 |
Description
Pacific Instruments' Vice President of Engineering, Scott Swinford, explores and compares 16-Bit SAR & 24-Bit Sigma-Delta A/D conversion and what it means for quality measurements.
Download or view the thought provoking presentation given to the Western Regional Strain Gage Committee on March 1st, 2010.
TOP
Elements Of A Measurement System
Measurements Systems Consist Of Many Elements
Including:
- Transducer
- Signal Conditioning
- Amplification
- Filtering
- Digitization (A/D)
- Storage
Each Element Prior To Storage Adds Errors To The Measurement
Quality Measurements Are Made By:
- Decreasing Error Sources
- Increasing Measurement Resolution
TOP
Digitizers: Quantifying Inputs Into Stored Results
Digitizers Quantify The Transducer Signal & The Error Signals
They Also Add Errors Of Their Own
Test Measurement Systems Tend To Use S.A.R or Sigma-Delta Digitizers
Digitizer Architectures Are Chosen Based On:
- Measurement Accuracy & Range Constraints
- Measurement Speed & Latency Constraints
- Power, Heating, & Space Constraints
TOP
Common Types of Digitizers
Flash
- 20M to 60Msps
- Radio, DSOs
Successive Approximation
- Low To ~ 4 Msps
- Mainstream Data Acquisition
- No Latency
Sigma Delta
- Low To ~ 10 Msps
- Originally Audio Now Data Acquisition
- Latency Due To Oversampling
Integrating
- 1k To 5ksps
- Used In High Precision DVMs
Pipelined Subranging
- 1M To 1Gsps
- Multiple Samples at a Time
Digitizer Speed Graph
TOP
Transducer Measurement System Requirements
Support A Wide Range Of Sampling Rates
Provide High Accuracy Results
Sample Wide Ranges Of Input Levels
- FS Ranges From 2 mV to 10 V
Provide High Resolutions
Filter Signals To Satisfy Nyquist Criteria
SAR & Sigma-Delta Digitizers Are The Choice For Transducer Measurements Since They Best Meet The Above Requirements While Being Cost Effective.
TOP
Successive Approximation (SAR) Architecture
SAR ADCs Convert Using A Binary Search Through Quantization Levels
Different SAR Register Values Are Clocked Into A DACStarting With The MSB = 1
A Comparator Then Decides If The Value Of The DAC Output Is Higher Or Lower Than Vin
If Lower The Current Bit Remains a 1 Otherwise It Becomes A Zero
The Process Continues Through All N Bits
The Resulting Code Is The Conversion Value
TOP
Sigma-Delta Architecture
1st Order Sigma-Delta A/D (Modulator) Contains:
- Difference Amplifier
- Integrator
- Comparator
- 1 Bit DAC.
Input Signal (X)
- Sums With DAC Feedback (B)
- Result Is Integrated (C)
- Then Compared To Zero (D)
- And Fed Back (W) To Summing Amp
Output 1s & 0s (D) Summed Over N Samples
Voltage Measured Is Calculated Using:
- Sum
- Number of Samples
- Vref
TOP
Sigma-Delta Conversion Example
+Vref= 1.0 V, X = 3/8 V
Summing D1 –D16
16 Intervals = 24 (i.e. 4 Bit A/D)
16 Codes Spanning –Vref to +Vref
Result = -Vref+ (Count * V/Code)
Result = -1V + (11 * 0.125) = 3/8 V
| Sample (n) |
X (Input) |
B (X-Wn-1) |
C (B+Cn-1) |
D (0 or 1) |
W (-Vref or Vref) |
| 0 |
3/8 |
0 |
0 |
0 |
0 |
| 1 |
3/8 |
3/8 |
3/8 |
1 |
+1.0 |
| 2 |
3/8 |
-5/8 |
-2/8 |
0 |
-1.0 |
| 3 |
3/8 |
11/8 |
9/8 |
1 |
+1.0 |
| 4 |
3/8 |
-5/8 |
4/8 |
1 |
+1.0 |
| 5 |
3/8 |
-5/8 |
-1/8 |
0 |
-1.0 |
| 6 |
3/8 |
11/8 |
10/8 |
1 |
+1.0 |
| 7 |
3/8 |
-5/8 |
5/8 |
1 |
+1.0 |
| 8 |
3/8 |
-5/8 |
0/8 |
0 |
-1.0 |
| 9 |
3/8 |
11/8 |
11/8 |
1 |
+1.0 |
| 10 |
3/8 |
-5/8 |
6/8 |
1 |
+1.0 |
| 11 |
3/8 |
-5/8 |
1/8 |
1 |
+1.0 |
| 12 |
3/8 |
-5/8 |
-4/8 |
0 |
-1.0 |
| 13 |
3/8 |
11/8 |
7/8 |
1 |
+1.0 |
| 14 |
3/8 |
-5/8 |
2/8 |
1 |
+1.0 |
| 15 |
3/8 |
-5/8 |
-3/8 |
0 |
-1.0 |
| 16 |
3/8 |
11/8 |
8/8 |
1 |
+1.0 |
TOP
Sampling, Nyquist, & Aliasing
Nyquist Requires Sampling Frequency (fs) >= 2
- Input Signal Frequency (fo)
SAR Architectures Band Limit foUsing Analog Filters
- Typically Multi-Pole
- Large Physically Due To Low fco Required
- Requires Much Circuitry Space & Increases Cost
Sigma-Delta Architectures Band Limit Using:
- Oversampling
- Digital Filtering
- Small Analog Filter Due To High fco Required
TOP
Noise & Oversampling Ratio
A Signal Sampled At fs Has All Of Its Noise Power Folded Into The Frequency Band 0 =f =fs/2
If The Noise Is Random (Typical of Quantization Noise) The Noise Spectral Density Is
- E(f) = eRMS(2/fs)½•(V/(sqrt(Hz)))
Converting To Noise Power Over The Bandwith Of Interest (fo) We Find The In BandQuantization Noise (n0)
- n0= eRMS(2fo/fs)½• V
- fs = sampling frequency
- fo= input signal bandwidth
- (fs/2fo) Is Oversampling Ratio (OSR)
OSR Reduces In Band Quantization Noise By The Square Root Of OSR
TOP
Sigma-Delta Noise Lowering (Oversampling) & Noise Shaping
Oversampling
- Spreads Quantization Noise Over A Larger Frequency Band
- Lowers The Noise In The Band of Interest (fo)
- Achieved By Sampling Faster
Noise Shaping
- Moves (High Pass Filters) In Band (fo)Noise To Out Of Band Areas
- Is Achieved By Modulator Error SignalFeedback Through The Integrator(s)
For An Mth Order Modulator Doubling The Sampling Frequency Decreases In Band (fo) Quantization Noise By 3(2M+1) dB
TOP
Sigma-Delta Digital Filtering
A Digital Filter Follows The Modulator Stage
It Low Pass Filters The Resulting Signal
The Filter Is Typically Finite Impulse Response (FIR)
Note, The Integrator Acts As A Low Pass Filter To The Input Signal Also
TOP
SAR & Sigma-Delta Characteristics Summarized
SAR
- No Integral Data Filtering
- No Latency
- Physically Constrained To ~ 18 Bits
- Widely Available
- Medium Cost
- Low Power (mW)
- Working Level 16 Bits
|
|
Sigma-Delta
- Integral Data Filtering
- Latency
- Not Physically Constrained To N Bits
- Widely Available
- Low Cost
- High Power (mW)
- Lots Of Quantization Noise Management
- Working Level 24 Bits
|
TOP
A/D Selection Criteria
Bits (Typical 12 –24)
Digitization Quality (Static)
Digitization Quality (Dynamic)
Speed
Power Consumption
Latency
Extended Characteristics
Size
TOP
| Bits |
Codes |
ENOB |
| 16 |
65536 |
16 |
| 24 |
16,777,216 |
24 |
| Measurement Tracker |
Most Widely Used: 16 Bit & 24 Bit
- 16 Bits = 65536 Quantification Codes
- 24 Bits = 16,777,216 Quantification Codes
- SAR –Typical Use 16 Bits
- Sigma-Delta–Typical Use 24 Bits
Some Digitized Bits Will Be Noise (Non Effective Bits) From Digitization Process
Digitization Quality Determines Effective Number Of Bits (ENOB) For Digitizer
TOP
| Bits |
Codes |
ENOB |
| 16 |
65536 |
16 |
| 24 |
16,777,216 |
24 |
Digitization Quality Is What Really Matters
Specificatiions Related To Static (DC) Digitization Quality
- INL = Integral Non Linearity
- DNL = Differential Non Linearity
- Gain Error
- Offset Error
- Temperature Drift
Specificatiions Related To Dynamic (AC) Digitization Quality
- SNR = Signal To Noise Ratio
- SINAD = Signal To Noise And Distortion Ratio
- THD = Total Harmonic Distortion
- THD + N = Total Harmonic Distortion + Noise
- SFDR = Spurious Free Dynamic Range
AC Specifications Significantly Affect ENOB
TOP
| Bits |
Codes |
ENOB |
| 16 |
65536 |
16 |
| 24 |
16,777,216 |
24 |
DC Specifications
INL & DNL Indicate If Codes Are Missing
- DNL Greater Than 1 Missing Codes Possible
- Data System Manufacturers Pay Special Attention To This
- Sigma-Delta & SAR Converters Available With Good INL & DNL Specs
Gain & Offset Error
- Typically Small & Can Be Calibrated Out
- Sigma-Delta Offset Drift Problems Have Been Significantly Improved
Temperature Drift
- Very Difficult To Calibrate Out
- Sigma-Delta & SAR Specifications Comparable
TOP
| Bits |
Codes |
ENOB |
| 16 |
65536 |
16 |
| 24 |
16,777,216 |
24 |
Measuring AC Specifications
Input Sine Wave
Sample At High Rate
Generate FFT of Results
Noise Levels & Harmonic Levels Used To Determine:
- THD
- THD + N
- SFDR
- SNR
- SINAD
SINAD Used To Determine ENOB
TOP
| Bits |
Codes |
ENOB |
| 16 |
65536 |
16 |
| 24 |
16,777,216 |
24 |
Total Harmonic Distortion (THD)
Gives Error Information Due To Non-Linearities Manifested As Harmonic Distortions
Ratio of RMS of Fundamental to Mean Value of RSS of Its Harmonics
THD+N Adds All Noise Components Except For DC Component
Generally Only First 5 Harmonics Used
THD+N = SINAD If Noise Measured Over Full Spectrum
TOP
| Bits |
Codes |
ENOB |
| 16 |
65536 |
16 |
| 24 |
16,777,216 |
24 |
Spurious Free Dynamic Range (SFDR)
Indicates In dB The Ratio Between The Input Signal Power And The Largest Harmonic
Think Of It As THD Using Only The Largest Harmonic
TOP
| Bits |
Codes |
ENOB |
| 16 |
65536 |
16 |
| 24 |
16,777,216 |
24 |
Signal To Noise And Distortion (SINAD)
A Good Indication Of A/D Dynamic Performance
Includes All Components Making Up Noise & Distortion
Usually Plotted For Different Input Frequencies
Determines Effective Number Of Bits
| ENOB = |
SINAD –1.76 dB |
| 6.02 |
TOP
| Bits |
Codes |
ENOB |
| 16 |
65536 |
16 |
| 24 |
16,777,216 |
24 |
Signal To Noise Ratio (SNR)
Is SINAD Without Distortion Information
Theoretically, SNR = (6.02 • N) + 1.76 dB Where N = A/D Bits
TOP
| Bits |
Codes |
ENOB |
| 16 |
65536 |
16 |
| 24 |
16,777,216 |
24 |
Some Important Equations
Given THD & SNR Solve For SINAD
SINAD = -10 log10(10-SNR/10+ 10-THD/10)
Given SINAD & THD Solve For SNR
SNR = -10 log10(10-SINAD/10+ 10-THD/10)
Given SINAD & SNR Solve For THD
THD = -10 log10(10-SINAD/10+ 10-SNR/10)
Note: Enter SINAD, THD, SNR In Positive dB
TOP
| Bits |
Codes |
ENOB |
| 16 |
19,563 |
14.25 |
| 24 |
108,518 |
16.72 |
| Updated Numbers |
Some Real World SINAD Numbers
Given
| ENOB = |
SINAD –1.76 dB |
| 6.02 |
At Best We Would Expect:
- SINAD24 = 6.02•(24) + 1.76 (dB) = 146.24 dB
- SINAD16 = 6.02•(16) + 1.76 (dB) = 98.08 dB
In Practice:
- SINAD24S?˜102.5 dB = Best Expected – 43.74 dB = 16.72 ENOB Performance
- SINAD16SAR˜87.6 dB = Best Expected – 10.48 dB = 14.25 ENOB Performance
TOP
| Bits |
Codes |
ENOB |
| 16 |
19,563 |
14.25 |
| 24 |
108,518 |
16.72 |
Sanity Check
TOP
| Bits |
Codes |
ENOB |
| 16 |
19,563 |
14.25 |
| 24 |
108,518 |
16.72 |
Why The Big Difference?
Quantification Noise In An A/D Is Inversely Proportional To A/D Comparator Levels Quantifiable
Sigma-Delta Converters Use A Single Comparator
SAR Converters Use N Comparators (N=#Bits)
Noise Shaping, Oversampling, & Digital Filtering In Sigma-Delta ArchitecturesLower The Quantization Noise But Do Not Eliminate It
Thus, We Get This Effect:
| Bits |
Codes |
ENOB |
| 16 |
19,563 |
14.25 |
| 24 |
108,518 |
16.72 |
TOP
| Bits |
Codes |
ENOB |
ESNR |
| 16 |
19,563 |
14.25 |
87.55 |
| 24 |
108,518 |
16.72 |
102.41 |
| Added Effective SNR |
Transducer & Cable Interaction
Gage & Cabling Noise Level?
1uV Noise On A 1mV Measurement…SNR = 60 dB << 87.55 or 102.41 dB
Filter The Noise?
OK, But Removes Any Dynamic Response Capabilities
In This Case Only A 10 Bit Digitizer Is Needed (N = (SNR –1.76) / 6.02)
Solution: Proper Grounding & Shielding To Increase Gage/Cable SNR
TOP
| Bits |
Codes |
ENOB |
ESNR |
| 16 |
19,563 |
14.25 |
87.55 |
| 24 |
108,518 |
16.72 |
102.41 |
Signal Conditioning & Amplification
Signal Conditioning:
- Excitation, Bridge Completion, Balance
- Will Add Small Errors To Transducer Signal
- Can Center Signals Enabling Higher Amplification
Amplification:
- Amplifies Signal & Noise Essentially Equally
- Adds Noise To Measurement
- For Low Noise & Low Level Transducer Signals Can Increase Usable Bits Per mV
TOP
| Bits |
Codes |
ENOB |
ESNR |
Codes/mV |
| 16 |
19,563 |
14.25 |
87.55 |
9781.5 |
| 24 |
108,518 |
16.72 |
102.41 |
339.1 |
Capabilities Of Some Commercially Available Data Acquisition Systems
| Architecture |
Bits |
ENOB |
Gain |
Codes |
Codes Per mV RTI |
Full Scale (+/-) |
| Sigma-Delta |
24 |
16.72 |
1 |
108,518 |
5.4 |
10 V FS |
| Sigma-Delta |
24 |
16.72 |
62.5 |
108,518 |
339.1 |
160 mV FS |
| SAR |
16 |
14.25 |
1 |
19,563 |
0.9 |
10 V FS |
| SAR |
16 |
14.25 |
100 |
19,563 |
97.8 |
100 mV FS |
| SAR |
16 |
14.25 |
300 |
19,563 |
296.5 |
33 mV FS |
| SAR |
16 |
14.25 |
1000 |
19,563 |
978.1 |
10 mV FS |
| SAR |
16 |
14.25 |
5000 |
19,563 |
9781.5 |
2 mV FS |
TOP
| Bits |
Codes |
ENOB |
ESNR |
Codes/mV |
| 16 |
19,563 |
14.25 |
87.55 |
9781.5 |
| 24 |
108,518 |
16.72 |
102.41 |
339.1 |
In Strain Perspective
| e (ue) |
Vo (uV) |
Vo (mV) |
| 1 |
2.5 |
0.0025 |
| 10 |
25 |
0.025 |
| 100 |
250 |
0.25 |
| 200 |
500 |
0.5 |
| 400 |
1000 |
1.0 |
| 800 |
2000 |
2.0 |
| 1000 |
2497 |
2.497 |
| 2000 |
4990 |
4.99 |
| 4000 |
9960 |
9.96 |
| 8000 |
19841 |
19.841 |
| 13000 |
32083 |
32.083 |
Essential Break Even Point |
| 63500 |
149271 |
149.271 |
Table 1. Strain Gage Outputs For GF=2, R=120 ohm, Vex = 5 V
TOP
| Bits |
Codes |
ENOB |
ESNR |
Codes/mV |
| 16 |
19,563 |
14.25 |
87.55 |
9781.5 |
| 24 |
108,518 |
16.72 |
102.41 |
339.1 |
Conclusion
Sigma-Delta & SAR Conversion Techniques Described
Dynamic & Static Real World Performance Numbers Explored
System Level Interaction Pointed Out
ENOB Calculated
Other Considerations Include Data Transmission & Storage Size
Better Is Not Determined By The Number Of Bits
Better Is Determined By The Entire System Architecture & Its Usage
TOP
Contact
Quality performance is a main focus of Pacific Instruments' products. For additional information about unbeatable test and measurement instrumentation, please feel free to contact us at:
 Phone: 925-827-9010
 Email: salesrequest@pacificinstruments.com
|
|
|
