Tables: LaPlace Transform to Difference Equation

The following tables were derived from LaPlace transfer functions using backward rectangular approximation for the integration. This method assures mapping of poles and zeros within the unit circle. In real applications, I have found that for most simple feedback control applications, no additional benefits are obtained by using higher order approximations, including Tustin's method. For precision digital filtering, or simulation higher order methods and compensation for warping may be required.

The following symbols are used throughout the tables:


Table 1 1st Order Transfer Functions

Table 2 2nd Order Transfer Functions

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