It is well known that mid-range wireless power transfer can be realized by a link consisting of mutually coupled series resonant circuits operating at the common resonant frequency. However, in such conditions, the link load which maximizes the output power or the transfer efficiency is coupling dependent. This letter provides an analytical solution to this problem by exploiting the frequency bifurcation phenomenon, which occurs after a certain threshold value of the coupling. When the system is operated at one of the secondary resonances, it behaves as an ideal transformer; thus, it is able to deliver to a prescribed load constant output power with constant efficiency. This is true for variable coil distances or coil misalignment, that is, for variable coupling coefficient.