Quantifying the Value of Transient Voltage Sources

Abstract

Some voltage sources are transient, lasting only for a moment of time, such as the voltage generated by converting a human motion into electricity. Such sources moreover tend to have a degree of randomness as well as internal resistance. We investigate how to put a number to how valuable a given transient source is. We derive several candidate measures via a systematic approach. We establish an interconvertibility hierarchy between such sources, where interconversion means adding passive interface circuits to the sources. Resistors at the ambient temperature are at the bottom of this hierarchy and sources with low internal resistance and high internal voltages are at the top. We provide three possible measures for a given source that assign a number to the source respecting this hierarchy. One measure captures how much ``$\mathrm{unitdc}$'' the source contains, meaning $1$ V dc with $1\mathrm{\ensuremath{\Omega}}$ internal resistance for $1$ s. Another measure relates to the signal-to-noise ratio of the voltage time series, whereas a third is based on the relative entropy between the voltage probability distribution and a thermal noise resistor. We argue that the $\mathrm{unitdc}$ measure is particularly useful by virtue of its operational interpretation in terms of the number of unit dc sources that one needs to combine to create the source or that can be distilled from the source.