EE247 Lecture 6. Frequency tuning for continuous-time filters

Transcription

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 2006 H.K. Page Summary Lecture 5 ontinuoustime filters Effect of integrator nonidealities on continuoustime filter behavior Effect of integrator finite D gain & nondominant poles on filter frequency response Integrator nonlinearities affecting filter maximum signal handling capability (harmonic distortion and intermodulation distortion) Facts about monolithic Rs & s and its effect on integrated filter characteristics Opamp R filters Frequency tuning for continuoustime filters Frequency adjustment by making provisions to have variable R or EES 247 Lecture 6: Filters 2006 H.K. Page 2

2 Integrator Implementation OpampR & OpampMOSFET & OpampMOSFETR R Vtune Vtune R OpampR OpampMOSFET OpampMOSFETR Vo ωo = where ωo = s Req EES 247 Lecture 6: Filters 2006 H.K. Page 3 Use of MOSFETs as Resistors R R replaced by MOSFET ontinuously variable resistor: Vtune OpampR OpampMOSFET I D Triode region V GS MOSFET IV characteristic: Nonlinear R V DS EES 247 Lecture 6: Filters 2006 H.K. Page 4

3 Opamp MOSFET Integrator SingleEnded Integrator W 2 V 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 By varying VG effective admittance is tuned Tunable integrator 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 2006 H.K. Page 5 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 i D2 = μ ox Vgs V L 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 M ut Nonlinear term of even order & cancelled! Admittance independent of Vi OpampMOSFET Problem: Threshold voltage dependence EES 247 Lecture 6: Filters 2006 H.K. Page 6

4 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 the unitygain frequency of the integrator Enhanced integrator Q Enhanced filter Q, Peaking in the filter passband EES 247 Lecture 6: Filters 2006 H.K. Page 7 Use of MOSFET as Resistor Issues MOS xtor operating in triode region ross section view Distributed channel resistance & gate capacitance Tradeoffs affecting the choice of device channel length: Filter performance mandates wellmatched MOSFETs long channel devices desirable Excess phase increases with L 2 Q enhancement and potential for oscillation! Tradeoff between device matching and integrator Q This type of filter limited to low frequencies EES 247 Lecture 6: Filters 2006 H.K. Page 8

5 Suitable for low frequency applications Issues with linearity Linearity achieved ~40 50dB Needs tuning Example: Opamp MOSFET Filter 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 2006 H.K. Page 9 Improved MOSFET 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 i D3 = μ ox Vgs3 Vth Vi/2 L 4 2 IX = ID ID3 W Vi V = μ i ox Vgs V L gs3 2 2 W Vi V I i Vi/2 X2 = μ ox Vgs3 V L gs 2 2 W I X I X2 = μ ox ( V gs V gs3 ) V L i ( IX IX2) G = = μ W ox ( V gs V gs3 ) Vi L No threshold dependence V G V G2 M I D I D2 I D3 I D4 M4 I X M3 I X2 M2 M,2,3,4 equal W/L ut 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. EES 247 Lecture 6: Filters 2006 H.K. Page 0

6 RMOSFET Integrator V G V G2 Vi/2 Vi/2 R R M2 M 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 2006 H.K. Page RMOSFET Lossy Integrator R2 Vi/2 Vi/2 R2 R V G M 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 EES 247 Lecture 6: Filters 2006 H.K. Page 2 R2

7 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 2006 H.K. Page 3 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 2006 H.K. Page 4

8 Integrator Implementation Transconductance & OpampTransconductance Intg. OTA Intg. Vo ωo = where ωo = s EES 247 Lecture 6: Filters 2006 H.K. Page 5 Filters Simplest Form of MOS Integrator Transconductance element formed by the sourcecoupled pair All MOSFETs operating in saturation region urrent in M& M2 can be varied by changing V control Transconductance of M& M2 varied through V control int g M M2 M0 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 2006 H.K. Page 6

9 Simplest Form of MOS Integrator A Half ircuit int g int g 2 2 int g int g M M2 M0V V control control M M0 M2 V control 2 M intg A half circuit EES 247 Lecture 6: Filters 2006 H.K. Page 7 Filters Simplest Form of MOS Integrator Use ac half circuit & small signal model to derive transfer function: M,2 Vo = gm 2int gs M,2 Vo g = m 2int g s Vo ω = o s M,2 gm ωo = 2 int g GS M gm 2 intg A half circuit Small signal model 2 intg EES 247 Lecture 6: Filters 2006 H.K. Page 8

10 Filters Simplest Form of MOS Integrator MOSFET in saturation region: μ W 2 I ox d = ( Vgs Vth ) 2 L is given by: M&M2 Id W gm = = μ ox Vgs Vth Vgs L I = 2 d V gs V th ( ) /2 W 2 = μ ox I 2 L d ( ) Id varied via Vcontrol gm tunable via Vcontrol M int g M2 M0 V control EES 247 Lecture 6: Filters 2006 H.K. Page 9 Filters 2 nd Order Filter Use the cell to build a 2 nd order bandpass filter M int g M2 M0 V control EES 247 Lecture 6: Filters 2006 H.K. Page 20

11 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 2006 H.K. Page 2 2nd Order IntegratorBased Bandpass Filter VBP 2s = 2 ττ 2s βτ2s τ * * = R 2 = L R * β = R R ω τ 0 = τ τ2 = Q= β τ τ τ 2 L Q V BP sτ sτ From matching pointof viewdesirable: = 2 = = Q = R ω0 * R τ τ τ EES 247 Lecture 6: Filters 2006 H.K. Page 22

12 2nd Order IntegratorBased Bandpass Filter V BP First implement this part With transfer function: Q sτ sτ V0 = s ω0 Q EES 247 Lecture 6: Filters 2006 H.K. Page 23 Terminated Integrator int g M3 M M0 M4 M2 M V control M M3 A half circuit 2intg EES 247 Lecture 6: Filters 2006 H.K. Page 24

13 Terminated Integrator M M3 2intg GS g M m M 3 g m 2 intg A half circuit Small signal model Vo = V M 3 in 2int g g s m M M gm gm V0 ompare to: = s ω0 Q EES 247 Lecture 6: Filters 2006 H.K. Page 25 Terminated Integrator Q V BP sτ sτ GS g M m M 3 g m 2 intg V0 = s ω0 Q Small signal model Vo = V M 3 in s 2int g g m M M gm gm M M gm g ω m 0 = & Q = 2 M3 int g gm Question: How to define Q accurately? EES 247 Lecture 6: Filters 2006 H.K. Page 26

14 Terminated Integrator /2 M WM M gm = 2 μ ox I d 2 LM /2 M3 WM3 M3 gm = 2 μ ox I 2 L d M3 Let us assume equal channel lengths for M, M3 then: M /2 M g m I d W = M M3 M3 g W m I d M3 int g M3 M4 M M2 M M0 VVcontrol EES 247 Lecture 6: Filters 2006 H.K. Page 27 Terminated Integrator Note that: M M0 I d I = d M3 M I d I d Assuming equal channel lengths for M0, M: int g M0 I M3 M4 d W = M0 M M M2 I d W M /2 M M W gm M0 WM M0 = VVcontrol M3 W g m W M M3 EES 247 Lecture 6: Filters 2006 H.K. Page 28

15 2nd Order Filter Simple design Tunable Q function of device ratios: g Q = g M,2 m M 3,4 m EES 247 Lecture 6: Filters 2006 H.K. Page 29 ontinuoustime 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 2006 H.K. Page 30

16 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 2006 H.K. Page 3 Factory Trimming Factory component 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 To switch D Fuse Fuse not blown D= Fuse blown D=0 EES 247 Lecture 6: Filters 2006 H.K. Page 32

17 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 2006 H.K. Page 33 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 Additional hardware, increased Si area & power EES 247 Lecture 6: Filters 2006 H.K. Page 34

18 MasterSlave Automatic Frequency Tuning Following facts used in this scheme: Use a replica of the main filter or its building block in the tuning circuitry The replica is called the master and the main filter is named the slave Place the replica in close proximity of the main filter to ensure good matching 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 2006 H.K. Page 35 MasterSlave Frequency Tuning Reference Filter (VF) Use a biquad built with replica of main filter integrator for master filter (VF) Utilize the fact the frequency f o, the lowpass (or highpass) outputs are 90 degree out of phase wrt to input VLP o ω = ω 2 o φ= 90 s s 2 ωo Qωo Apply a sinusoid at the desired f o desired ompare the LP output phase to the input Based on the phase difference Increase or decrease filter critical freq. ωo Q s V HP V BP V LP ωo s EES 247 Lecture 6: Filters 2006 H.K. Page 36

19 MasterSlave Frequency Tuning Reference Filter (VF) V rms rms tune K V ref V LP cosφ Vtune fo f o Q Input Signal Frequency ωo Q s V ref V LP ωo s Amp. Filter Phase omparator V Tune EES 247 Lecture 6: Filters 2006 H.K. Page 37 MasterSlave Frequency Tuning Reference Filter (VF) By closing the loop, feedback tends to drive the error voltage to zero. Locks f o to f o desired, 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 2006 H.K. Page 38

20 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 2006 H.K. Page 39 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 of about 00μVrms) Ref. signal feedthrough is a function of: Reference signal frequency with respect to filter passband Filter topology are in the layout Fully differential topologies beneficial EES 247 Lecture 6: Filters 2006 H.K. Page 40

21 MasterSlave Frequency Tuning 2 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 2006 H.K. Page 4 MasterSlave Frequency Tuning 2 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 Reference input signal square wave (not sin.) EES 247 Lecture 6: Filters 2006 H.K. Page 42

22 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 2006 H.K. Page 43 MasterSlave Frequency Tuning 3 Reference Integrator Locked to Reference Frequency Replica of main filter Vref I=*Vref Vout V tune Replica of main filter integrator e.g. building block used Utilizes the fact that a D voltage source connected to the input of the cell generates a constant current proportional to the transconductance and the voltage reference I =.Vref EES 247 Lecture 6: Filters 2006 H.K. Page 44

23 Reference Integrator Locked to Reference Frequency onsider the following sequence: Integrating capacitor is fully t=0 At t=0 the capacitor is connected to the output of the cell then: Vref I=*Vref Vout V tune V T V = V ref T t=0 time Q = V = V ref T V = V ref T EES 247 Lecture 6: Filters 2006 H.K. Page 45 Reference Integrator Locked to Reference Frequency Since at the end of the period T: V V ref T If V is forced to be equal to Vref then: Vref I=*Vref Vout V tune = T = N fclk How do we manage to force V=Vref? Use feedback!! V T V V ref T t=0 time EES 247 Lecture 6: Filters 2006 H.K. Page 46

24 Reference Integrator Locked to Reference Frequency Replica of main filter Vref S2 S3 S 2 A Three clock phase operation To analyze study one phase at a time 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 2006 H.K. Page 47 Reference Integrator Locked to Reference Frequency P high S closed Vref S2 S3 S 2 A discharged V =0 2 retains its previous charge EES 247 Lecture 6: Filters 2006 H.K. Page 48

25 Reference Integrator Locked to Reference Frequency P2 high S2 closed Vref S2 I=*Vref S3 2 A charged with constant current: I=*Vref 2 retains its previous charge P2 V V = V ref T2 T T2 EES 247 Lecture 6: Filters 2006 H.K. Page 49 Reference Integrator Locked to Reference Frequency P3 high S3 closed Vref S2 S3 ΔV 2 A T T2 charge shares with 2 Few cycles following startup Assuming A is large, feedback forces: ΔV 0 V 2 = Vref EES 247 Lecture 6: Filters 2006 H.K. Page 50

26 Reference Integrator Locked to Reference Frequency P3 high S3 closed Vref S2 S3 2 A T T2 V = V2 = Vref since: V = V ref T2 then: Vref = V ref T2 or: = T2 = N / fclk EES 247 Lecture 6: Filters 2006 H.K. Page 5 Summary Replica Integrator Locked to Reference Frequency Vref S2 S3 2 A Tuning Signal To Main Filter Integrator time constant locked to an accurate frequency Tuning signal used to adjust the time constant of the main filter integrators Feedback forces to assume a value so that : τintg = = N /fclk or intg ω 0 = = fclk / N EES 247 Lecture 6: Filters 2006 H.K. Page 52