Zero-Order-Hold function as a model for DAConverters

Josef Hoffmann

Still RelevantAdvanced

The output of a digital to analog converter, short DAC, is a constant analog signal between two discrete samples. The DAC's output register retains its value from one sample up to the next sample. The network, which converts the binary value of the register into an analog voltage thus supplies a constant voltage and that leads to a stepped output signal. The analog smoothing filter connected at the output together with the frequency response of the DAC, modeled with a Zero-Order-Hold function, results in distortions. These are examined here and solutions to compensate for them are presented.

Summary

The article models a DAC's stepped output as a Zero-Order-Hold (ZOH) and derives its frequency response to show how a following analog smoothing filter interacts with the ZOH to produce spectral and temporal distortions. It analyzes these distortions and presents analytical and practical compensation techniques to correct amplitude and phase errors in DAC reconstruction.

Key Takeaways

Model the DAC output as a Zero-Order-Hold (ZOH) and derive its frequency-domain representation for analysis.
Quantify the spectral distortion and imaging introduced by the ZOH plus analog smoothing filter using FFT/spectral methods.
Design compensating pre-filters and reconstruction filters to correct amplitude and phase deviations caused by the ZOH.
Implement practical equalization methods (digital pre-distortion or analog compensation) for audio and communications DACs.
Evaluate trade-offs between oversampling, filter complexity, and residual reconstruction error when compensating ZOH effects.

Who Should Read This

Advanced DSP engineers and system designers in audio, communications, or instrumentation who need to model DAC behavior and implement compensation for ZOH-induced reconstruction errors.

Still RelevantAdvanced

Topics

Filter Design FFT/Spectral Analysis Communications