Figure-of-merit for optimizing the current-efficiency of low-power RF circuits

The widely used RF Figures-of-Merit such as transit frequency (f_t) and maximum frequency of oscillation (f_max), are only partial measures of performance and not well adapted to ultra-low power RF design. These FoMs are narrowly defined to characterize the speed of operation but without any consideration about the power efficiency of the device. A new FoM comprising both, the current-efficiency and the ability of the device to show gain at RF has been defined. This FoM lends itself naturally for the optimization of the operating points of RF circuits. In this paper we derive analytical expressions for I_D and G_m, continuous from weak inversion to strong inversion and including velocity saturation, to evaluate the FoM. We extract the value of a critical inversion coefficient I_crit as the theoretical edge between velocity saturation and non-velocity saturation regions and show that the FoM has a peak which lies in the moderate inversion region at equation.