EE247 Lecture 8. Lowpass to Bandpass Transformation Table

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1 EE47 ecture 8 ontinuoutime filter Bandpa filter Example: Gm BP filter uing imple diff. pair inearity & noie iue Variou Gm Filter implementation omparion of continuoutime filter topologie Switchedcapacitor filter owpa to Bandpa Tranformation Table owpa filter tructure & table ued to derive bandpa filter filter From: Zverev, Handbook of filter ynthei, Wiley, 967 p.57. P BP BP Value & are normilzed P value Rrωr Rr ωr Rr ωr Rrωr EES 47 ecture 8: Filter 005 H.K. Page EES 47 ecture 8: Filter 005 H.K. Page 3 Bandpa Filter owpa to Bandpa Tranformation Bandpa Filter: < 5 ombination of lowpa & highpa owpa H( jω) > 5 Direct implementation ω Highpa H( jω) ω H( jω) H( jω) >5 ω <5 ω R R R R 3 3 R R 3 3 Where: R 3 3 V o R,, 3, normalized lowpa value bandpa filter quality factor & ω 0 filter center frequency EES 47 ecture 8: Filter 005 H.K. Page EES 47 ecture 8: Filter 005 H.K. Page 4

Signal Flowgraph 6 th Order Bandpa Filter V o Signal Flowgraph 6 th Order Bandpa Filter R 3 3 R * * R R * R R * R * * R R 3 * 3R * R R ω 0 ω 0 3 3 Note each & in the original lowpa prototype replaced

2 Signal Flowgraph 6 th Order Bandpa Filter V o Signal Flowgraph 6 th Order Bandpa Filter R 3 3 R * * R R * R R * R * * R R 3 * 3R * R R ω 0 ω Note each & in the original lowpa prototype replaced by a reonator Subtituting the bandpa,,.. by their normalized lowpa equivalent previou page The reulting SFG i: Note: Three reonator All integrator timecontant are equal et u try to build thi bandpa filter uing the imple Gm tructure EES 47 ecture 8: Filter 005 H.K. Page 5 EES 47 ecture 8: Filter 005 H.K. Page 7 Signal Flowgraph 6 th Order Bandpa Filter Second Order Gm Filter Uing Simple Sourceouple Pair Gmell * R R ω 0 3 ω 0 ω 0 3 * R R Note the integrator have different time contant Ratio of time contant for each reonator ~/ typically, require high component ratio poor matching Deirable to convert SFG o that all integrator have equal time contant for optimum matching. Scale node to obtain equal integrator time contant enter frequency: M, gm ω o intg function of: M, g m g M3,4 m To ue thi tructure it i more power efficient to couple reonator through capacitive coupling EES 47 ecture 8: Filter 005 H.K. Page 6 EES 47 ecture 8: Filter 005 H.K. Page 8

3 Signal Flowgraph 6 th Order Bandpa Filter Sixth Order Bandpa Filter Signal Flowgraph 3 γ γ ω Modified ignal flowgraph to have equal coupling between reonator In mot filter cae 3 Example: For a butterworth lowpa filter 3 & Aume deired overall bandpa filter 0 γ oupling path (γ) between reonator can be implemented with extra differential input pair additional power diipation Or modify SFG a hown in next page: γ EES 47 ecture 8: Filter 005 H.K. Page 9 EES 47 ecture 8: Filter 005 H.K. Page Sixth Order Bandpa Filter Signal Flowgraph Sixth Order Bandpa Filter Signal Flowgraph SFG Modification γ γ γ γ γ γ γ Where for a Butterworth hape Since 0 then: γ γ 4 γ EES 47 ecture 8: Filter 005 H.K. Page 0 EES 47 ecture 8: Filter 005 H.K. Page

4 Sixth Order Bandpa Filter Signal Flowgraph SFG Modification For narrow band filter (high ) where frequencie within the paband are cloe to ω 0 narrowband approximation can be ued: The reulting SFG: ω ω γ γ γ Sixth Order Gm Bandpa Filter Utilizing Simple Sourceoupled Pair Gmell k γ intg γ /4 k 7 intg Paraitic at integrator output, if unaccounted for, will reult in inaccuracy in g EES 47 ecture 8: Filter 005 H.K. Page 3 EES 47 ecture 8: Filter 005 H.K. Page 5 Sixth Order Bandpa Filter Signal Flowgraph SFG Modification Sixth Order Gm Bandpa Filter Frequency Repone Simulation γ γ γ γ Bidirectional coupling path, can eaily be implemented with coupling capacitor no extra power diipation EES 47 ecture 8: Filter 005 H.K. Page 4 EES 47 ecture 8: Filter 005 H.K. Page 6

5 Simplet Form of MOS Gmell Nonidealitie MOS Gmell HighFrequency Pole D gain (integrator ) M, g a m M, g 0 g load a θ ( Vg Vth ) M, Small Signal Differential Mode Halfircuit effective P i Pi effective M, P.5ω t High frequency behavior of an MOS tranitor Where a denote D gain & θ i related to channel length modulation by: θ λ Seem no extra pole! ω ( Vg Vth ) M, µ M, gm 3 t W ox M, Ditributed nature of gate capacitance & channel reitance reult in an effective pole at.5 time input device cutoff frequency EES 47 ecture 8: Filter 005 H.K. Page 7 EES 47 ecture 8: Filter 005 H.K. Page 9 MOS Gmell HighFrequency Pole MOS Gmell uality Factor ro ection view of a MOS tranitor operating in aturation a θ ( Vg Vth ) M, ( Vg Vth ) M, µ effective 5 P 4 Ditributed channel reitance & gate capacitance Ditributed nature of gate capacitance & channel reitance reult in infinite no. of highfrequency pole intg. real ω a o p i i ( V V ) θ g th M, 4 ωo intg. 5µ ( VgV real th) M, Note that the phae lead aociated with D gain i inverely prop. to The phae lag due to highfreq. pole directly prop. to For a given ω ο there exit an optimum which cancel the lead/lag phae error reulting in high integrator EES 47 ecture 8: Filter 005 H.K. Page 8 EES 47 ecture 8: Filter 005 H.K. Page 0

6 MOS Gm ell hannel ength for Optimum Integrator uality Factor Meaure of inearity. 5 θµ opt. 4 ( VgVth) ωo /3 M, Vout α α α amplitude3 rdharmonicdit. comp. HD3 amplitude fundamental α 4 α 3... Vout w w w 3w w Optimum channel length computed baed on proce parameter (could vary from proce to proce) amplitude3 rdorderim comp. IM 3 amplitudefundamental 3α 5 α 4α 8 α Vout w w w w w w w w w w EES 47 ecture 8: Filter 005 H.K. Page EES 47 ecture 8: Filter 005 H.K. Page 3 Sourceoupled Pair MOS Gmell inearity Ideal G m g m arge ignal G m drop a input voltage increae Give rie to filter nonlinearity Sourceoupled Pair MOS Gmell inearity / vi v i Id I ( V () g V th) 4 ( V V ) M, g th M, 3 Id a vi a vi a3 v i... Serie expanion ued in () I a & a 0 ( V g V th) M, I a 3 & a V ( g V th) M, I a 5 & a V ( g V th) M, EES 47 ecture 8: Filter 005 H.K. Page EES 47 ecture 8: Filter 005 H.K. Page 4

7 inearity of the Sourceoupled Pair MOS Gmell 3a3 5a5 4 IM3 vˆi v ˆi... 4a 8a Subtituting for a,a,... 3 vˆi 5 vˆi IM ( VGSVth) 04 ( VGSVth) ˆvimax 4V ( GS Vth) IM rm IM %&V ( V ) V Vˆ 30mV 3 GS th in Key point: Max. ignal handling capability function of gateoverdrive Simplet Form of MOS Gm ell Removing Dependence of Maximum Signal Handling apability on Tuning an overcome problem of max. ignal handling capability being a function of tuning by providing tuning through : oare tuning via witching in/out binaryweighted crocoupled pair Try to keep gate overdrive voltage contant Fine tuning through varying current ource Dynamic range dependence on tuning removed (to t order) Ref: R.atello,I.Bietti, F. Svelto, HighFrequency Analog Filter in Deep Submicron Technology, International Solid State ircuit onference, pp 7475, 999. EES 47 ecture 8: Filter 005 H.K. Page 5 EES 47 ecture 8: Filter 005 H.K. Page 7 Simplet Form of MOS Gm ell Diadvantage Max. ignal handling capability function of gateoverdrive IM ( V V ) 3 GS th ritical freq. function of gateoverdrive too M, gm ωo intg W ince g m µ V g th then ωo ox ( V ) ( Vg Vth ) Filter tuning affect max. ignal handling capability! Dynamic Range for Sourceoupled Pair Baed Filter rm IM3 % & ( VGS Vth) V 30mV Minimum detectable ignal determined by total noie voltage It can be hown for the 6 th order Butterworth bandpa filter noie i given by: v o kt 3 intg Auming 0 intg 5pF rm vnoie 60µ V rm ince vmax 30mV DynamicRange 63dB EES 47 ecture 8: Filter 005 H.K. Page 6 EES 47 ecture 8: Filter 005 H.K. Page 8

8 Improving the Max. Signal Handling apability of the Sourceoupled Pair Gmell Improving the Max. Signal Handling apability of the Sourceoupled Pair Gm nd ourcecoupled pair added to ubtract current proportional to nonlinear component aociated with the main SP W ( ) W ( ) ( V g V th) ( V g V th) I M, b & a and thu I3 M3,4 M, b a M3,4 Improve maximum ignal handling capability by about db Dynamic range theoretically improved to 6375dB EES 47 ecture 8: Filter 005 H.K. Page 9 EES 47 ecture 8: Filter 005 H.K. Page 3 Improving the Max. Signal Handling apability of the Sourceoupled Pair Gm Simplet Form of MOS Gmell Pro apable of very high frequency performance (highet?) Simple deign on Tuning affect power diipation Tuning affect max. ignal handling capability (can overcome) imited linearity (poible to improve) Ref: H. Khorramabadi, "HighFrequency MOS ontinuoutime Filter," U.. Berkeley, Department of Electrical Engineering, Ph.D. Thei, February 985 (ER Memorandom No. UB/ER M85/9). Ref: H. Khorramabadi and P.R. Gray, High Frequency MOS continuoutime filter, IEEE Journal of SolidState ircuit, Vol.S9, No. 6, pp , Dec EES 47 ecture 8: Filter 005 H.K. Page 30 EES 47 ecture 8: Filter 005 H.K. Page 3

9 Gmell Sourceoupled Pair with Degeneration µ W I ox d ( Vg Vth ) Vd V d Id W gd µ ox Vg Vth Vd geff M3 M, g d gm M, M3 for gm >> g d M3 geff g d ( ) Vd mall M3 operating in triode mode ource degeneration determine overall gm MOSFET in triode mode: Note that if Vd i kept contant: BiMOS Gmell µ W I ox d ( Vg Vth ) Vd V d Id W gm µ ox V V d g inearity performance keep gm contant function of how contant Vd can be held Node X mut be minimized A g M g B x m m Since for a given current, gm of BJT i larger compared to MOS preferable to ue BJT Extra pole at node X Vb Vcm I Iout B X M gm can be varied by changing Vb and thu Vd EES 47 ecture 8: Filter 005 H.K. Page 33 EES 47 ecture 8: Filter 005 H.K. Page 35 Gmell Sourceoupled Pair with Degeneration Alternative Fully MOS Gmell BJT replaced by a MOS tranitor with booted gm Pro Moderate linearity ontinuou tuning provided by Vc Tuning doe not affect power diipation on Extra pole aociated with the ource of M, ow frequency application only Ref: Y. Tividi, Z. zarnul and S.. Fang, MOS tranconductor and integrator with high linearity, Electronic etter, vol., pp. 4546, Feb. 7, 986 ower frequency of operation compared to the BiMOS verion due to more paraitic capacitance at node A & B A B EES 47 ecture 8: Filter 005 H.K. Page 34 EES 47 ecture 8: Filter 005 H.K. Page 36

10 BiMOS Gm Integrator Differential need commonmode feedback ckt Freq. tuned by varying Vb Deign tradeoff: Extra pole at the input device drain junction Input device have to be mall to minimize paraitic pole Reult in high inputreferred offet voltage could drive ckt into nonlinear region Small device high /f noie intg/ intg/ Vout omparion of 7 th Order Gm veru OpampR PF Gm filter require 4 time le intg. cap. area compared to OpampR For lownoie application where filter area i dominated by cap. area could make a ignificant difference in the total area OpampR linearity uperior compared to Gm Power diipation tend to be lower for Gm ince output i high impedance and thu no need for buffering A B B Gm Filter A OpampR Filter A A B A B A B B A B Vo Vout EES 47 ecture 8: Filter 005 H.K. Page 37 EES 47 ecture 8: Filter 005 H.K. Page 39 7 th Order Elliptic Gm PF For DMA RX Baeband Application A B A B A B A B A B A B A B Vout Gmell in previou page ued to build a 7th order elliptic filter for DMA baeband application (650kHz corner frequency) Inband dynamic range of <50dB achieved BiMOS GmOTA Integrator Ued to build filter for dikdrive application Since high frequency of operation, timecontant enitivity to paraitic cap ignificant. Opamp ued M & M3 added to compenate for phae lag (provide phae lead) Ref:. aber and P.Gray, A 0MHz 6th Order BiMOS Paraitic Inenitive ontinuoutime Filter & Second Order Equalizer Optimized for Dik Drive Read hannel, IEEE Journal of Solid State ircuit, Vol. 8, pp , April 993. EES 47 ecture 8: Filter 005 H.K. Page 38 EES 47 ecture 8: Filter 005 H.K. Page 40

11 6th Order BiMOS ontinuoutime Filter & Second Order Equalizer for Dik Drive Read hannel Gmopamp of the previou page ued to build a 6th order filter for Dik Drive Filter conit of 3 Biquad with max. of each Performance in the order of 40dB SNDR achieved for up to 0MHz corner frequency Ref:. aber and P.Gray, A 0MHz 6th Order BiMOS Paraitic Inenitive ontinuoutime Filter & Second Order Equalizer Optimized for Dik Drive Read hannel, IEEE Journal of Solid State ircuit, Vol. 8, pp , April 993. EES 47 ecture 8: Filter 005 H.K. Page 4 Gmell Sourceoupled Pair with Degeneration Gmell Sourceoupled Pair with Degeneration M7,8 operating in triode mode determine the gm of the cell Feedback provided by M5,6 maintain the gateource voltage of M, contant by forcing their current to be contantà help linearize rd of M7,8 urrent mirrored to the output via M9,0 with a factor of k Performance level of about 50dB SNDR at fcorner of 5MHz achieved EES 47 ecture 8: Filter 005 H.K. Page 43 BiMOS Gm Integrator Need higher upply voltage compared to the previou deign ince quite a few device are tacked vertically M, à triode mode, à hold Vd of M, contant urrent ID ued to tune filter critical frequency by varying Vd of M, and thu gm of M, Gmcell intended for low dik drive filter M3, M4 operate in triode mode and added to provide MFB Ref: I.Mehr and D.R.Welland, "A MOS ontinuoutime Gm Filter for PRM Read hannel Application at 50 Mb/ and Beyond", IEEE Journal of SolidState ircuit, April 997, Vol.3, No.4, pp EES 47 ecture 8: Filter 005 H.K. Page 4 Ref: R. Alini, A. Bachirotto, and R. atello, Tunable BiMOS ontinuoutime Filter for HighFrequency Application, IEEE Journal of Solid State ircuit, Vol. 7, No., pp , Dec. 99. EES 47 ecture 8: Filter 005 H.K. Page 44

M5 & M6 configured a capacitor added to compenate for RHP zero due to gd of M, (move it to HP) ize of M5,6 /3 of M, BiMOS Gm Integrator / GS M /3 GS M Ref: R. Alini, A. Bachirotto, and R.

12 M5 & M6 configured a capacitor added to compenate for RHP zero due to gd of M, (move it to HP) ize of M5,6 /3 of M, BiMOS Gm Integrator / GS M /3 GS M Ref: R. Alini, A. Bachirotto, and R. atello, Tunable BiMOS ontinuoutime Filter for High Frequency Application, IEEE Journal of Solid State ircuit, Vol. 7, No., pp , Dec. 99. Summary ontinuoutime Filter Opamp R filter Good linearity High dynamic range (6090dB) Only dicrete tuning poible Medium uable ignal bandwidth (<0MHz) Opamp MOSFET inearity compromied (typical dynamic range 4060dB) ontinuou tuning poible ow uable ignal bandwidth (<5MHz) Opamp MOSFETR Improved linearity compared to Opamp MOSFET (D.R. 5090dB) ontinuou tuning poible ow uable ignal bandwidth (<5MHz) Gm Highet frequency performance (at leat an order of magnitude higher compared to the ret <00MHz) Dynamic range not a high a Opamp R but better than Opamp MOSFET (4070dB) EES 47 ecture 8: Filter 005 H.K. Page 45 EES 47 ecture 8: Filter 005 H.K. Page 47 BiMOS Gm Filter For DikDrive Application Switchedapacitor Filter Example: odec hip f 04kHz f 8kHz f 8kHz f 8kHz Uing the integrator hown in the previou page Biquad filter for dik drive gmgmgm4gm3 Tunable from 8MHz to 3MHz Ref: R. Alini, A. Bachirotto, and R. atello, Tunable BiMOS ontinuoutime Filter for High Frequency Application, IEEE Journal of Solid State ircuit, Vol. 7, No., pp , Dec. 99. f 8kHz f 8kHz f 8kHz f 8kHz Ref: D. Senderowicz et. al, A Family of Differential NMOS Analog ircuit for PM odec Filter hip, IEEE Journal of SolidState ircuit, Vol.S7, No. 6, pp.0403, Dec. 98. EES 47 ecture 8: Filter 005 H.K. Page 46 EES 47 ecture 8: Filter 005 H.K. Page 48

13 Switchedapacitor Reitor Switchedapacitor Reitor apacitor i the witched capacitor f f i f S (v IN v OUT ) f f Nonoverlapping clock φ and φ control witche S and S, repectively v IN i ampled at the falling edge of φ Sampling frequency f S Next, φ rie and the voltage acro i tranferred to v OUT Why i thi a reitor? v IN f f S S v OUT With the current through the witched capacitor reitor proportional to the voltage acro it, the equivalent witched capacitor reitance i: R eq f Example f MHz, pf R eq MegaΩ v IN f f S S v OUT T/f T/f EES 47 ecture 8: Filter 005 H.K. Page 49 EES 47 ecture 8: Filter 005 H.K. Page 5 Switchedapacitor Reitor Switchedapacitor Filter harge tranferred from v IN to v OUT during each clock cycle i: Average current flowing from v IN to v OUT i: (v IN v OUT ) i/t xf i f S (v IN v OUT ) v IN f f f f S S T/f v OUT et build a S filter We ll tart with a imple R PF Replace the phyical reitor by an equivalent S reitor 3dB bandwidth: ω f 3dB R eq f f 3dB π v IN v IN R E f f S S v OUT v OUT EES 47 ecture 8: Filter 005 H.K. Page 50 EES 47 ecture 8: Filter 005 H.K. Page 5

14 Switchedapacitor Filter Advantage veru ontinuoutime Filter Uniform Sampling f f R eq V in S S V in Nomenclature: ontinuou time ignal x(t) Sampling interval T Sampling frequency f /T Sampled ignal x(kt) x(k) x(t) x(kt) x(k) f π 3dB f f3 db π R eq orner freq. proportional to: orner freq. proportional to: Sytem clock (accurate to few ppm) Abolute value of R & ratio accurate < 0.% Poor accuracy 0 to 50% Main advantage of S filter inherent corner frequency accuracy Problem: Multiple continuou time ignal can yield exactly the ame dicrete time ignal et look at ample taken at µ interval of everal inuoidal waveform T time EES 47 ecture 8: Filter 005 H.K. Page 53 EES 47 ecture 8: Filter 005 H.K. Page 55 Typical Sampling Proce ontinuoutime(t) Sampled Data (SD) Sampling Sine Wave ontinuou Time Signal time T m f /T MHz f in 0kHz Sampled Data Sampled Data ZOH voltage y(nt) time lock v(t) in [p(0000)t] EES 47 ecture 8: Filter 005 H.K. Page 54 EES 47 ecture 8: Filter 005 H.K. Page 56

15 Sampling Sine Wave T m f MHz f in 899kHz voltage time v(t) in [p(899000)t] EES 47 ecture 8: Filter 005 H.K. Page 57 Sampling Sine Wave T m f MHz f in 0kHz voltage time v(t) in [p(0000)t] EES 47 ecture 8: Filter 005 H.K. Page 58

EE247 Lecture 8. Lowpass to bandpass transformation Example: Gm-C BP filter using simple diff. pair

EE247 Lecture 8. Lowpass to bandpass transformation Example: Gm-C BP filter using simple diff. pair EE47 Lecture 8 Summary of lat lecture Continuoutime filter Bandpa filter Lowpa to bandpa tranformation Example: GmC BP filter uing imple diff. pair Linearity & noie iue Variou GmC Filter implementation