reference signl frequency wrt filter pssbnd Filter topology re in the lyout Fully differentil topologies beneficil EES 247 ecture 5: Filters 2004 H.K. Pge 53 MsterSlve Frequency Tuning Reference oltgeontrolledoscilltor (O) Insted of F voltgecontrolledoscilltor (O) is used O mde or replic integrtor used in min filter Tuning circuit opertes exctly s conventionl phselocked loop (P) Tuning signl used to tune min filter Ref: K.S. Tn nd P.R. Gry, Fully integrted nlog filters using bipolr FET technology, IEEE, J. SolidStte ircuits, vol. S3, no.6, pp. 8482, December EES 247 ecture 5: Filters 2004 H.K. Pge 54

28 MsterSlve Frequency Tuning Reference oltgeontrolledoscilltor (O) Issues to be wre of: Design of stble & repetble oscilltor chllenging O opertion should be limited to the liner region or else the opertion loses ccurcy imiting the O signl rnge to the liner region not trivil design issue In the cse of F bsed tuning ckt there ws only ref. signl feedthrough. In this cse, there is lso the feedthrough of the O signl!! Advntge over F bsed tuning Reference input signl squre wve (not sin.) EES 247 ecture 5: Filters 2004 H.K. Pge 55 MsterSlve Frequency Tuning hoice of Ref. Frequency wrt Feedthrough Immunity Ref:. Gopinthn, et. l, Design onsidertions for HighFrequency ontinuoustime Filters nd Implementtion of n Antilising Filter for Digitl ideo, IEEE JSS, ol. S25, no. 6 pp , Dec EES 247 ecture 5: Filters 2004 H.K. Pge 56