Introduction to ADC testing I Definition of basic parameters

1
Introduction to ADC testing IDefinition of basic
parameters

• Ján Šaliga
• Dept. of Electronics and Telecommunications
• Technical University of Kosice, Slovakia

2
Agenda

• Introduction
• Deterministic and probabilistic models
• Basic static parameters
• Basic dynamic parameters
• Other parameters

3
A/D converter A/D interface
A/D interface
Reference and power sources
Signal condi-tioning
SH(optional)
x
ADC
Buffer
ADC
Timing and control circuit
4
ADC parameters (characteristics errors)

• Static (quasistatic) parameters derived from
  transfer characteristic
• Point (gain, gain error, offset, missing code,
  ...)
• Function (transfer characteristic, INL, DNL, ...)
• Dynamic parameters characterize a behavior of
  ADC at time-varying signals
• SINAD, ENOB, SNR, SFDR, THD, IMD, ...
• ADC parameter testing requires extraordinaire
  accuracy
• E.g. 12-bit ADC detetermination of transition
  level with uncertainty lt 1 ?uncertainty of
  measurement lt 1/(1004096) 0,000252,5ppm of
  ADC FS

5
Accuracy versus precision
6
ADC transfer characteristic
Gain (slope) error
Inputcode k
Tk - transition level (thresholdof code
k), Wk Tk- Tk-1 code bin width N
nominal resolution (number of bits) of ADC
Non-linearity
Ideal and real straight lines
Input analogue value x(t) Vfs/Q
Missingcode
-4 -3 -2 -1
0 1 2 3 4
Ideal ADC
Error in monotonicity
Real ADC
Vfs - full scale range Vfs Vref(2N-1)/(2N)
Offset error
7
Gain and offset their errors

• Fitting the straight line
• End points straight line - connecting the two end
  code transition or code midstep values
• Least-square fit straight line according a
  least-square fitting algorithm
• Minimum-maximum straight line - the line which
  leads to the most positive and the most negative
  deviations from the ideal straight line

8
ADC transfer characteristic

• Stochastic model

• Deterministic model

1 0 1 2 3 4
Conditional probability
9
DNL and INL

• Differential non-linearity
• Integral non-linearity

10
Dynamic parameters I

• Bandwidth (BW) - the band of frequencies of input
  signal that the ADC under test is intended to
  digitize with nominal constant gain. It is also
  designated as the Half-power Bandwidth, i.e., the
  frequency range over which the ADC maintains a
  dynamic gain level of at least ?3 dB with respect
  to the maximum level.
• Gain flatness error (?G(f)) - the difference
  between the gain of the ADC at a given frequency
  in the ADC bandwidth, and its gain at a specified
  reference frequency, expressed as a percentage of
  the gain at the reference frequency. The
  reference frequency is typically the frequency
  where the bandwidth of ADC presents the maximum
  gain. For DC-coupled ADCs the reference frequency
  is usually fref 0.

11
Quantisation noise and errors

• Caused by rounding in quantisation process (and
  ADC non-linearity)
• Power of quantisation noise for ideal ADC (s2eq,
  h2rms)
• Is it dependent/independent on input signal?
• Is the value Q 2/12 correct?
• Distribution?
• Answer see the simulation

12
ADC noise and distortion

• ADC output random noise random signal
• Quantisation noise - uniform
• Noise generated in input analogue circuits -
  Gaussian
• Noise caused by sampling frequency jitter and
  aperture uncertainty (Kobayashi)
• Spurious unwanted deterministic spectral
  components uncorrelated with input signal (e.g.
  50Hz)
• Total noise any deviation between the output
  signal (converted to input units) and the input
  signal, except deviations caused by linear time
  invariant system response (gain and phase shift),
  harmonics of the fundamental up to the frequency
  fm, or a DC level shift.
• Distortion new unwanted deterministic spectral
  components correlated with input signal

13
Noise floor

• determines the lowest input signal power level
  which is reliably detectable at the ADC output,
  i. e., it limits the ultimate ADC sensitivity to
  the weak input signals, since any signal whose
  amplitude is below the noise floor (SNR lt 0 dB)
  will become difficult to recover.

14
Dynamic parameters IISignal to noise and
distortion ratio

• SINAD for a pure sinewave input of specified
  amplitude and frequency, the ratio of the rms
  amplitude of the ADC output fundamental tone to
  the rms amplitude of the output noise, where
  noise is defined as to include not only random
  errors but also non-linear distortion and the
  effects of sampling time errors, i.e., the sum of
  all non-fundamental spectral components in the
  range from DC (excluded) up to half the sampling
  frequency (fs/2).

15
Dynamic parameters IIISNR

• Signal to noise ratio (SNR) - harmonic signal
  power (rms) to broadband noise power ratio
  excluding DC, fundamental, and harmonics

16
Dynamic parameters IVTHD, THDnoise, IMD

• THD
• THDnoise 1/SINAD
• Intermodulation distortion (IMD) - for an input
  signal composed of two or more pure sinewaves,
  the distortion due to output components at
  frequencies resulting from the sum and difference
  of all possible integer multiples of the input
  frequency tones.

17
Dynamic parameters VEffective Number of Bits

• Effective Number of Bits (Nef, ENOB) - for a
  sinusoidal input signal, Nef is defined as
• where hrms is the rms total noise including
  harmonic distortion and seq the ideal rms
  quantisation noise for a sinusoidal input.
  (SINADdBFS SINADdB - 20log(SFSR)) SFSR
  signal to full scale ratio
• Nef can be interpreted as follows if the actual
  noise is attributed only to the quantisation
  process, the ADC under test can be considered as
  equivalent to an ideal Nef-bit ADC insofar as
  they produce the same rms noise level.

18
Dynamic parameters VISFDR

• Spurious-free dynamic range (SFDR) - expresses
  the range, in dB, of input signals lying between
  the averaged amplitude of the ADC's output
  fundamental tone, fi, to the averaged amplitude
  of the highest frequency harmonic or spurious
  spectral component observed over the full Nyquist
  band, for a pure sinewave input of specified
  amplitude and frequency, i.e., maxY(fh) ,
  Y(fsp)
• where Yavm is the averaged spectrum of the ADC
  output, fi is the input signal frequency, fh and
  fsp are the frequencies of the set of harmonic
  and spurious spectral components.

19
Dynamic parameters VII Experimental demonstration

• Measurement setup (run generator first and then
  demonstration)

Sound out
NI USB 6009 ADC 12 bits, 10kHz, differential
AI1 (DUT)
USB

• Software (LabVIEW)
• Sinewave generator Sound card
• Control AI1 DUT (FS, record)Data processing
  and visualisation

20
Other parameters

• Various electrical parameters, e.g. input
  impedance, power requirements, grounding,
• Time parameters, e.g. clock frequency, conversion
  time, sampling frequency,
• Digital output data coding, levels (logic),
  serial/parallel, error bit rate,

21
Introduction to ADC testing IIBasic standardized
test methods
22
Agenda

• Standardization
• Static test method
• Histogram test
• Dynamic test with data processing in time domain
• Dynamic test with data processing in spectral
  domain

23
Standardization

• IEEE Std. 1057 - 1994, "IEEE Standard for
  Digitizing Waveform Recorders",
• IEEE Std. 1241 - 2000, "IEEE Standard for
  Terminology and Test Methods for
  Analog-to-Digital Converters
• European project DYNAD SMT4-CT98-2214,
  Methods and draft standards for the DYNamic
  characterisation of Analogue to Digital
  convertershttp//www.fe.up.pt/hsm/dynad
• IEC Standard 62008 Performance characteristics
  and calibration methods for digital data
  acquisition systems and relevant software
• Additional and related standards
• IEEE Standard on Transition and Pulse Waveforms,
  Std-181-2003 (IEC 60469-1, -2)
• IEEE and IEC standards for DAQ and ADM in
  preparation
• IEC 60748 - covers only static ADC and DAC
  operations
• Detail overview of standards and standardisation
  see the lecture of Pasquale Arpaia A/D and D/A
  Standards, CD from SS on DAQ 2005
• Standard comparison Sergio Rapuano Figures of
  Merit for Analog-to-Digital Converters Analytic
  Comparison of International Standards, In Proc.
  of IMTC 2006, Sorrento, Italy, pp. 134-139

24
ADC static testStandardized method
25
ADC static test - basic ideas

• Yields ADC transfer characteristic
• Static point and function parameters can be
  derived and calculated
• Gain, offset, FS, DNL, INL,
• Based on the stochastic model of ADC
• Simple test setup DC voltmeter is the only
  accurate instrument
• Time consuming each Tk is determined
  individually. The total time 2N x longer than
  determination of one T k

26
Static test setup (IEEE 1057)
27
ADC static test - algorithm

• Start with the code k 1
• Find an input voltage level for which the
  probability of codes lower than k in the record
  is slightly higher than 0.5 the voltage is
  below Tk.
• Find a bit higher voltage (the usual step is a
  quarter of Q) for which the probability of codes
  lower than k is slightly lower than 0.5 the
  voltage is above Tk
• Fit these two point by line and calculate the
  voltage for which the probability of codes
  smaller than k is 0.5 this is the transition
  level of code k the voltage equal to Tk
• Repeat the procedure for all k 1, 2, ., 2N-1
  the complete transfer characteristic will be
  measured out

28
Uncertainty in the static test

• The uncertainty can be reduced by increasing the
  number of acquired samples (M).
• The table shows the measurement precision for a
  confidence level of 99,87.

Number of acquired samples (M) 64 256 1024 4096
Transition level measurement precision ( of noise standard deviation) 45 23 12 6
29
The main disadvantage of the static testing

• The test is long time consuming
• Lets test 16bit ADC with sampling frequency
  10kHz, testing step is Q/4, additive noise
  s1LSB, required precision better than 10.
• The chosen record length 2000 samples
• Measurement on one level takes2000 x 0.1ms
  0.2s
• Total required time 0.2s x 2(164) 58.2 hours!!!

30
Static test Experimental demonstration

• Measurement setup (run demonstration)

NI USB 6009 ADC 12 bits, 10kHz, differentialDAC
12 bit, static, RSE
AI0 (DUT)
USB
AI1 (Voltmeter)

• Software (LabVIEW) controls
• AO0 DC test voltage
• AIO DUT - FS, record
• AI1 virtual DC voltmeter with averaging
• Statistical data processing and visualisation

110
AO0 (DC source)
31
Alternative static methodwith feedback - IEEE
1241
32
Alternative static methodwith feedback - IEEE
1241
33
Some experimental results INI USB 6008 (12 bits,
10kHz, 10000s/T)
34
Some experimental results IINI USB 6008/9
(10000s/T)
Difference of two following measurements Switch
ing monitor during the measurement
35
Histogram (statistical) testStandardized method
36
Histogram (statistical) testBasic ideas I

• Goal to determine ADC transfer characteristic
  (the same as in static test method)
• The calibrating signal is a time invariant
  repetitive signal covering the ADC full scale
• The stream of ADC output codes is recorded
• Histogram is built from the record
• The relative count of hits in code bin k in the
  histogram in comparison to the calibrating signal
  probability density function (or counts for code
  bin k in cumulative histogram in relation to
  signal probability distribution function) gives
  information about the code bin width (or code
  transition levels)

37
Histogram (statistical) testBasic ideas II

• The best shape would be ramp or triangular
  signal. Why? Problem?
• The basic recommended signal by all standards
  sinewave. Why?
• To achieve a required accuracy a relative long
  record (or records) is required
• Faster than the static test
• Requirement an accurate generator with an
  extremely high accuracy (low distortion, high
  linearity, high spectral purity)

38
Histogram (statistical) testGeneral test setup
39
Ramp signal (IEEE 1241)

• TkCG.HCk-1/S for k1, 2, .... , (2N- 2)
• G is a gain factor, C is an offset factor,
• The code bins 0 and 2N-1 are usually excluded
  from data processing (why?)

40
Sinewave signal(All standards) theoretical
background I

• Signal
• Densityof probability
• Distribution of probability

41
Sinewave signal(All standards) theoretical
background I

• Ideal theoretical histogram
• DNL
• Transition levels

42
Sinewave signal(All standards) theoretical
background II

• Problem in praxis what are the sinewave
  parameters A, C ?Hidk?
• Various ways of estimation, e.g Dynad
• Incorrectestimation ?error ingain and offset

43
Sinewave signalTest conditions I

• The total record must contain exactly an integer
  number J of sinewave cycles
• R partial records can be used instead of one long
  record
• Total recorded number M of samples must be
  relatively prime with J, i.e. they have no common
  factor
• Then the sampling and sinewave frequency are

44
Sinewave signalTest conditions II

• The number of samples (M) to acquire in the
  histogram test, depends on
• The noise level in the measurement system,
• The required tolerance (B is measured in LSBs)
  and confidence level (a) and the M is different
  if DNL (quantization interval) or INL (transition
  levels) it to be determined.
• The specification of tolerance for an individual
  transition level or code bin width, or for the
  worst case in all range.

45
Sinewave signalTest conditions III

• The equation generally used to determine the
  number of records to acquire is
• J1 for INL, J2 for DNL, s is the standard
  deviation of noise level in volt for the INL
  determination and the smaller of the values of s
  and Q/1,1 for the DNL determination.

46
Sinewave signalSimulation

• Simulation (see the simulation)
• Form of histogram for various test signals
• Error caused by limited number of samples
• Error caused non-coherent sampling
• Error caused by noise in input signal
• Error caused by higher harmonics

47
Histogram test Experimental demonstration

• Measurement setup (run generator first and then
  demonstration)

Sound out
12
NI USB 6009 ADC 12 bits, 10kHz, differential
AI1 (DUT)
USB
Software (LabVIEW) Sinewave generator Sound
card AI1 control DUT - FS, record Data
processing and visualisation
48
Results of experimental testsComparison
generators (USB 6009)
Stanford DS 360 (20-bits, 100 mil. samples)
Agilent 33220A (14-bits, 100 mil. samples)
49
Histogram (statistical) testSome
non-standardized methods
50
Non standardized histogram tests Basic ideas

• Reasons
• To use signals that are closer to real signal
  digitized by ADC in common applications
• To use signal that can be simply generated with
  required precision
• Common signals
• Gaussian noise
• Exponential signal
• Uniform noise, small sinewave or triangular with
  DC steps,

51
Non standardized histogram test Gaussian noise I

• Martins, R. C., Serra, A. C. ADC
  Characterisation by using Histogram Test
  stimulated by Gaussian Noise. Theory and
  experimental results, Measurement, Elsevier
  Science B. V., vol. 27, n. 4, pp. 291-300, June
  2000
• The noise is centred within ADC input range and
  overlap the whole ADC range
• Problem generate the noise with really precise
  Gaussian distribution convenient methods for
  low resolution ADCs and very high and very low
  frequencies where it is difficult to generate
  sinewave with required purity

52
Non standardized histogram test Gaussian noise II

• Holub J., Komárek M., Machácek J., Vedral J.
  STEP-GAUSS STOCHASTIC TESTING METHOD APPLICATION
  FOR TRANSPORTABLE REFERENCE ADC DEVICE, Proc. 8th
  IWADC 2003, Perugia, Italy, pp. 223-226
• Gaussian noise with a small standard deviation is
  moved within the ADC input range by adding a DC
  voltage (mean) in small steps so that the results
  will be the same as using uniform noise
  overlapping the whole ADC full scale
• Discussion is really possible in praxis to
  fulfil the requirement of the limit with finite
  DC steps with acceptable precision?

53
Non standardized histogram test Small amplitude
sinewave or triangular with a DC component

• Michaeli L., Serra A.C., .. In IEEE
  transactions on instrumentation and measurement,
  Measurement, proc. of IMTC, IMEKO IWADC
• Idea multistep test with fractional histograms
  (and INLs) acquired at small signal (sinewave,
  triangular) covering only a few tens/hundreds of
  codes shifted within ADC FS by known DC voltage
• Advantage the quality of test signal may be much
  worse than those of signal covering the whole FS
  of ADC
• Disadvantage connecting the partial histograms
  to build the final histogram

54
Non standardized histogram test Exponential signal

• Holcer R., Michaeli L., Šaliga J. DNL ADC
  testing by the exponential shaped voltage, In
  IEEE transactions on instrumentation and
  measurement, Vol. 52, no. 3 (2003), pp. 946-949.
• Šaliga J., Holcer R., Michaeli L. Noise
  sensitivity of the exponential histogram ADC
  test, In Measurement, Vol. 39, no. 3 (2006), pp.
  238-244
• We will continue with a new PhD. Student next
  year
• Exponential signal is simple to generate native
  signal in electronic circuit
• Problem distortion by other exponential with
  different time constant and keeping the final
  value of the signal known and constant.

55
Non standardized histogram test Small signals
with a DC component

• Measurement setup (run generator first and then
  demonstration)

Sound out
NI USB 6009 ADC 12 bits, 10kHz, differential
12 110
AI0 (DUT)
USB
Software (LabVIEW)
Arbitrary generator Sound card DC shift
AO0 AI0 DUT (FS, record) Data processing and
visualisation
AO0 (DC shift)
56
Histogram testConclusions

• Histogram versus static test histogram test
  gives usually better more reliable results
  because
• Faster the test conditions are constant and
  measurement of any T k is distributed and
  repeated in time over the all testing time
• Disadvantage an precise generator is needed
• Non standardised test procedures can bring
  simplifying in test setup and decrease the
  requirements on instrumentation precision.

57
ADC dynamic testing
58
Dynamic testIntroduction

• Goal
• Determination of various dynamic ADC parameters
  such as SINAD, ENOB, SNR, THD, IMD SFDR,
• Two ways of data processing
• Time domain directly SINAD, ENOB
• Spectral domain (DFT test) SINAD, ENOB, SNR,
  THD, IMD SFDR,
• No way can be generally supposed to be the best
  one

59
Dynamic testGeneral test setup
60
Dynamic testRequirements

• Coherent sampling the same as for sinewave
  histogram test - the precise coherence is not
  necessary
• Minimal size of record
• Record can consist of a few partial records
• Sinewave must cover the ADC input range as much
  as possible (more than 90 95) but must not
  overload it.

61
Dynamic testData processing in time domain
62
Dynamic testData processing in time domain I

• See the following lectures by prof. Kollár and
  prof. Händel
• Basic idea to calculated the noise in the record
  (residuals) as the deference between the input
  signal sinewave (analogue samples) and the
  record (digitized samples).
• Knowing the noise the SINAD and ENOB can be
  calculated according the definitions

63
Dynamic testData processing in time domain II

• Difficult task and question the input signal
  must be precisely know how to do it?
• Common solution recovering the input signal from
  the record by a fitting method (LMS)
• Three-parameter fit (A, C, f)
• Four-parameter fit (A, C, f, f)
• Question is the recovered fitted signal really
  the origin input signal?!

64
Dynamic testThree-parameter fit I

• Simple calculation system of linear system of 3
  equations is to be solved

65
Dynamic testThree-parameter fit II

• In matrix form

66
Dynamic testThree-parameter fit III

• Necessary condition
• The input (and sampling) frequency must be
  precisely known!!!
• If not incorrect results SINAD,
• SEE THE SIMULATION

67
Dynamic testFour-parameter fit I

• Unknown parameters A, C, f, f
• Difficult calculation system of non-linear
  system of 4 equations is to be solved
• The system can be solved only by iteration
  process

68
Dynamic testFour-parameter fit II

• Let

69
Dynamic testFour-parameter fit III

• Problem with convergence one global minimum and
  a few local minima
• If the first estimation is incorrect the
  iteration converges to the fault minimum
• One of best estimations is the estimation from
  spectrum within the interval (J-s, Js)
• See the simulation

70
Dynamic testData processing in spectral domain
DFT test
71
Dynamic testData processing in spectral domain I

• The same test setup, requirements and the first
  step as for Data processing in time domain
• The DFT spectrum is calculated from the record
• Using the definitions (see the beginning part of
  this lecture) the unknown ADC parameters can be
  estimated

72
Dynamic testData processing in spectral domain II

• Common problem in praxis incoherent sampling
  leakage effect in the record spectrum
• Solution applying a window function (Hanning, 7
  term Blackman-Harris, ) to suppress the leakage
  effect and then correction of results according
  the window parameters (see the general theory of
  windowing in DSP)
• Introduced in detail in DYNAD
• Rule the higher the ADC resolution is, the lower
  the side-lobes of the window have to be.
  Nevertheless, lowering the side-lobes results in
  increasing the main lobe width
• Calculation is much more complex

73
Dynamic testData processing in spectral domain
III

• Spectrum calculation
• Error in coherency

Processing gain
Equivalent Noise Bandwidth
74
Dynamic testData processing in spectral domain IV

• Changes in formulas example 1 Noise floor

75
Dynamic testData processing in spectral domain V

• Changes in formulas example 2 SINAD

76
Dynamic testConclusions

• No method of data processing can be suppose to be
  absolutely the best
• Processing in time domain is less sensitive on
  coherency but the 4-parameter fit can be
  problematic
• Processing in frequency domain gives directly
  much more parameters but it is very sensitive on
  coherency

77
The final conclusions

• ADC testing is not a simple task
• Extremely difficult task to test ADC with high
  resolution (more than 20 bits)
• Methods are in the process a challenge for you
• Another challenge test procedures for special
  ADC, e.g. band-pass for direct digitalization and
  demodulation of high frequency signals, etc.

78
Thank you for your attention