Analysis of multiple sampler systems with finite pulse width, open loop

The Laplace transform method has been applied to the analysis of multiple-sampler systems. The method of analysis is based on a contour integral, which is derived from the Laplace transformation, and which mathematically describes the operation of a sampler with finite pulse width. This contour integral referred to as p-transformation in references 1 and 2 is employed for the exact analysis of linear multiple-sampler open-loop systems with finite pulse width. It is shown that by a combination of a few fundamental steps it is possible to treat any open-loop system. These steps have been outlined and simple examples given to demonstrate their application. The technique is general, no restriction being imposed on the number or the periodicity of samplers present. It may be applied to systems with delayed samplers, and periodic samplers with different periods and pulse widths, as well as to systems which include nonperiodic samplers both with respect to period and/or pulse width. In each case the solution is exact and in systems with periodic samplers it can always be expressed in a closed form. The limiting cases are also considered. As a consequence of these, a method is obtained for analysis of open-loop sample-data systems with zero pulse width which include two or more samplers.