In this letter, we propose an optimal second-order approximation of the ideal unit delay function \(e^{-s}\) and provide some possible circuit realizations. Because it is based on standard second-order filter blocks, the approximation is flexible and can be realized using multiple different circuits based on operational amplifiers, operational transconductance amplifiers, second generation current conveyors or other active building blocks offering a quick yet accurate realization of the unit delay function. Simulations and experimental results are presented to validate the theory.
