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

Abstract

The number of strands to minimize loss in a litz-wire transformer winding is determined. With fine stranding, the ac resistance factor decreases, but dc resistance increases because insulation occupies more of the window area. A power law to model insulation thickness is combined with standard analysis of proximity-effect losses.

Computationally efficient winding loss calculation with multiple windings, arbitrary waveforms, and two-dimensional or three-dimensional field geometry

“…The average loss depends on the time average of the squared derivative of the field, (Hence the term squared-field-derivative, or SFD). The squared field derivative, or corresponding squared winding current derivatives, have been used by many authors, including [19]- [21], [23]. The "K-factor" used in rating low-frequency power transformers for nonsinusoidal currents can also be understood on the same basis [30].…”

“…For designs in which 1-D field analysis is accurate, and where wire strands are not large compared to a skin-depth, these various methods are approximately equivalent [6], despite one small discrepancy explained in [21]. Although the basic analysis is usually based on sinusoidal waveforms, a number of authors have developed methods of extending this analysis to nonsinusoidal waveforms through Fourier analysis or other methods [11], [13], [19], [20]- [23].…”

Contactless energy transfer at the bedside featuring an online power optimization strategy

“…The coil has an outer diameter of 140 mm, an inner diameter of 100 mm and contain ten Litz wire windings. Litz wire, a wire that consists of many thin wire strands, individually insulated and twisted, is designed to reduce the skin effect and proximity effect losses in conductors used at frequencies up to about 1 MHz [39]. The average inductance of the coils measures 20.2 H. Reproducibility of our coil manufacturing process revealed an inductance deviation of 100 nH.…”

State-of-the-art of contactless energy transfer (CET) systems: design rules and applications

“…Generally, a strong reduction of these effects is obtained by adopting stranded wire, also called litz wire. Sullivan in [41] proposes a method to optimize the number of strands in a litz wire, by considering wire's thickness as well as core's geometries. Given the dc resistance of the winding, R dc , its dc + ac resistance can be estimated as follows:…”