Designing Coupled Inductors

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

In regards to the reluctance model, the reverse-series measurement is equivalent to putting the two windings in parallel, and the equivalent circuit reduces to that shown in Fig. 3f. It is clear from this figure that the equivalent reluctance is equal to:

Again, knowing that L = N² / R and using Eqs. 5 and 6 yields:

And using Eq. 8 to solve Eq. 3 yields:

With the definition of L_K and L_M in terms of R and R_C it would be possible now to design a coupled inductor. However, it would not be possible to determine if the inductor was going to saturate in an actual application without first determining the amount of flux in the various sections of the core. To determine this, we need to solve for the flux (Φ₁, Φ₂ and Φ₃) in the reluctance model. The reluctance model (Fig. 3c) resembles the electrical circuit used in Millman's Theorem, and as such this theorem can be used to solve for the flux in each leg:

where I1 and I2 are the currents in phase one and phase two, respectively.

It can be seen that the expression R_C / (R² + 2RR_C) in Eqs. 10 and 11 is similar to the definition of L_M in Eq. 9, and it should be noted that the expression (R + R_C) / (R² + 2RR_C) is similar to adding L_M plus L_K in Eq. 3. Substitution and noting that L_M = p × L_K yields:

Want to use this article? Click here for options!
© 2007 Penton Media, Inc.