Optimal coil size ratios for wireless power transfer applications

Optimization of coil sizes for wireless power transfer applications has a significant impact on the range and efficiency of the wireless power system. Often it is difficult to accurately analyze how a set of coils will perform before they are constructed due to the complexity of approximating the parasitic components and coupling coefficients associated with the coils. Also, for certain wireless power applications such as consumer electronic devices, implanted medical devices and industrial equipment that have physical constraints on the size and shape of the coils, it can be a difficult and time-consuming process to design and evaluate several different coil configurations for optimal range and efficiency. This paper provides simplified design equations to accurately calculate the self inductance, capacitance, resistance, quality factor and coupling coefficient in terms of coil geometries for flat, spiral coils. Experimental results validate the analysis and a design example is provided to optimize the size of a transmit coil for maximum range and wireless power efficiency to a 5.8cm receive coil used in a four-element wireless power transfer system.