Modeling the influence of the transistor gain ratio and the input-to-output coupling capacitance on the CMOS inverter delay

An improved model for the ramp response of a CMOS inverter has been derived where the influences of the short-circuit current and the input-to-output coupling capacitance are considered. These effects modify the ideal linear relationship between the inverter propagation delay and the input ramp rise/fall time by adding a term proportional to the charge supplied by the short-circuiting transistor. This term is shown to contain first- and second-order contributions of the input ramp rise/fall time where the second-order contribution effectively models the propagation delay roll-off for slow input ramps. Both the first and the second-order effects are found to be affected by the P-to-N-channel gain ratio. The model shows excellent agreement with SPICE level 3 simulations; even when the short-circuiting transistor has a driving capability twice that of the charging/discharging transistor the error in the propagation delay is only about 2% for a slow input ramp (input-to-output slope-ratio at V_DD/2 equal to 1:2)