Notes on "A static power model for architects" by Butts and Sohi
Power = Dynamic Power + Static Power = P_dyn + P_static
Definition: Dynamic power is power used to do computations,
that is when switching
Definition: Static power is power used even if not switching
Fact: Static power as a percentage of total power is increasing
(see figure 1)
Equation: P_dyn = supply voltage^2 * frequency
= V_cc * frequency
Minimum value of V_CC is roughly linear with f (This fact is not in the paper)
Fact: P_dyn = f^3, sometimes called cube-root rule
Equation: P_static = design constant * number of of transistors *
suppply voltage * subthreshold leakage
= k_design * N * V_cc * I_leak
(For subthreshold leakage see figures 2 and 3 in the paper)
Definition: Constant field scaling = reduces supply voltage by
the same factor as device dimensions and speed increases
Equation: switching time = Supply Voltage/ Drain current
= V_cc/I_sat
So under constant field scaling, let us say you are halving
V_cc and switching time. Then I_sat must remain constant.
Equation: I_sat = (supply voltage - threshold voltage)^1.5
= (V_cc - V_t)^1.5
Definition: Threshold voltage = voltage to turn on transistor
So in order to keep I_sat constant when V_cc is halved,
then V_t has to be reduced
Definition: Subthreshold leakage = e^(-V_T/temperature)