On the determination of dynamic errors for rise time measurement with an oscilloscope

The dynamic behavior of an oscilloscope is usually described by its bandwidth, which is not sufficient for well-founded error estimation for rise time measurement. Two rules of thumb have become most common that describe (a) a relation between bandwidth and rise time of an oscilloscope and (b) an estimation of the error resulting from the rise time limitation of the oscilloscope. Although it is well understood that these rules are approximations, no information on their accuracy and extent of validity appears in the literature. In this paper, we analyze these rules of thumb with their underlying assumptions and respect a more realistic model for oscilloscope behavior. We give accurate error estimates for a selection of typical input signals, show how well the rules perform for these signals and that, although the rules provide good upper bounds for the error, they can not be reliably used for error correction.