# Multiple Cores vs Single Core Power Efficiency Equations

I was searching for OpenMP tutorials and I came up a video that showed some simple equations that promotes multiple core hierarchies against single core ones. The equations used are

Capacitance = Ability to store energy

C=q/V ⇒ q=CV

Work = Moving charge across voltage

W=Vq ⇒ W=CV^2

Power = Work over a period of time

P=Wf ⇒ P=CV^2f It then proceeds to calculate power requirement of a single core processor as

Ps = CsVs^2fs

where Xs stands for X used on single core system. It then goes on to calculate it for a dual core system responsible for doing the same work. But it uses following parameters (Not exactly 2 or 0.5 multipliers but they just make the problem more easier to understand):

Cd = 2Cs Vd = 0.5Vs fd = 0.5fs

Power is calculated as

Pd = 0.25Ps

I don't get why voltage and capacitance are altered.

The video is over here youtu.be/cMWGeJyrc9w?t=3m45s, if time link doesn't work for you, it starts about 3:45.

## 1 Answer

It looks to me like they are using a real world example processor, saying "SingleCoreWigdget" has a capacitance of 1 and uses voltage of 1, but "DualCoreWidget" has a capacitance of 2 and uses half the voltage. There is no physical reality to "processing efficiency" so all you can use are example processors.

• Well the most reasonable thing I've come up is that parallel capacitances add up and make system cap 2c, and to keep charge same, they reduce the voltage, too. – Mert Can Ergün Dec 30 '16 at 17:33
• That's trying to apply physical reality to the situation, I am fairly certain you can't do that. I'm pretty sure they are saying "we found this dual core processor design that "Can do the same work" so we will use its numbers as an example." – user7358648 Dec 30 '16 at 17:35
• But I can't answer the question why didn't they increase capacitance in the first place? Voltage goes down and so does the power as well – Mert Can Ergün Dec 30 '16 at 17:36
• What do you mean? Capacitance is usually a function of transistor size if you have a smaller process, capacitance is going to go down. – user7358648 Dec 30 '16 at 17:49
• Two identical processors means twice the gate capacitance of one processor. You can run half as fast (ideally, in theory). So that explains F and C. I think the idea with V is that if you're running slower you can lower your voltage (I can't remember how that scales). It certainly doesn't scale indefinitely. I'm working on a chip running at 1.6 GHz, 0.54 V. I don't think we could run it at 0.27 V and 800 MHz :). – Matt Aug 25 '18 at 3:15