Phase-Plane Derived Distortion Modeling of a Fast and Accurate Digitizing Sampler

We report on continued efforts to model the distortion behavior of custom-designed digitizing samplers for accurate measurement of dynamic signals. The 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, we describe an analytic error model for a sampler having a -3 dB bandwidth of 6 GHz. 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 chosen from consideration of the voltage dependence of digitizer input capacitance and previously studied error behavior in a predecessor digitizer. At 1 GHz, an improvement in total harmonic distortion from -32 dB 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