An Analytical Model for the Effective Drive Current in CMOS Circuits

Inverter delay is often evaluated as CV
_dd
/I
_eff
, where C is the load capacitance, V
_dd
is the supply voltage, and I
_eff
is the effective drive current derived by approximating the inverter switching trajectory with a linear model. The I
_eff
model utilizes high and low drain currents conventionally measured in wafer acceptance tests and does not require extraction of any parameters. Ease of use combined with reasonable accuracy (~15%) is the main reason for wide application of CV
_dd
/I
_eff
delay metrics. However, CV
_dd
/I
_eff
expression produces large errors when applied to another two important basic circuits: nand and nor. This is because nand and nor circuits contain transistor series connections not accounted for in the inverter model. In this paper, an analytical solution for the transistor series connection influence on the discharge/charge operation in nand/nor circuits is provided. The model for nand/nor effective drive current (denoted as Istack) developed in this paper maintains simplicity of the original I
_eff
expression. It requires only one additional measurement of the linear current. Model accuracy was assessed by comparing to extensive SPICE delay simulations of nand and nor circuits designed using state-of-the-art MOS technologies. Comparison results show that CV
_dd
/I
_stack
equation provides ~15% accuracy for nand/nor circuits in line with CV
_dd
/I
_eff
accuracy for inverter. In an era of emphasis on low-power design, the developed model presents convenient means of exploring design space when optimizing circuit supply voltage for low-power operation.