willy sansen CT filters

7/25/2019 willy sansen CT filters

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Willy Sansen 10-05 191

Continuous-time filters

Willy Sansen

KULeuven, ESAT-MICAS

Leuven, Belgium

[email protected]


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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 ?


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Table of contents

Active RC filters

MOSFET-C filters

GmC filters

Comparison

Ref.: Tsividis, Voorman, Integrated Cont.-time filters, IEEE Press 1993

J. Silva-Martinez, Kluwer 1993,

W. Dehaene, JSSC, July 1997, 977-988


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Active RC filters

Opamps and passive components (R, C)

+

-

C2

R1vINvOUT

C1

Cn

Disadvantages :

Opamps :

only for low frequenciesErrors on R, C 20 %

>> tune Cs

Advantages :

S/N up to 100 dB

THD very low < - 90 dB


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Table of contents

Active RC filters MOSFET-C filters

GmC filters Comparison

Ref.: Silva-Martinez, Dehaene, ..


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MOST resistors

VDS0

IDSlinear

saturation

VGS-VT

On-resistance :

Ron =

VDS > VGS-VT

1

(VGS-VT)

= KPWL

iDS = KP [(vGS-vT)vDS - ]W

L

vDS2

2

HD2


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Examples of differential MOST-Rs

partial cancellation of even nonlincancellation of even

and odd nonlinearities

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


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From active RC to MOSFET-C filter

Ref. Tsividis JSSC Feb.86, 15-30


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Large RON values at high frequencies

KP W/L (VGS-VT)

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

f-3dB = 2 RonC

1

2 C

For f-3dB = 4 kHz; KP= 60 A/V2; VGS-VT = 1 V; W = 2 m; C = 10 pF

Ron= 4 M. For matching W = 2 m: L 500 m ! The area is 10-5 cm2

For Cox = 5.10-7 F/cm2 (0.35 m); CGS = 5 pF;

High-frequency limit at 8 kHz or fT8 kHz !!!!!!


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LC ladder filter

Ref. Banu

JSSC Dec.85,

1114-1121


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Fifth-order low-pass filter

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

-vINvIN

v


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Fifth-order elliptic low-pass filter

Ref. Tsividis

JSSC Feb.86,

15-30


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PLL tuning

Ref.

Banu JSSC Dec.85,

1114-1121

Krummenacher, JS

SC June 88, 750-758

Khoury, JSSC

Dec.91, 1988-1997

Problems:

Master/slave for

each pole/zero

VCO + PLL at fc

Signal feedthrough

at fc

Filter


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Table of contents

Active RC filters

MOSFET-C filters GmC filters

Transconductors Tuning

Comparison



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Some GmC filters

Single-ended GmC filters

Fully-differential ...


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GmC filter definition

Operational

amplifier

Opamp OTA

Operational

Transconduct.

amplifier

+

-+

-

Av =vOUT

vINAg =

iOUT

vIN

Av = = Ag RL

+

-vIN

Ag or Gm (Ibias)

Ibias

vOUT

C

Disadv.: Distortion

Mismatch errors

Parasitic Cs (low Q)

Adv.: High freq. operation

Easy tuning

iOUT


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Simple GmC filters

+-ZIN

+

-vIN1vOUT

C

gm

+

-vIN

C

vIN2

R

vOUT

vOUT

vIN1- vIN2

=gm

sC

vOUT

vIN =

gmR

1+ sRC


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Simple GmC filters

+-

gm2

+

-vIN

C

vOUT

vOUT

vIN =

gm1

gm2 + sC

gm1

f

gm1gm2

gm1

2

C

gm22C


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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


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Voltage-mode & current-mode filters


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A differential pair as a transconductor

M1Vid/2 -Vid/2

Ibias

-ioutiout

M1

VId

VGS

- VT

U =

IM3 = 3HD3 = U2

U is the relative current swing

3

32

IP3 3.3 (VGS - VT)

Max. Vidptp 2 2 (VGS - VT)

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


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Amplifier or transconductor ?

vod

vind

slope gm

RLIB

-RLIB

2 (VGS -VT)0

bipolarMOST transconductor

Transconductor :Wide input range : low distortion

Small gain gm


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Table of contents

Active RC filters

MOSFET-C filters

GmC filters

Transconductors

use of transconductors

local feedback

parallel differential pairs

others

Tuning

Comparison


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Increasing the IP3 by feedback

M1Vid/2 -Vid/2

2Ibias

-ioutiout

M1 M1Vid/2 -Vid/2

Ibias

-ioutiout

M1

Ibias

R R 2R

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

2 n= 1+gm1R

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


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Increasing the IP3 by FB and high loop gain

Additional local FB

2R

More FB with opamps

2R


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Tuneable resistances


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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


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By nonlinear feedback (input)

M2Vid/2 -Vid/2

IbiasIbias

-ioutiout

M1

IP3 3.3 (VGS1 - VT) n2

Ref. Krummenacher JSSC June 88, 750-758

n = 1+HD3

n2

1

42

No extra currentNo extra CM node !

But limited VGS-VT !

gmtot =Ibias

n (VGS1

- VT

)


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By nonlinear feedback (as load)

M2

M1

Ref. Menolfi JSSC July 97, 968-976

Vid/2

Voutd

-Vid/2M3 Av =

n gm3gm1

n = 1+ 3

42

2Rind2 n

gm1


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Low-distortion combination : power !

M2Vid/2 -Vid/2

IbiasIbias

iout

M1

M2

Ibias

-iout

M1


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Reduced distortion by cross-coupling

M2Vid/2 -Vid/2

IbiasIbias

iout

M1

Ibias

-iout2Ibias

M3

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


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Comparison (simulations)


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Measured THD for transconductor

THD

- 60 dB

2.4 Vptp

Input Voltage

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


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Linear transconductor with opamps

Ref. Chang JSSC March 97,388-397


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Table of contents

Active RC filters

MOSFET-C filters

GmC filters

Transconductors


local feedback


others

Tuning

Comparison


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Parallel differential pairs with offset Voltages

M2avid/2 -vid/2

IBIB

-ioutiout

M1a

Ref. Gilbert, JSSCDec. 82, 1179-1191

Voorman ECCTD 83

Tanimoto, .. JSSC

July 91, 937-945

M2b M1b+ +--

VGG VGG VGG 1.3 kT/q

34 mV


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Transfer characteristics of parallel diff. pairs

iCE

IB

vId

iCE1a iCE2a

1

0.5

0

0

VGG = 34 mV

0.2

0.8

iCE =IB

1 + exp(-qvId/kT)


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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,

1179-1191

Voorman, ECCTD 83

ESSCIRC 85

JSSC, Aug.00, 1097-1108Tanimoto, .. JSSC

July 91, 937-945

De Veirman, JSSC

March 92, 324-331

M2aM1a M2b M1b


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Paralleling four differential pairs

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

Input range 160 mVptp (1% THD)

5th order filter

9 kHz


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Dual-input transconductor

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

7th order filter

2 10 MHz

Input range

96 mVptp (1% THD)


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Parallel diff.pairs with different transistor sizes

vid/2 -vid/2

IB2IB1

-ioutiout

MOST : n 5

1 : nn : 1

Ref. in CMOS :

Nedungadi, CASOct 84, 891-894

Voorman, JSSC

Aug.00, 1097-1108

Luh, ESSCIRC 00

M2aM1a M1b M2b

Parameters :

= IB2

/ IB1

v = VGST1/ VGST2

VGST = VGS-VT

n = v2


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Cross-coupling for linearity and swing

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


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Multiplier or Amp. with distortion cancellation

vid/2 -vid/2

IB2IB1

iout

M1

iout

M2M1

Parameters :

= IB2/ IB1

v = VGST1/ VGST2

VGST = VGS-VT

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


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Cross-coupling and source resistors

Ref. Prodanov, ESSCIRC 2001, 488-491

M2

vid/2

-vid/2

Ibias

-ioutiout

M3 M3M2

M1 M1


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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


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Table of contents

Active RC filters

MOSFET-C filters

GmC filters

Transconductors


local feedback


others

Tuning

Comparison


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Linearity CMOS amplifier

vout

IDS

M1

M2

vin

CL

VDD

Vin = Vout =2

VDD

Ln

Wn

Lp

Wpif Kn = Kp

vout

vin

VDD

VDD0 VTn VTp

QVDD/2

VDD/2

very linear !


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Linearized transconductors

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

CMFB


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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

i i OS


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Transconductors with linear MOSTs

VDS1 = RDID0.2 V

IDS1 = 1VDS1(VGS1-VT)

gm1 = 1VDS1 is constant

over wide range !

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

Al i l i


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Alternative solutions

Larger tuning range

Controls VDSVDSmin0

Vtuning down to 0

Vtuning

Vtuning

VIN

VIN

Smaller tuning range

Controls VGS -VTVGSTmin limited by linearity

Vtuning from VT up

P d diff ti l t ith li MOST


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

No rejection of

CM signals

(CMRR = 0 dB)

Biasing

imposed by

previous circuit !

Pseudodifferential transc. with linear MOSTs

T d t ith li MOST


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gm1 = 1VDS1

is constantover wide range !

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

Transconductors with linear MOSTs

T bl f t t


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Table of contents

Active RC filters

MOSFET-C filters GmC filters

Transconductors

Tuning

Comparison


Gm R C versus Gm C filters


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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


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Gm-R-C filters

if fo


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Tunable R to tune Q

ROUT

ROUT 1

KP1 (VC-VGS2)W1

L1

Tuning systems : transconductance tuning


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Tuning systems : transconductance tuning

+

-+

-gm

Cint

Iref = Vref/ R

Iref = gmVref

gm = 1/ R

vOUT = vtune

R

-

+

VrefIref

Tuning systems : frequency tuning


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Tuning systems : frequency tuning

+

-+

-gm

vtuneC

fc

vOUT

Ref. Viswanathan, JSSC Aug.82, 775-778

Silva, JSSC Dec. 92, 1843-1853

-

+

Vref

R = 1/ Cfc

Iref = Cfc Vref

Iref = gmVref

gm = Cfc

Cint

Fully-differential tuning system realization


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Fully-differential tuning system realization

Ref. Chang, JSSC March 1997, 388-397

Tuning systems : frequency tuning with low f


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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= Nfc

CTc

Charge

balancing :

No crosstalk

vOUT

Ref. Silva

Cint

Fully-differential frequency tuning system


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gm= Nfc

C

Fully differential frequency tuning system

NIBIB

IB NIB

C

C

VfOTA OTA

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

Tuning systems : Q tuning


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Tuning systems : Q tuning

H(t) =

1 -1

4Q2exp( - ) sin( ot + )

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


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Q tuning with active resistor

LPF

Rtune

AMP

Comparison of 10.7 MHz filters


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p

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

Biquad for 7th-order Filter at 50 MHz


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Ref. Dehaene JSSC July 97, 977-988

Biquad with matched nodes

C = Cparasitic

gm2* = gm2 + go

CC

Av =gm3

gm1 (2

+1)

gm1

2

(2+1)

(2+1)fo =

1

2 =

gm2* =

gm2*C

q

Q =

Tuning system for Q : conductance ratio


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Ref. Dehaene JSSC July 97, 977-988

gm1 =

gm2*

closed : tuning mode closed :offset calibration

mode for all OTAs(Vref set to 0)

gm1Vn+,n- = gOTA Vref = kVref gOTAgm2*1

k

gOTA gOTA

=

g y Q

Tuning system for the ratio of time constants


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Charge balancing :

V1,int = V2,int or

k12

1

Vref

Cint

gm1 = 2

2

Vref

k12Cint

gm

2

1

2

1

= k122

1

g y

Table of contents


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Active RC filters

MOSFET-C filters

GmC filters

Comparison




Signal to Noise + Distortion ratio


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RC (GBW)dB

f

100

80

60

40

20

10 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


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Active RC filters

MOSFET-C filters

GmC filters

Comparison




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willy sansen CT filters