We present a new approach to design resonant dc-dc converters, that allows us to achieve both a more accurate implementation and a simpler architecture, by reducing the number of required passive components. The approach is applied to a class-E topology, and it is based on the analytic solution of the system of differential equations regulating the converter evolution. Our technique is also capable of taking into account the most important circuit nonidealities. This represents an important breakthrough with respect to the state of the art, where class-E circuit analysis is based on strong simplifying assumptions, and the final circuit design is achieved by means of numerical simulations after many time-consuming parametric sweeps. The developed methodology is dimensionless, and the achieved design curves can be denormalized to easily get the desired circuit design. Measurements on two different prototypes confirm an extremely high adherence to the developed mathematical approach.