Wireless power transfer (WPT) is an emerging technology with many promising applications where transmitting power via wired connections is undesirable. However, near-field WPT between magnetically coupled inductors is highly susceptible to positional changes, with power transfer efficiency (PTE) suffering if the coils are misaligned. To combat this effect, many position-independent, self-adaptive, inductive WPT schemes have been developed. Recent work indicates that it is possible to passively achieve high PTE across the operating range with nonlinear capacitors. In this work, the functionality of nonlinear WPT circuits is investigated, and fundamental design equations are derived and validated. A simplified design procedure is proposed for the position-independent self-adaptive WPT using nonlinear capacitors, wherein the ideal capacitance is extracted for each coupling factor. The efficacy of the method is demonstrated with an experimental circuit. Future work in this area is also proposed.