Phase-plane-derived distortion modeling of a fast and accurate digitizing sampler

Continued efforts to model the distortion behavior of custom-designed digitizing samplers for accurate measurement of dynamic signals are reported. This work is part of ongoing efforts at the National Institute of Standards and Technology (NIST) to advance the state of the art in waveform sampling metrology. In this paper, an analytic error model for a sampler having a -3-dB 6-GHz bandwidth is described. The model is derived from examination of the sampler's error behavior in the phase plane. The model takes as inputs the per-sample estimates of signal amplitude, first derivative, and second derivative, where the derivatives are with respect to time. The model's analytic form consists of polynomials in these terms, which are chosen from consideration of the voltage dependence of the digitizer input capacitance and the previously studied error behavior in a predecessor digitizer. At 1 GHz, an improvement in total harmonic distortion from -32 to -46 dB is obtained when model-generated sample corrections are applied to the waveform. The effect of timebase distortion in the sampling system is also accounted for and corrected. The inclusion of second-derivative dependence in the model is shown to improve the model's fit to the measured data by providing fine temporal adjustment of the fitted waveform.