z-transform

The widespread use of mathematical applications, which include differential equations solvers, and the increase in the speed of computing devices have led to a decrease in interest in operator methods, in particular, the z-transform. Nevertheless, the use of the z-transform capabilities allows the implementation of efficient high-speed computing schemes with high numerical stability. The need for this may arise in the case of real-time simulation or the synthesis of digital control systems.

The well-known numerical-analytic method based on zeroes/poles matching (as z-transform realization) of equivalent transfer function or complex impedance (conductivity) in Laplace domain was proposed for high-speed computer analysis of electric circuits’ transients. The advantages of this method were illustrated on simple examples of the computer models of the first order electric circuit (RC-circuit that correspond to real pole) and second order electric circuit (RLC-circuit that correspond to complex pair of poles).