# Dynamic energy and dynamic power in microprocessors

In a class I'm learning about dynamic energy and dynamic power and the notes seem to be incomplete.

• Dynamic energy
Transistor switch from 0 -> 1 or 1 -> 0
• Dynamic power
0.5x Capacitive load x Voltage2 x Switching Frequency


I've seen simillar formulas used in other places, for example I've seen other formulas that don't have 0.5 but require the value of a constant. Is 0.5 the average or something? Also what is switching frequency in the context of computer hardware? Is that the speed the CPU operates at (e.g. 2.5GHz)?

Energy in a capacitor = $\dfrac{C\cdot V^2}{2}$

That is the standard formula for the energy stored in a capacitor by virtue of it being charged to V volts.

If this energy is liberated (lost) into heat at f times per second then the power liberated is

$\dfrac{f\cdot C\cdot V^2}{2}$

Also what is switching frequency in the context of computer hardware? Is that the speed the CPU operates at (e.g. 2.5GHz)?

Most of the energy lost due to "driving" capacitance will probably be from IO from the CPU such as driving the bus - although the frequency (f) will be much smaller than 2.5GHz (for example) the PCB track capacitance and input capacitance of bus chips will make this the dominant losses in a lot of cases.

Here's a good website that gives the derivation for energy: -

• Big thanks! You mention the word "capacitor" and my notes use the word "transistor". What is the difference? – Celeritas Mar 6 '14 at 18:33
• A mosfet is noted for it's large gate capacitance. Within a chip this will be a factor.Also in some memory devices mosfet capacitance is used as the storage element. The lower the parasitic capacitance the lower the power. – Andy aka Mar 6 '14 at 19:17