Power/Heat/Performance frequency question?

[WhatMeWorry]

Sorry if this is a obvious question but Is power and heat and performance of a processor a linear or near-linear function of frequency? In other words if a given processor at 3.0 GHz is overclocked to 6.0 Ghz, would the power required, heat generated and performance obtained be approximately doubled as well?

And would underclocking (if possible) behave in a similar fashion?

Thanks.

[Althernai]

As a function of frequency, it's linear -- but it also depends quadratically on the voltage. The simplified equation is:

Power = C * Frequency * Voltage^2

The value of C depends on a bunch of different things (e.g. the capacitance of the chip so necessarily the temperature, size, etc.). If you could change the frequency from 3GHz to 6GHz without changing the voltage or anything else, the power usage would indeed go up by a factor of two... but since there are no chips that are capable of this, it usually needs a lot more than that.

[morphine]

I have no idea about the theory, but in practice, once you go a bit past the rated clockspeed, the power draw and heat increase a LOT, that is to say, either quadratically or exponentially. It's definitely not linear, as there's a very defined point of diminishing returns.

[Flying Fox]

Performance is definitely not linear to frequency. There are other parts of the system that does not scale in the same magnitude as the CPU clock (such as memory, disk, etc.) that a program is not going to run twice as fast with twice the frequency.

[WhatMeWorry]

I came across this from today's short bread link to AnandTech Brazos review. Seems germane to the discussion.

Generally a single microprocessor architecture can cover an order of magnitude of power envelopes. You can take an architecture from 10W - 100W using clock speed, voltage scaling and disabling features (e.g. cutting cache sizes). You can’t efficiently take a 100W architecture and scale it down to 1W. Intel realized this with Atom, and what resulted was a new architecture designed to span the 0.5W - 5W range