Mathematical Derivation of Cell-Driving-Jitter Effects on the Risetime of IVA-Output Voltages

Based on the step function and the probability distribution function, the risetime (10%–90%) increase of induction voltage adder-output voltage pulses, resulting from cell-driving jitters, was analyzed in detail. Using Taylor series expansion, an analytic solution of the risetime increase was obtained for jitters with normal distributions (assuming that the mean is
$\mu $
, the standard deviation is
$\sigma $
). It is found that the risetime increase of output voltages is a function of the
$\sigma $
, which can be simply expressed as
$2.563\sigma $
. This analytic solution was directly verified by the numerical calculation results. Analytic solutions of the risetime increase for jitters with three-parameter Weibull distribution are also given. It can be used to approximate several distributions (such as normal distribution, exponential distribution, and Rayleigh distribution). The application limitations of these solutions are discussed and presented, especially the reliable probability. Also, the total risetime of the output voltage is presented by considering the risetime increase resulting from cell-driving jitters.