An analytical expression for early voltage factor useful for hand calculations

The maximum voltage gain of a MOSFET transistor is limited by its output conductance (g_ds), which depends on gate and drain-source voltage bias and drain current and channel length (L). In this work, it is demonstrated that output conductance, extracted from SPICE simulations using EKV 2.6 model parameters, can be expressed as the product of two potential functions; the first one being a function of channel length; the second one, depending on inversion level (i_f). This expression can be used for hand calculations of either output conductance as a function of channel length and inversion level, or the Early voltage factor (V_E) as a function of the inversion level.