## Electrical Units

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

 Electronics Electrons Wire Battery Resistor Voltage (volts) Current (amps) Capacitor Transistor Plumbing e.g., MONIAC Hydraulic Computer Water Pipe Pump Clog Pressure (psi) Flow rate (gpm) Accumulator Tank Valve

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.