Synthesizing two different values of inductance from a given sample coil for use in a single-input double-tuned circuit is possible by means of three extra LC elements. A detailed analysis with derived equations shows how to calculate the circuit component values and what to expect from this kind of probe. It also derives the upper limit of the trap coil/sample coil inductance ratio beyond which no solution exists to double-tune the 31P-1H probe. The general expression for the channel efficiency shows that the latter is a function not only of the inductance of the coils, but also of their quality factor and of the operating frequencies. A numerical example is given illustrating good agreement between experiment and theory provided high quality rf capacitors are used.