Fundamentals of Quantitative Design and Analysis - Computer Architecture: A Quantitative Approach - page 22

Energy And Power Within A Microprocessor
For CMOS chips, the traditional primary energy consumption has been in switching tran-
sistors, also called dynamic energy . The energy required per transistor is proportional to the
product of the capacitive load driven by the transistor and the square of the voltage:
This equation is the energy of pulse of the logic transition of 0→1→0 or 1→0→1. The energy
of a single transition (0→1 or 1→0) is then:
The power required per transistor is just the product of the energy of a transition multiplied
by the frequency of transitions:
For a fixed task, slowing clock rate reduces power, but not energy.
Clearly, dynamic power and energy are greatly reduced by lowering the voltage, so voltages
have dropped from 5V to just under 1V in 20 years. The capacitive load is a function of the
number of transistors connected to an output and the technology, which determines the capa-
citance of the wires and the transistors.
Example
Some microprocessors today are designed to have adjustable voltage, so a 15%
reduction in voltage may result in a 15% reduction in frequency. What would
be the impact on dynamic energy and on dynamic power?
Answer
Since the capacitance is unchanged, the answer for energy is the ratio of the
voltages since the capacitance is unchanged: