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Sigma Delta A/D Converter

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Title: Sigma Delta A/D converters Author: Anonymous Last modified by: Anonymous Created Date: 10/20/1998 11:08:38 AM Document presentation format – PowerPoint PPT presentation

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Title: Sigma Delta A/D Converter


1
Sigma Delta A/D Converter
en
Decimation Filter
fs
fs
2 fo
Sampler
Modulator
x(t)
xn
yn
16 bits
Bandlimited to fo
Digital
Analog
Over Sampling Ratio 2fo is Nyquist
frequency Transfer function for an Lth order
modulator given by
2
Modulator Characteristics
  • Highpass character for noise transfer function
  • In-band noise power is given by
  • no falls by 3(2L1) for doubling of Over Sampling
    Ratio
  • L0.5 bits of resolution for doubling of Over
    Sampling Ratio
  • no essentially is uncorrelated for
  • Dithering is used to decorrelate quantization
    noise

3
Implementation
  • Select Over Sampling Ratio and L such that
    quantization noise is not the limiting factor
  • Switched capacitor circuits
  • easy to build in a digital CMOS process
  • gains and time constants decided by capacitor
    ratios and clock frequency
  • Fully differential circuits achieve better power
    supply rejection and common mode noise rejection
  • Analog characteristics are very sensitive to
    layout
  • layouts are made symmetrical to overcome
    variations in process

4
Influence of Circuit Parameters
  • Infinite DC gain for the integrators is
    unrealistic
  • Finite DC gain (integrator leakage) causes DC
    offset and increased baseband noise
  • Always build the best possible op-amp for the
    first integrator
  • Non-linearity in the feedback D/A converter
  • Harmonic distortion in the output signal
  • Possible modulation of the reference voltage
    (bad!!)
  • A simple 2 level D/A (two switches and a
    reference voltage) is used
  • Circuit noise is usually the performance limiting
    factor
  • kT/C noise in the capacitors
  • kTR noise in the resistors and switches
  • Thermal and 1/f noise in the MOSFETS

5
Example Implementation
6
Decimation
  • Sample rate conversion from a high rate to
    Nyquist rate
  • Performed using cascaded digital FIR filters
  • One class of filters used are called CICs
    (cascaded integrator comb filters) with the
    transfer function

N
  • Bit-width of the stage is given by
    b is the output of the modulator
  • Decimation in stages to ease hardware
    implementation
  • Typically,

7
Sigma Delta D/A Converters
  • Modulator loop is digital
  • Theory and math applicable exactly quantization
    error is replaced by truncation error
  • Interpolation filter instead of sampler to raise
    sample rate
  • Analog part A 1 bit D/A followed by one or more
    filters
  • Harder to build than A/D counterparts (!!)
    (analog part has no feedback loop to take
    advantage of)
  • Switched capacitor D/As, Current steering D/As
    are popular
  • Switched capacitor filters followed by a
    continuous time smoothing filter
  • Tapped delay line FIR filters are also used
    (tends to be larger in area)

8
General Circuit Considerations
  • Keep analog and digital circuitry on separate
    power supplies and spaced as far as possible
  • Use the biggest capacitors possible (area and
    loading on amplifiers are issues)
  • Use the smallest switches possible (lower noise,
    lower parasitic capacitive coupling)
  • Low thermal and 1/f noise in op-amps
  • Keep signal level as large as possible in the
    signal path
  • Keep the reference voltage clean (easier said
    than done!!)
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