Functionals of Brownian bridges arising in the current mismatch in D/A converters

Digital-to-analog converters (DAC) transform signals from the abstract digital domain to the real analog world. In many applications, DACs play a crucial role. Due to variability in the production, various errors arise that influence the performance of the DAC. We focus on the current errors, which describe the fluctuations in the currents of the various unit current elements in the DAC. A key performance measure of the DAC is the Integrated Nonlinearity (INL), which we study in this article. There are several DAC architectures. The most widely used architectures are the thermometer and the binary and the segmented architectures. We study the two extreme architectures, namely the thermometer and the binary architectures. We assume that the current errors are independent and identically normally distributed and reformulate the INL as a functional of a Brownian bridge. We then proceed by investigating these functionals. For the thermometer case, the functional is the maximal absolute value of the Brownian bridge, which has been investigated in the literature. For the binary case, we investigate properties of the functional, such as its mean, variance, and density