Technical University of Ko

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Technical University of Košice Faculty of
Electrotechnic and Informatics Department of
Electronics and Telecommunications
Education and Training
ADC Modelling Introduction part 2
Linus Michaeli
6th Summer School on Data Acquisition
Systems Benevento, Italy, 27.June 2006
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Concept of modern instruments

• Analog-to-Digital Converters (ADC) and
  Digital-to-Analog Converters (DAC) together with
  Analog Conditioning Block represents the main
  error source in the measuring instruments.
• The input/output transfer characteristic is
  similar to the stepwise characteristic of the ADC
  with continuous impact of analog block errors.
  The input/output blocks can be considered as a
  generalised ADC or DAC
• The digital output from the ADC and digital input
  to DAC is processed in the DSP or just displayed
  on the Human-Instrument Interface.

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Modelling objective

• Error models describe by a simple way properties
  of ADCs and DACs under various dynamic
  conditions, with a reduced set of parameters.
• The identified error model gives users concise
  information about the whole system convenient
  for
• ADC and DAC metrological description.
• Performing signal processing precedure/algorithms
  performing error reduction.

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Error models
Behavioural error models (B EM) represented by
the Memorised functional error parameters
Mathematical models
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ADC PSPICE Model
ADC and DAC models as components from the circuit
simulators
Proportional to the model complexity the
simulation time raises. Singularities in the
trasnfer characteristic at each T(k) cause
the generation of the limit cycles in .TRAN
analysis
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Electrical macromodel of SAR ADC
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SAR Model extension for dynamic case
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Static model of Flash/Cyclic ADC

• Parallel ADC - casual distribution of INL, DNL
• Serio-parallel ADC - cyclic repetition of one INL
  replica

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Macromodels of the ADC using intermediate
trasformation (averaging ADC)
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Dynamic extension of the averaging ADC
Actual continuous internal parameter T/f before
ideal quantisation
INL as two dimmensional polynom
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Signal processing models ADC
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Memorised functional error parameters
ADC error model where errors are memorised in the
one or two dimensional look up table
Huge amount of memorised parameters is in
contradiction to requirement of simplification by
error models.
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Approximation function with reduced number of
parameters
Polynomial description of real transfer
characteristic. Number of model parameters
related with order of approximation function.
(First order regression line - two parameters
offset and gain error).

• Spline, Lagrange and LMS approximations from the
  tested data

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Error properties described as one two
dimensional image

• Description using low code frequency (LCF) and
  high code frequency (HCF) components

LCF component polynomial continuous
function HCF component modelled by the DNLmHCF(l)
from the multiperiodical model code bins with
extraordinary high differential nonlinearity
estimated by histogram test.
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High Low Code Frequency Components
DNL0(3)
DNL0(1)
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Unified model of ADC
I 4 k3 I 5 k4 (Lab 1200)
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DAC error model
Electrical model of multiplying DAC using
macromodels .
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