Okay, this is applying to an old argument that I brought up a while ago.
some of you might recall the title: "5.6 GHz?? Impossible!!!"
Well, the commond idea of the 2 GHz and 3 GHz being the theoretical limit of processors arises from basic assumptions and calculations. I will provide these in just a moment.
For those that don't understand this all too well, you should understand what a capacitor is, a transistor, and bascially how a capacitor and transistor are used to juggle around 1's and 0's. Think of a capacitor as a storage area, and the transistor as the gate. Okay here we go:
Now, the industry standard for 1 bit is around 1,000,000 electrons. This is something they really don't mess around with, because at any smaller charge, you have a really bad signal to noise ratio. (there are trillions upon quadrillions of electrons all around) So, the other CPU detail is the fact that the difference between a "1 bit" and a "0 bit" is just a matter of voltage. (When a capacitor holds a charge, it also creates a voltage). The other standard of computers, is that the "0bit" is 0 volts, and the "1 bit" is 3 volts. This has basically not changed in a while.
Now, the idea of capacitance comes into play, capacitance is the ability for a capacitor to hold charge. This can be calculated by the equation: C= charge/voltage.
The charge of 1,000,000 electrons is something on the order of 1.6 X 10^13 Coulombs. And at 3 volts, you get the capacitance of 50 femtofarads. (femto is 1,000,000 times smaller than nano)
Now the transistor used in CPU's and in many computing parts is a Field Effect Transistor. This transistor is the common one that everyone learns about in simple solid state electronics. The channel of the FET (Field Effect Transistor) has a resistance of around 1 kilo Ohm.
Okay, here comes the big UHOH -
the value of 1 kilo Ohm arises from the equation Resistance = Resistivity X (Width of channel/ Cross sectional area)
So to get the 1 kilo Ohm, the resistivity of the materials used in the FET has not changed that much, but the width of the channl has... In the case of "1 kilo Ohm" we assume that the width of the channel is .25 microns. As you all know this is an OLD photolitographic process, and they are now commonly using .18 and even .13. For the purpose of this argument I will continue on with .25 microns. Oh and for those that want to do the calculation for .13 microns, the cross area is around 1 micron X 10 nanometers.
Finally, we wrap this all up with what is known as a RC time constant. (Resistance-Capacitance Time constant). This is just a simple matter of multiplying the resistance and capacitance together. And for those that know a little E&M physics, u will know how important that value is. This brings us to around 50 pico Seconds.
(The RC constant is a time unit that determines how long it takes to charge the capacitor at an exponential rate. So a value of 50 picoseconds means that it takes 50 picoseconds to charge the capacitor to 63 % of full capacity. HOWEVER, it doesn't mean it charges to 126% in 100 pico seconds. It's an exponential increase, that slows down dramatically, in fact it takes infinite time to reach 100% charge. (which is why recharageable batteries have a life, but that's a different story)
So, it is also a common standard that the CPU will wait for 6 time constants to get as FULL of a charge as possible in as LITTLE time as possible. If you dont wait long enough, you are open to a LOT of errors, which will make ur CPU VERY buggy, and make it extremely bad for overclocking. Since heat will amplify electron "jumping" errors. (when electrons are not where they are supposed to be). So 6 X 50 picoseconds comes to 0.3 nanoseconds. And finally if u take the frequency of that, it comes to 3 GHz.
=)
Now, this is based on many assumptions, however, keep in mind some of these are pretty constant. Like the 1 million electrons, 3 V for a bit. But then again there are many OTHERS that have changed within the past couple years, and will change dramatically in the future. As you can see, when u decrease the channel width (from .25 microns to .13 microns) it decreases the Resistance, which in turn will decrease the time constant, and finally increase the value of the theoretical limit fo 2 Ghz, or 3 Ghz, whatever u may.
If i have any errors, I'm the one that is most likely wrong. I haven't looked at the semiconductor industry in a while, so they might have changed some standards, like the 3 V for a bit standard. Although that has been there for quite a while.
Oh and FYI, you may think that u set ur CPU at 1.5 V, but its at -1.5 V and +1.5 V. This in turn comes out to an actual difference of 3.0 V.
And if I do have errors, please correct me, dont flame me.
Tom
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