Mathematical Spreadsheets and Simulators: Both Belong in Your Toolbox

Aug 29, 2007 4:38 PM
By Alan Elbanhawy, Director, Advanced Power System Center, Fairchild Semiconductor International, San Jose, Calif.

Obtaining a closed-form solution to a complex set of differential equations using mathematical software packages may not always be possible. The greatest advantage of the mathematical solution to a problem is once you get the closed-form solution for a set of equations, you can now do several probing activities that will help you understand the scope of your application and give you a very good understanding of the above mentioned dependencies of the solution on different parameters.

Using math software, you can generate a family of curves that relates any two parameters, helping you to understand the effect of a given perturbation of a given parameter on the solution. Better yet, by using the same mathematical package you can generate a 3-D graph that relates any two independent parameters and time. This type of result gives you an unparalleled visual understanding of the relationship of these two parameters over time.

One more thing that can easily be done is to derive equations for dependent parameters by solving one or more of the independent parameter equations for a specific condition. You can also perform optimization calculations by finding the maxima or minima of a certain parameter and design for either, if needed. One last use of the same set of solutions is performing sensitivity analysis using the closed-form solution with obvious advantages for numerical sensitivity analysis. You can use the same math software to do numerical solutions (used in simulation software), too, if you so desire.

Of course, mathematical software is not going to replace simulation, which plays a great role in power engineering design today and will continue to do so in the future. Instead, it offers engineers another tool for understanding and optimizing their power circuit designs. So, for any power designers who have yet to experience the benefits of math software, its time to take a closer look at this very powerful design tool and discover just how well it complements simulation.

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© 2007 Penton Media, Inc.