Measurement of definite integral product of two more signals using two-bit ADCs

This paper presents the two-bit stochastic converter theory of operation. This converter could be used for the precise measurement of the effective (root-mean-square) value of voltage, current, electric power or energy and thus, could be applicable to grid measurements. The key contribution of this paper is the theoretical derivation of error limits when measuring signals using the stochastic method. Standard deviation of measured value over a specified measuring period is defined as an error. When finding expressions for the measured quantity and its error, time is treated as an independent uniform random variable; therefore, probability theory and statistical theory of samples can be applied. This condition is necessary because the presented problem is highly nonlinear and stochastic and thus, cannot be solved by the linear theory of discrete signals and systems, or by the theory of random processes. The presented solution is generalized in order to include the measurements of the definite integral of the product of a finite number of signals.