Discovery of the Nearly Zero Flux Between Two Parallel Conductors in Planar Transformers

The momentum to achieve high efficiency, high frequency, and high power density in power supplies limits the use of conventional wire-wound transformers, but widely employs planar transformers. Planar transformers intrinsically benefit from low profile, predictable parasitic components, ease of manufacture, and excellent repeatability of construction, which are generally applied to high frequency and high current applications, such as data centers and telecoms. Reducing the current density through parallel connections is becoming common practice in planar transformers. However, the current on every parallel conductor is usually unbalanced and hard to be predicted. Start from the motivation to predict parallel current distribution, a phenomenon is discovered in this article that the parallel current distribution is constant from medium frequency (MF) and follows the same pattern in higher frequency range. Besides, this article points out that the insulation thickness also affects the current distribution. Furthermore, the phenomenon that the magnetic flux in the space between two parallel conductors approaches zero when parallel currents are frequency independent is proved theoretically and demonstrated experimentally. Together with Ampere's circuital law, which links the current to the magnetic field, the current distribution can be derived. No complex mathematical calculation or simulation tool is required. Any applications using planar transformers with parallel conductors at MF or higher frequency can adopt this method to predict the parallel current distribution for design optimization.