Compute B/H Curve for Inductor with DC and Ripple Currents

May 1, 2010 12:00 PM
Keng Wu Independent Consultant, Cranbury, NJ

Numerous variables and parameters are involved in building and specifying an inductor. Only a selected few give a designer limited degree of freedom. The rest, a majority, is utterly beyond the reach of users. For instance, among the latter, magnetic core flux density specification falls totally in the hand of core producers. Users have no choice but to accept what are offered and available. As a result, design iterations are often required to keep the part application within the constraints set by manufacturer.

Depending on the application, magnetic core flux may be attributed to driving voltage, current, or both. If not careful, all flux components may not be accounted for properly. The following graphs discuss a computational approach using a current-driven concept. Applying the technique of continuity of state, the total, steady state current of an inductor is derived. Given core geometry and material properties, flux density is computed and plotted against the actual data.

BOOST CONVERTER

A battery powered boost converter, shown in the simplified schematic (Fig. 1), is employed to power a TWT (traveling wave tube). Providing isolation and voltage step-up, the transformer operates in a 50% push-pull mode while the regulator loop works in PWM with duty cycle D. The core flux density of the boost choke needs to be evaluated to ensure no magnetic saturation.

It is also understood that the main power train alternates between two states, Fig. 2 and Fig. 3, when the PWM switch turns on, or off, with clock period T. Two state variables, the inductor current I and the output capacitor voltage V are involved. Along with that, two time constants, τL = L/rL and τC = RL×C, are identified.

SWITCH ON

In switch-on state, with “a” suffix, two differential equations govern the circuit.

Assume a cyclical, yet unknown, starting conditions X1 = (Ia0, Va0)T a column vector, the solution in matrix form is given by:

(See equation 2)

Where:

Continue to next page

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