Mathematica--A System for Doing Mathematics by Computer.

The number and diameter of strands to minimize loss in a litz-wire transformer winding is determined. With fine stranding, the AC resistance factor can be decreased, but DC resistance increases as a result of the space occupied by insulation. A power law to model insulation thickness is combined with standard analysis of proximity-effect losses to find the optimal stranding. Suboptimal choices under other constraints are also determined.

/pdf/optimal-choice-for-number-of-strands-in-a-litz-wire-4jp058ex2a.pdf

Optimal choice for number of strands in a litz-wire transformer winding

The next generation of implantable high-power neuroprosthetic devices such as visual prostheses and brain computer interfaces are going to be powered by transcutaneous inductive power links formed between a pair of printed spiral coils (PSC) that are batch-fabricated using micromachining technology. Optimizing the power efficiency of the wireless link is imperative to minimize the size of the external energy source, heating dissipation in the tissue, and interference with other devices. Previous design methodologies for coils made of 1-D filaments are not comprehensive and accurate enough to consider all geometrical aspects of PSCs with planar 3-D conductors as well as design constraints imposed by implantable device application and fabrication technology. We have outlined the theoretical foundation of optimal power transmission efficiency in an inductive link, and combined it with semi-empirical models to predict parasitic components in PSCs. We have used this foundation to devise an iterative PSC design methodology that starts with a set of realistic design constraints and ends with the optimal PSC pair geometries. We have executed this procedure on two design examples at 1 and 5 MHz achieving power transmission efficiencies of 41.2% and 85.8%, respectively, at 10-mm spacing. All results are verified with simulations using a commercial field solver (HFSS) as well as measurements using PSCs fabricated on printed circuit boards.

Design and Optimization of Printed Spiral Coils for Efficient Transcutaneous Inductive Power Transmission

The one well-known one-dimensional method for calculating the AC resistance of multilayer transformer windings contains a built-in orthogonality which has not been reported previously. Orthogonality between skin effect and proximity effect makes a more generalized approach for the analytical solution of AC resistance in windings possible. This includes a method to calculate the AC resistance of round conductor windings which is not only convenient to use, but gives more accurate answers than the basic one-dimensional method because the exact analytical equations for round conductors can be used. >

Improved analytical modeling of conductive losses in magnetic components

This paper reviews some of the major approaches to modeling and simulation in power electronics, and provides references that can serve as a starting point for the extensive literature on the subject. The major focus of the paper is on averaged models of various kinds, but sampled-data models are also introduced. The importance of hierarchical modeling and simulation is emphasized.

Modeling and simulation of power electronic converters

Conventional techniques and new techniques based on digitizing instruments for making high-frequency B-versus-H loop and core-loss measurements on magnetic cores are presented and compared. Potential sources of measurement errors and their magnitudes, limitations imposed by the instrumentation, and thermal considerations are discussed. Circuits suitable for high-frequency sine-wave or square-wave core excitation are also discussed. The utility of such measurements is illustrated with sample data. >

High-frequency measurement techniques for magnetic cores

Several papers pertaining to the design and modeling of high-frequency transformer windings are reviewed. Each paper is summarized, stressing its significant contributions and its relationship to the others. The emphases and relative merits of each are discussed, and the understandability and applicability are evaluated. >

Characterizing high-frequency effects in transformer windings-a guide to several significant articles

A method for calculating the reluctance of air gaps in magnetic circuits making use of a Schwarz-Christoffel transformation is described. The method is applied to the calculation of the inductance of example inductor and transformer configurations and its validity established through comparisons with calculations based on the finite-element method of numerical analysis. >

Air-gap reluctance and inductance calculations for magnetic circuits using a Schwarz-Christoffel transformation

Conventional and new techniques for making high-frequency B versus H loop and core-loss measurements on magnetic cores are presented and compared. Potential sources of measurement errors and their magnitudes are discussed along with circuits suitable for high-frequency sine-wave or square-wave core excitation. The utility of such measurements is illustrated with sample data.

By considering the set of short-circuit tests which can be performed on a multiwinding transformer, analytical expressions are derived for the leakage inductances between all pairs of transformer windings, expressions which depend only on the winding geometry and the frequency of excitation. For each short-circuit test, a simplified field analysis gives the complete solution for the frequency-independent magnetic field intensity between winding layers, and the frequency-dependent distribution of magnetic field intensity within each layer. Then, for any frequency of interest, the magnetic energy stored in each winding layer and interlayer space is calculated, and the results are summed to give the total energy stored in the entire winding space of the transformer. Finally, the leakage inductance between excited and short-circuited windings is derived from the total stored energy. Experimental data are provided that illustrate the accuracy and the limitations of such leakage-inductance calculations as well as the accuracy of AC-winding-resistance calculations carried out using a similar, previously published method. >

Thomas G. Wilson

Papers

High-frequency measurement techniques for magnetic cores

Characterizing high-frequency effects in transformer windings-a guide to several significant articles

Air-gap reluctance and inductance calculations for magnetic circuits using a Schwarz-Christoffel transformation

High-frequency measurement techniques for magnetic cores

Calculating the short-circuit impedances of a multiwinding transformer from its geometry