Continuous-time filters - Springerextras.springer.com/2006/978-0-387-25746-4/Chapter_19.pdfWilly...

Willy Sansen 10-05 191

Continuous-time filters

Willy Sansen

KULeuven, ESAT-MICASLeuven, Belgium

[email protected]


Applications and problems

• Applications• Anti-aliasing filters• Video and HF filters : hard-disk drives• Channel select filters• Low-power filters

• Problems:• Tuning for high precision: mismatch < 5 %• Distortion : THD < -60 dB• Low power supply voltages• High quality factors : Q > 50 ?


Table of contents

Active RC filtersMOSFET-C filtersGmC filtersComparison

Ref.: Tsividis, Voorman, Integrated Cont.-time filters, IEEE Press 1993J. Silva-Martinez, Kluwer 1993, W. Dehaene, JSSC, July 1997, 977-988


Active RC filters

Opamps and passive components (R, C)

+-

C2

R1vIN vOUT

C1

Cn

Disadvantages :Opamps :

only for low frequencies Errors on R, C ≈ 20 %

>> tune C’s

Advantages :S/N up to 100 dBTHD very low < - 90 dB


Table of contents


Ref.: Silva-Martinez, Dehaene, ..


MOST resistors

VDS0

IDS linear

saturation

VGS-VT

On-resistance :Ron =

VDS > VGS-VT

1

β (VGS-VT)

β = KPWL iDS = KP [(vGS-vT)vDS - ]

WL

vDS2

2

HD2


Examples of differential MOST-R’s

partial cancellation of even nonlincancellation of even and odd nonlinearities

Ref. Tsividis JSSC Feb.86, 15-30; Ma.94, 166-176


From active RC to MOSFET-C filter

Ref. Tsividis JSSC Feb.86, 15-30


Large RON values at high frequencies

KP W/L (VGS-VT)

For low-frequency low-pass filter with f-3dB

f-3dB = ≈2π RonC

12π C

For f-3dB = 4 kHz; KP= 60 µA/V2; VGS-VT = 1 V; W = 2 µm; C = 10 pF Ron= 4 MΩ. For matching W = 2 µm: L ≈ 500 µm ! The area is 10-5 cm2

For Cox = 5.10-7 F/cm2 (0.35 µm); CGS = 5 pF; High-frequency limit at ≈ 8 kHz or fT ≈ 8 kHz !!!!!!


LC ladder filter

Ref. BanuJSSC Dec.85, 1114-1121


Fifth-order low-pass filter

Ref. Tsividis, JSSC Feb.86, 15-30

-vINvIN

v


Fifth-order elliptic low-pass filter

Ref. Tsividis JSSC Feb.86, 15-30


PLL tuning

Ref.Banu JSSC Dec.85, 1114-1121 Krummenacher, JS SC June 88, 750-758Khoury, JSSC Dec.91, 1988-1997

Problems:Master/slave for

each pole/zeroVCO + PLL at fcSignal feedthrough

at fc

Filter


Table of contents

Active RC filtersMOSFET-C filtersGmC filters• Transconductors• TuningComparison



Some GmC filters

Single-ended GmC filters

Fully-differential ...


GmC filter definition

Operational amplifier

Opamp OTAOperational

Transconduct.amplifier

+-

+-

Av =vOUTvIN

Ag =iOUTvIN

Av = = Ag RL

+-vIN

Ag or Gm (Ibias)

Ibias

vOUT

C

Disadv.: Distortion Mismatch errorsParasitic C’s (low Q)

Adv.: High freq. operationEasy tuning

iOUT


Simple GmC filters

+-ZIN +

-vIN1vOUT

Cgm

+-vIN

C

vIN2

R

vOUT

vOUTvIN1- vIN2

=gmsC

vOUTvIN

=gmR

1+ sRC


Simple GmC filters

+-

gm2

+-vIN

C

vOUT

vOUT

vIN=

gm1gm2 + sC

gm1

f

gm1gm2

gm12πC

gm22πC


Simple fully-differential GmC filters

-vIN CL

+Gm1 Gm2

-

+

Cp

CpResistorIntegrator Lossy integrator

Sensitive toparasitic capacitancesvOUT

-vIN C1

+Gm1 Gm1 C2 Gm2 Gm1

+

-

vOUT

Biquadratic cell


Voltage-mode & current-mode filters


A differential pair as a transconductor

M1Vid/2 -Vid/2

Ibias

-ioutiout

M1

VId

VGS - VTU =

IM3 = 3HD3 = U2

U is the relative current swing

332

IP3 ≈ 3.3 (VGS - VT)

Max. Vidptp ≈ 2 √2 (VGS - VT)

HD3 = - 60 dB for Vid = 1 V requires VGS-VT = 6 V !!!


Amplifier or transconductor ?

vod

vindslope gm

RLIB

-RLIB

√2 (VGS -VT)0

bipolar MOST transconductor

Transconductor :Wide input range : low distortionSmall gain gm


Table of contents

Active RC filtersMOSFET-C filtersGmC filters

Transconductors• use of transconductors• local feedback• parallel differential pairs• othersTuning

Comparison


Increasing the IP3 by feedback

M1Vid/2 -Vid/2

2Ibias

-ioutiout

M1 M1Vid/2 -Vid/2

Ibias

-ioutiout

M1

IbiasR R 2R

IP3 ≈ 3.3 (VGS-VT)(1+gm1R)2 HD3/n2 n= 1+gm1R

HD3 = - 60 dB for Vid = 1 V requires VGS-VT = 0.38 V and gm1R = 3 !!!


Increasing the IP3 by FB and high loop gain

Additional local FB

2R

More FB with opamps

2R


Tuneable resistances


By tuneable feedback

M2Vid/2 -Vid/2

IbiasIbias

~ 2Ibias -ioutiout

M1

IP3 ≈ 3.3 (VGS - VT)n2

n= 1+

HD3

n2

gm1

gm2

Ref.Torrance etal CAS Nov.85, 1097-1104


By nonlinear feedback (input)

M2Vid/2 -Vid/2

IbiasIbias

-ioutiout

M1IP3 ≈ 3.3 (VGS1 - VT) n2

Ref. Krummenacher JSSC June 88, 750-758

n = 1+ HD3

n2

β1

4β2

No extra currentNo extra CM node !But limited VGS-VT !

gmtot =Ibias

n (VGS1 - VT)


By nonlinear feedback (as load)

M2

M1

Ref. Menolfi JSSC July 97, 968-976

Vid/2

Voutd

-Vid/2M3 Av =

n gm3gm1

n = 1+β3

4β2

2Rind ≈ 2 n

gm1


Low-distortion combination : power !

M2Vid/2 -Vid/2

IbiasIbias

iout

M1

M2

Ibias

-iout

M1


Reduced distortion by cross-coupling

M2Vid/2 -Vid/2

Ibias

Ibias

iout

M1

Ibias

-iout2Ibias

M3

Ref. Silva-Martinez JSSC July 91,946-955


Comparison (simulations)


Measured THD for transconductor

THD ≈- 60 dB2.4 VptpInput Voltage



Linear transconductor with opamps

Ref. Chang JSSC March 97,388-397


Table of contents



Comparison


Parallel differential pairs with offset Voltages

M2avid/2 -vid/2

IBIB

-ioutiout

M1a

Ref. Gilbert, JSSCDec. 82, 1179-1191

Voorman ECCTD 83Tanimoto, .. JSSC

July 91, 937-945

M2b M1b+ +--

VGG VGG VGG ≈ 1.3 kT/q≈ 34 mV


Transfer characteristics of parallel diff. pairs

iCE

IB

vId

iCE1a iCE2a

1

0.5

00

VGG = 34 mV

0.2

0.8

iCE =IB

1 + exp(-qvId /kT)


Parallel diff.pairs with different transistor sizes

vid/2 -vid/2

IBIB

-ioutiout

Bipolar : n ≈ 4

1 : nn : 1 Ref. in bipolar :Gilbert, JSSC, Dec. 82,

1179-1191Voorman, ECCTD 83

ESSCIRC 85JSSC, Aug.00, 1097-1108

Tanimoto, .. JSSCJuly 91, 937-945

De Veirman, JSSCMarch 92, 324-331

M2aM1a M2b M1b


Paralleling four differential pairs

Ref. Tanimoto,.. JSSC July 91, 937-945

Input range 160 mVptp (1% THD)

5th order filter… 9 kHz


Dual-input transconductor

Ref. De Veirman, JSSC, March 92, 324-331

7th order filter2 … 10 MHz

Input range96 mVptp (1% THD)


Parallel diff.pairs with different transistor sizes

vid/2 -vid/2

IB2IB1

-ioutiout

MOST : n ≈ 5

1 : nn : 1

Ref. in CMOS :Nedungadi, CAS

Oct 84, 891-894Voorman, JSSC

Aug.00, 1097-1108Luh, ESSCIRC 00

M2aM1a M1b M2b

Parameters :α = IB2 / IB1

v = VGST1 / VGST2VGST = VGS-VT

n = α v2


Cross-coupling for linearity and swing

Ref. Luh, USC, ESSCIRC 2000, 72-75


Multiplier or Amp. with distortion cancellation

vid/2 -vid/2

IB2IB1

iout

M1

iout

M2M1

Parameters :α = IB2 / IB1

v = VGST1 / VGST2

VGST = VGS-VT

Ref. Gilbert, JSSC Dec. 68, 365-373


Cross-coupling and source resistors

Ref. Prodanov, ESSCIRC 2001, 488-491

M2

vid/2 -vid/2

Ibias

-ioutiout

M3 M3M2

M1 M1


Cross-coupling and source followers

M2

vid/2 -vid/2

Ibias

-ioutiout

M3 M3

M2

Ref. Van Engelen, JSSC Dec.99, 1753-1764

M1 M1

iout =vid

Vg/2 -Vg/2

gm1

gm21 -

gm3

=vid

gm1

gm21 -

vg 1


Table of contents



Comparison


Linearity CMOS amplifier

vout

IDS

M1

M2

vinCL

VDD

Vin = Vout = 2

VDD

Ln

Wn

Lp

Wpif K’n = K’p

vout

vin

VDD

VDD0VTn VTp

QVDD/2

VDD/2

very linear !


Linearized transconductors

Ref. Voorman, JSSC, Aug.2000, 1097-1108

CMFB


Transconductor for High Frequencies (2 nodes)

Ref. Nauta JSSC Febr.92,142-146

Iod = Io1 - Io2 = gmd VidTuning with Vdd

RDM1 = 1

gm5-gm6

RDM2 = 1

gm4-gm3

RCM2 = 1

gm4+gm3

RCM1 = 1

gm5+gm6


Transconductors with linear MOSTs

VDS1 = RDID ≈ 0.2 V

IDS1 = β1VDS1(VGS1-VT)

gm1 = β1VDS1 is constant

over wide range !

Ref. Alini, JSSC, Dec.92, pp.1905-1915


Alternative solutions

Larger tuning rangeControls VDSVDSmin ≈ 0Vtuning down to 0

Vtuning

Vtuning

VIN

VIN

Smaller tuning rangeControls VGS -VTVGSTmin limited by linearityVtuning from VT up


Ref. Alini, JSSC, Dec.92, pp.1905-1915

No rejection ofCM signals (CMRR = 0 dB)

Biasing imposed by previous circuit !

Pseudodifferential transc. with linear MOSTs


gm1 = β1VDS1is constantover wide range !

Ref. Laber, JSSC, April 93, 462-470

Transconductors with linear MOSTs


Table of contents

Active RC filtersMOSFET-C filtersGmC filters• Transconductors• TuningComparison



Gm-R-C versus Gm-C filters

-vIN vOUTCL

+Gm Gm

-

+

Cp

Cp

-vIN CL

+Gm

Cp

Cp

R

fo foQ Q

vOUT

-

+


Gm-R-C filters

if fo << fpar

2π

1 gm1gm2

C1C2

if g1 ≈ 0 (cascodes)

fo ≈

Q ≈gm2

g2+go2



Tunable R to tune Q

ROUT

ROUT ≈1

KP1 (VC-VGS2)W1L1


Tuning systems : transconductance tuning

+-

+-gm

Cint

Iref = Vref / R

Iref = gmVrefgm = 1/ R

vOUT = vtune

R

-+

VrefIref


Tuning systems : frequency tuning

+-

+-gm

vtune

CfcvOUT

φφ

Ref. Viswanathan, JSSC Aug.82, 775-778Silva, JSSC Dec. 92, 1843-1853

-+

Vref

R = 1/ Cfc

Iref = Cfc Vref

Iref = gmVrefgm = Cfc

Cint


Fully-differential tuning system realization

Ref. Chang, JSSC March 1997, 388-397


Tuning systems : frequency tuning with low fc

+-

IB

+-

IB/N

gm

vtune

C

t

vOUT Qgm = C IB/gm

QIBN = IB/N Tc

fc

gm = NfcCTc

Chargebalancing :No crosstalk

vOUTφφ

Ref. Silva

Cint


gm = NfcC

Fully-differential frequency tuning system

NIBIB

IB NIB

C

CVf

OTA OTA

Ref. Silva, JSSC Dec. 92, 1843-1853


Tuning systems : Q tuning

H(t) = 1 -

1 4Q2

exp( - ) sin( ωot + θ)1 t.BW

2 1 -1

4Q2

No HF PLL or VCO !

Detection at fc !

Unity-pulse response Biquad :

Envelop

Average


Q tuning with active resistor

LPF

Rtune

AMP


Comparison of 10.7 MHz filters

SC OTA-C Gm-RC

fc (BW = 250 kHz) 10.7 MHz 12.5 MHz 10.7 MHz

Order filter 6 4 4

Vin @ IM3= 1% 0.24 VRMS 0.32 VRMS 0.71 VRMS

DR @ IM3= 1% 34 dB 51 dB 68 dB

Power (± V) 500 mW(± 5) 360 mW(± 6) 220 mW(± 2.5)

Chip area 2 mm2 7.8 mm2 6 mm2


Ref. Dehaene JSSC July 97, 977-988

Biquad with matched nodes

C = ΣCparasitic

gm2* = gm2 + Σgo

CC

Av =gm3

gm1 (γ2+1)

gm1

2γ

(γ2+1)

γ

(γ2+1)fo =1

2π ττ =

gm2*γ =

gm2*C

Biquad for 7th-order Filter at 50 MHz

Q =


Ref. Dehaene JSSC July 97, 977-988

gm1γ =

gm2*Φ1 closed : γ tuning mode Φ1 closed :

offset calibration mode for all OTA’s

(Vref set to 0)gm1

Vn+,n- = gOTA Vref = kVref gOTAgm2*1k

gOTA gOTA

γ =

Tuning system for Q : conductance ratio γ


Charge balancing : V1,int = V2,int or

k12

γ1

Vref

Cint

gm τ1 = τ2γ2

Vrefk12Cint

gm

γ2

γ1

τ2τ1

= k12γ2γ1

Tuning system for the ratio of time constants


Table of contents




Signal to Noise + Distortion ratio

RC (GBW)dB

f

100

80

60

40

2010 k 100 k 1 M 10 M 100 M 1 GHz

MOST-C (GBW)

SC (settling)

gmC (linearity)

SI (mismatch) gmC

+ Disto - Tuning

+ Tuning - Disto

+ Tuning - HiFr+ Power, Disto+ Tuning - Disto+ HiFr

+HiFr - DR


Table of contents



Continuous-time filters - Springerextras.springer.com/2006/978-0-387-25746-4/Chapter_19.pdfWilly...

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