The two biggest limiting factors are power consumption and cooling. Smartphones are battery powered and passively cooled (they have no fans). So they favour efficiency over raw power.
Heat is essentially wasted electricity, so power consumption and temperature regulation go hand in hand. This means basically that different architecture CPUs are better in different use cases. In PCs we have a more powerful energy source and we use that for active cooling with fans or water and so we focus on raw speed at the expense of heat generation. In mobile phones we mostly want long battery life so we have to settle for less CPU speed.
Size is definitely an issue. Phones are packed to the brim with electronics, there’s not really space for a big cpu. Cooling and power are both issues, phone cpus are fairly power/heat efficient for their size. You can’t really slap a heatsink onto a phone like you can a computer. Plus, even if you could dissipate enough heat, the surface of the phone is the heatsink, and it would become uncomfortably or dangerously hot to hold.
You could put any CPU you wish into a mobile device. But, as you guessed, power is a major issue for mobility.
Firstly desktop CPUs chew up a lot of power. And that power is turned into heat – which is why most modern desktop CPUs have large fans attached – to dissipate the energy into the air.
Even if you put a big fan on the back of a CPU in a mobile device you really don’t want a lot of heat in your pocket. So that puts quite a limit on the power that a phone can dissipate safely.
And we haven’t even talked about the size of a battery required to power a desktop CPU – which would be considerable.
You’re not wrong that desktop CPUs are small. It’s true. But it’s really all down to power supply and heat dissipation.
And cost/price.
Main issues are power and cooling.
A mobile device is super compact, so there’s no internal airflow or ability to add fans.
Even if you could somehow dissipate the heat, people expect their phone’s power consumption to allow going a certain amount of time without a charge. With a high-speed power-hungry CPU, you’d need a big battery, which wouldn’t fit.
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