Over the last decade, notebook computers have become commonplace household and business gadgets: everyone from business travelers to weekend warriors understands the importance of battery life and the frustration of dealing with drained laptop batteries. Because approximately 200 million computers are manufactured in the world each year, this issue is not trivial.
Alan Elbanhawy, a power systems industry expert, recognized this problem and decided to investigate ways to optimize battery life in notebook computers. At the time, he was working with a major semiconductor manufacturer making MetalOxide Semiconductor FieldEffect Transistors (MOSFETs), which are power switching devices used in synchronous buck DCDC converters for computers. With computers using in excess of 500 million synchronous buck DCDC converters each year, this is one of the most popular topologies in the power industry. To maximize battery life, it is important that these converters are as efficient as possible. Elbanhawy realized the importance of better understanding the power losses inherent in these devices to enable engineers to refine their design process, save energy, and at the same time, help the environment.
Determined to find a solution, Elbanhawy worked with the widely popular engineering and mathematics software Maple™ from Maplesoft. Using Maple, he developed three applications dealing in great depth with power loss mechanisms in these converters. Maple, essential technical computing software for engineers and scientists, provides all of the necessary technology, whether an engineer needs to do quick calculations, develop design sheets, or produce sophisticated highfidelity simulation models.
Several loss mechanisms exist in these converters, including conduction losses. A set of rudimentary equations describing these losses exists, but the general consensus is that these equations typically estimate only 50% of the actual power loss, and researchers could not previously explain this discrepancy. Through investigation using Maple, Elbanhawy derived frequencydependent conduction loss equations that were much more accurate. He determined that, at a switching frequency of only a few megahertz, the MOSFET package’s parasitic resistance constitutes a large part of the total device onresistance and influences the losses greatly. This is due to the skin effect phenomenon, in which the bonding wires of the drain, gate, and source leads exhibit different parasitic resistance at different frequencies. The higher the frequency, the more electrons are concentrated around the periphery of the conducting wire. Using Fourier analysis in Maple, he broke the switching square wave current down to its constituent frequency components—both the basic DC component and many harmonics. Finally, he derived new power loss equations, using simulated skin effect resistance values and taking the first 100 harmonics into consideration—an extremely challenging problem that would have been very difficult without Maple. Depending on the package used and the fundamental switching frequency chosen, he determined that the error involved in calculating the DC conduction losses using the traditional equations could be as large as 200%!
A second source of losses involves the phenomenon known as cross conduction, or shootthrough; essentially, this involves the condition where both MOSFETs in the synchronous buck converter are turned on at the same time. Because they each have a very small onresistance value, this condition can result in extremely high current flow, and therefore, greater losses, leading to lower power conversion efficiency. However, if the devices are chosen appropriately, shootthrough can be reduced or eliminated. With Maple, Elbanhawy could easily visualize the various ranges at which shootthrough occurs. Using Maple, he developed mathematical formulas that allow designers to test the suitability of various MOSFETs for use in these converters.

Finally, he explored the effects of the source inductance present in the most common MOSFET packages used today. Using Maple’s powerful mathematics and visualization tools, he determined that the drain current rise and fall times are proportional to the total source inductance, making the switching losses nonlinearly proportional to the drain current, and not linearly proportional, as previously believed. This helped to explain why measured switching losses have always been higher than those calculated by textbook equations. As a result, he determined that improvements to the MOSFET parameters, such as gatedrain charge, are not sufficient to improve converter performance on their own; it is also necessary to improve package and printed circuit board layout techniques.
Results of the study
Based on this research, several papers have been published in international power industry conferences. New MOSFET packages have been developed by several manufacturers to address the power loss problems, and these new methods have been incorporated widely in the industry in North America, Europe, and Asia Pacific. Engineers now have a much better understanding of the various loss mechanisms, and have incorporated the results as an inherent part of the design process.
Not only did Maple enable this deep, mathintensive research, but by using Maple to create the actual research paper, several advantages were provided. Using Maple, it was easy to include the full derivation of equations in Elbanhawy’s papers to help readers understand the thought process behind the research. Maple’s strong visualization capabilities are indispensable in understanding the subject matter: several 2D and 3D graphs clearly illustrate the intermediate and final results. Most importantly, because math in a Maple document is live, readers can take a deeper look at the results: they can interact with the document, draw different graphs, view graphs at any angle, and examine the concepts as they apply to their existing or indevelopment designs.
Elbanhawy is excited about Maple’s contribution to make his research possible. “I would never have endeavored to do all of this mathintensive work without Maple,” he said. “With Maple, I can write the equations and within minutes I have the solution and any verification I need. I can then plot it and investigate the interdependencies of the different device parameters. Without Maple, one mistake along the process and you are back to the drawing board!”
Maple worksheets related to these applications:
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