# Computing stuff tied to the physical world

## Easy Electrons – Electric charge

In Hardware on Dec 27, 2010 at 00:01

Welcome to another installment of the Easy Electrons series.

The previous article was about capacitance. And specifically about the dynamic properties of capacitors. Complex stuff (literally so, in fact).

This time, I will focus on the charge and energy aspects of capacitors (and similar components).

First a small diversion into the land of electrical units: a farad can be interpreted as the amount of charge you need to create a voltage potential of 1 volt. Charge is described in terms of coulombs (named after Charles-Augustin de Coulomb). One coulomb is equivalent to 1 amp current during 1 second.

Once you start diving into this, you will be thankful for the International System of Units which created a set of units of measurement that are very easy to use and to remember. Being able to write that previous paragraph about what a farad is, without a single conversion factor or physical constant is a great help, also intuitively. I can clearly picture an amount of water (coulomb), being lifted a certain height (volt), and flowing at a certain rate (ampere). And even though the water analogy is quite limited, it’s a great help to visualize what’s “happening” inside an electrical circuit.

The farad unit is awkward, though.

It’s far too big a unit for most capacitors. You will often see caps described in terms of µF (microfarad, 10^-6), nF (nanofarad, 10^-9), or even pF (picofarad, 10^-12). Capacitors in the mF (millifarad) range are less common.

There’s another very widespread type of electricity containers: batteries. A battery is a bit like a huge capacitor, even though its “charge” is not held as electrical energy but as chemical energy. For batteries, the farad unit is also awkward, because it’s in fact too small. Let’s find out how many farad a standard 1.5V 2500 mAh AA battery would be, if it were a capacitor:

• 2500 mAh means it can supply 2500 mA during one hour
• that’s 2.5 x 3600 = 9000 “ampere-second”
• an ampere is defined as 1 coulomb per second
• so the AA battery holds 9000 coulomb of charge
• in our battery, that charge is “held” at 1.5V
• so we’d need 9000/1.5 = 6000 coulomb to reach 1V
• than means one AA battery is essentially a 6000 farad capacitor, charged to 1.5V

As you can imagine, it’s easy to make mistakes with farads because you may encounter values in normal use which vary over some fifteen orders of magnitude. Always check your zeros carefully!

Somewhere between the basic capacitor and the battery, lies the Supercap:

This is still a capacitor, but with a phenomenally high capacitance, compared to normal caps. The one shown here is 0.47 farad. No milli, micro, nano, or pico. These small devices are relatively new, and usually only work up to 2.7 or 5.5V, max.

If anything, supercaps look a lot like little batteries. They only hold their charge for a few hours though, due to a certain amount of internal leakage. Think of it as a resistor tied permanently to its output pins, draining the charge, slowly but incessantly.

One important use for capacitors (of all sizes) is as what I’d like to call “charge buffers”. This is the case whenever you see a capacitor with one side tied to negative, i.e. ground level:

What these do could be summarized as: resist change. If + in the left-hand image is tied to +3.3V, then the capacitor will charge up to 3.3V and then … it’ll essentially stop doing anything. But whenever there is a distubance in that 3.3V level, the capacitor will either draw current (if the voltage went up), or supply current (if the voltage went down).

It’s not that different from a rechargeable battery. Attach a voltage higher than the current battery and the battery starts charging. Attach a lower voltage, including any circuit consuming power, and the battery starts discharging.

The circuit on the right is slightly more involved, due to the extra resistor. The same happens as before, but now, as the capacitor draws or supplies current, the current has to pass through the resistor. As a consequence, the resistor will create a voltage drop (E = I x R, again!). The effect is similar to the LED circuit with a series resistor: the resistor will reduce the current flowing in or out, thus “dampening” the effect. So what you get, is that OUT lags IN, if IN changes, but eventually it’ll follow it to whatever voltage IN is.

The right-hand side is also called a low-pass RC filter. It tracks slow-moving changes fairly accurately, but rapid changes are evened out a bit.

The left-hand circuit is used all over digital circuits, to remove “noise” (i.e. very fast but random changes) in the power supply line. The noise comes from the fact that digital circuits switch connections all the time, changing electricity flow and power draw. Often a 0.1µF capacitor is used. This is usually called a “decoupling” capacitor. It rips high frequencies out of a supply line which you’d like to remain stable.

The right-hand circuit is also useful to even out variations, but in a more gradual and controlled manner. It’s used as last step in a power supply, and to even out pulse trains. One nice use of this, is to turn an PWM signal into an analog voltage:

• a PWM signal which is always on will produce an output of that same voltage
• a PWM signal which is always off will produce a zero volt output
• everything in between will produce and averaged value in between the two extremes

There are some simple calculations to determine how fast things happen. Look for the term “RC time constant” on the web. And if you run into articles such as this one, don’t let the math discourage you. As I said in the previous post, the intricate details of capacitors involve complex calculations. Just skip them. There’s plenty you can do with caps without diving in.

Supercaps are also a lot of fun to play with. You get all the properties described above – after all, it is a capacitor like any other. The difference is that things happen a lot slower, due to the larger amounts of charge involved. Supercaps have enough energy to power an LED, for example (don’t forget the series resistor!). And when it does, you’ll see how it eventually fades and dies out, as the charge drops.

A simple experiment would be to measure the voltage over time with such a supercap driving an LED + resistor circuit. With Ohm’s law, you can then calculate the amount of current drawn. Which in turn gives you an idea how brightness in LEDs is related to the current through them. If you think that’s boring, how about measuring the voltage with a JeeNode, and then sending the results to your PC and plotting the values in real time? You may not realize it, but a lot of lab experiments related to electricity can be done with an ATmega, i.e. a JeeNode or an Arduino. Who needs a multimeter? Make one!

Easy Electrons!