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EECS 247 Lecture 6: Filters © 2005 H.K. Page 1
EE247 Lecture 6
• Summary last lecture• Continuous-time filters
– Opamp MOSFET-C filters– Opamp MOSFET-RC filters– Gm-C filters
• Frequency tuning for continuous-time filters– Trimming via fuses– Automatic on-chip filter tuning
• Continuous tuning– Master-slave tuning
• Periodic off-line tuning– Systems where filter is followed by ADC & DSP, existing hardware
can be used to periodically update filter freq. response
EECS 247 Lecture 6: Filters © 2005 H.K. Page 2
Summary Last Lecture
• Continuous-time filters– Effect of integrator non-idealities on continuous-
time filter behavior– Facts about monolithic Rs & Cs and its effect on
integrated filter characteristics– Opamp RC filters– Opamp MOSFET-C filters
• Frequency tuning for continuous-time filters– Frequency adjustment by making provisions to
have variable R or C
EECS 247 Lecture 6: Filters © 2005 H.K. Page 3
Use of MOSFETs as ResistorsSingle-Ended Integrator
Problem: Single-ended MOSFET-C Integratorà Effective R non-linearNote that the non-linearity is mainly 2nd order type
( )
( )
( )
2ds
2i
W VCI V V VD ox gs th dsL 2
W VC V V VI ox gs th iD L 2I WD V V VCG gs th ioxV Li
µ
µ
µ
= − −
= − −
∂ − −= =∂
VG
oV
C
-
+
inV
ID
àTunable by varying VG:
EECS 247 Lecture 6: Filters © 2005 H.K. Page 4
Use of MOSFETs as ResistorsDifferential Integrator
Opamp-MOSFET-C
VGC
• Non-linear term cancelled!• Admittance independent of Vi
Problem: Threshold voltage dependence
+
+-
- outV
Vi/2
-Vi/2
( )( ) ( )
W VdsCI VV VD ox dsgs thL 2VVW iiCI V VD1 ox gs thL 24
VVW iiCI V VD2 ox gs thL 24W V VCI I Vgs thD1 D2 ox iL
I I WD1 D2 V VCG gs thoxV Li
µ
µ
µ
µ
µ
= − −
= − −
= − − +
−− =
∂ −−= =
∂
ID1
M1
M2ID2
C
EECS 247 Lecture 6: Filters © 2005 H.K. Page 5
MOSFET-C Integrator
VGC
à Common-mode voltage sensitivity
+
+-
- outV
Vi/2
-Vi/2
Vx
Vx
+
+-
-
Vi/2
-Vi/2
outV0V
0V
•For the Opamp-RC integrator, opamp input stays at 0V (virtual gnd.)
•For the MOSFET-C integrator, opamp input stays at the voltage Vx which is a function of 2nd order MOSFET non-linearities
EECS 247 Lecture 6: Filters © 2005 H.K. Page 6
Use of MOSFET as Resistor Issues
• Distributed nature of gate capacitance & channel resistance results in infinite no. of high-frequency poles à excess phase
• Filter performance mandates well-matched MOSFETs à long channel devices
• Excess phase increases with L2
àTradeoff between matching and integrator QàThis type of filter limited to low frequencies
MOS xtor operating in triode regionCross section view
Distributed channel resistance & gate capacitance
EECS 247 Lecture 6: Filters © 2005 H.K. Page 7
Example:Opamp MOSFET-C Filter
•Suitable for low frequency applications•Issues with linearity•Linearity achieved ~40-50dB•Needs tuning
5th Order Elliptic MOSFET-C LPF with 4kHz Bandwidth
Ref: Y. Tsividis, M.Banu, and J. Khoury, “Continuous-Time MOSFET-C Filters in VLSI”, IEEE Journal of Solid State Circuits Vol. SC-21, No.1 Feb. 1986, pp. 15-30
EECS 247 Lecture 6: Filters © 2005 H.K. Page 8
Improved MOSFET-C IntegratorVG1
C
No threshold dependenceFirst order Common-mode non-linearity cancelledLinearity achieved in the order of 60-70dB
+
+-
- outV
Vi/2
-Vi/2
VG2
ID1
M1
M2
ID2
M3
M4
I D3
ID4
IX1
IX2
( )( )
W VdsCI VV VD ox dsgs thL 2VW V iiCI V VD1 ox gs1 thL 24
VW V iiCI V VD3 ox gs2 thL 24I I IX 1 D1 D3
VW V iiC V Vox gs1 gs2L 22VW V iiCI V VX 2 ox gs2 gs1L 22
W V VCI I Vgs1 gs2X 1 X 2 ox iLI IX 1 X 2G
µ
µ
µ
µ
µ
µ
= − − = − −
= − − +
= +
= − − = − −
−− =
∂ −= ( )W V VC gs1 gs2oxV Li
µ −=∂
C
Ref: Z. Czarnul, “Modification of the Banu-Tsividis Continuous-Time Integrator Structure,” IEEE Transactions on Circuits and Systems, Vol. CAS-33, No. 7, pp. 714-716, July 1986.
EECS 247 Lecture 6: Filters © 2005 H.K. Page 9
R-MOSFET-C IntegratorVG1
C
•Improvement over MOSFET-C by adding resistor in series with MOSFET•Voltage drop primarily across fixed resistor à small MOSFET Vds àimproved linearity & reduced tuning range•Linearity in the order of 90dB possible•Generally low frequency applications
+
+-
- outV
Vi/2
-Vi/2
VG2
M1
M2
M3
M4
C
Ref: U-K Moon, and B-S Song, “Design of a Low-Distortion 22-kHz Fifth Order Bessel Filter,”IEEE Journal of Solid State Circuits, Vol. 28, No. 12, pp. 1254-1264, Dec. 1993.
R
R
EECS 247 Lecture 6: Filters © 2005 H.K. Page 10
R-MOSFET-C Lossy Integrator
VG1
C
Negative feedback around the non-linear MOSFETs improves linearityCompromises frequency response accuracy
+
+-
- outV
Vi/2
-Vi/2
VG2M1
M2
M3
M4
C
Ref: U-K Moon, and B-S Song, “Design of a Low-Distortion 22-kHz Fifth Order Bessel Filter,” IEEE Journal of Solid State Circuits, Vol. 28, No. 12, pp. 1254-1264, Dec. 1993.
R1
R2
R2
R2
EECS 247 Lecture 6: Filters © 2005 H.K. Page 11
Example:Opamp MOSFET-RC Filter
Ref: U-K Moon, and B-S Song, “Design of a Low-Distortion 22-kHz Fifth Order Bessel Filter,” IEEE Journal of Solid State Circuits, Vol. 28, No. 12, pp. 1254-1264, Dec. 1993.
•Suitable for low frequency applications•Significant improvement in linearity compared to MOSFET-C•Needs tuning
5th Order Bessel MOSFET-RC LPF -22kHz bandwidthTHD à-90dB for 4Vp-p 2kHz input signal
EECS 247 Lecture 6: Filters © 2005 H.K. Page 12
Operational Amplifiers (Opamps) versus Operational Transconductance Amplifiers (OTA)
• Low output impedance• Output in the form of voltage • Can drive R-loads• Good for RC filters,
OK for SC filters
• Extra buffer adds complexity, power dissipation
• High output impedance• In the context of filter design called
gm-cells• Output in the form of current • Cannot drive R-loads• Good for SC & gm-C filters• Typically, less complex compared to
opampà higher freq. potential• Typically lower power
Opamp OTAVoltage controlled Voltage controlled
voltage source current source
EECS 247 Lecture 6: Filters © 2005 H.K. Page 13
Integrator ImplementationTransconductance-C & Opamp-Transconductance-C
inV
oVGm
oV
C
inV
Gm
whereo o mo
in
V G
V s C
ωω
−= =
-
+∫
GmC Intg. GmC-OTA Intg.
-
+
EECS 247 Lecture 6: Filters © 2005 H.K. Page 14
Gm-C FiltersSimplest Form of CMOS Gm-C Integrator
• Transconductance element formed by the source-coupled pair
• All MOSFETs operating in saturation region
• Current in M1& M2 can be varied by changing Vcontrol
à Transconductance of M1& M2 varied through Vcontrol
Ref: H. Khorramabadi and P.R. Gray, “High Frequency CMOS continuous-time filters,” IEEE Journal of Solid-State Circuits, Vol.-SC-19, No. 6, pp.939-948, Dec. 1984.
controlV
oV
inV
-
+
+
-
int gCM1 M2
M10
EECS 247 Lecture 6: Filters © 2005 H.K. Page 15
Simplest Form of CMOS Gm-C IntegratorAc Half Circuit
int gC
oV
inV
-
+
+
-
M1 M2
M10 controlV
oV
inV
-
+
+
-
int g2C
M1 M2
M10
int g2C
controlV
inV intg2CM1
oV
AC half circuit
EECS 247 Lecture 6: Filters © 2005 H.K. Page 16
Gm-C FiltersSimplest Form of CMOS Gm-C Integrator
• Use ac half circuit & small signal model to derive transfer function:
M 1,2o m in int g
M 1,2o m
in int g
o o
inM 1,2m
oint g
V g V 2C s
V gV 2C s
VV s
g
2 C
ω
ω
= − × ×
= −
−=
→ =×
inV
intg2C
oVing Vm
CGS
inV intg2CM1
oV
AC half circuit
Small signal model
EECS 247 Lecture 6: Filters © 2005 H.K. Page 17
Gm-C FiltersSimplest Form of CMOS Gm-C Integrator
• MOSFET in saturation region:
• Gm is given by:
( )
( )
( )
2
M 1&M 2m
1 / 2
C Wox V VI gs thd 2 L
I Wd V VCg gs thoxV LgsId2
V Vgs th
1 WC2 Iox d2 L
µ
µ
µ
−=
∂ −= =∂
=−
=
Id varied via Vcontrol à gm tunable via Vcontrol
controlV
oV
inV
-
+
+
-
int gCM1 M2
M10
EECS 247 Lecture 6: Filters © 2005 H.K. Page 18
Gm-C Filters2nd Order Gm-C Filter
• Use the Gm-cell to build a 2nd order bandpass filter
controlV
oV
inV
-
+
+
-
int gCM1 M2
M10
EECS 247 Lecture 6: Filters © 2005 H.K. Page 19
2nd Order Bandpass Filter1 1
*RR *
1
sCR
'1V
2V
inV1− 1
1V
*R
sL
1−
oV
'3V
inV
1*R R 21
sτ11
sτ
∑
oV
--
* *1 2R C L Rτ τ= × =
oV
R CinI L CV
LI
+
- CILV
+
-
+
-RV
RI
EECS 247 Lecture 6: Filters © 2005 H.K. Page 20
2nd Order Integrator-Based Bandpass Filter
inV
11Q−
1sτ1
sτ
BPV
-
∑
BP 22in 1 2 2
* *1 2
*
0 1 2
1 2
1 2 *0
V sV s s 1
R C L R
R R
11
Q 1
Frommatch ing pointof viewdes i rab le :1 RQ
R
L C
β
β
β
ω
ττ τ τ
ω τ τ
τ τ
τ τ
τ τ
=+ +
= × =
=
= =
= ×
= = → =
EECS 247 Lecture 6: Filters © 2005 H.K. Page 21
2nd Order Integrator-Based Bandpass Filter
∑
inV
11Q−
1sτ
1sτ
BPV
-First implement this partWith transfer function:
0in
0
V 1V s 1
Qω
−=+
EECS 247 Lecture 6: Filters © 2005 H.K. Page 22
Terminated Gm-C Integrator
oV
inV
+
-
+
-
M1 M2
M10controlV
M3 M4
M11
int gC
inV intg2CM1
oV
AC half circuit
M3
EECS 247 Lecture 6: Filters © 2005 H.K. Page 23
Terminated Gm-C Integrator
inV intg2CM1
oV
AC half circuit
M3
oM 3in int g m
M 1 M 1m m
V 1V s 2C g
g g
−=
×+
inV
intg2C
oVinM 1g Vm
CGS
Small signal model
M 3gm
1
EECS 247 Lecture 6: Filters © 2005 H.K. Page 24
Terminated Gm-C Integrator
oM 3in int g m
M 1 M 1m m
M 1 M 1m m
0 M 3int g m
V 1V s 2C g
g g
g g& Q
2C gω
−=
×+
= =→
inV
intg2C
oVinM 1g Vm
CGS
Small signal model
M 3gm
1
∑
inV
11Q−
1sτ
1sτ
BPV
-
0in
0
V 1V s 1
Qω
−=+
Question: How to define Q accurately?
EECS 247 Lecture 6: Filters © 2005 H.K. Page 25
Terminated Gm-C Integrator
int gC
controlV
oV
inV
+
-
+
-
M1 M2
M10
M3 M4
M11
1 / 2M 1 M 1M 1m d
M 11 / 2
M 3 M 3M 3m d
M 3
1 / 2M 1M 1m d M 1M 3 M 3 M 3m d
W1 Cg 2 Iox2 L
W1 Cg 2 Iox2 L
Let us assume equal channel lengths for M1, M3 then:
Ig WWg I
µ
µ
=
=
= ×
EECS 247 Lecture 6: Filters © 2005 H.K. Page 26
Terminated Gm-C Integrator
int gC
controlV
oV
inV
+
-
+
-
M1 M2
M10
M3 M4
M111 / 2
M 1 M 10d dM 3 M 11d d
M 10d M 10M 11
M 11d
Note that:
I I
I I
Assuming equal channel lengths for M10, M11:
I W
I W
M1 Wg Wm M 10 M 1M 3 Wg W M 3m M 11
=
=
=
→
×
EECS 247 Lecture 6: Filters © 2005 H.K. Page 27
2nd Order Gm-C Filter
M 1,2mM 3,4m
gQg
=
• Simple design• Tunable• Q function of device ratios:
EECS 247 Lecture 6: Filters © 2005 H.K. Page 28
Filter Frequency Tuning Techniques
• Component trimming
• Automatic on-chip filter tuning– Continuous tuning
• Master-slave tuning
– Periodic off-line tuning• Systems where filter is followed by ADC & DSP, existing
hardware can be used to periodically update filter freq. response
EECS 247 Lecture 6: Filters © 2005 H.K. Page 29
Example: Tunable Opamp-RC Filter
oV
C-
+
inV
D0
R1 R2 R3 R4
R1
D1D2
R2 R3 R4
Post manufacturing:•Usually at wafer-sort tuning performed
•Measure -3dB frequency•If frequency too high decrement D to D-1•If frequency too low increment D to D+1•If frequency within 10% of the desired corner freq. stop
Not practical to require end-user to tune the filter à Need to fix the adjustment at the factory
EECS 247 Lecture 6: Filters © 2005 H.K. Page 30
Trimming• Component trimming
– Build fuses on-chip• Based on measurements @
wafer-sort 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
Fuse not blown à D1=1Fuse blown à D1=0
Fuse
To switch
D1
EECS 247 Lecture 6: Filters © 2005 H.K. Page 31
Example:Tunable/Trimmable Opamp-RC Filter
oV
C-
+inV
R1 R2 R3 R4
R1 R2 R3 R4
Fuse
D0
Fuse
D1
Fuse
D2
D2 D1 D0 Rnom1 1 1 7.2K1 1 0 8.28K1 0 1 9.37K………………………………………………………………………
0 0 0 14.8K
EECS 247 Lecture 6: Filters © 2005 H.K. Page 32
Automatic Frequency Tuning
• By adding additional circuitry to the main filter circuit– Have the filter critical frequency automatically
tuned à Expensive trimming avoidedà Accounts for critical frequency variations due to temperature, supply voltage, and effect of aging
EECS 247 Lecture 6: Filters © 2005 H.K. Page 33
Master-Slave Automatic Frequency Tuning
• Following facts used in this scheme:– Use a replica (master) of the main filter
(called the slave) in the tuning circuitry– Place the replica in close proximity of the main
filter – Use the tuning signal generated to tune the
replica, to also tune the main filter– In the literature, this scheme is called master-
slave tuning!
EECS 247 Lecture 6: Filters © 2005 H.K. Page 34
Master-Slave Frequency TuningReference Filter (VCF)
• Use a biquad for master filter (VCF)• Utilize the fact that @ the frequency fo the lowpass (or highpass)
outputs are 90 degree out of phase wrt to input
• Apply a sinusoid at the desired fo• Compare the LP output phase to the input• Based on the phase difference
– Increase or decrease filter critical freq.
oLP o2in2o o
V 1 @ 90V s s 1Q
ω ω φ
ω ω
= = = −+ +
inV
11Q
os
ω
BPV
--LPV
HPV
∑
os
ω
EECS 247 Lecture 6: Filters © 2005 H.K. Page 35
Master-Slave Frequency TuningReference Filter (VCF)
rms rmstune LPrefV K V V cosφ≈ − × × ×
Input Signal Frequency
of
of Q
LPV
re fV
11Q
os
ω
--
os
ω
Phase Comparator
Amp.+ Filter
TuneV
∑
Vtu
ne
EECS 247 Lecture 6: Filters © 2005 H.K. Page 36
Master-Slave Frequency TuningReference Filter (VCF)
• By closing the loop, feedback tends to drive the error voltage to zero.à Locks fo, 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
LPV
re fV
11Q
os
ω
--
os
ω
Phase Comparator
Amp.+ Filter
TuneV
EECS 247 Lecture 6: Filters © 2005 H.K. Page 37
Master-Slave Frequency TuningReference Filter (VCF)
tuneV
inV
1 + -
-+ -+
+ - + -
*R Rs−
*R RL21
sτ 31
sτ 41
sτ 51
sτ11
sτ
LPV
re fV
11Q
--
01
sτ
Phase Comparator
Amp.+ Filter
Main Filter (Slave)
Replica Filter(Master)
oV
Ref: H. Khorramabadi and P.R. Gray, “High Frequency CMOS continuous-time filters,” IEEE Journal of Solid-State Circuits, Vol.-SC-19, No. 6, pp.939-948, Dec. 1984.
01
sτ
EECS 247 Lecture 6: Filters © 2005 H.K. Page 38
Master-Slave Frequency TuningReference Filter (VCF)
• Issues to be aware of:– Input reference tuning signal needs to be sinusoid à Disadvantage since clocks are usually available as square waveform
– Reference signal feed-through to the output of the filter can limit filter dynamic range (reported levels or about 100µVrms)
– Ref. signal feed-through is a function of:• Reference signal frequency wrt filter passband• Filter topology • Care in the layout• Fully differential topologies beneficial
EECS 247 Lecture 6: Filters © 2005 H.K. Page 39
Master-Slave Frequency TuningReference Voltage-Controlled-Oscillator (VCO)
•Instead of VCF a voltage-controlled-oscillator (VCO) is used •VCO made of replica integrator used in main filter •Tuning circuit operates exactly as a conventional phase-locked loop (PLL)•Tuning signal used to tune main filterRef: K.S. Tan and P.R. Gray, “Fully integrated analog filters using bipolar FET technology,” IEEE, J.
Solid-State Circuits, vol. SC-13, no.6, pp. 814-821, December 1978..
EECS 247 Lecture 6: Filters © 2005 H.K. Page 40
Master-Slave Frequency TuningReference Voltage-Controlled-Oscillator (VCO)
• Issues to be aware of:– Design of stable & repeatable oscillator challenging– VCO operation should be limited to the linear region of
the amp or else the operation loses accuracy– Limiting the VCO signal range to the linear region not
a trivial design issue– In the case of VCF based tuning ckt there was only ref.
signal feedthrough. In this case, there is also the feedthrough of the VCO signal!!
– Advantage over VCF based tuning à Reference input signal square wave (not sin.)
EECS 247 Lecture 6: Filters © 2005 H.K. Page 41
Master-Slave Frequency TuningChoice of Ref. Frequency wrt Feedthrough Immunity
Ref: V. Gopinathan, et. al, “Design Considerations for High-Frequency Continuous-Time Filters and Implementation of an Antialiasing Filter for Digital Video,” IEEE JSSC, Vol. SC-25, no. 6 pp. 1368-1378, Dec. 1990.
EECS 247 Lecture 6: Filters © 2005 H.K. Page 42
Master-Slave Frequency TuningReference C/Gm Locked to Ref. Frequency
C1 refV Gm V T C1≈ × ×
tuneV
Gm
C
Vin
•Replica of main filter Gm-C building block used •Utilizes the fact that a DC voltage source connected to the input of the Gm cell generates a constant current
I=Gm.Vref•If the integrating capacitor is fully discharged and at t=0 is connected to the output of the Gm cell then:
•If VC1 is forced to be equal to Vref then:
Replica of main filter Gm
Vout
VC1
T
Vref
I=Gm*Vref
clkC NTGm f= =
EECS 247 Lecture 6: Filters © 2005 H.K. Page 43
Master-Slave Frequency TuningReference C/Gm Locked to Ref. Frequency
S2
S1
S3Gm
C1 C2
Vref
A
•Three phase operation •Feedback loop forces:
Replica of main filter Gm
clkC N
Gm f≈
Ref: A. Durham, J. Hughes, and W. Redman- White, “Circuit Architectures for High Linearity Monolithic Continuous-Time Filtering,” IEEE Transactions on Circuits and Systems, pp. 651-657, Sept. 1992.
EECS 247 Lecture 6: Filters © 2005 H.K. Page 44
Reference C/Gm Locked to Ref. FrequencyP1 highà S1 closed
S2
S1
S3Gm
C1 C2
Vref
Discharge C1
A
EECS 247 Lecture 6: Filters © 2005 H.K. Page 45
Reference C/Gm Locked to Ref. FrequencyP2 high à S2 closed
S2 S3Gm
C1 C2
Vref
A
Charge C1 with I=Gm*Vref
I=Gm*Vref
P2
VC1
C1 refV Gm V T 2 C1≈ × ×
T1 T2
EECS 247 Lecture 6: Filters © 2005 H.K. Page 46
Reference C/Gm Locked to Ref. Frequency P3 high à S3 closed
Charge on C1 shared with C2Feedback forces Gm to assume a value:
S2 S3Gm
C1 C2
Vref
A
C1 C2
C1 ref
ref re f
V V Vref
s ince V Gm V T 2 C1then: V Gm V T2 C1
C1o r : T 2 N / fclkGm
:= =
= × ×
= × ×
= =
T1 T2
EECS 247 Lecture 6: Filters © 2005 H.K. Page 47
SummaryReference C/Gm Locked to Ref. Frequency
Feedback forces Gm to vary so that :
S2 S3Gm
C1 C2
Vref
A
in t g
int g0
C1 N / fclkGmor
Gm fclk / NC1
τ
ω
= =
= =
Integrator time constant locked to an accurate frequencyTuning signal used to adjust the time constant of the main filter integrators
Problems to be aware of:à Tuning error due to Gm-cell DC offset
EECS 247 Lecture 6: Filters © 2005 H.K. Page 48
Issues Reference C/Gm Locked to Ref. Frequency
What is DC offset?
Simple example:
For the gm-cell shown here, difference between the threshold voltage of the input devices ( M1 & M2) would cause DC offset.à A non-zero voltage should be applied to input to have Vo=0Offset is usually models as a small DC voltage source at the input
Example: Gm-cell
controlV
oV
inV
-
+
+
-
int gCM1 M2
M10
EECS 247 Lecture 6: Filters © 2005 H.K. Page 49
Gm-Cell Offset Induced Error
( )
C1 C2
C1 ref
C1 osref
os
ref
V V Vref
Ideal V Gm V T2 C1with of fset : V Gm V V T2 C1
VC1or : T2 1Gm V
:= =
= × ×
= × − ×
= −
Vref
Vos S2 S3Gm
C1 C2
A
I=Gm(Vref-Vos)
•Effect of Gm-cell DC offset:
Voltage sourceRepresenting
DC offset
EECS 247 Lecture 6: Filters © 2005 H.K. Page 50
Reference C/Gm Locked to Ref. FrequencyGm-Cell Offset Induced Error
os
ref
os
ref
VC1 T2 1Gm V
Vfor 1/10V
10% error in tuning!
= −
=
Vref
Vos S2 S3Gm
C1 C2
A
I=Gm(Vref+Vos)
•Example:
EECS 247 Lecture 6: Filters © 2005 H.K. Page 51
Gm-cell à two sets of input pairs Aux. input pair + C3a,b à Offset cancellation Same clock timing
Reference C/Gm Locked to Ref. FrequencyIncorporating Offset Cancellation
+
-
-+
P2
P2B-
+
P3
P1+
-
+
-
P1
P2
P3
P2B
P3
P2 P3
P2
Vcm
+Vref/2
-Vref/2
Vtune
C1 C2C3a
C3b
EECS 247 Lecture 6: Filters © 2005 H.K. Page 52
Reference C/Gm Locked to Ref. FrequencyP3 High (Update & Store Vos)
out osV V= −osV
+
-
-+
-
+
+
-
+
-
Vcm
+Vref/2
-Vref/2
Vtune
C1 C2
C3a
C3b
Gm-cell à Unity gain config.C3a,b à Store Gm-cell offsetC1, C2à Charge sharing
EECS 247 Lecture 6: Filters © 2005 H.K. Page 53
Reference C/Gm Locked to Ref. FrequencyP1 High (Reset)
+
-
-+
-
+
+
-
+
-
Vcm
+Vref/2
-Vref/2
Vtune
C1 C2C3a
C3b
Gm-cell à Reset.C1 à DischargeC2 à Hold ChargeC3a,b à Hold Chargeà Offset stored on C3a,b cancels gm-cell offset
osV
osC3aV V= −
EECS 247 Lecture 6: Filters © 2005 H.K. Page 54
Reference C/Gm Locked to Ref. FrequencyP2 High (Charge)
osV+
-
-+
-
+
+
-
+
-
Vcm
+Vref/2
-Vref/2
Vtune
C1 C2C3a
C3b
osC3aV V= −
Gm-cell à Charging C1C3a,b à Store Gm-cell offsetC2 à Hold charge
Key point: Tuning error due to Gm-cell offset cancelled
EECS 247 Lecture 6: Filters © 2005 H.K. Page 55
SummaryReference C/Gm Locked to Ref. Frequency
osV+
-
-+
-
+
+
-
+
-
Vcm
+Vref/2
-Vref/2
Vtune
C1 C2C3a
C3b
osC3aV V= −
Gm-cell à Charging C1C3a,b à Store Gm-cell offsetC2 à Hold charge
Key point: Tuning error due to Gm-cell offset cancelled
EECS 247 Lecture 6: Filters © 2005 H.K. Page 56
SummaryReference C/Gm Locked to Ref. Frequency
Feedback forces Gm to vary so that :
S2 S3Gm
C1 C2
Vref
A
in t g
int g0
C1 N / fclkGmor
Gm fclk / NC1
τ
ω
= =
= =
Tuning error due to gm-cell offset voltage resolvedHas the advantage over previous scheme that fclk can be chosen to be at much higher frequencies compared to filter bandwidth (N>1) à Feedthrough of Vref attenuated by filter
EECS 247 Lecture 6: Filters © 2005 H.K. Page 57
DC Tuning of Resistive Timing ElementVtune
Rext used to lock Gm or on-chip R
Feedback forces Gm=1/Rext
Account for Cap. variations in the gm-C implementation by trimming
Rext.
-
+-
+
I
I
Gm
Ref: C. Laber and Gray, “A 20MHz 6th Order BiCMOS Parasitic Insensitive Continuous-time Filter and Second Order Equalizer Optimized for Disk Drive Read Channels,” IEEE Journal of Solid State Circuits, Vol. 28, pp. 462-470, April 1993