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Continuous-time filters
Willy Sansen
KULeuven, ESAT-MICAS
Leuven, Belgium
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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
Ref.: Silva-Martinez, Dehaene, ..
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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
use of transconductors
local feedback
parallel differential pairs
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
use of transconductors
local feedback
parallel differential pairs
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
Ref.: Silva-Martinez, Dehaene, ..
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
Ref.: Tsividis, Voorman, Integrated Cont.-time filters, IEEE Press 1993
J. Silva-Martinez, Kluwer 1993,
W. Dehaene, JSSC, July 1997, 977-988
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
Ref.: Tsividis, Voorman, Integrated Cont.-time filters, IEEE Press 1993
J. Silva-Martinez, Kluwer 1993,
W. Dehaene, JSSC, July 1997, 977-988