Electronic circuit Emuling a first-order time-delay differential equation

This article provides undergraduates a useful tool for a better understanding of the time delay effect on an electronic circuit. The time delay effect is analyzed in this paper a first-order differential equation. This linear time delay is associated with the amplitude of a firstorder differential equation and is responsible for three responses: one of the responses is a differential equation type in first-order without delay, another one of the responses is a differential equation type in second-order and finally, we have the response of a harmonic oscillator. The proposed circuit is an emulator that develops the three different responses mentioned above. Simulink-Matlab software was used to implement the time delay and simulate the differential equation. These simulation results coincide with the theoretical results. In the same manner, the experimental results match those of the theory. The electronic circuits suggested consist of three blocks: an integrator block, a phase shift block, and a gain block. The electrical circuit is composed of resistors, capacitors, and operational amplifiers. © 2021 Sociedad Mexicana de Fisica. All rights reserved.

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