chap15 - 15 Transformer Design In the design methods of the...

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15 Transformer Design In the design methods of the previous chapter, copper loss and maximum flux density are speci- fied, while core loss is not specifically addressed. This approach is appropriate for a number of appli- cations, such as the filter inductor in which the dominant design constraints are copper loss and saturation flux density. However, in a substantial class of applications, the operating flux density is lim- ited by core loss rather than saturation. For example, in a conventional high-frequency transformer, it is usually necessary to limit the core loss by operating at a reduced value of the peak ac flux density This chapter covers the general transformer design problem. It is desired to design a k -winding transformer as illustrated in Fig. 15.1. Both copper loss and core loss are modeled. As the operat- ing flux density is increased (by decreasing the number of turns), the copper loss is decreased but the core loss is increased. We will determine the operating flux density that minimizes the total power loss It is possible to generalize the core geometrical constant design method, derived in the previ- ous chapter, to treat the design of magnetic devices when both copper loss and core loss are significant. This leads to the geometrical constant a measure of the effective magnetic size of core in a trans- former design application. Several examples of transformer designs via the method are given in this chapter. A similar procedure is also derived, for design of single-winding inductors in which core loss is significant. 15.1 TRANSFORMER DESIGN: BASIC CONSTRAINTS As in the case of the filter inductor design, we can write several basic constraining equations. These equations can then be combined into a single equation for selection of the core size. In the case of trans- former design, the basic constraints describe the core loss, flux density, copper loss, and total power loss
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566 Transformer Design vs. flux density. The flux density is then chosen to optimize the total power loss. 15.1.1 Core Loss As described in Chapter 13, the total core loss depends on the peak ac flux density the operating frequency f , and the volume of the core. At a given frequency, we can approximate the core loss by a function of the form Again, is the core cross-sectional area, is the core mean magnetic path length, and hence is the volume of the core. is a constant of proportionality which depends on the operating frequency. The exponent is determined from the core manufacturer’s published data. Typically, the value of for fer- rite power materials is approximately 2.6; for other core materials, this exponent lies in the range 2 to 3. Equation (15.1) generally assumes that the applied waveforms are sinusoidal; effects of waveform har- monic content are ignored here.
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This note was uploaded on 01/17/2010 for the course EL 5673 taught by Professor Dariuszczarkowski during the Spring '09 term at NYU Poly.

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chap15 - 15 Transformer Design In the design methods of the...

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