Electrical Units

OK, so we're going to use electricity.  That means we need to know the units used.
 

Electron: it's a fundamental particle with negative charge (drawn as e^-).  As far as we know, there's nothing inside an electron (other than... electron!).  Electrons are the charge carriers in most solid-state conductors.  For example, metals conduct electricity because they don't mind trading their spare "valence" electrons with their neighbors.

Current: one amp is a coulomb of moving electrons per second (6.24x10¹⁸ e^-/sec) .  Typical microcontroller output signals are measured in milliamps; on-chip logic signals might only be a few picoamps.  Typical wall plug currents are up to a few dozen amps, and typical arc welding current is about a hundred amps.  A desktop PC CPU also typically uses about a hundred amps!

Voltage: measures how much electrons want to be somewhere, in volts.  Electrons will try to flow from a lower voltage to a higher voltage region.  We define the planet Earth's voltage as "ground", or zero volts, and connect to it with a metal rod stuck into the dirt (usually outside your electrical pole!).  Back in the 1980's, it was common to use 5 volts direct current (5vdc) to represent "true", and 0v as false; in the 1990's they switched to 3.3v == true; now most desktop CPUs use only about 1v core voltage, to save power.  For example:

• PC power supply, black wire = 0vdc
• PC power supply, red wire = 5vdc
• PC power supply, yellow wire = 12vdc  (Most machines pull primarily 12V today, and then DC-DC convert down to whatever core voltage you need.)
• PC power supply, orange wire = 3.3vdc
• One AA battery = 1.4vdc
• Lead-acid car battery = 12vdc
• A typical Fairbanks electrostatic charge = 10,000v or more(!)

Resistance: V = I R (volts = amps * ohm).  A 1 ohm resistor will lose 1 volt when conducting 1 amp of current; a 10 ohm resistor will drop 10 volts when conducting one amp.  Ohm's law (V=I R or volts = amps * ohms) is more of a guideline, an assumption of linearity that is only valid for "resistive" materials (OK for most metals; but poor for most insulators, liquids, or semiconductors).  The beautiful part about semiconductors is their resistance can be varied electronically (typically depending on nearby voltages).  For example:

• Typical wire resistance is milliohms.
• Typical "pull-up" logic resistor is Kohms.

Power: P = I V (watts = volts * amps, at least for DC circuits).  A 0.1 ohm piece of wire will drop 0.1 volt if you push 1 amp through it, which takes 1 watts: the wire might get fairly warm, but will still be there.  The same 1 watt into a tiny component like a resistor is enough to let the smoke out, as demonstrated in class.  The same wire taking 100 amps will drop 10 volts, so must dissipate 1000 watts: the wire is rapidly going to glow red-hot, and unless it's made of tungsten or inconel, it's likely to burn in air.  Generally:

• Anything over a megawatt needs a dedicated liquid cooling *tower*, as commonly seen on nuclear power plants.
• Anything over a kilowatt is going to glow red to white hot without dedicated liquid cooling, like a radiator.  Your car is a few hundred kilowatts.  Ordinary personal computers haven't hit this point yet, although supercomputers and data centers have been liquid cooled since the Cray-2 in 1985.
• Air cooling with a heatsink works well between a few dozen and a few hundred watts.  This is the thermal regime of most modern PCs.
• Air cooling without a heatsink is fine below a dozen or so watts, at least for a reasonably large component.  This is the design range of most cellphone and some portable processors.

For example, a current-signaling network might represent individual byte values as groups of 0 to 255 electrons.  255 electrons per sample at 10 billion samples per second is 25.5x10¹¹ Ge^-/s.  One Coulomb of charge is 6.24x10¹⁸ e^-, so that's a current of 4x10^-7 C/s, or 0.4 micro-amps.  At 1V signal strength, a one-ohm wire will lose 0.4 micro-volts, dissipating a power of 0.16 picowatts.  Not much!  Of course, in practice we usually use voltage-signaled networks, since single electrons have a bad habit of obeying only the funky quantum laws instead of ordinary classical dynamics, which makes things much more complicated.

Why you care

Supporting a chip with a Thermal Design Power (TDP) beyond a few hundred watts becomes very difficult using only air cooling.  In mobile devices (tablets, phones, laptops while unplugged), the limited energy available in a battery means we can't afford to consistently burn more than a few watts.

Today, energy usage is a dominant constraint in computer design--we can actually build many more transistors than we can afford to switch on and off every clock cycle: this is called dark silicon.