data convertor
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1
Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Data Converter Basics
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A/D and D/A Conversion
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
S/H
Analog
in
Digital
out
Quantization
DSP
AAF
S/H
AnalogoutDigitalin
D/A
DSP
Smoothing
filter
A/D Conversion
D/A Conversion
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Quantization
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
N inout
FS
VDivision : D = 2
V
Quantization = division + normalization + truncation
Full-scale range (VFS) is determined by Vref
A/Dbn
Digital outputAnalog input
b1...
Vref
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Quantization Error
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
FSout in out inN
V = D - V =D - V
2
FS
N
V = =LSB
2
in FSV 0, V
- 2 2
Dout
0
Vin
2 3
1
3
5
0
2
4
6
7
VFS
2
--2-3
VFS
2
Random quantization error
is usually regarded as noise
Vin0
-/2
/2
2 30--2-3
N = 3
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Quantization Noise
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Vin
2 3
0
4 5 6 7-/2
/2
VFS
/2 2
2 2
-/2
1 = d =
12
P
0-/2 /2
1/
Assumptions:
N is large
0 Vin VFSand Vin>>
Vinis active
is Uniformly distributed
Spectrum of is white
Ref: W. R. Bennett, Spectra of quantized signals, Bell Syst. Tech. J., vol. 27, pp. 446-472, July 1948.
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Signal-to-Quantization Noise Ratio (SQNR)
6
Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
2N2
2NFS
22
2 / 8V / 8SQNR = = =1.5 2 ,
12
Assume Vinis sinusoidal with Vp-p= VFS,
SQNR = 6.02 N+1.76 dB
N
(bits)
SQNR
(dB)
8 49.9
10 62.012 74.0
14 86.0
SQNR depicts the theoretical performance of an ideal ADC In reality, ADC performance is limited by many other factors:
Electronic noise (thermal, 1/f, coupling/substrate, etc.)
Distortion (measured by THD, SFDR, IM3, etc.)
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FFT Spectrum of Quantized Signal
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
N = 10 bits
8192 samples, only
f= [0, fs/2] shown
Normalized to Vin
fs= 8192, fin= 779
finand fsmust be
incommensurate
0 500 1000 1500 2000 2500 3000 3500 4000-120
-100
-80
-60
-40
-20
0
PSD
Frequency
dB
SQNR-1.76 dBENOB=6.02 dB
SQNR = 61.93 dB
ENOB = 9.995 bits
Ref: W. R. Bennett, Spectra of quantized signals, Bell Syst. Tech. J., vol. 27, pp. 446-472, July 1948.
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Commensuratefsand fin
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
0 500 1000 1500 2000 2500 3000 3500 4000-120
-100
-80
-60
-40
-20
0
PSD
Frequency
d
B
0 500 1000 1500 2000 2500 3000 3500 4000-120
-100
-80
-60
-40
-20
0
PSD
Frequency
d
B
fs= 8192
fin= 256
fs= 8192
fin= 2048
Periodic sampling points result in periodic quantization errors
Periodic quantization errors result in harmonic distortion
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Spectrum Leakage
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
0 500 1000 1500 2000 2500 3000 3500 4000-120
-100
-80
-60
-40
-20
0
PSD
Frequency
d
B
0 500 1000 1500 2000 2500 3000 3500 4000-120
-100
-80
-60
-40
-20
0
PSD
Frequency
d
B
fs= 8192
fin= 779.3
fs= 8192
fin= 779.3
TD samples must include integer number of cycles of input signal
Windowing can be applied to eliminate spectrum leakage
Trade-off b/t main-lobe width and sideband rejection for different windows
w/
Blackman
window
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FFT Spectrum with Distortion
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
0 500 1000 1500 2000 2500 3000 3500 4000-120
-100
-80
-60
-40
-20
0
PSD
Frequency
dB
High-order harmonics are aliased back, visible in [0, fs/2] band
E.g., HD3 @ 779x3+1=2338, HD9 @ 8192-9x779+1=1182
HD3HD9
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Dynamic Performance
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
SNDR
[dB]
Vin[dB]0 VFS
Overload
Peak SNDR limited by large-signal distortion of the converter
Dynamic range implies the theoretical SNR of the converter
2
in10 2 2
N
in
SNR
V / 2=10LOG
/12+
V dB
Peak
SNDR
Dynamic
range
Circuit
noise
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Dynamic Performance Metrics
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Signal-to-noise ratio (SNR)
Total harmonic distortion (THD)
Signal-to-noise and distortion ratio (SNDR or SINAD)
Spurious-free dynamic range (SFDR)
Two-tone intermodulation product (IM3)
Aperture uncertainty (related to the frontend S/H and clock)
Dynamic range (DR)misleading (avoid it if possible!) Idle channel noise or pattern noise in oversampled converters
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Evaluating Dynamic Performance
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
0 500 1000 1500 2000 2500 3000 3500 4000-120
-100
-80
-60
-40
-20
0
PSD
Frequency
dB
Signal-to-noise
plus distortion ratio
(SNDR)
Total harmonic
distortion (THD)
Spurious-free
dynamic range
(SFDR)
SNDR = 59.16 dB
THD = 63.09 dB
SFDR = 64.02 dB
ENOB = 9.535 bits
HD3HD9
SNDR -1.76 dBENOB =
6.02 dB
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Static Performance Metrics
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Offset (OS)
Gain error (GE)
Monotonicity
Linearity
Differential nonlinearity (DNL)
Integral nonlinearity (INL)
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Static Performance
of DAC
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DAC Transfer Characteristic
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Note: Vout(bi= 1, for all i) = VFS-= VFS(1-2-N) VFS
N N
N-iiout FS ii
i=1 i=1
bV = V = b 2
2
D/Abn
Digital input
Vout
Analog output
b1...
Vref
N = # of bits
VFS= Full-scale input
= VFS/2N= 1LSB
bi= 0 or 1
Multiplication
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Ideal DAC Transfer Curve
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Vout
000Din
001 011 101010 100 110 111
VFS-
VFS2
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Offset
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Vout
000Din
001 011 101010 100 110 111
VFS2
VFS-
Vos
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Gain Error
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Vout
000Din
001 011 101010 100 110 111
VFS2
VFS-
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Monotonicity
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Vout
000Din
001 011 101010 100 110 111
VFS2
VFS-
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Differential and Integral Nonlinearities
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
DNL = deviation of an output step from 1 LSB (== VFS/2N)
INL = deviation of the output from the ideal transfer curve
DNL < -1 ?
Vout
000
Din
001 011 101010 100 110 111
VFS2
INL
VFS-
th
i
i Step Size- DNL =
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DNL and INL
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Vout
000
Din
001 011 101010 100 110 111
VFS2
VFS-
i
i j
j=0
INL = DNL
INL = cumulative sum of DNL
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DNL and INL
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
DNL measures the uniformity of quantization steps, or incremental (local)
nonlinearity; small input signals are sensitive to DNL.
INL measures the overall, or cumulative (global) nonlinearity; large input
signals are often sensitive to both INL (HD) and DNL (QE).
Vout
000Din
001 011 101010 100 110 111
VFS2
VFS-
Vout
000Din
001 011 101010 100 110 111
VFS2
VFS-
Smooth Noisy
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Measure DNL and INL (Method I)
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Vout
000
Din
001 011 101010 100 110 111
VFS2
VFS-
Endpoints of the transfer characteristic are always at 0 and VFS-
Endpointstretch
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Measure DNL and INL (Method II)
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Vout
000
Din
001 011 101010 100 110 111
VFS2
VFS-
Least-squarefit and stretch
(detrend)
Endpoints of the transfer characteristic may not be at 0 and VFS-
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Measure DNL and INL
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Method I (endpoint stretch)
(INL) 0
Method II (LS fit & stretch)
(INL) = 0
Vout
000Din
001 011 101010 100 110 111
VFS2
VFS-
Vout
000Din
001 011 101010 100 110 111
VFS2
VFS-
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Static Performance
of ADC
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Ideal ADC Transfer Characteristic
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Dout
000 Vin
001
011
101
010
100
110
111
VFSVFS/20
Note the systematic offset! (floor, ceiling, and round)
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DNL and Missing Code
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Dout
000 Vin
001
011
101
010
100
110
111
VFSVFS/20
DNL = deviation of an input step width from 1 LSB (= VFS/2N=)
DNL = ?
Can DNL < -1?
th
i
i Step Size- DNL =
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DNL and Nonmonotonicity
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Dout
000 Vin
001
011
101
010
100
110
111
VFSVFS/20
DNL = deviation of an input step width from 1 LSB (= VFS/2N=)
DNL = ?
How can we even
measure this?
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INL
31
Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Dout
000 Vin
001
011
101
010
100
110
111
VFSVFS/20
INL = deviation of the step midpoint from the ideal step midpoint
(method I and II )
Any code
Missing?
Nonmonotonic?
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10-bit ADC Example
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
0 200 400 600 800 1000-2
-1
0
1
2DNL
LSB
0 200 400 600 800 1000-2
-1
0
1
2INL
Code
LSB
1024 codes
No missing code!
Plotted againstthe digital code,
not Vin
Code density test
(CDT)
DNL must always be greater or equal to -1 LSB!
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Code Density Test
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Count
000Vin
001 011 101010 100 110 111
VFS0
Uniformly distributed 0 Vin VFS
n
n
n
n
n
n
n
n
Ball casting problem: # of balls collected by each bin (ni) is proportional to
the bin size (converter step size)
th
i ii
i
n - ni Step Size-DNL =
n
Count
000Vin
001 011 101010 100 110 111
VFS0
Uniformly distributed 0 Vin VFS
>
ni
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CDT and Nonmonotonicity
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Two transition steps for one code?! How to plot INL/DNL?
CDT can be misleading in determining the static nonlinearity
Dout
000 Vin
001
011
101
010
100
110
111
VFSVFS/20
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Nyquist-Rate ADC
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Nyquist-Rate ADC
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Digitizes input signal up to Nyquist frequency (fN=fs/2)
Minimum sample rate (fs) for a given input bandwidth
Each sample is digitized to the maximum resolution of converter
Often referred to as the black box version of digitization
A/Dbn
Digital outputAnalog inputb1
...
Vref
fs
D C D C B i P f Y Chi
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Nyquist-Rate ADC (N-Bit, Binary)
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Word-at-a-time (1 step) fast
Flash
Level-at-a-time (2Nsteps) slowest
Integrating (Serial)
Bit-at-a-time (N steps) slow
Successive approximation
Algorithmic (Cyclic)
Partial word-at-a-time (1 < M N steps) medium
Subranging
Pipeline
Others (1 M N step)
Folding relatively fast
Interleaving (of flash, pipeline, or SA) fastest
the number in the parentheses is the latency of conversion, not throughput
D t C t D t C t B i P f Y Chi
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Accuracy-Speed Tradeoff
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
0
Resolution
[Bits]
5
10
15
20
1k 10k 100k 1M 10M 100M 1G 10G
Sample Rate [Hz]
Nyquist
Oversampling
Integrating Oversampling
Successive Approximation
AlgorithmicSubranging
Pipeline
Folding & Interpolating
FlashInterleaving
1 level/Tclk1 word/OSR*Tclk
1 bit/Tclk
Partial word/Tclk
1 word/Tclk
100G
D t C t D t C t B i P f Y Chi
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Building Blocks for Data Converters
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Data Converters Data Converter Basics Professor Y. Chiu
EECT 7327 Fall 2012
Sample-and-Hold (Track-and-Hold) Amplifier
Switched-Capacitor Amplifiers, Integrators, and Filters
Operational Amplifier
Comparators (Preamplifier and Latch)
Voltage and Current DACs
Current Sources
Voltage/Current/Bandgap References