Data Converters
EECT 7327
Data Converter Basics
Data Converter Basics
–1–
Professor Y. Chiu
Fall 2014
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
A/D and D/A Conversion
A/D Conversion
Analog
in
DSP
AAF
S/H
Digital
out
Quantization
D/A Conversion
Digital
in
Analog
out
DSP
D/A
S/H
–2–
Smoothing
filter
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Quantization
A/D
Analog input
...
Vref
bn
b1
Digital output
Division : Dout
 N Vin 
= 2 

V
FS 

•
Quantization = division + normalization + truncation
•
Full-scale range (VFS) is determined by Vref
–3–
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Quantization Error
Dout
7
Δ=
6
VFS
= LSB
2N
5
4
3
VFS
2
VFS
2
2
Vin
V 
ε = Dout Δ - Vin = Dout  FS
- Vin
N 
 2 
1
0
-3Δ -2Δ -Δ
ε
0
Vin  0, VFS 
Δ 2Δ 3Δ
-
N=3
Δ
Δ
ε
2
2
Δ/2
Vin
0
-Δ/2
-3Δ -2Δ -Δ
0
Δ 2Δ 3Δ
–4–
“Random” quantization error
is usually regarded as noise
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Quantization Noise
ε
Assumptions:
Δ/2
Vin
0
-Δ/2
Δ 2Δ 3Δ 4Δ 5Δ 6Δ 7Δ VFS
Pε
•
N is large
•
0 ≤ Vin ≤ VFS and Vin >> Δ
•
Vin is active
•
ε is Uniformly distributed
•
Spectrum of ε is white
1/Δ
Δ/2
1
Δ2
σ ε =  ε   dε =
Δ
12
-Δ/2
2
-Δ/2
0
Δ/2
ε
2
Ref: W. R. Bennett, “Spectra of quantized signals,” Bell Syst. Tech. J., vol. 27, pp. 446472, July 1948.
–5–
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Signal-to-Quantization Noise Ratio (SQNR)
Assume Vin is sinusoidal with Vp-p = VFS,
2
SQNR =
VFS / 8
=
σε2
 2N Δ  / 8
2
Δ
12
2
= 1.5  22N,
SQNR = 6.02 N+1.76 dB
N
(bits)
SQNR
(dB)
8
49.9
10
62.0
12
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.)
–6–
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
FFT Spectrum of Quantized Signal
PSD
SQNR = 61.93 dB
ENOB = 9.995 bits
0
-20
• 8192 samples, only
f = [0, fs/2] shown
• Normalized to Vin
-40
dB
• N = 10 bits
• fs = 8192, fin = 779
-60
• fin and fs must be
incommensurate
-80
-100
-120
0
500
1000
1500 2000 2500
Frequency
3000
3500
4000
ENOB =
SQNR -1.76 dB
6.02 dB
Ref: W. R. Bennett, “Spectra of quantized signals,” Bell Syst. Tech. J., vol. 27, pp. 446472, July 1948.
–7–
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Commensurate fs and fin
PSD
0
PSD
0
fs = 8192
fin = 256
-20
-20
-40
dB
dB
-40
-60
-60
-80
-80
-100
-100
-120
fs = 8192
fin = 2048
0
500
1000
1500 2000 2500
Frequency
3000
3500
-120
4000
0
500
1000
1500 2000 2500
Frequency
3000
•
Periodic sampling points result in periodic quantization errors
•
Periodic quantization errors result in harmonic distortion
–8–
3500
4000
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Spectrum Leakage
PSD
0
PSD
0
fs = 8192
fin = 779.3
-20
-20
-40
dB
dB
-40
-60
-60
-80
-80
-100
-100
-120
w/
Blackman
window
0
500
1000
1500 2000 2500
Frequency
3000
3500
-120
4000
0
500
1000
1500 2000 2500
Frequency
fs = 8192
fin = 779.3
3000
3500
4000
•
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
–9–
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
FFT Spectrum with Distortion
PSD
0
-20
dB
-40
HD3
HD9
-60
-80
-100
-120
0
500
1000
1500 2000 2500
Frequency
3000
3500
4000
•
High-order harmonics are aliased back, visible in [0, fs/2] band
•
E.g., HD3 @ 779x3+1=2338, HD9 @ 8192-9x779+1=1182
– 10 –
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Dynamic Performance
SNDR
[dB]
Peak
SNDR
Circuit
noise
Overload
0
VFS
SNR
 Vin 2 / 2 
= 10LOG10  2
2 
Δ
/
12
+
σ

N 
 Vin  dB 
Vin
[dB]
Dynamic
range
•
Peak SNDR limited by large-signal distortion of the converter
•
Dynamic range implies the “theoretical” SNR of the converter
– 11 –
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Dynamic Performance Metrics
• 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
– 12 –
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Evaluating Dynamic Performance
PSD
SNDR = 59.16 dB
THD = 63.09 dB
SFDR = 64.02 dB
ENOB = 9.535 bits
0
-20
dB
-40
HD9
-60
HD3
• Signal-to-noise
plus distortion ratio
(SNDR)
• Total harmonic
distortion (THD)
• Spurious-free
dynamic range
(SFDR)
-80
-100
ENOB =
-120
0
500
1000
1500 2000 2500
Frequency
3000
3500
– 13 –
4000
SNDR -1.76 dB
6.02 dB
Data Converters
EECT 7327
Data Converter Basics
Static Performance Metrics
• Offset (OS)
• Gain error (GE)
• Monotonicity
• Linearity (unique to converters)
– Differential nonlinearity (DNL)
– Integral nonlinearity (INL)
– 14 –
Professor Y. Chiu
Fall 2014
Data Converters
EECT 7327
Data Converter Basics
Static Performance
of DAC
– 15 –
Professor Y. Chiu
Fall 2014
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
DAC Transfer Characteristic
bn
b1
...
Vref
D/A
Digital input
Vout
• N = # of bits
Analog output
• VFS = Full-scale input
• Δ = VFS/2N = 1LSB
• bi = 0 or 1
N
Vout
N
bi
= VFS   i = Δ   bi  2N-i
i=1 2
i=1
• Multiplication
Note: Vout (bi = 1, for all i) = VFS - Δ = VFS(1-2-N) ≠ VFS
– 16 –
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Ideal DAC Transfer Curve
Vout
VFS-Δ
VFS
2
000
001
010
011
100
– 17 –
101
110
111
Din
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Offset
Vout
VFS-Δ
VFS
2
Vos
000
001
010
011
100
– 18 –
101
110
111
Din
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Gain Error
Vout
VFS-Δ
VFS
2
000
001
010
011
100
– 19 –
101
110
111
Din
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Monotonicity
Vout
VFS-Δ
VFS
2
000
001
010
011
100
– 20 –
101
110
111
Din
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Differential and Integral Nonlinearities
Vout
VFS-Δ
ith Step Size - Δ
DNLi =
Δ
VFS
2
INL
DNL < -1 ?
000
001
010
011
100
101
110
111
Din
•
DNL = deviation of an output step from 1 LSB (= Δ = VFS/2N)
•
INL = deviation of the output from the ideal transfer curve
– 21 –
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
DNL and INL
Vout
VFS-Δ
i
VFS
2
INLi =  DNL j
j=0
000
001
010
011
100
101
110
111
Din
INL = cumulative sum of DNL
– 22 –
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
DNL and INL
Vout
Vout
VFS-Δ
VFS-Δ
VFS
2
VFS
2
000
001
010
011
100
101
110
111
Din
Smooth
000
001
010
011
100
101
110
111
Noisy
•
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).
– 23 –
Din
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Measure DNL and INL (Method I)
Vout
VFS-Δ
VFS
2
Endpoint
stretch
000
001
010
011
100
101
110
111
Din
Endpoints of the transfer characteristic are always at 0 and VFS-Δ
– 24 –
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Measure DNL and INL (Method II)
Vout
VFS-Δ
VFS
2
Least-square
fit and stretch
(“detrend”)
000
001
010
011
100
101
110
111
Din
Endpoints of the transfer characteristic may not be at 0 and VFS-Δ
– 25 –
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Measure DNL and INL
Vout
Vout
VFS-Δ
VFS-Δ
VFS
2
VFS
2
000
001
010
011
100
101
110
111
Din
000
001
010
011
100
101
110
111
Method I (endpoint stretch)
Method II (LS fit & stretch)
Σ(INL) ≠ 0
Σ(INL) = 0
– 26 –
Din
Data Converters
EECT 7327
Data Converter Basics
Static Performance
of ADC
– 27 –
Professor Y. Chiu
Fall 2014
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Ideal ADC Transfer Characteristic
Dout
111
110
101
100
011
010
001
000
0
VFS/2
VFS
Vin
Note the systematic offset! (floor, ceiling, and round)
– 28 –
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
DNL and Missing Code
Dout
111
110
• DNL = ?
101
• Can DNL < -1?
100
011
ith Step Size - Δ
DNLi =
Δ
010
001
000
0
VFS/2
VFS
Vin
DNL = deviation of an input step width from 1 LSB (= VFS/2N = Δ)
– 29 –
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
DNL and Nonmonotonicity
Dout
111
110
• DNL = ?
101
• How can we even
measure this?
100
011
010
001
000
0
VFS/2
VFS
Vin
DNL = deviation of an input step width from 1 LSB (= VFS/2N = Δ)
– 30 –
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
INL
Dout
111
110
101
Any code
100
• Missing?
011
• Nonmonotonic?
010
001
000
0
VFS/2
VFS
Vin
INL = deviation of the step midpoint from the ideal step midpoint
(method I and II …)
– 31 –
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
10-bit ADC Example
DNL
2
LSB
1
• 1024 codes
0
• No missing code!
-1
-2
0
200
400
600
800
1000
INL
2
LSB
1
• Plotted against
the digital code,
not Vin
• Code density test
(CDT)
0
-1
-2
0
200
400
600
800
1000
Code
DNL must always be greater or equal to -1 LSB!
– 32 –
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
0
Count
Count
Code Density Test
Uniformly distributed 0 ≤ Vin ≤ VFS
Uniformly distributed 0 ≤ Vin ≤ VFS
n
n
n
n
n
n
n
n
ni
Δ
Δ
Δ
Δ
Δ
Δ
Δ
Δ
>Δ
000
001
010
011
100
101
110
111
VFS
Vin
000 001 010
0
011
100 101
110 111
VFS
ith Step Size - Δ ni - ni
DNLi =

Δ
ni
Ball casting problem: # of balls collected by each bin (ni) is proportional to
the bin size (converter step size)
– 33 –
Vin
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
CDT and Nonmonotonicity
Dout
111
110
101
100
011
010
001
000
0
VFS/2
VFS
Vin
•
Two transition steps for one code?! How to plot INL/DNL?
•
CDT can be misleading in determining the static nonlinearity
– 34 –
Data Converters
EECT 7327
Data Converter Basics
Nyquist-Rate ADC
– 35 –
Professor Y. Chiu
Fall 2014
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Nyquist-Rate ADC
•
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/D
Analog input
...
Vref
bn
b1
Digital output
fs
– 36 –
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Nyquist-Rate ADC (N-Bit, Binary)
•
Word-at-a-time (1 step)† ← fast
– Flash
•
Level-at-a-time (2N steps) ← 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”
– 37 –
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Accuracy-Speed Tradeoff
1 word/OSR*Tclk
1 level/Tclk
Resolution
[Bits]
1 bit/Tclk
20
Integrating
Partial word/Tclk
Oversampling
15
Successive Approximation
1 word/Tclk
Algorithmic
Subranging
Pipeline
Folding & Interpolating
Interleaving
Flash
10
5
Nyquist
Oversampling
0
1k
10k
100k
1M
10M
100M
1G
10G
100G
Sample Rate [Hz]
– 38 –
Data Converters
EECT 7327
Data Converter Basics
Professor Y. Chiu
Fall 2014
Building Blocks for Data Converters
•
Sample-and-Hold (Track-and-Hold) Amplifier
•
Switched-Capacitor Amplifiers, Integrators, and Filters
•
Operational Amplifier
•
Comparators (Preamplifier and Latch)
•
Voltage and Current DAC’s
•
Current Sources
•
Voltage/Current/Bandgap References
– 39 –