[Galaxy S II Q&A, Help & Troubleshooting] AndreiLux:
For god's ****ing sake that is the most idiotic analogy I've ever heard of. Please show me that article and if it even mentions that theory in regards to electronics the author needs to be beaten to a pulp.

I'm getting a little sick of this thread and misinformation spreading out of it.

A CPU or any other part of a electronics device is build up from millions of the simplest electronic element, transistors. A transistor is just a switch which either current through or not. How often this transistor does that is called the switching speed. The switching speed is nothing else than the frequency on which the transistor is running at. Switching a transistor takes current, and due to inefficiencies in the physical properties of the silicon / semi-conductor, creates waste heat. Switching a transistor at a higher frequency takes more voltage because again of psysical limits on the material the transistor is made of.

Now that we got that out of the way, to the next step.

You can sum up in a formula on how much power such a circuit uses up:

The capacitance of the material x the voltage to the squared x the frequency or simply C x V² x f.

C is something you cannot alter and is a physical property, the only way you'd be able to change that is if you dump your phone into liquid nitrogen or some other method to cool your chip to crazy low temperatures. Thus, for practical use, C is a constant which we can just ignore.

This leaves one with the simplified formula of V² x f. Now if any of you have had 7th grade maths you'll notice that the product of that formula will scale quadratically to the voltage and linearly to the frequency. This just means that voltage has much more effect on power draw than the switching frequency.

So we have our imaginary circuit: it runs on either 1 or 2V, and at 1 or 2 GHz. To make any kind of computation it always takes up a certain amount of cycles on the circuit, no matter what.

So we have a example computation, it calculates the mass of your best friend's mother and it takes up 500 million cycles (0.5G) worth of time on the circuit.

So we have for example these power draws, theorizing that the circuit is under load for 1 second:

A) 1V & 1000MHz : 1000M power units

B) 1V & 2000MHz : 2000M power units

C) 2V & 1000MHz : 2000M power units

D) 2V & 2000MHz : 4000M power units

The thing is, it's physically not possible to run B) because of technological and materal limits, and it's retarded to run C) because we can achieve the same end-result by using the values under A). We are left with:

A) 1V & 1000MHz : 1000M power units

D) 2V & 2000MHz : 4000M power units

Please keep in mind that because we are ignoring the capacitance of the circuit, we cannot calculate SI units like the actual power draw in watts. This is irrelevant since our imaginary power units are directly relative to real power draw.

Now to get back to the computation of your friend's mother's mass; which takes up 500M cycles.

A) at 1000MHz it takes 0.5 seconds or 500M power units to complete

D) at 2000MHz it takes 0.25 seconds or 1000M power units to complete

Now if you hadn't noticed by now: to do the same stupid computation with the same result, it takes twice the amount of power to do it at a higher frequency.

This is a result of the power efficiency/inefficiency of the electronics.

This is a rule-of-thumb for most semi-conductor circuit in the last 30 years and it holds true.

Power draw scales linearly with frequency.

Power draw scales quadratically with voltage.

By lowering the voltage you increase the power efficiency at any frequency. By limiting yourself to a lower frequency you don't use less power-efficient states.

And now a little bit about CPU states themselves:

The only reason we want to use CPU states is because we want to have the most power-efficient state running on the CPU without sacrificing performance. There is no reason to run a computation at 20% load at 1000MHz, where we could run it at 100% load at 200MHz, the end power draw will be less if it's done in the slower power state. The only reason why we want high power states is for time-critical computations; that means animations and anything related to what needs to be shown on the screen, because we love things to be fluid and smooth.

If somebody says he doesn't notice too much the difference between 1600MHz on his phone and 800MHz, and wants to limit it to 800MHz it's his damn right, and he is absolutely correct that it will save battery life.

TL;DR: underclocking and undervolting saves battery life. period.