| Modern CPUs are built using CMOS MOSFET transistors[1]. The gate, which controls if the transistor conducts or not, is effectively a small capacitor. The gate capacitor has to be charged up for the transistor to conduct[2], ie you have to stuff some electrons into it to turn the transistor on. Once you've done that, the transistor is on until the gate capacitor is discharged. This requires getting rid of the electrons you stuffed into it. The easiest is to just connect the gate to ground, essentially throwing the electrons away. So for each time the transistor goes through an on-off cycle, you need to "spend" some electrons, which in turn need to be supplied from the power supply. Thus higher frequency means more current just from more on-off cycles per second. There's also resistive losses and leakage currents and such. Now in theory I suppose you could recycle some of these electrons (using a charge pump arrangement[3]), reducing the overall demand. But that would require relatively large capacitors, and on-chip capacitors take a lot of chip area which could have been used for many transistors instead. [1]: https://en.wikipedia.org/wiki/CMOS [2]: https://en.wikipedia.org/wiki/MOSFET#Modes_of_operation [3]: https://en.wikipedia.org/wiki/Charge_pump |