switched-capacitor filters - extra...
Post on 07-Apr-2018
250 Views
Preview:
TRANSCRIPT
Willy Sansen 10-05 N171
Switched-capacitor filters
Willy Sansen
KULeuven, ESAT-MICASLeuven, Belgium
willy.sansen@esat.kuleuven.be
Willy Sansen 10-05 N172
Switched-Capacitor Filters
• Introduction : principle• Technology:
• MOS capacitors• MOST switches
• SC Integrator• SC integrator : Exact transfer function• Stray insensitive integrator• Basic SC-integrator building blocks
• SC Filters : LC ladder / bi-quadratic section• Opamp requirements
• Charge transfer accuracy• Noise
• Switched-current filters McCreary, JSSC Dec 75, 371-379Gregorian, IEEE Proc. Aug 83, 941-986
Willy Sansen 10-05 N173
Principle
φ1φ2
• Non overlapping clocks• Switches are MOSTs
CQ Q
φ1 φ2V1 V2
Iav = =
Iav
C(V1-V2)
Tc = 1/ fc
Qav
Tc Tc
Iav = (V1-V2)
R
R = = Tc
For C = 1 pF & fc = 100 kHz R = 10 MΩ
1
fcCC
I2 Iav
t
t
Willy Sansen 10-05 N174
Low-Pass Filter with R’s and C
+
Av0 =
f-3db =
Ratio’s of R: 0.5% accuracy
R1 R2
C
-
R1
R2
2πR2C1
f-3dB f
Av0
Av
1
-20 dB/dec
Absolute value of RC : 20 % accuracy
vIN vOUT
Willy Sansen 10-05 N175
Low-Pass Filter with switched C’s
+
High accuracy: only ratio’s of C: 0.2%Only capacitors to drive : low power !Tunable & easy to integrate !But : only for frequencies << fc
-1 2
1 2
C
C1
C2R1 R2
C
-
+
Av0 =
f-3db =
C2
C1
2πfc
CC2
vOUTvIN
vOUT
vIN
Willy Sansen 10-05 N176
Example of 4th-Order SC Low-Pass filter
LC proto-type
SC ladder filter
Willy Sansen 10-05 N177
4th-Order SC Low-Pass filter
Capacitors
SwitchesOpamps
Clock
Willy Sansen 10-05 N178
Switched-Capacitor Filters
• Introduction : principle• Technology:
• MOS capacitors• MOST switches
• SC Integrator• SC integrator : Exact transfer function• Stray insensitive integrator• Basic SC-integrator building blocks
• SC Filters : LC ladder / bi-quadratic section• Opamp requirements
• Charge transfer accuracy• Noise
• Switched-current filters McCreary, JSSC Dec 75, 371-379Gregorian, IEEE Proc. Aug 83, 941-986
Willy Sansen 10-05 N179
Capacitors: metal-n+ & Metal-poly
Carea ≈ 5 fF/µm2
Cp ≈ 1.2 fF/µm2
Carea / Cp ≈ 1/4• Voltage dependent• Rsub: noise
Carea ≈ 2 fF/µm2
Cp ≈ 1 fF/µm2
Carea / Cp ≈ 1/2
• Linear• Large parasitics: Multi-layer !
Willy Sansen 10-05 N1710
Capacitor Matching
Common centroide lay-out !
Constant Area / Perimeter !
Willy Sansen 10-05 N1711
Random Error (σ)
1%
σ
Log (C)
local vs global tox effects
0.1%
Willy Sansen 10-05 N1712
Capacitances in nanometer CMOS
vias• Digital technology, no MIM cap.• lateral metal-metal capacitance• 8 metal layers, 1.7 fF/μm2
• Good matching
• MIM capacitors• 5 metal layers, 0.35 fF/μm2
• Excellent matching
Aparicio, JSSC March 02, 384-393
Willy Sansen 10-05 N1713
Switched-Capacitor Filters
• Introduction : principle• Technology:
• MOS capacitors• MOST switches
• SC Integrator• SC integrator : Exact transfer function• Stray insensitive integrator• Basic SC-integrator building blocks
• SC Filters : LC ladder / bi-quadratic section• Opamp requirements
• Charge transfer accuracy• Noise
• Switched-current filters McCreary, JSSC Dec 75, 371-379Gregorian, IEEE Proc. Aug 83, 941-986
Willy Sansen 10-05 N1714
A MOST as a switch
1 2
W= 2 µm L = 0.7 µmKPn = 80 µA/V2
VT = 0.7 VVh = 3 V
02468101214161820
0 1 2 3
Input Signal
1 2
Ron =KPn (Vh-VT-Vsign)W
L
1
Willy Sansen 10-05 N1715
Double Switch or transmission gate
nMOST: Vin < VDD-VGS,n ≈ VDD - 0.7 VpMOST: Vin > VGS,p ≈ 0.7 VMinimum Vh = VDD : VDD-VGS,n = VGS,p => VDD > 1.4 V
Switch:
Φ1
Φ1
VinC
Φ1
Φ1
VinC
Willy Sansen 10-05 N1716
Double Switch
02468101214161820
0 1 2 3
Input Signal
RnmosRpmosRon
RpMOST RnMOST
Willy Sansen 10-05 N1717
Low Voltage SC : MOST-Switch
VDD0 VTpVDD-VTn
nMOSTpMOST
1.3 V
?
VDD-VGS
VDD0 VTp VDD-VTn
nMOSTpMOST
3 VgDS gDS
Willy Sansen 10-05 N1718
Low Voltage SC : MOST-Switch
0 1.0 2.0 3.0 4.0 5.0VIN
4.0 k
3.0 k
2.0 k
0 0.5 1.0 1.5 2.0VIN
60 k
40 k
20 k
0 k
VDD =5 V
VDD =1.8 V
Ron
Willy Sansen 10-05 N1719
Time constant of Ron
Vin
time
Vout
ε
ts
Vout = Vin (1-exp(- ))
ts = RC ln(1/ε)ts ≈ 7 RC for ε = 0.1 %
Speed if large C (low noise)large R (small switch)
1Vin VoutVin
RCtRonVout
C C
Willy Sansen 10-05 N1720
For W/L = 2 and VGS-VT ≈ 1 VRon ≈ 10 kΩFor C ≈ 1 pFFor ε ≈ 0.1% ts = 7 RC ≈ 70 nsTc = 140 ns fmax ≈ 7 MHz
Maximum frequency of operation
Due to only one switch
practical fmax : 1-10 MHz
φ1
Tmax = 1/fmax
ts
L Ron
Willy Sansen 10-05 N1721
For Cmin ≈ 0.25 pF (mismatch)∆Vc = 1% of 0.1 V or ∆Vc = 1 mV dt = Tc/2 with Tc = 1/fcmin
Minimum frequency of operation
φ1 φ1φ2 φ2
VC
t0
∆VC
Tc
Leakage i = CdVC
dti is 10 nA/cm2 at 25o
is 10 µA/cm2 at 125o
For 10x1 µm: 2 fA (25o)or 2 pA (125o)
fcmin =i
2 Cmin ∆Vc= 4 Hz or 4 kHz (125o)
Willy Sansen 10-05 N1722
Clock Feed-Through
Overlap Capacitors Covl ≈ W Covlo
W ↑ ⇒ R ↓ but Covl ↑
Example : W = 3µm L = 0.7µm Covlo = 0.5 fF/µm
⇒ Covl ≈ 1 fF
∆V: Q = Covl (Vh-Vl) ≈ 1fF. 3V ≈ 3fC
⇒ ∆V ≈ ≈ 3fC/1pF ≈ 3 mVQC
Covl
C
Willy Sansen 10-05 N1723
Charge redistribution
Inversion layer charge Qm ≈ CoxWL(Vh-Vsign-VT)
Ex. W = 3µm L = 0.7µm Cox = 1.6 fF/µm2
VT = 0.7V Vsign = 1.5V
⇒ Q ≈ 6 fC∆V: Half is stored in each cap⇒ ∆V ≈ Q/2C ≈ 3 fC/1pF ≈ 3 mV
Total: ∆V ≈ 10 mV/pF C ↑ ⇒ CD ↓ Speed ↓ Power ↑
Willy Sansen 10-05 N1724
Clock injection & Charge redistribution
If Covl,n = Covl,p
No Clock FT !
Problems: matchingWn = Wp ?
Φ
Φ
Φ
Φ
Dummy Switch
6/0.7
3/0.7
OK if Q is split equal 1/2
Problems: clock skewrise/fall timeimpedance
Willy Sansen 10-05 N1725
Quantitative Charge Redistribution
Ci/C
Ci >> C, B >>1 ∆Q 0
NO dummy
Ci << C, B >>1∆Q QDummy
Ci = C: ∆Q=Q/2Dummy
B<<1 : ∆Q=Q/2 Dummy
High Speed Clocks
Low Speed Clocks
Ref. Wegmann, Vittoz, JSSC Dec.87, 1091-1097
β = µCox.W/La = dV/dtVTe = effective VT (with bulk effect)
Willy Sansen 10-05 N1726
Layout considerations
Reduce Cox area Use metal to ‘shield’
clock lines
Parasitic C⇓
CFT
Willy Sansen 10-05 N1727
Switched-Capacitor Filters
• Introduction : principle• Technology:
• MOS capacitors• MOST switches
• SC Integrator• SC integrator : Exact transfer function• Stray insensitive integrator• Basic SC-integrator building blocks
• SC Filters : LC ladder / bi-quadratic section• Opamp requirements
• Charge transfer accuracy• Noise
• Switched-current filters McCreary, JSSC Dec 75, 371-379Gregorian, IEEE Proc. Aug 83, 941-986
Willy Sansen 10-05 N1728
Sampling analog signals
VoutVin
Φ1
Φ1
C
Vin
Vout
Willy Sansen 10-05 N1729
Spectra
Input signal vin
Sampled signal fc/2 >> fsignal
Sampled signal fc/2 < fsignalNyquist !
fs
fs fc
fs fc fc 3fc
f
f
f
fc/2
fs
|Vin|
|Vout|
|Vout|
Willy Sansen 10-05 N1730
Anti-Aliasing filter
fcfs ffc-fs
Willy Sansen 10-05 N1731
Anti-aliasing / Reconstruction
N-order filter:N
fsfc − fs[ ] =
−Attenuation2010 fc = fs.
Attenuation20.N10
Ex. Attenuation = 40 dB; fs = 10 kHz ; N = 1 fc = 1 MHz
Willy Sansen 10-05 N1732
Sampled Data Basics : z-transform
Analog System: s = jω
Sampled data: z-transforms1 delay is z-1
z = e = ejωTc j2πf
e = 1 + jωTc + jωTc (jωTc)2
2
VoutVin
11 + sRC
=
fc
R C
+ …… if ωTc << 1
Willy Sansen 10-05 N1733
SC-Integrator in phase 1
+-
RC
Vout(s) =−Vin(s)sRC
+-1 2
C
aC
timetntn-1/2tn-1
Φ1
Φ2Φ1 QaC1 = aC Vin(n-1/2)
QC1 = - C Vout (n-1)Vout(n-1/2) = Vout(n-1)
Willy Sansen 10-05 N1734
SC-Integrator in phase 2 : charge conservation
+-
RC
Vout(s) =−Vin(s)sRC
+-1 2
C
aC
timetntn-1/2tn-1
Φ1
Φ2 Φ2
- C Vout (n) = aC Vin (n-1/2) - C Vout (n-1)
QaC2 = 0QC2 = - C Vout (n)
QaC2 +QC2 = QaC1 +QC1
Willy Sansen 10-05 N1735
SC-Integrator : approximate transfer function
- C Vout (n) = aC Vin (n-1/2) - C Vout (n-1)
Vout (n-1) = z-1 Vout
C.Vout = z-1 C Vout - z-1/2 aC Vin
⇒VoutVin
≈ −a(1− jωTc/ 2)
jωTc≈ −
ajωTc
Integrator
RC = aTc
= - az-1/2
1 - z-1
Vout
Vinz-1 = e ≈ 1 - jωTc
-jωTc
Willy Sansen 10-05 N1736
Exact Transfer function
Euler’s relationship:
sin(x) =+ jxe − − jxe2 j
f/fc = 0.1error ≈ 0.1%
H(z) = -az-1/2
1 - z-1
H(e ) = -ae1 - e
jωTc-jωTc/2
-jωTc
H(e ) = -a
e - ejωTc
jωTc/2
jωTc
-jωTc/2
H(e ) = -ajωTc ωTc/2
sin(ωTc/2)
Willy Sansen 10-05 N1737
The sin(x)/x function
x
sin(x) ≈ x - + .. x3
3
sin(x) ≈ 1 - + ..x2
3
For x = 0.1sin(x)/x ≈ 1 - 0.003
For x = 0.05sin(x)/x ≈ 1 - 0.0008
≈ 1 - 0.001
Willy Sansen 10-05 N1738
Switched-Capacitor Filters
• Introduction : principle• Technology:
• MOS capacitors• MOST switches
• SC Integrator• SC integrator : Exact transfer function• Stray insensitive integrator• Basic SC-integrator building blocks
• SC Filters : LC ladder / bi-quadratic section• Opamp requirements
• Charge transfer accuracy• Noise
• Switched-current filters McCreary, JSSC Dec 75, 371-379Gregorian, IEEE Proc. Aug 83, 941-986
Willy Sansen 10-05 N1739
Stray Capacitances
+-1 2
C
aC
Stray Cap at input:Substrate couplingContinuous timePSRR very bad
Stray Cap at output:Cp is extra load
for opamp
Willy Sansen 10-05 N1740
Stray Capacitances
+-1 2
CaC
Cp ≈ 2.CjS.Area ≈ 20 fF
Gain =aC + 2Cp
C
error ≈2CpaC
≈ 5 −10%
Willy Sansen 10-05 N1741
Stray Insensitive SC integrator
+-1 2
C2 = CC1 = aC
12
Av =C1C2
= a
vIN+
-vOUT
Willy Sansen 10-05 N1742
Stray Insensitive SC integrator
+-
CaC
Av =C1C2
= a
vIN+
-vOUT
Φ1
Willy Sansen 10-05 N1743
Stray Insensitive SC integrator
+-
CaC
Av =C1C2
= a
vIN+
-vOUT
Φ2
Willy Sansen 10-05 N1744
Stray Insensitive Integrator during phase 1
+-1 2
CaC
12
Φ1 aC
Q = 0 no effectQaC = aC VinQcp = Cp Vin
Av =C1C2
τ =1afc
CpCp
Cp Cp
= a
Willy Sansen 10-05 N1745
Stray Insensitive Integrator during phase 2
+-1 2
CaC
12
Φ2 aC
Qcp is discharged
to gnd Virtual groundQcp remains 0Only QaC is transferred
CpCp
Cp Cp
+-
C
Willy Sansen 10-05 N1746
Switched-Capacitor Filters
• Introduction : principle• Technology:
• MOS capacitors• MOST switches
• SC Integrator• SC integrator : Exact transfer function• Stray insensitive integrator• Basic SC-integrator building blocks
• SC Filters : LC ladder / bi-quadratic section• Opamp requirements
• Charge transfer accuracy• Noise
• Switched-current filters McCreary, JSSC Dec 75, 371-379Gregorian, IEEE Proc. Aug 83, 941-986
Willy Sansen 10-05 N1747
Loss-less Integrators
-
1 2
C1
C2
+
H(z) =C1
C2
z-1
1 - z-1
12
2
1H(z) =
C1
C2
z-1/2
1 - z-1
H(z) = -C1
C2
z-1/2
1 - z-1
H(z) = -C1
C2
11 - z-1
-
1
2
C1
C2
+1
2
2
1
Willy Sansen 10-05 N1748
Low-pass filter of 1st order
-1 2
1 2
C1
C2+
Av =C1C2
BW =fc
2π
vINvOUT
C
C2C
Damped because of R//C !
Willy Sansen 10-05 N1749
Damped integrators
Non-inverting damped integrator
Inverting Damped integrator
-
(c)
Willy Sansen 10-05 N1750
Offset compensation
-1
aC+2
21vIN
vOUTvos
1
+-
C
Av = a z-1/2
independent of vos
Gregorian, IEEE Proc. Aug 83, 941-986
Willy Sansen 10-05 N1751
Offset compensation
-
aC
+vIN
vOUTvos+-
C
QaC1 = aC (vos - vIN(n-1/2))QC1 = C vos
-
aC
+vos+-
Φ1 Φ2
+
+
vOUT
Av = a z-1/2
QaC2 = aC vosQC2 = C (vos - vOUT(n))
QaC1 + QC1 = QaC2 + QC2
C
Willy Sansen 10-05 N1752
Switched-Capacitor Filters
• Introduction : principle• Technology:
• MOS capacitors• MOST switches
• SC Integrator• SC integrator : Exact transfer function• Stray insensitive integrator• Basic SC-integrator building blocks
• SC Filters : LC ladder / bi-quadratic section• Opamp requirements
• Charge transfer accuracy• Noise
• Switched-current filters
Gregorian, Temes, Analog MOS Integrated Circuits for Signal Processing, Wiley, 1986
Laker, Sansen, Design of Analog Integrated Circuits and Systems, McGrawHill, 1994
Johns, Martin, Analog Integrated CircuitDesign, Wiley 1997
Willy Sansen 10-05 N1753
Capacitors
SwitchesOpamps
Clock
Clock freq 100 kHzCut-off 5 kHzPass ripple 0.25dBStop reject >45 dBPower 190µW (± 2.5V)S/N 75 dBHarm dist 0.25%Area 0.9 mm2
4th Order SC low-pass ladder filter
Willy Sansen 10-05 N1754
Biquadratic filter
Willy Sansen 10-05 N1755
Switched-Capacitor Filters
• Introduction : principle• Technology:
• MOS capacitors• MOST switches
• SC Integrator• SC integrator : Exact transfer function• Stray insensitive integrator• Basic SC-integrator building blocks
• SC Filters : LC ladder / bi-quadratic section• Opamp requirements
• Charge transfer accuracy• Noise
• Switched-current filters McCreary, JSSC Dec 75, 371-379Gregorian, IEEE Proc. Aug 83, 941-986
Willy Sansen 10-05 N1756
Opamp parameters
A0
1
|A|
fd f
Loop gain (1+T) ≈ T
GBW
Feedback factor α
Ac0 = 1/ α
T = A0 / Ac0 = α A0 Ac0
BW = α GBW
BW
GBW = gm
2π Ceff
α
Willy Sansen 10-05 N1757
Static error
Vout , t = ∞ = −Ao.Vstep1 +α.Ao
εS =Vstep /α −VoutVstep /α
=1−Ao
1+ Ao.α≈
1α .Ao
Ao >1
α.εSMinimum Gain
ε = 0.05%
A0 ≈ 1-10k≈ 60-80 dB
Willy Sansen 10-05 N1758
Dynamic error
εD = EXP(−α.gm.tSCL, ef
)
GBW >fc
π.αln(1εD)Minimum GBW:
GBW =gm2πCL, ef
εD = EXP(−α.2π.GBW.tS) tS =12 fc
GBW =1
α.2π .tSln(1εD) =
2 fc2π.α
ln(1εD)
ε = 0.05%
GBW ≈ 2-3*fc
Willy Sansen 10-05 N1759
Switched-Capacitor Filters
• Introduction : principle• Technology:
• MOS capacitors• MOST switches
• SC Integrator• SC integrator : Exact transfer function• Stray insensitive integrator• Basic SC-integrator building blocks
• SC Filters : LC ladder / bi-quadratic section• Opamp requirements
• Charge transfer accuracy• Noise
• Switched-current filters McCreary, JSSC Dec 75, 371-379Gregorian, IEEE Proc. Aug 83, 941-986
Willy Sansen 10-05 N1760
kT/C versus kTR noise
Narrow-band noise >> noise density : dvni2 = 4kT R df
kTC
Wide-band noise >> integrated noise : vni2 =
fc GBW
dvni2
vni2 =
kTC
GBW
f
fc/2
2fc 3fcfc2
Willy Sansen 10-05 N1761
Switched-Capacitor Filters
• Introduction : principle• Technology:
• MOS capacitors• MOST switches
• SC Integrator• SC integrator : Exact transfer function• Stray insensitive integrator• Basic SC-integrator building blocks
• SC Filters : LC ladder / bi-quadratic section• Opamp requirements
• Charge transfer accuracy• Noise
• Switched-current filters McCreary, JSSC Dec 75, 371-379Gregorian, IEEE Proc. Aug 83, 941-986
Willy Sansen 10-05 N1762
Switched-current delay block
Ref. Zele JSSC Feb. 96, 157- 168
M1 M2
IBIB
Iout
1 : 1
IinSwitch closed : track VGS
Iout = IinClock
Switch open : hold VGSIout = Iin (∆Tc)
Iout = Iin z-1/2
Willy Sansen 10-05 N1763
Switched-current low-pass filter
Ref. Zele JSSC Feb. 96, 157- 168
M1 M2 IB
IBiout = Kif
1 : 1
if
if = if z-1 - iin z-1/2K z-1/2
1 - z-1
Clock1 Clock2
iin
ioutiin
=
1 : K
KIB
if
Willy Sansen 10-05 N1764
2nd-generation switched-current filter
A1z-1
1 - Bz-1io(z) = i1(z) - i2(z) -
A2z-1
1 - Bz-1
A3(1-z-1)
1 - Bz-1i3(z)
A1 = 1 + α4
α1
A2 = 1 + α4
α2
A3 = 1 + α4
α3
B = 1 + α4
1
Willy Sansen 10-05 N1765
Comparison SC - SI
SC SI
Signal : Voltage CurrentCharge on linear C Charge on MOST CGS
Q = C V Q = I tAccuracy : Capacitor ratio MOST area ratio
0.2 % 2 %Amps : Opamps Current mirrorsS/N+D 70 dB 50 dB
Willy Sansen 10-05 N1766
Switched-Capacitor Filters
• Introduction : principle• Technology:
• MOS capacitors• MOST switches
• SC Integrator• SC integrator : Exact transfer function• Stray insensitive integrator• Basic SC-integrator building blocks
• SC Filters : LC ladder / bi-quadratic section• Opamp requirements
• Charge transfer accuracy• Noise
• Switched-current filters McCreary, JSSC Dec 75, 371-379Gregorian, IEEE Proc. Aug 83, 941-986
top related