While meeting the future demand of microprocessor using multiphase synchronous buck converter, integrated magnetic components are used to reduce the size of the converter and improve efficiency. However, no analysis leading to simple equivalent circuit of the coupled system with arbitrary number of phases has been presented so far. This paper proposes a circuit based analysis method for such converters, which leads to precise performance prediction and design equations. It is shown that, with the proper design, coupling of inductors can improve both the steady state and dynamic performance of VRM's with increase in efficiency. A four phase coupled inductor synchronous buck converter has been designed and simulated using PSPICE. Simulation results were found to be in good agreement with theoretical predictions. These predictions are supported by experimental results of a prototype, 12 V/1.1 V, 20 A, 50 kHz, coupled four-phase synchronous buck converter.