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)