# Overview

In the analysis of a switching piecewise-linear system, the steady-state solution is essential. For example, in the study of the line/load regulation of a regulated switching power system, the relevant information is the steady-state load voltage over a range of line/load conditions. Although carrying important information in its own right, the transient information on how the system settles to the new steady-state under the new line/load condition is not the focus of such a study. To carry out such a study, the load voltage is measured after the system has settled to new steady-state operations under new line/load conditions. Depending on the damping and the regulation circuitry of the system, it may take the system hundreds to thousands of switching cycles before settling to a new steady-state operation after each change in the line/load condition. While carrying out such a study with a brute-force simulation is possible, it can be time-consuming. Hence, there is a need for a special analysis tool that can "accelerate" the convergence of the system towards its steady-state operating condition without going through the actual transient.

Another example where the steady-state operation of a switched piecewise-linear system is essential is in the study of the load transient of a regulated switching power system. In such a study, the transient experienced by the system, in response to a load change, is monitored. When this study is carried out through simulation, one must initialize the circuit simulation to the initial steady-state solution of the system before the load change is initiated. Without using a steady-state solution to start the simulation, the transient obtained will be different from the transient measured in the laboratory.

A special algorithm for speeding up the computation of the steady-state solution of switched piecewise-linear systems have been incorporated into SIMPLIS as a special analysis tool. While it is mathematically more challenging and computationally more intensive, the computation of the steady-state solution of a switched system is conceptually quite similar to finding the DC operating point of a non- switching system under only DC excitations. In both cases, we are interested in finding the operation of the system in the absence of an external stimulus. Since the term "Operating Point Analysis" has been traditionally and widely used as the name for a DC operating-point analysis, the name "Periodic Operating Point Analysis,"(POP) is given to this special algorithm for speeding up the computation of the steady-state solution of switched piecewise-linear systems that are periodically driven or self-oscillating.

The Periodic Operating Point Analysis tool in SIMPLIS is able to speed up the convergence to the steady-state solution of a switched piecewise-linear system that is either self-oscillating or driven by one or more periodic sources that are commensurate in their periods. To invoke such an analysis, the user only needs to add a few lines in the input file. Statements Relating to POP Analysis explains in detail the format of the input statements related to the Periodic Operating Point analysis. Synopsis of the Periodic Operating Point Analysis explains what happens during a Periodic Operating Point analysis. After reading this section, a user will understand the internal workings of this analysis tool and, as a result, will be able to use the analysis tool more productively. An example in Example of Applying the POP Analysis Tool illustrates the application of the POP analysis to a closed-loop regulated switching power system