Discrete-time analysis of linear and nonlinear systems using analog circuit simulators

A method to teach discrete-time systems analysis concepts and skills to engineering students is presented and discussed. The method presented in this investigation uses commercially available analog–digital circuit simulators and a delay element and sampler constructed from analog components. The delay element and sampler used with standard, continuous-time amplifiers and summers, allow the user to simulate discrete-time systems in a manner identical to that used for continuous-time systems. Construction of the discrete-time delay element and sampler using the PSpice circuit simulator is presented as is their use in a variety of well-known linear discrete-time systems including problems from economics, population dynamics, and digital signal processing. The well-known nonlinear quadratic model of chaos is also simulated in this investigation. The results of the linear and nonlinear discrete-time system analysis are compared to the analytical results and show that the delay element and sampler are stable and accurate components useful in modeling a wide variety of linear and nonlinear discrete-time systems.