Modeling and Analysis of Multi-Phase Coupled Inductor Structures for Voltage Regulators

As the performance and power demands of modern microprocessors continuously grow, multi-phase voltage regulators are expected to be faster, more efficient, and more compact. Compared with non-coupled inductors used in today's products, the negative coupled inductor has a better circuit performance, as well as a smaller inductor size. However, unsymmetrical coupling is an inherent issue to overcome for the traditional coupled inductor; when the phase number increases, the performance deteriorates. To solve this issue, two different coupled inductor structures, designated as an indirect-coupled inductor and a hybrid-coupled inductor, were proposed. These two structures can achieve smaller current ripple and much faster transient speed compared with non-coupled inductors, thus gaining a great amount of interest in industry. However, the detailed modeling and analysis of these two structures is lacking in the literature. In this paper, the equivalent circuit models of these two structures are derived with a clear physical meaning. Then, the method to adjust the coupling for these structures is analyzed in detail. Finally, experimental results with a four-phase buck platform validate the proposed modeling method. With the proposed modeling method, the benefits and limitations of these coupled inductor structures are identified quantitatively for the first time. It also provides a powerful tool to design these coupled inductors.