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Sigma Delta A/D Converter

Sigma Delta A/D Converter. e [n]. f s. f s. Decimation Filter. 2 f o. x (t). Sampler. Modulator. x [n]. y [n]. 16 bits. Bandlimited to f o. Digital. Analog. Over Sampling Ratio = 2 f o is Nyquist frequency Transfer function for an L th order modulator given by.

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Sigma Delta A/D Converter

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  1. Sigma Delta A/D Converter e[n] fs fs Decimation Filter 2 fo x(t) Sampler Modulator x[n] y[n] 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(2L+1) for doubling of Over Sampling Ratio • L+0.5 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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