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EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 1
EE247Lecture 20
ADC Converters (continued)– Comparator design (continued)
• Latched comparators• Comparator architecture examples
– Techniques to reduce flash ADC complexity• Interpolating• Folding• Interpolating & folding
– Interleaved ADCs– Multi-Step ADCs
• Two-Step flash• Pipelined ADCs
– Effect of sub-ADC, sub-DAC, gain stage non-idealities on overall ADC performance
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 2
Project
• Design & simulate an ADC– ENOB=6bit for fsignal<10MHz– Signal bandwidth 0 to 100MHz– Architecture of your choice targeted for minimum
power dissipation– Description posted in the homework section – Teams of two preferred– Report due Dec. 3rd
– Powerpoint presentation ~5min/person in class on Dec. 8th
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 3
CMOS Latched Comparators
Comparator amplification need not be linearcan use a latch regeneration
Latch Amplification + positive feedback
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 4
CMOS Latched ComparatorsSmall Signal Model
Latch can be modeled as a:Single-pole amp + positive feedback
Small signal ac half circuit
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 5
CMOS Latched ComparatorLatch Delay
2 2
1 1
2D 2 1
1
1 11 1
1 1 1Integrating both sides: 1 ln ln ln ln
Latch Delay:1 ln11
mL
m m
m L m L
t V a amb
t V bm L
m
m L
V dVg V CR dt
g dV g dVV dtC g R dt C g R V
g adt dV dx x a bC g R V x b
C Vt t tg V
g R
= +
⎛ ⎞ ⎛ ⎞− = − =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
⎛ ⎞ ⎛ ⎞− = = = − =⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠
⎛ ⎞ ⎛ ⎞= − = ⎜ ⎟ ⎜⎝−⎜ ⎟⎜ ⎟
⎝ ⎠
∫ ∫ ∫
2D
1
For 1
ln
m L
m
g R
C Vtg V
⎟⎠
>>
⎛ ⎞≈ ⎜ ⎟⎝ ⎠
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 6
Latch-Only Comparator• Much faster compared to cascade of open-
loop amplifiers
• Main problem associated with latch-only comparator topology:
– High input-referred offset voltage (as high as 100mV!)• Solution:
– Use preamplifier to amplify the signal and reduce overall input-referred offset
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 7
Pre-Amplifier + LatchOverall Input-Referred Offset
LatchVi+
Vi-
Do+
Do-
fs
Preamp
Av
VosLatchVosPreamp
2 2Re _ _ Pr _2
Pr
_ Pr _ Pr
2 2Re _ 2
1
: 4 & 50 & 10
14 50 6.410
Input ferred Offset Vos eamp Vos Latcheamp
Vos eamp Vos Latch eamp
Input ferred Offset
A
Example mV mV A
mV
σ σ σ
σ σ
σ
−
−
= +
= = =
= + =
Latch offset attenuated by preamp gain when referred to preamp input.Assuming the two offset sources are uncorrelated:
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 8
Pre-Amplifier Tradeoffs
• Example:– Latch offset 50 to 100mV– Preamp DC gain 10X– Preamp input-referred latch offset 5 to 10mV– Input-referred preamplifier offset 2 to 10mV– Overall input-referred offset 5.5 to 14mV
Addition of preamp reduces the latch input-referred offset reduced by ~7 to 9X ~allows extra 3-bit resolution for ADC!
LatchVi+
Vi-
Do+
Do-
fs
Preamp
Av
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 9
Comparator Preamplifier Gain-Speed Tradeoffs• Amplifier maximum Gain-Bandwidth product (fu) or a given technology, typically a
function of maximum device ft
- Tradeoff:• To reduce the effect of latch offset high preamp gain desirable• Fast comparator low preamp gain
Choice of preamp gain: compromise speed v.s. input-referred latch offset
fu=0.1-10GHz
f0 fu freq.
Magnitude
Av
0 0
0
preamp
0
preamp
preamp 0
0
=unity gain frequency, 3 frequency & settling time
For example assuming preamp has a gain of 10:1 100
10
1 1.6 sec2 2
u
u
u
u
f f dBff
A
f GHzf MHzA
An
f f
τ
τπ π
= − =
=
= = =
= = =
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 10
Latched Comparator
Av LatchVi+
Vi-
Do+
Do-
fs
Preamp
Important features:– Maximum clock rate fs settling time, slew rate, small signal bandwidth– Resolution gain, offset– Overdrive recovery– Input capacitance (and linearity of input capacitance!)– Power dissipation– Input common-mode range and CMR – Kickback noise– …
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 11
CMOS Preamplifier + Latch Type Comparator Delay in Response
2D
1
1
0D
Latch delay previously found:
ln
Assuming gain of for the preamplifier then :
ln
m
v v in
m v in
VCg V
A V A V
VCg A V
τ
τ
⎛ ⎞⎜ ⎟⎝ ⎠
= ×
⎛ ⎞⎜ ⎟⎝ ⎠
≈
≈
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 12
Latched Comparator Including PreamplifierExample
oV
inV
-+
+
-
M1 M2CLK
M3 M4
VDD
M7 M8bias
M5 M6
M9
Preamp Latch
( )( )
3 31
3 1 1
0D
Preamplifier gain:
Comparator delay: (for simplicity, preamp delay ignored)
ln
M MMGS thm
v M M Mm GS th
m v
V VgAg V V
C Vg A Vin
τ
−= =
−
⎛ ⎞≈ ⎜ ⎟⎝ ⎠
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 13
Comparator Dynamic Behavior
vOUT
CLK
TCLK
τdelay
Comparator Reset Comparator Decision
vO+
vO-
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 14
Comparator Resolution
VIN =10mV 1mV
0.1mV10μVvOUT
CLK
Δt = (gm/C).ln(Vin1/Vin2)
Note: For small Vin the comparator may not be able to make a decision within the allotted time output ambiguous
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 15
Comparator Voltage Transfer FunctionNon-Idealities
Vout
Vin
VOffset
ε
-0.5LSB 0.5LSB
VOffset Comparator offset voltage
ε Meta-Stable region (output ambiguous)
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 16
CMOS Comparator ExampleFlash ADC
Ref: A. Yukawa, “A CMOS 8-Bit High-Speed A/D Converter IC,” JSSC June 1985, pp. 775-9
• Flash ADC: 8bits, +-1/2LSB INL @ fs=15MHz (Vref=3.8V, LSB~15mV)• No offset cancellation
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 17
Comparator with Auto-Zero
Ref: I. Mehr and L. Singer, “A 500-Msample/s, 6-Bit Nyquist-Rate ADC for Disk-Drive Read-Channel Applications,” JSSC July 1999, pp. 912-20.
Note: Reference & input both differential
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 18
Ref: I. Mehr and D. Dalton, “A 500-Msample/s, 6-Bit Nyquist-Rate ADC for Disk-Drive Read-Channel Applications,” JSSC July 1999, pp. 912-20.
Voffset
( )C C
Re f Re f Offset
V VV V V
+ −
+ −
− =− −
Flash ADCComparator with Auto-Zero
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 19
Ref: I. Mehr and D. Dalton, “A 500-Msample/s, 6-Bit Nyquist-Rate ADC for Disk-Drive Read-Channel Applications,” JSSC July 1999, pp. 912-20.
Voffset
Vo
( ) ( )[ ]( )
( ) ( )
Offseto P1 P2 In In C C
C C
Re f Re fo P1 P2 In In
VV A A V V V V
Subst i tut ing for from previous cycle:V V
V VV A A V V
Note: Of fset i s cancel led & di f ference betweeninput & reference es tabl ished
+ − + −
+ −
+ −+ −
− −= ∗ − −
−
−= ∗ −⎡ ⎤−⎣ ⎦
Flash ADCComparator with Auto-Zero
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 20
Ref: I. Mehr and D. Dalton, “A 500-Msample/s, 6-Bit Nyquist-Rate ADC for Disk-Drive Read-Channel Applications,” JSSC July 1999, pp. 912-20.
Flash ADCUsing Comparator with Auto-Zero
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 21
Auto-Zero Implementation
Ref:I. Mehr and L. Singer, “A 55-mW, 10-bit, 40-Msample/s Nyquist-Rate CMOS ADC,” JSSC March 2000, pp. 318-25
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 22
Comparator Example
Ref: T. B. Cho and P. R. Gray, "A 10 b, 20 Msample/s, 35 mW pipeline A/D converter," IEEE Journal of Solid-State Circuits, vol. 30, pp. 166 - 172, March 1995
• Variation on Yukawa latch used w/o preamp
• Good for low resolution ADCs (in this case 1.5bit/stage for a pipeline we will see later are tolerant of high offset)
• Note: M1, M2, M11, M12 operate in triode mode
• M11 & M12 added to vary comparator threshold
• Conductance at node X is sum of GM1 & GM11
x
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 23
Comparator Example (continued)
Ref: T. B. Cho and P. R. Gray, "A 10 b, 20 Msample/s, 35 mW pipeline A/D converter," IEEE Journal of Solid-State Circuits, vol. 30, pp. 166 - 172, March 1995
Vo1
G1 G2
( ) ( )
( ) ( )
( ) ( )
Cox V V V VG W WI1 th R th1 1 11L
Cox V V V VG W WI2 th R th2 1 11L
WC W 11ox 1 V V V VG I1 I2 R RWL 1
μ
μ
μ
− −= × +⎡ ⎤−⎣ ⎦
− −= × +⎡ ⎤+⎣ ⎦
⎡ ⎤− −−→ Δ = × + −⎢ ⎥⎣ ⎦
Vo1 Vo2
• M1, M2, M11, M12 operate in triode mode with all having equal L
• Conductance of input devices:
• To 1st order, for W1= W2 & W11=W12Vth
latch = W11/W1 x VR
where VR = VR+ - VR-
VR fixed W11, 12 varied from comparator to comparator Eliminates need for resistive divider
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 24
Comparator Example• Used in a pipelined ADC with digital
correctionNo offset cancellation required
Differential reference & input
• M7, M8 operate in triode region
• Preamp gain ~10
• Input buffers suppress kick-back
• φ1 high Cs charged to VR & φ2B is also high current diverted to latchcomparator output in hold mode
• φ2 high Cs connected to S/Hout & comparator input (VR-S/Hout), current sent to preamp comparator in amplify mode
Ref: S. Lewis, et al., “A Pipelined 5-Msample/s 9-bit Analog-to-Digital Converter”IEEE JSSC , NO. 6, Dec. 1987
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 25
Bipolar Comparator Example
• Used in 8bit 400Ms/s & 6bit 2Gb/s flash ADC
• Signal amplification during φ1 high, latch operates when φ1 low
• Input buffers suppress kick-back & input current
• Separate ground and supply buses for front-end preamp kick-back noise reduction
Ref: Y. Akazawa, et al., "A 400MSPS 8b flash AD conversion LSI," IEEE International Solid-State Circuits Conference, vol. XXX, pp. 98 - 99, February 1987
Ref: T. Wakimoto, et al, "Si bipolar 2GS/s 6b flash A/D conversion LSI," IEEE International Solid-State Circuits Conference, vol. XXXI, pp. 232 - 233, February 1988
Preamp Latched Comparator
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 26
Reducing Flash ADC ComplexityE.g. 10-bit “straight” flash
– Input range: 0 … 1V– LSB = Δ: ~ 1mV – Comparators: 1023 with offset < 1/2 LSB– Assuming Cin for each comparator is 0.1pF & power 3mW
• Total input capacitance: 1023 * 100fF = 102pF• Power: 1023 * 3mW = 3W
High power dissipation & large area & high input cap.
Techniques to reduce complexity & power dissipation :– Interpolation– Folding– Folding & Interpolation– Two-step, pipelining
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 27
Interpolation• Idea
– Reduce number of preamps & instead interpolate between preamp outputs
• Reduced number of preamps– Reduced input capacitance– Reduced area, power dissipation
• Same number of latches (2B-1)
• Important “side-benefit”– Decreased sensitivity to preamp offset
Improved DNL
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 28
Flash ADCPreamp Output
Zero crossings (to be detected by latches) at Vin =
Vref1 = 1 ΔVref2 = 2 Δ
0 0.5 1 1.5 2 2.5 3
-0.5
0
0.5
Vin /Δ
Pre
amp
Out
put [
V]
A2A1
VinA2
Vref1 Vref2
Vref1
Vref2
A1
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 29
Simulink Model
2Y
1Vin
2*DeltaVref2
1*DeltaVref1
Vi
Preamp2
Preamp1
Vin
A2
A1
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 30
Differential Preamp OutputDifferential output crossings @ Vin =
Vref1 = 1 ΔVref2 = 2 Δ
Note: Additional crossing ofA1&-A2 (A2&-A1)
A1-(-A2 )=A1+A2cross zero at:
Vref12 = 0.5*(1+2) Δ=1.5Δ
0 0.5 1 1.5 2 2.5 3-0.5
0
0.5
Pre
amp
Out
put
0 0.5 1 1.5 2 2.5 3
A 1+A
2
A2-A2A1-A1
A1-(-A2)
Vin / Δ
-0.5
0
0.5
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 31
Interpolation in Flash ADCHalf as many reference voltages and preamps Interpolation factor:x2
Example: For 10bit straight FlashADC need 2B=1024 preamps compared 2B-1=512 for x2 interpolation
Possible to accomplish higher interpolation factor
Interpolation at the output of preamps
Vin
A1
A2
Compare A2& -A1Comparator output is sign of A1+A2
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 32
Interpolation in Flash ADCPreamp Output Interpolation
Interpolate between two consecutive output via impedance Z
Choices of Z:1. Resistors (Kimura)2. Capacitors (Kusumoto)3. Current mode (Roovers)
Vin
A1
A2
Z
Z
Z
Vo1
Vo2
Vo1.5 = (Vo
1+Vo2)/2
Ref: H. Kimura et al, “A 10-b 300-MHz Interpolated-Parallel A/D Converter,” JSSC, pp. 438-446, April 1993K. Kusumoto et al, "A 10-b 20-MHz 30-mW pipelined interpolating CMOS ADC," JSSC, pp.1200 -1206, December 1993. R. Roovers et al, "A 175 Ms/s, 6 b, 160 mW, 3.3 V CMOS A/D converter," JSSC, pp. 938 - 944, July 1996.
Z
...
...
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 33
Interpolation in Flash ADCPreamp Output Interpolation
Vin
A1
A2
......
...
0 0.5 1 1.5 2 2.5 3-0.5
0
A2-A2A1-A1
With 2 sets of interpolation resistors at each preamp outputs three extra intermediate points 2extra bits
0.5
Pre
amp
Out
put
...
...
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 34
Higher Order Resistive Interpolation
Ref: H. Kimura et al, “A 10-b 300-MHz Interpolated-Parallel A/D Converter,”JSSC April 1993, pp. 438-446
• Resistors produce additional levels
• With 4 resistors per side, the “interpolation factor”M=8
extra 3bits
• (M ratio of latches/preamps)
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 35
Preamp Output InterpolationDNL Improvement
• Preamp offset distributed over M resistively interpolated voltages:
Impact on DNL divided by M
• Latch offset divided by gain of preamp
Use “large” preamp gainNext: Investigate how large preamp gain can be
Ref: H. Kimura et al, “A 10-b 300-MHz Interpolated-Parallel A/D Converter,”JSSC April 1993, pp. 438-446
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 36
Preamp Input RangeIf linear region of preamp transfer curve do not overlap
Dead-zone in the interpolated transfer curve! Results in error
Linear consecutive preamp input ranges must overlapi.e. input range w/o output saturation> Δ
Sets upper bound on preamp gain: Preampgain <VDD / Δ
0 0.5 1 1.5 2 2.5 3
A2-A2A1-A1
0 0.5 1 1.5 2 2.5 3-0.5
0
0.5
Pre
amp
Out
put
A 1+A
2
Vin / Δ
Linear region of transfer curve not overlapping
-0.5
0
0.5
A1+A2
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 37
Interpolated-Parallel ADC
Ref: H. Kimura et al, “A 10-b 300-MHz Interpolated-Parallel A/D Converter,” JSSC April 1993, pp. 438-446
• 10-bit overall resolution:• 7-bit flash (127 preamps and Vref 128 resistors) & x8 interpolation
• Use of Gray Encoder minimizes effect of sparkle code & meta-stability
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 38
Measured Performance
Ref: H. Kimura et al, “A 10-b 300-MHz Interpolated-Parallel A/D Converter,” JSSC April 1993, pp. 438-446
(7+3)
Low inputcapacitance
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 39
Interpolation Summary• Consecutive preamp transfer curve linear region need to have
overlap Limits gain of preamp to ~VDD/Δ
• The added impedance at the output of the preamp typically reduces the bandwidth and affects the maximum achievable frequencies
• DNL due to preamp offset reduces by interpolation factor M
• Interpolation reduces # of preamps and thus reduces input C-however, the # of required latches the same as “straight” Flash
Use folding to reduce the # of latches
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 40
Folding Converter
• Two ADCs operating in parallel– MSB ADC– Folder + LSB ADC
• Significantly fewer comparators compared to flash • Fast• Typically, nonidealities in folder limit resolution
LOGICLSB
ADC
MSBADC
Folding Circuit
VIN
DigitalOutput
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 41
Example: Folding Factor of 4
Vin
VFSVFS/2
Vout
00
01
10
11
ToLSB
Quantizer
MSBbits
• Folding factornumber of folds
• Folder maps input to smaller range
• MSB ADC determines which fold input is in
• LSB ADC determines position within fold
• Logic circuit combines LSB and MSB results
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 42
Example: Folding Factor of 4
Vin
VFSVFS/2
Vout
00
01
10
11• How are folds generated?
• Note: Sign change every other fold + reference shift
Fold 1 Vout=+ VinFold 2 Vout= - Vin + VFS/2Fold 3 Vout=+ Vin - VFS/2Fold 4 Vout= - Vin + VFS
1 32 4
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 43
Generating Foldsvia Source-Coupled Pairs
M1 M2
IS
Vref1M3 M4
IS
Vref2 M5 M6
IS
Vref3M7 M8
IS
Vref4
R1 R2
VDD
-Vo+
Vin
Vref1 < Vref2 < Vref3 < Vref4As Vin changes, only one of M1, M3, M5, M7 is on depending on the input level
IS
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 44
CMOS Folder Output
CMOS folder transfer curve max. min. portions:
RoundedAccurate only
at zero-crossings
In fact, most folding ADCs do not use the folds, but only the zero-crossings!
0 0.5 1 1.5 2 2.5 3 3.5 4
0
Fold
er O
utpu
t
0 0.5 1 1.5 2 2.5 3 3.5 4-20%
0
20%
Erro
r (Id
eal-R
eal)
Vin /Δ
Ideal Folder
CMOS Folder
-ISxR
ISxR
Vref1 Vref2 Vref3 Vref4
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 45
Parallel Folders Using Only Zero-Crossings
Vref + 3/4 * Δ
Comparator
Folder 3
Folder 2
Folder 1
Folder 4
LogicVref + 2/4 * Δ
Vref + 1/4 * Δ
Vref + 0/4 * Δ
Vin
LSB bits
(to be combined with MSB bits)
Comparator
Comparator
Comparator
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 46
Parallel Folder Outputs
• 4 folders with 4 folds each
• 16 zero crossings• 4 LSB bits
• Higher resolution• More folders
Large complexity• Interpolation
0 1 2 3 4 5
-0.4
-0.2
0
0.2
0.4
Vin /Δ
Fold
er O
utpu
t
F1F2F3F4
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 47
Folding & Interpolation
FineFlashADC
ENCODER
Vref + 3/4 * Δ
Folder 3
Folder 2
Folder 1
Folder 4
Vref + 2/4 * Δ
Vref + 1/4 * Δ
Vref + 0/4 * Δ
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 48
Folder / Interpolator OutputExample:4 Folders + 4 Resistive Interpolator per Stage
0 1 2 3 5-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Vin / Δ
Fold
er /
Inte
rpol
ator
Out
put F1
F2I1I2I3
1.5 1.6 1.7 1.8
-0.02
0
0.02
0.04
4
Note: Output of two folders only + corresponding interpolator only shown
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 49
Folder / Interpolator OutputExample:2 Folders + 8 Resistive Interpolator per Stage
Non-linear distortionInterpolate only between closely spaced folds to avoid nonlinear distortion
1.5 1.6 1.7 1.8 1.9 2 2.1-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0 1 2 3 4 5-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Fold
er /
Inte
rpol
ator
Out
put F1
F2I1I2I3
Vin / Δ
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 50
A 70-MS/s 110-mW 8-b CMOS Folding and Interpolating A/D Converter
Ref: B. Nauta and G. Venes, JSSC Dec 1985, pp. 1302-8
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 51
A 70-MS/s 110-mW 8-b CMOS Folding and Interpolating A/D Converter
Note: Total of 40 (MSB=8, LSB=32) comparators compared to 28-1= 255 for straight flash
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 52
A 70-MS/s 110-mW 8-b CMOS Folding and Interpolating A/D Converter
Ref: B. Nauta and G. Venes, JSSC Dec 1985, pp. 1302-8
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 53
Two-Step Example: (2+2)Bits
• Using only one ADC: output contains large quantization error
• "Missing voltage" or "residue" ( -εq1)
• Idea: Use second ADC to quantize and add -εq1
0 1 2 300
01
10
11
0 1 2 3-1
-0.5
0
0.5
1
[LS
B]
ADC Input [LSB]
Vin
+Dout = Vin + εq1
2-bit ADC 2-bit ADC
???
ε q1
D out
Vin
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 54
Two Stage Example
• Use DAC to compute missing voltage• Add quantized representation of missing voltage• Why does this help? How about εq2 ? • Since maximum voltage at input of the 2nd ADC is Vref1/4 then for 2nd ADC
Vref2=Vref1/4 and thus εq2= εq1/4 =Vref1/16 4bit overall resolution
Vin “Coarse“
+
Dout= Vin + εq1
2-bit ADC 2-bit ADC
“Fine“+-2-bit DAC
-εq1
-εq1+εq2
-εq1+εq2
Vref2Vref1
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 55
Two Step (2+2) Flash ADC
Vin Vin Vin
4-bit Straight Flash ADC Ideal 2-step Flash ADC
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 56
Two Stage Example
• Fine ADC is re-used 22 times• Fine ADC's full scale range needs to span only 1 LSB of coarse
quantizer
221
22
2 222 ⋅== refref
q
VVε
00 01 10 11
Vref1/22
−εq1
00
01
10
11
First ADC“Coarse“
Second ADC“Fine“VinVref1
Vref2
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 57
Two-Stage (2+2) ADC Transfer Function
0000000100100011010001010110011110001001101010111100110111101111
CoarseBits(MSB)
FineBits(LSB)
Dout
VinVref1
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 58
Residue or Multi-Step Type ADCIssues
• Operation:– Coarse ADC determines MSBs– DAC converts the coarse ADC output to analog- Residue is found by
subtracting (Vin-VDAC)– Fine ADC converts the residue and determines the LSBs– Bits are combined in digital domain
• Issue: 1. Fine ADC has to have precision in the order of overall ADC 1/2LSB 2. Speed penalty Need at least 1 clock cycle per extra series stage to resolve
one sample
(optional)Coarse ADC
(B1-Bit)Vin
Residue
DAC(B1-Bit)
Fine ADC(B2-Bit)
Bit
Com
bine
r
(B1+
B2)
-Bit
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 59
Solution to Issue (1)Reducing Precision Required for Fine ADC
• Accuracy needed for fine ADC relaxed by introducing inter-stage gain
– Example: By adding gain of x(G=2B1=4) prior to fine ADC in (2+2)bit case, precision required for fine ADC is reduced to 2-bit only!
– Additional advantage- coarse and fine ADC can be identical stages
Vin “Coarse“
+
Dout= Vin + εq1
2-bit ADC 2-bit ADC
“Fine“+-
2-bit DAC-εq1
-εq1+εq2
-εq1+εq2
G=2B1
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 60
Solution to Issue (2)Increasing ADC Throughput
• Conversion time significantly decreased by employing T/H betweenstages– All stages busy at all times operation concurrent– During one clock cycle coarse & fine ADCs operate concurrently:
• First stage samples/converts/generates residue of input signal sample # n• While 2nd samples/converts residue associated with sample # n-1
Vin “Coarse“
+Dout= Vin + εq1
2-bit ADC
2-bit ADC
“Fine“+-
2-bit DAC-εq1
- εq1+εq2
T/H+(G=2B1)
T/H
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 61
Pipelined A/D Converters
• Ideal operation• Errors and correction
– Redundancy– Digital calibration
• Implementation – Practical circuits– Stage scaling
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 62
Pipeline ADCBlock Diagram
• Idea: Cascade several low resolution stages to obtain high overall resolution (e.g. 10bit ADC can be built with series of 10 ADCs each 1-bit only!)
• Each stage performs coarse A/D conversion and computes its quantization error, or "residue“
• All stages operate concurrently
Align and Combine Data
Stage 1B1 Bits
Stage 2B2 Bits
Digital output(B1 + B2 + ... + Bk) Bits
Vin
MSB... ...LSB
Stage k Bk Bits
Vres1 Vres2
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 63
Pipeline ADCCharacteristics
• Number of components (stages) grows linearly with resolution
• Pipelining– Trading latency for conversion speed– Latency may be an issue in e.g. control systems– Throughput limited by speed of one stage → Fast
• Versatile: 8...16bits, 1...200MS/s
• One important feature of pipeline ADC: many analog circuit non-idealities can be corrected digitally
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 64
Pipeline ADC Concurrent Stage Operation
• Stages operate on the input signal like a shift register• New output data every clock cycle, but each stage
introduces at least ½ clock cycle latency
Align and Combine Data
Stage 1B1 Bits
Stage 2B2 Bits
Digital output(B1 + B2 + ... + Bk) Bits
VinStage kBk Bits
φ1φ2
acquireconvert
convertacquire
...
...
CLKφ1
φ2
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 65
Pipeline ADCLatency
[Analog Devices, AD 9226 Data Sheet]
Note: One conversion per clock cycle & 8 clock cycle latency
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 66
Pipeline ADCDigital Data Alignment
• Digital shift register aligns sub-conversion results in time
Stage 2B2 Bits
VinStage kBk Bits
φ1φ2
acquireconvert
convertacquire
...
...
+ +Dout
CLK CLK CLK
Stage 1B1 Bits
CLKφ1
φ2
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 67
Cascading More Stages
• LSB of last stage becomes very small • All stages need to have full precision• Impractical to generate several Vref
VinADC
+-DACADC
B3 bitsB2 bitsB1 bits
Vref Vref /2B1 Vref /2(B1+B2) Vref /2(B1+B2+B3)
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 68
Pipeline ADC Inter-Stage Gain Elements
• Practical pipelines by adding inter-stage gain use single Vref• Precision requirements decrease down the pipe
– Advantageous for noise, matching (later), power dissipation
Vin ADCB3 bitsB2 bitsB1 bits
Vref
2B1
+-DACADC
Vref Vref Vref
2B22B3
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 69
Complete Pipeline StageVin +
-B-bitDAC
B-bitADC
D
-GVres
Vin00
Vref
−εq1
“ResiduePlot“
E.g.:B=2
G=22 =4
Vres
VrefNote: Non of the blocks have ideal performanceQuestion: What is the effect of the non-idealities?
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 70
Pipeline ADCErrors
• Non-idealities associated with sub-ADCs, sub-DACs and gain stages error in overall pipeline ADC performance
• Need to find means to tolerate/correct errors
• Important sources of error– Sub-ADC errors- comparator offset– Gain stage offset– Gain stage gain error– Sub-DAC error
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 71
Pipeline ADC Single StageModel
Vin
−
Dout
-G V res
−εq
Σ
εq
Σ
Vres = Gxεq
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 72
Pipeline ADC Multi-Stage Model
1 q2 2out in,ADC q1
d1 d1 d 2
q( n 1) ( n 1) qnn 2 n 1
d( n 1)dj djj 1 j 1
G GD V 1 1
G G GG
.. . 1GG G
εε
ε ε− −− −
−
= =
⎛ ⎞ ⎛ ⎞= + − + − +⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠⎛ ⎞⎜ ⎟+ − +⎜ ⎟⎝ ⎠∏ ∏
ΣΣ
εq1
- G1
Σ
ΣΣ
εq2
- G2
Σ
ΣΣ
εq(n-1)
- Gn-1
Σ
Vin,ADC
Dout 1/Gd1 1/Gd2
Vres1 Vres2 Vres(n-1)
Σ
1/Gd(n-1)
εqnD1 D2 D(n-1)Dn
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 73
Pipeline ADC Model• If the "Analog" and "Digital" gain/loss is precisely matched:
∏
∏
∏
∏
−
=≈
−
=≈
−
=−
=
+
⎟⎟⎠
⎞⎜⎜⎝
⎛×
⎟⎟⎠
⎞⎜⎜⎝
⎛××=
×
==
1
12
1
12
1
11
1
log
2log
223log20
212
22log20.
log20..
n
jjnADC
n
jj
BADC
n
jj
B
n
jj
B
ref
ref
GBB
GB
G
G
V
V
NoiseQuantrmsSignalFSrmsRD
n
n
n
∏−
=
+= 1
1
, n
jj
qnADCinout
GVD
ε
EECS 247 Lecture 20: Data Converters: Nyquist Rate ADCs © 2009 Page 74
Pipeline ADCObservations
• The aggregate ADC resolution is independent of sub-ADC resolution!
• Effective stage resolution Bj=log2(Gj)
• Overall conversion error does not (directly)depend on sub-ADC errors!
• Only error term in Dout contains quantization error associated with the last stage
• So why do we care about sub-ADC errors?Go back to two stage example