TDP is short for "thermal design power" (or "thermal design point"). This is the amount of power that a cooling system must dissipate, provided by the chip manufacturer*. This is important because fast chips consume a lot of power and, through conservation of energy, turn that power into heat. If the chip isn't cooled properly, it's going to fail and you will be sad.
* This can vary. AMD defines TDP to mean the maximum current the CPU can draw, at the default voltage, under the worst-case temperature conditions. Intel publishes TDPs that are the average power that the processor can dissipate (to be used for processor thermal solution design targets).
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Regarding the equation, it was said in class that we can reason, "To push frequency higher, there is a non-linear power cost."
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I think it's interesting to note the relatively tiny TDP values of mobile phone processors. Phones are uniquely limited in that their usefulness is dependent on their battery capacity and physical size. Since it appears that advances in processors are coming much faster than advances in battery capacity, phone processor designers have to pay extra close attention to power usage since it's not feasible to just increase the sizes of batteries for more power-hungry processors. This issue isn't as limiting (yet?) with GPUs for example, since high-end GPUs can still be accomodated by using PSUs with higher ratings.
An increase in frequency leads to an increase in voltage. So, in terms of the equation, an increase in frequency leads to a non-linear increase in power. That is why there seems to be a frequency ceiling of around 4 GHz for today's CPUs. Even Intel's top of the line i7 processors have a stock frequency of around 3.5 GHz.
The industry seems to have fully embraced this, with Intel desktop CPUs having lower TDPs every year or every other year: quad core Nehalem CPUs typically had TDPs of 95w or 130w, quad core Sandy Bridge CPUs typically had TDPs of 95w, and quad core Ivy Bridge CPUs typically have TDPs of 77w.
Another contributing factor to this decrease in TDPs on Intel's part is that Intel wants to improve efficiency for various reasons, especially mobile.
The power wall is important from everything from mobile phones to supercomputers. For supercomputers, heat generated is heat that needs to be removed via air conditioning systems, which have their own power cost associated with them. Mobile phones need to not build up heat because no one wants to hold a burning brick in their hands or next to their ear.