Sigma Delta A/d converter Modulator Characteristics

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Sigma Delta A/D Converter

Modulator Characteristics

  • Highpass character for noise transfer function:

  • In-band noise power is given by


  • 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

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

Example Implementation


  • 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

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)

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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