The minimum supply voltage limit is studied in the case of a 2.45 GHz LC cross-coupled oscillator, in a 28 nm FD-SOI technology. An approach with simple equations aided with look up tables is used to obtain a theoretical prediction of the minimum voltage and current required for operation. The look up tables are loaded with all the transistor parameters of interest, which are extracted by means of DC simulations. The prediction is in good agreement with the simulation results, as long as the transition frequency of the transistors is at least 10 times the oscillation frequency. A feasible supply voltage for this circuit topology, oscillation frequency and technology is shown to be 37 mV. Depending on the back-plane voltage value and the inductor selected, the supply voltage reduction is limited by either the parasitic capacitances or the intrinsic gain of the transistors. Equations are provided to aid the designer in the selection of all of the design parameters to achieve the lowest possible supply voltage and lowest possible current.