Designing Coupled Inductors

Apr 1, 2006 12:00 PM
By John Gallagher, Field Applications Engineer, Pulse, San Diego

Three things should be noted about these equations. First, the flux in the center of the reluctance model (Φ₃) is not dependent on the coupling factor (p) or the imbalance between the currents in phases one and two (I1 and I2). Second, and most important, the flux in the outer legs of the reluctance model (Φ₁ and Φ₂) is very much dependent on the current imbalance as well as the coupling factor (p). As a result, high values of p (as p is increased, the phase ripple decreases but at a decreasing rate) actually destabilize the inductor and make it more susceptible to saturation caused by a current imbalance between phases; therefore, high p values should be avoided.

By substituting the phase current equations derived in the January 2006 article, Eqs. 13, 14 and 15 can be rewritten in terms of the peak flux (affecting saturation) and the ac flux (affecting core losses) as:

Note that the Φ_3AC occurs at twice the switching frequency (F_S), but that the flux in the outer legs Φ_1AC and Φ_2AC occurs at the switching frequency. Intuitively, this makes sense because the outer legs are only being driven once per cycle, whereas the center leg is being driven by both the N × I1 and N × I2 terms. In addition, note that the ac flux is not affected by the coupling ratio (p) or the actual value of L_K as it is influenced entirely by the applied volt-µs in the application.

Uncoupled vs. Coupled Design

To get a feel for the tradeoffs between uncoupled and coupled inductor applications, it is helpful to run through an actual design comparison. A potential application for the CIMP topology would be in powering the processor for IMVP6 notebook computing applications. Although the electrical requirements vary, a standard specification is shown in the table.

Existing implementations use inductors similar to the Pulse PG0255.401NL (360 nH, 1 mΩ, 11.2 mm × 10 mm × 4 mm), and the electrical and mechanical specifications are shown in the table. For the sake of comparison, the design will seek to keep the same efficiency per phase (equal ΔI_PHASE), but improve the transient response time by a factor of two (dI/dt_MAXIMUM = 60 A/µs). This requires an L_K of 0.5 × 360 nH or 180 nH. For consistency, we will assume that the 1 m is a necessary condition due to the use of inductor current sensing — sensing the current by measuring the voltage across the inductor resistance — and that the 4-mm maximum height is required for this notebook application.

Note that a patent on the coupled inductor multiphase topology has been granted to Volterra, and so it is my understanding that at the present time the coupled inductor multiphase topology can only be used with approval by or license from Volterra. The coupled inductor product defined previously was developed as a comparison and is not commercially available.

As can be seen in the table, the coupled inductor designed using the previous equations enables a 2x increase in the transient response without affecting the ripple current per phase. This performance improvement is accompanied by a reduction in total inductor footprint of more than 30% and a cost reduction of more than 35%. In addition, because the coupled inductor is made using a ferrite-core material, the core losses can be reduced by a total of 1.7 W, which represents a 2% to 3% increase in system efficiency.

Through simple analysis of the circuit and reluctance models, design equations for a two-phase coupled inductor have been derived. This analysis can be extended to higher phase counts. The proposed two-phase coupled inductor design for notebook applications showed that the CIMP topology can enable faster transient response, improved efficiency, smaller board space and reduced cost over the conventional two inductor noncoupled multiphase approach.

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