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1 EE247 Lecture 6 Summary last lecture ontinuoustime filters Opamp MOSFET filters Opamp MOSFETR filters filters Frequency tuning for continuoustime filters Trimming via fuses Automatic onchip filter tuning ontinuous tuning Masterslave tuning Periodic offline tuning Systems where filter is followed by AD & DSP, existing hardware can be used to periodically update filter freq. response EES 247 Lecture 6: Filters 2005 H.K. Page Summary Last Lecture ontinuoustime filters Effect of integrator nonidealities on continuoustime filter behavior Facts about monolithic Rs & s and its effect on integrated filter characteristics Opamp R filters Opamp MOSFET filters Frequency tuning for continuoustime filters Frequency adjustment by making provisions to have variable R or EES 247 Lecture 6: Filters 2005 H.K. Page 2

2 Use of MOSFETs as Resistors SingleEnded Integrator W V 2 ID= µ ox ds ( Vgs V L th ) Vds 2 W 2 V i I = µ ox ( Vgs V D th ) V L i 2 ID W G = = µ ox ( Vgs Vth Vi) Vi L VG I D Tunable by varying VG: Problem: Singleended MOSFET Integrator Effective R nonlinear Note that the nonlinearity is mainly 2 nd order type EES 247 Lecture 6: Filters 2005 H.K. Page 3 Use of MOSFETs as Resistors Differential Integrator W V ds ID = µ ox Vgs Vth V L ds 2 W Vi V I i D= µ ox Vgs V L th 4 2 W Vi V I V V i D2= µ ox L gs th 4 2 W I D I D2 = µ ox ( V gs V th ) V L i ( ID ID2) W G = = µ ox Vgs Vth Vi L ( ) Vi/2 Vi/2 I D I D2 M2 VG ut Nonlinear term cancelled! Admittance independent of Vi OpampMOSFET Problem: Threshold voltage dependence EES 247 Lecture 6: Filters 2005 H.K. Page 4

3 MOSFET Integrator For the OpampR integrator, opamp input stays at 0V (virtual gnd.) Vi/2 Vi/2 0V 0V ut For the MOSFET integrator, opamp input stays at the voltage Vx which is a function of 2 nd order MOSFET nonlinearities Vi/2 Vi/2 VG Vx Vx ut ommonmode voltage sensitivity EES 247 Lecture 6: Filters 2005 H.K. Page 5 Use of MOSFET as Resistor Issues MOS xtor operating in triode region ross section view Distributed channel resistance & gate capacitance Distributed nature of gate capacitance & channel resistance results in infinite no. of highfrequency poles excess phase Filter performance mandates wellmatched MOSFETs long channel devices Excess phase increases with L 2 Tradeoff between matching and integrator Q This type of filter limited to low frequencies EES 247 Lecture 6: Filters 2005 H.K. Page 6

Example: Opamp MOSFET Filter Suitable for low frequency applications Issues with linearity Linearity achieved ~4050dB Needs tuning 5 th Order Elliptic MOSFET LPF with 4kHz Bandwidth Ref: Y.

oury, ontinuoustime MOSFET Filters in VLSI, IEEE Journal of Solid State ircuits Vol. S2, No. Feb. 986, pp. 530 EES 247 Lecture 6: Filters 2005 H.K.

4 Example: Opamp MOSFET Filter Suitable for low frequency applications Issues with linearity Linearity achieved ~4050dB Needs tuning 5 th Order Elliptic MOSFET LPF with 4kHz Bandwidth Ref: Y. Tsividis, M.Banu, and J. Khoury, ontinuoustime MOSFET Filters in VLSI, IEEE Journal of Solid State ircuits Vol. S2, No. Feb. 986, pp. 530 EES 247 Lecture 6: Filters 2005 H.K. Page 7 Improved MOSFET Integrator W V ds ID= µ ox Vgs Vth V L ds 2 V G W V V i I i D= µ ox Vgs Vth L 4 2 W V V i I i D3= µ ox Vgs2 Vth Vi/2 L 4 2 I D IX = ID ID3 W Vi V = µ V V i ox L gs gs2 2 2 V I W V i Vi/2 D2 I V V i X2 = µ ox L gs2 gs 2 2 M2 W I X I X2 = µ ox ( V gs V gs2) V L i ( IX IX2) G = = µ W ox ( gs V gs2) Vi L No threshold dependence First order ommonmode nonlinearity cancelled Linearity achieved in the order of 6070dB Ref: Z. zarnul, Modification of the BanuTsividis ontinuoustime Integrator Structure, IEEE Transactions on ircuits and Systems, Vol. AS33, No. 7, pp. 7476, July 986. I D3 I D4 M4 V G2 M3 I X I X2 ut EES 247 Lecture 6: Filters 2005 H.K. Page 8

RMOSFET Integrator V G V G2 Vi/2 Vi/2 R R M2 M4 M3 ut Improvement over MOSFET by adding resistor in series with MOSFET Voltage drop primarily across fixed resistor small MOSFET Vds improved linearity

of Solid State ircuits, Vol. 28, No. 2, pp. 254264, Dec. 993. EES 247 Lecture 6: Filters 2005 H.K.

5 RMOSFET Integrator V G V G2 Vi/2 Vi/2 R R M2 M4 M3 ut Improvement over MOSFET by adding resistor in series with MOSFET Voltage drop primarily across fixed resistor small MOSFET Vds improved linearity & reduced tuning range Linearity in the order of 90dB possible Generally low frequency applications Ref: UK Moon, and BS Song, Design of a LowDistortion 22kHz Fifth Order Bessel Filter, IEEE Journal of Solid State ircuits, Vol. 28, No. 2, pp , Dec EES 247 Lecture 6: Filters 2005 H.K. Page 9 RMOSFET Lossy Integrator R2 Vi/2 Vi/2 R2 R V G M2 M4 V G2 M3 ut Negative feedback around the nonlinear MOSFETs improves linearity ompromises frequency response accuracy Ref: UK Moon, and BS Song, Design of a LowDistortion 22kHz Fifth Order Bessel Filter, IEEE Journal of Solid State ircuits, Vol. 28, No. 2, pp , Dec R2 EES 247 Lecture 6: Filters 2005 H.K. Page 0

Example: Opamp MOSFETR Filter 5 th Order Bessel MOSFETR LPF 22kHz bandwidth THD 90dB for 4Vpp 2kHz input signal Suitable for low frequency applications Significant improvement in linearity compared

6 Example: Opamp MOSFETR Filter 5 th Order Bessel MOSFETR LPF 22kHz bandwidth THD 90dB for 4Vpp 2kHz input signal Suitable for low frequency applications Significant improvement in linearity compared to MOSFET Needs tuning Ref: UK Moon, and BS Song, Design of a LowDistortion 22kHz Fifth Order Bessel Filter, IEEE Journal of Solid State ircuits, Vol. 28, No. 2, pp , Dec EES 247 Lecture 6: Filters 2005 H.K. Page Operational Amplifiers (Opamps) versus Operational Transconductance Amplifiers (OTA) Opamp Voltage controlled voltage source OTA Voltage controlled current source Low output impedance Output in the form of voltage an drive Rloads Good for R filters, OK for S filters Extra buffer adds complexity, power dissipation High output impedance In the context of filter design called gmcells Output in the form of current annot drive Rloads Good for S & gm filters Typically, less complex compared to opamp higher freq. potential Typically lower power EES 247 Lecture 6: Filters 2005 H.K. Page 2

7 Integrator Implementation Transconductance & OpampTransconductance Intg. OTA Intg. Vo ωo = where ωo = Vin s EES 247 Lecture 6: Filters 2005 H.K. Page 3 Filters Simplest Form of MOS Integrator Transconductance element formed by the sourcecoupled pair All MOSFETs operating in saturation region urrent in & M2 can be varied by changing V control Transconductance of & M2 varied through V control intg M2 0 V control Ref: H. Khorramabadi and P.R. Gray, High Frequency MOS continuoustime filters, IEEE Journal of SolidState ircuits, Vol.S9, No. 6, pp , Dec EES 247 Lecture 6: Filters 2005 H.K. Page 4

Page 5 Filters Simplest Form of MOS Integrator Use ac half circuit & small signal model to derive transfer

8 Simplest Form of MOS Integrator Ac Half ircuit 2 intg 2 intg intg 0 M2 V control 0 M2 V control 2 intg A half circuit EES 247 Lecture 6: Filters 2005 H.K. Page 5 Filters Simplest Form of MOS Integrator Use ac half circuit & small signal model to derive transfer function:,2 Vo = gm Vin 2intgs,2 Vo g = m Vin 2intgs Vo ω = o Vin s,2 gm ωo = 2 intg GS gm 2 intg A half circuit Small signal model 2 intg EES 247 Lecture 6: Filters 2005 H.K. Page 6

Filters Simplest Form of MOS Integrator MOSFET in saturation region: µ W 2 I ox d = ( Vgs Vth ) 2 L is given by: &M2 Id W gm = = µ ox Vgs Vth Vgs L I = 2 d V V ( gs th ) /2 W 2 = µ ox I 2 L d ( ) Id

9 Filters Simplest Form of MOS Integrator MOSFET in saturation region: µ W 2 I ox d = ( Vgs Vth ) 2 L is given by: &M2 Id W gm = = µ ox Vgs Vth Vgs L I = 2 d V V ( gs th ) /2 W 2 = µ ox I 2 L d ( ) Id varied via Vcontrol gm tunable via Vcontrol intg M2 0 V control EES 247 Lecture 6: Filters 2005 H.K. Page 7 Filters 2 nd Order Filter Use the cell to build a 2 nd order bandpass filter intg M2 0 V control EES 247 Lecture 6: Filters 2005 H.K. Page 8

10 2 nd Order Bandpass Filter Iin V R R V L L V I I R L I V ' V * R R V 2 sr * ' V 3 * R sl τ τ * * = R 2= L R * R R sτ sτ 2 EES 247 Lecture 6: Filters 2005 H.K. Page 9 2nd Order IntegratorBased Bandpass Filter VBP τ2s V = in 2 ττ 2 s βτ2 s τ * * = R 2 = L R β = R * R ω0 = ττ 2= L Q= β τ τ τ2 Q V BP sτ sτ Frommatchingpointofviewdesirable: τ= τ R 2 = Q = ω0 R * EES 247 Lecture 6: Filters 2005 H.K. Page 20

11 2nd Order IntegratorBased Bandpass Filter V BP First implement this part With transfer function: Q sτ sτ V0 = Vin s ω0 Q EES 247 Lecture 6: Filters 2005 H.K. Page 2 Terminated Integrator intg M3 0 M4 M2 V control Vin M3 A half circuit 2intg EES 247 Lecture 6: Filters 2005 H.K. Page 22

Terminated Integrator Vin M3 2intg GS gm Vin g M3 m 2 intg A half circuit Small signal model Vo = V M3 in s 2intg g m gm gm EES 247 Lecture 6: Filters 2005 H.K.

12 Terminated Integrator Vin M3 2intg GS gm Vin g M3 m 2 intg A half circuit Small signal model Vo = V M3 in s 2intg g m gm gm EES 247 Lecture 6: Filters 2005 H.K. Page 23 Terminated Integrator Q V BP sτ sτ GS gm Vin g M3 m 2 intg V0 = Vin s ω0 Q Small signal model Vo = V M3 in s 2intg g m gm gm gm g ω m 0 = & Q = 2 M3 intg gm Question: How to define Q accurately? EES 247 Lecture 6: Filters 2005 H.K. Page 24

13 Terminated Integrator /2 W g m = 2 µ ox I d 2 L /2 M3 WM3 M3 g m = 2 µ ox I 2 L d M3 Let us assume equal channel lengths for, M3 then: /2 g m I d W = M3 M3 g W m I d M3 intg M3 M4 M2 0 V control EES 247 Lecture 6: Filters 2005 H.K. Page 25 Terminated Integrator Note that: I 0 d I = d M3 I d I d Assuming equal channel lengths for 0, : intg 0 I d W = 0 I d W g W m 0 W = gm3 W W m M3 /2 M3 0 M4 M2 V control EES 247 Lecture 6: Filters 2005 H.K. Page 26

14 2nd Order Filter Simple design Tunable Q function of device ratios: g Q = g,2 m M3,4 m EES 247 Lecture 6: Filters 2005 H.K. Page 27 Filter Frequency Tuning Techniques omponent trimming Automatic onchip filter tuning ontinuous tuning Masterslave tuning Periodic offline tuning Systems where filter is followed by AD & DSP, existing hardware can be used to periodically update filter freq. response EES 247 Lecture 6: Filters 2005 H.K. Page 28

Example: Tunable OpampR Filter Post manufacturing: Usually at wafersort tuning performed D2 D D0 Measure 3dB frequency If frequency too high decrement D to D If frequency too low increment D to D If

15 Example: Tunable OpampR Filter Post manufacturing: Usually at wafersort tuning performed D2 D D0 Measure 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 R R2 R3 R4 R R2 R3 R4 Not practical to require enduser to tune the filter Need to fix the adjustment at the factory EES 247 Lecture 6: Filters 2005 H.K. Page 29 Trimming omponent trimming Build fuses onchip Based on wafersort blow fuses selectively by applying high current to the fuse Expensive Fuse regrowth problems! Does not account for temp. variations & aging Laser trimming Trim components or cut fuses by laser Even more expensive Does not account for temp. variations & aging Fuse To switch D Fuse not blown D= Fuse blown D=0 EES 247 Lecture 6: Filters 2005 H.K. Page 30

16 Example:Tunable/Trimmable OpampR Filter D2 D D0 Rnom 7.2K K K K D0 Fuse D Fuse D2 R R2 R3 R4 Fuse R R2 R3 R4 EES 247 Lecture 6: Filters 2005 H.K. Page 3 Automatic Frequency Tuning By adding additional circuitry to the main filter circuit Have the filter critical frequency automatically tuned Expensive trimming avoided Accounts for critical frequency variations due to temperature, supply voltage, and effect of aging EES 247 Lecture 6: Filters 2005 H.K. Page 32

17 MasterSlave Automatic Frequency Tuning Following facts used in this scheme: Use a replica (master) of the main filter (called the slave) in the tuning circuitry Place the replica in close proximity of the main filter Use the tuning signal generated to tune the replica, to also tune the main filter In the literature, this scheme is called masterslave tuning! EES 247 Lecture 6: Filters 2005 H.K. Page 33 MasterSlave Frequency Tuning Reference Filter (VF) Use a biquad for master filter (VF) Utilize the fact the frequency fo the lowpass (or highpass) outputs are 90 degree out of phase wrt to input VLP ω = ω o 2 o φ= 90 Vin s s 2 ωo Qωo V BP ωo Q s ωo s Apply a sinusoid at the desired fo ompare the LP output phase to the input Based on the phase difference Increase or decrease filter critical freq. V HP V LP EES 247 Lecture 6: Filters 2005 H.K. Page 34

Page 35 MasterSlave Frequency Tuning Reference Filter (VF) By closing the loop, feedback tends to drive the error voltage to zero.

18 MasterSlave Frequency Tuning Reference Filter (VF) V rms rms tune K V ref V LP cosφ Vtune fo Q ωo Q s V LP ωo s Amp. Filter Phase omparator V Tune f o Input Signal Frequency V ref EES 247 Lecture 6: Filters 2005 H.K. Page 35 MasterSlave Frequency Tuning Reference Filter (VF) By closing the loop, feedback tends to drive the error voltage to zero. Locks fo, the critical frequency of the filter to the accurate reference frequency Typically the reference frequency is provided by a crystal oscillator with accuracies in the order of few ppm ωo Q s V ref ωo s V LP V Tune Amp. Filter Phase omparator EES 247 Lecture 6: Filters 2005 H.K. Page 36

MasterSlave Frequency Tuning Reference Filter (VF) Q sτ 0 Replica Filter (Master) sτ 0 V LP Amp. Filter * R Rs sτ Phase omparator V tune 2 Main Filter (Slave) sτ sτ 3 sτ 4 sτ 5 * R RL V ref Ref: H.

Frequency Tuning Reference Filter (VF) Issues to be aware of: Input reference tuning signal needs to be sinusoid Disadvantage since clocks are usually available as square waveform Reference signal

19 MasterSlave Frequency Tuning Reference Filter (VF) Q sτ 0 Replica Filter (Master) sτ 0 V LP Amp. Filter * R Rs sτ Phase omparator V tune 2 Main Filter (Slave) sτ sτ 3 sτ 4 sτ 5 * R RL V ref Ref: H. Khorramabadi and P.R. Gray, High Frequency MOS continuoustime filters, IEEE Journal of SolidState ircuits, Vol.S9, No. 6, pp , Dec EES 247 Lecture 6: Filters 2005 H.K. Page 37 MasterSlave Frequency Tuning Reference Filter (VF) Issues to be aware of: Input reference tuning signal needs to be sinusoid Disadvantage since clocks are usually available as square waveform Reference signal feedthrough to the output of the filter can limit filter dynamic range (reported levels or about 00µVrms) Ref. signal feedthrough is a function of: Reference signal frequency wrt filter passband Filter topology are in the layout Fully differential topologies beneficial EES 247 Lecture 6: Filters 2005 H.K. Page 38

MasterSlave Frequency Tuning Reference VoltageontrolledOscillator (VO) Instead of VF a voltagecontrolledoscillator (VO) is used VO made of replica integrator used in main filter Tuning circuit

20 MasterSlave Frequency Tuning Reference VoltageontrolledOscillator (VO) Instead of VF a voltagecontrolledoscillator (VO) is used VO made of replica integrator used in main filter Tuning circuit operates exactly as a conventional phaselocked loop (PLL) Tuning signal used to tune main filter Ref: K.S. Tan and P.R. Gray, Fully integrated analog filters using bipolar FET technology, IEEE, J. SolidState ircuits, vol. S3, no.6, pp. 8482, December EES 247 Lecture 6: Filters 2005 H.K. Page 39 MasterSlave Frequency Tuning Reference VoltageontrolledOscillator (VO) Issues to be aware of: Design of stable & repeatable oscillator challenging VO operation should be limited to the linear region of the amp or else the operation loses accuracy Limiting the VO signal range to the linear region not a trivial design issue In the case of VF based tuning ckt there was only ref. signal feedthrough. In this case, there is also the feedthrough of the VO signal!! Advantage over VF based tuning à Reference input signal square wave (not sin.) EES 247 Lecture 6: Filters 2005 H.K. Page 40

21 MasterSlave Frequency Tuning hoice of Ref. Frequency wrt Feedthrough Immunity Ref: V. Gopinathan, et. al, Design onsiderations for HighFrequency ontinuoustime Filters and Implementation of an Antialiasing Filter for Digital Video, IEEE JSS, Vol. S25, no. 6 pp , Dec EES 247 Lecture 6: Filters 2005 H.K. Page 4 MasterSlave Frequency Tuning Reference / Locked to Ref. Frequency Replica of main filter building block used Utilizes the fact that a D voltage source connected to the input of the cell generates a constant current I=.Vref If the integrating capacitor is fully discharged and at t=0 is connected to the output of the cell then: Vin Vref Replica of main filter I=*Vref Vout V tune V V V ref T T If V is forced to be equal to Vref then: = T = N fclk EES 247 Lecture 6: Filters 2005 H.K. Page 42

22 MasterSlave Frequency Tuning Reference / Locked to Ref. Frequency Replica of main filter Three phase operation Feedback loop forces: Vref S2 S3 S 2 A N fclk Ref: A. Durham, J. Hughes, and W. Redman White, ircuit Architectures for High Linearity Monolithic ontinuoustime Filtering, IEEE Transactions on ircuits and Systems, pp , Sept EES 247 Lecture 6: Filters 2005 H.K. Page 43 Reference / Locked to Ref. Frequency P high S closed Vref S2 S3 S 2 A Discharge EES 247 Lecture 6: Filters 2005 H.K. Page 44

23 Reference / Locked to Ref. Frequency P2 high S2 closed Vref S2 I=*Vref S3 2 A harge with I=*Vref P2 V V Vref T2 T T2 EES 247 Lecture 6: Filters 2005 H.K. Page 45 Reference / Locked to Ref. Frequency P3 high S3 closed Vref S2 S3 2 A T T2 harge on shared with 2 Feedback forces to assume a value: V= V2 = Vref since: V = Vref T2 then: Vref = V ref T2 or: = T2= N/fclk EES 247 Lecture 6: Filters 2005 H.K. Page 46

24 Summary Reference / Locked to Ref. Frequency Vref S2 S3 2 A Integrator time constant locked to an accurate frequency Tuning signal used to adjust the time constant of the main filter integrators Problems to be aware of: Tuning error due to cell D offset Feedback forces to vary so that : τintg = = N/fclk or intg ω 0 = = fclk/n EES 247 Lecture 6: Filters 2005 H.K. Page 47 Issues Reference / Locked to Ref. Frequency What is D offset? Simple example: For the gmcell shown here, difference between the threshold voltage of the input devices ( & M2) would cause D offset. A nonzero voltage should be applied to input to have Vo=0 Offset is usually models as a small D voltage source at the input intg M2 0 V control Example: cell EES 247 Lecture 6: Filters 2005 H.K. Page 48

25 ell Offset Induced Error Voltage source Representing D offset Vref Vos S2 S3 I=(VrefVos) 2 A Effect of cell D offset: V= V2 = Vref Ideal: V = Vref T2 ( ref os) withoffset: V= V V T2 V or: = T2 os V ref EES 247 Lecture 6: Filters 2005 H.K. Page 49 Reference / Locked to Ref. Frequency ell Offset Induced Error Vref Vos S2 S3 I=(VrefVos) 2 A Example: V = T2 os V ref V for os = /0 V ref 0% errorintuning! EES 247 Lecture 6: Filters 2005 H.K. Page 50

26 Reference / Locked to Ref. Frequency Incorporating Offset ancellation P2 P3 Vref/2 Vcm Vref/2 P2B P2B 3a 3b P P2 P2 P P3 P3 2 P2 P3 Vtune cell two sets of input pairs Aux. input pair 3a,b Offset cancellation Same clock timing EES 247 Lecture 6: Filters 2005 H.K. Page 5 Reference / Locked to Ref. Frequency P3 High (Update & Store Vos) Vref/2 Vcm Vref/2 3a s 3b Vout = Vos 2 Vtune cell Unity gain config. 3a,b Store cell offset, 2 harge sharing EES 247 Lecture 6: Filters 2005 H.K. Page 52

27 Reference / Locked to Ref. Frequency P High (Reset) Vref/2 Vcm Vref/2 V3a = Vos 3a s 3b 2 Vtune cell Reset. Discharge 2 Hold harge 3a,b Hold harge Offset stored on 3a,b cancels gmcell offset EES 247 Lecture 6: Filters 2005 H.K. Page 53 Reference / Locked to Ref. Frequency P2 High (harge) V3a = Vos Vref/2 Vcm Vref/2 3a 3b V os 2 cell harging 3a,b Store cell offset 2 Hold charge Vtune Key point: Tuning error due to cell offset cancelled EES 247 Lecture 6: Filters 2005 H.K. Page 54

28 Summary Reference / Locked to Ref. Frequency V3a = Vos Vref/2 Vcm Vref/2 3a 3b V os 2 cell harging 3a,b Store cell offset 2 Hold charge Vtune Key point: Tuning error due to cell offset cancelled EES 247 Lecture 6: Filters 2005 H.K. Page 55 Summary Reference / Locked to Ref. Frequency Vref S2 S3 2 A Tuning error due to gmcell offset voltage resolved Has the advantage over previous scheme that fclk can be chosen to be at much higher frequencies compared to filter bandwidth (N>) Feedthrough of Vref attenuated by filter Feedback forces to vary so that : τintg = = N/fclk or intg ω 0 = = fclk/n EES 247 Lecture 6: Filters 2005 H.K. Page 56

29 D Tuning of Resistive Timing Element Vtune Rext used to lock or onchip R I Feedback forces =/Rext Account for ap. variations in the gm implementation by trimming I Rext. Ref:. Laber and Gray, A 20MHz 6th Order BiMOS Parasitic Insensitive ontinuoustime Filter and Second Order Equalizer Optimized for Disk Drive Read hannels, IEEE Journal of Solid State ircuits, Vol. 28, pp , April 993 EES 247 Lecture 6: Filters 2005 H.K. Page 57

EE247 Lecture 6. Frequency tuning for continuous-time filters

EE247 Lecture 6. Frequency tuning for continuous-time filters EE247 Lecture 6 Summary last lecture ontinuoustime filters Opamp MOSFET filters Opamp MOSFETR filters filters Frequency tuning for continuoustime filters Trimming via fuses Automatic onchip filter tuning