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|
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:
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:
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:
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.
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.