The part value tolerance specified by component manufacturers for surface mount RLCs is given as either a percentage of the nominal value or as a +/- deviation. This type of specification generally carries with it the assumption that the part value distribution is Gaussian about the nominal value. In practice, however, the actual distribution may be bi-modal—this occurs when the manufacturer must selectively sort parts that are closer to the nominal value in order to supply the “tight tolerance” version of the components. Thus, tight tolerance parts tend to follow Gaussian distributions about the nominal value, while looser tolerance parts tend to have bi-modal distributions.

Unfortunately, there is no convenient way to represent bi-modal distributions in most of today’s popular electronic design automation tools. The available options are typically either a Gaussian distribution or a uniform distribution. The purpose of this application note is to investigate different simulation scenarios concerned with statistical distributions of capacitor values used in a band-pass filter.