Typically, to select an inductor, you'd simply figure out the maximum load current, and establish an inductance by allowing 20% ripple current. It would have a temperature rise similar to the data sheet as the core loss would be insignificant. However, as switching frequencies rise above 500 kHz, core loss and winding ac losses can dramatically reduce the allowable dc current in an inductor. Using 20% ripple current to calculate the inductance sets the same flux excursion in the core material, independent of frequency. The core loss equation takes the general form:

Pcore = K × F^1.3

So if the frequency (F) goes from 100 to 500 kHz, the core loss increases by a factor of eight. This increase is shown in Figure 1, which also depicts the allowable copper loss, which decreases with increasing core loss. At 100 KHz, most of the loss is in the copper and it's possible to utilize the full dc current rating. At higher frequencies, core loss becomes significant. Since the total allowable loss is set by the sum of the core and copper loss, copper loss must be reduced as core loss rise. This continues until the losses become equal. This is an optimum, at higher frequency where the losses are best kept equal and allows the maximum output current to be achieved from the magnetic structure.

Figures 1 and 2 are based on a fixed core volume and winding area, with only the number of turns varied. Figure 2 shows the inductance and allowable dc current for the core loss shown in Figure 1. Below 1.3 MHz, the inductance is inversely proportional to the switching frequency. The inductance reaches a minimum around 1.3 MHz. Above this frequency, the inductance must be increased to limit the core flux and, hence, limit the core loss to 50% of the total. The inductor's resulting current rating is also calculated. At low frequency, where core losses aren't significant, the current rating is set by power losses in the windings. In the equation below, the number of turns is proportional to the reciprocal of the frequency's square root, so a two-fold increase in frequency (inductance decreased by half) results in 0.707 as many turns.

L = μ × A × N²/l_m

This impacts the winding resistance in two ways. There are 30% fewer turns, and there's 41% more area available for each turn. Since the winding resistance is related to the number of turns divided by the turn area, the resistance reduces linearly with increased frequency, or as in this example, by a factor of two.

At higher frequencies, core loss starts to limit allowable copper loss until the point that they become equal. At that point, the inductance is raised to reduce flux by adding more turns and the winding resistance increases. The current rating of the inductor then decreases. The result is an optimum frequency from a size point of view for the inductor.

To summarize, the notion that increasing switching frequency will shrink magnetic size is true, but only up to the point that the core loss and ac winding losses equal the copper loss. Past that point, the size of the magnetics will actually increase. Also, designers need to note that with many of the high-switching frequency products available today, potential issues with excessive core loss are not clearly noted in the corresponding application notes.

Previously published Power Tips articles by Robert Kollman are available.

For more information about this and other power solutions, visit ti.com/power-ca.

About the author
Robert Kollman is a senior applications manager and a Distinguished Member of the Technical Staff at Texas Instruments. He has more than 30 years of experience in the power electronics business and has designed magnetics for power electronics ranging from sub-watt to sub-Megawatt with operating frequencies into the megahertz range. Robert earned a BSEE from Texas A&M University, and a MSEE from Southern Methodist University. You can reach Robert at powertips@list.ti.com.