Determination of Stray Inductance of Low-Inductive Laminated Planar Multiport Busbars Using Vector Synthesis Method

Laminated busbars connect capacitors with switching power modules, and they are designed to have low stray inductance to minimize electromagnetic interference. Attempts to accurately measure the stray inductance of these busbars have not been successful. The challenge lies with the capacitors, as they excite the busbar producing their individual stray inductances. These individual stray inductances cannot be arithmetically averaged to establish the total stray inductance that applies when all the capacitors excite the busbar at the same time. It is also not possible to measure the stray inductance by simultaneous excitation of each capacitor port using impedance analyzers. This paper presents a solution to the above dilemma. A vector synthesis method is proposed, whereby the individual stray inductance from each capacitor port is measured using an impedance analyzer. Each stray inductance is then mapped into an xyz frame with a distinct direction. This mapping exercise allows the data to be vectored. The total stray inductance is then the sum of all the vectors. The effectiveness of the proposed method is demonstrated on a busbar designed for H-bridge inverters by comparing the simulation and practical results. The absolute error of the total stray inductance between the simulation and the proposed method is 0.48 nH. The proposed method improves the accuracy by 14.9% compared to the conventional technique in measuring stray inductances

The diagonal dimension of sub-C*-algebras

We introduce diagonal dimension, a version of nuclear dimension for diagonal sub-C*-algebras (sometimes also referred to as diagonal C*-pairs). Our concept has good permanence properties and detects more refined information than nuclear dimension. In many situations it is precisely how dynamical information is encoded in an associated C*-pair. For free actions on compact Hausdorff spaces, diagonal dimension of the crossed product with its canonical diagonal is bounded above by a product involving Kerr's tower dimension of the action and covering dimension of the space. It is bounded below by the dimension of the space, by the asymptotic dimension of the group, and by the fine tower dimension of the action. For a locally compact, Hausdorff, \'etale groupoid, diagonal dimension of the groupoid C*-algebra is bounded below by the dynamic asymptotic dimension of the groupoid. For free Cantor dynamical systems, diagonal dimension (defined at the level of the crossed product C*-algebra) and tower dimension (an entirely dynamical notion) agree on the nose. Similarly, for a finitely generated group diagonal dimension of its uniform Roe algebra with the canonical diagonal agrees precisely with asymptotic dimension of the group. This statement also holds for uniformly bounded metric spaces. We apply the lower bounds above to a number of further examples which show how diagonal dimension keeps track of information not seen by nuclear dimension.Comment: 70 page