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!!)