## CMOS gate delay, power measurements and characterization with logical effort and logical power

##### Abstract

The primary metrics associated with a logic gate's performance are speed, power,
and area. We define a gate as a specific CMOS transistor level implementation of a particu-
lar boolean function in a specific fabrication technology at a constant rail voltage, constant
length, and where the ratio of any two transistor widths are constant. Asking how fast a
gate switches then is highly situational; it changes with load capacitance, choice of inputs,
input slew rate, and the size of the gate. Predicting how much energy the gate consumes
depends on the time frame, how many times the gate has switched in this time frame, input
selection, input slew rate, load capacitance, and gate width. Logical Effort (LE) predicts
gate delay with a simple linear equation: d = t(gh+p). Where g and p are gate and input
dependent parameters independent of load size and gate size, and h is the ratio of output ca-
pacitance to input capacitance (directly related to gate width), and t is a process dependent
conversion factor. The product, gh, then is the delay associated with driving a subsequent
gate, and p is the delay of the gate driving itself. The prediction ignores input slew rate and
the linear dependence fails for very large values of h, but for input slew rates on the same
order as the output slew rate, and for reasonable fan-outs, LE provides remarkably accurate
predictions of gate switching time. The methodology goes on to solve for the widths nec-
essary for each gate in an arbitrary logic path to minimize delay. Designs can quickly be
compared, analyzed and optimized. By breaking down delay into components, one is able
to intuitively choose better logic implementations, if parasitic delay is dominating, often a
better implementation is one with smaller fan-in gates and less logic depth, if effort delay
is dominating then then higher logic depth can lead to faster results. What the method does
not do is predict the power consumption ramifications of all of these choices. What about
minimizing power on non-critical paths, for instance?
To our knowledge, no methodology exists to predict power consumption in a similar
fashion. We propose a power prediction methodology, Logical Power (LP), compatible
with LE that breaks down power consumption into dynamic, static, and short-circuit com-
ponents with linear equations dependent on h. This would allow a compact and efficient
way to characterize a gate that scales with its environment, as well as to allow designers
optimizing with LE to consider not only the speed ramifications of individual gate sizings
but power as well. For instance given a target path delay higher than the theoretical mini-
mum predicted by LE, sizings could be chosen with LE and LP that minimize power that
still result in meeting the target delay.
The other major contribution of this work is a new short-circuit power measurement
technique for simulation that more accurately distinguishes between short-circuit and the
parasitic portions of dynamic power in total active power dissipation than all known tech-
niques.