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Renco Electronics, Inc.
The Effects of Increasing Frequency on Magnetic Components
Nelson Garcia – Engineering Manager APN -100

Abstract
The operating frequency of most electronic circuits has been increasing since the late 1950’s. While the increase in frequency has reduced the overall weight and size of most consumer electronics now available, some engineers may not realize that the bulkof the reduction in weight and size has occurred in the magnetic components designed in to the circuits. The increase in frequency still continues today and as a result there is some occasional confusion as to the effects of increasing the frequency on the magnetic components. This paper discusses the consequences, good or bad, of increasing the frequency on magnetic components primarily used inpower supply applications.

Introduction
Electronics consumers have been requesting smaller and lighter electronics products for decades. Design Engineers have been able to reduce the size and weight of electronic products by increasing the frequency the magnetic components need to operate at. However, the consequences of increasing the frequency on the magnetic components can be confusingdepending on the literature that is reviewed. In order to be able to continue increasing frequency the effects of increasing frequency on magnetic components must be understood.

Increasing Transformer Operating Frequency
When considering increasing the operating frequency to reduce transformer size and, therefore overall product size, the WaAe (Window Area X Core Area product) formula should beevaluated. A quick review of this formula will immediately show the impact of an increase in operating frequency on the size of the transformer. The WaAe formula has been derived in detail in Abraham Pressman’s book, “Switching Power Supply Design, 2nd Edition,” and 1 is defined below:

WaAe =
Where:

Pout × Dcma K t × Bmax × f

Eq. 1

WaAe = Product of the window area and core area in cm4Pout = Output power in Watts Dcma = Current Density in circular mils/amp Bmax = Flux Density in Gauss f = Frequency in Hertz Kt = Topology constant Kt = 0.00100 Push Pull Kt = 0.00140 Half Bridge Kt = 0.00140 Full Bridge Kt = 0.00050 Forward Converter Kt = 0.00033 Flyback (Single Winding) Kt = 0.00025 Flyback (Multiple Winding)

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8/29/09

Renco Electronics, Inc.
The Effects of Increasing Frequency on Magnetic Components
Nelson Garcia – Engineering Manager APN -100

If everything except frequency and WaAe is kept constant in equation 1, then it is clear that as frequency is increased the window area and core area product isdecreased. In other words, as the frequency is increased the size of the transformer can be decreased. Some magnetic core vendors list the WaAe for their cores and this is very handy when trying to determine which transformer package can be used when considering increasing or decreasing the frequency. Once the frequency analysis is completed using equation 1, a common form of the basic Faraday’s Lawformula should be used to determine the necessary primary turns and complete the transformer design. See equation 5

Skin Effect and Proximity Effect
Skin effect and proximity effect are probably the two biggest topics in the world of magnetics design that cause headaches for some engineers. While an in depth analysis of these topics is beyond the scope of this paper, basic concepts will becovered. In addition, there are many well written and thorough papers and chapters of books written on skin effect and proximity effect. Skin effect is simply when the current going through a copper wire travels on the outside skin of the copper rather than throughout the entire diameter of the copper wire. See Figure 1. As the frequency is increased more of the current travels on the outside “skin”...
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