A further demystification of the U-shaped probability distribution

Of all the probability distributions considered during the calculation of measurement uncertainty, the U-shaped distribution is generally least familiar to the typical EMC engineer. A previous paper (Carpenter, E., 2003) attempted to demystify the distribution by demonstrating that it occurs naturally when considering the voltage standing wave (VSW) amplitude generated along the length of a semi-infinite cable by impedance mismatch at its termination. This paper seeks to continue the demystification by presenting additional background unlikely to be familiar to the typical EMC engineer. Specifically, the origin of the 1/√2 normalisation factor, used to determine the standard uncertainty contribution due to mismatch, is presented, as is the relationship between the U-shaped distribution and the beta and gamma distributions.