A sensitivity analysis method for the equivalent parameter extraction of transient magnetic field problems with internally coupled circuits is presented. In contrast to conventional methods using physical meaning and physical relationships for parameter extraction, this method is based on a collection of mathematical system equations which include transient magnetic field equations and internal circuit equations. The extracted parameters include the collective effects of eddy currents, internal circuits, and mechanical motion. Compared with previous sensitivity analysis methods which extract only the equivalent inductance, the proposed algorithm extracts also the equivalent resistance. A laminated transformer with internal circuit is reported to validate and showcase the proposed method. ; Department of Electrical Engineering