Mutual Inductance of Multilayer Spiral-Inductor Clusters for Small-Form-Factor Wireless Power Transfer (μWPT)

Spiral inductors are commonly used in wireless power transfer (WPT) systems due to their simplicity and low cost, but their large physical size poses challenges for μWPT systems (i.e., WPT systems with small form factors). To address these challenges, multilayer spiral-inductor clusters (MSICs) are employed to increase the mutual inductance between the transmitting and receiving couplers for acceptably high power-transfer efficiency. This paper uses the Neumann formula, first, to derive an exact analytical expression for the equivalent inductance <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L_N^Eq1</i> of an MSIC of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> layers and, second, to conceptualize a mutual inductance <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M_N^dy</i>(<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</i>) between two MSICs that are separated by an air gap <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</i> and derive an exact analytical expression for it. These novel expressions were verified experimentally within 1% margin of error and can be easily applied to design μWPT systems.