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The Crossover Design Cookbook
Chapter 2: How Components Work
by Mark Lawrence

## Capacitors

A capacitor stores charge. This is exactly like a water tank, which stores water. Capacitors come in units called Farads. A 1 farad capacitor is a fairly large box, which can store a dangerous amount of power. Capacitors are also rated according to their maximum allowable voltage. If you exceed the voltage rating of a capacitor, it will explode. Depending on the voltage and capacitance, this can be dangerous.

The Farad is named after Michael Faraday, the smartest Scotsman to ever live. Faraday figured out the connection between electricity and magnetism, but Nobel hadn't even been born yet so, no prize.

In a cross over we will typically find capacitors between 1 micro farad and 1000 micro farads, rated at 100 to 200 volts. A micro farad is one millionth of a farad. In a power supply for a piece of electronic equipment, we will typically find capacitors between 5,000 and 50,000 micro farads (.005 to .05 farads), rated at 25 to 100 volts. In electronic circuits, we will typically find capacitors between 10 pico farads (10 trillionths of a farad) and 1 micro farad. Micro farads are written like this: "µF" or "uF", or sometimes simply "µ" or "u". "u" is a left over from the typewriter days before word processors and computers.

In the US, we write capacitor values like this: "4.7µ". In Europe, this might be "4u7". In Asia, this would likely be written "4k7", meaning 4,700 nano farads. In the US, we never use nano farads as units, but we buy most of our capacitors from Asia. Again, I think they do this just to be different.

If you connect two capacitors side by side (in parallel), the capacities add. If you connect two capacitors end to end in a line (in series), you use the parallel resistor law to calculate the new capacitance. This is backwards from resistors. The resulting capacitance will be smaller than either of the two capacitors. Since capacitors are expensive, we only rarely want to buy two so that we can make one smaller one.

When you connect two capacitors in parallel, you must use the lower of the two voltage ratings. When you connect two capacitors in series, the formula for figuring out the new voltage rating is a bit complicated. Fortunately, we almost never connect capacitors in series, so we'll ignore this case.
 C1 * C2 C = C1 + C2
C = C1 + C2
SeriesParallel

There are many types of capacitors, including paper, mica, ceramic, metal film, tantalum, and electrolytic. Ceramic and mica capacitors are typically 1 pico farad to 10,000 pico farads (trillionths of a farad). We don't use such small capacitors in cross overs, so we'll ignore them. Tantalum capacitors rarely have voltage ratings over about 15 volts, and power amplifiers put out 50 to 200 volts, so tantalum capacitors have no place in cross overs.

Electrolytic capacitors are small, light weight, and inexpensive. They also have complicated non-linear properties which can and usually do color sound, so we mostly try to avoid using them in crossovers. Electrolytic capacitors come in "polar" and "non-polar" varieties. In cross overs, we must only use "non-polar" electrolytics. Polar electrolytics have a plus side and a minus side. If you buy a 250 volt polar electrolytic and put more than about 5 volts across it in the reverse direction, it will be ruined and possibly explode.

Metal film capacitors are the preferred capacitor for use in crossovers. Metal film capacitors come in Mylar, Polyethylene, Polypropylene, and Polycarbonate. There are, in principle, reasons to prefer polypropylene capacitors for audio applications, but I must admit that all film capacitors sound just fine to me. Mylar capacitors are readily available and only somewhat expensive, so I typically use them.

Whenever you need a capacitor over about 10µF, it's best to build up the capacitor from several smaller capacitors. For example, I keep a couple hundred 2.25µF mylar capacitors on hand, and if I need a 13µF capacitor, I use six 2.25µF capacitors in parallel. Alternatively, you could use a MultiCap, but a 13µF MultiCap costs about \$35, and six 2.25µF mylars cost about \$4.50. A 13µF non-polar electrolytic costs about 75¢, and, unfortunately, sounds like about 75¢.

The reason for adding up many small capacitors is that the capacitors have inductance and lead resistance, which make the capacitor less useful. When you place resistors and inductors in parallel, their effect shrinks, but the capacitor's effects add. So, building up large capacitors by placing several small capacitors in parallel makes our capacitors act more like perfect capacitors. This is a good thing.

For large capacitors on a budget, you can mix capacitor types. For example, to make a 100µF, you could use a 50µF electrolytic, three 10µF mylars, and nine 2.25µF mylars. This will sound just fine, and cost about half as much as if you used only mylars. If you're worried about sound quality, the electrolytic should not exceed 60% - 75% of the total capacitor value. Some people will buy a 100µF electrolytic and parallel it with a 1µF polypropylene hoping to cancel the distortion, but they are only fooling themselves, not the electrons. This is like placing a 1/16" fuel line next to a 4" fire hose and then telling people there's more water coming through.

A 4 inch fire hose will drain a water tank much faster than a garden hose. How long it takes to drain the tank depends on the size of the hose, the height of the tank, and the amount of water in the tank. Similarly, a small resistance will drain a capacitor faster than a large resistance, and a large capacitor holds more charge than a small capacitor. The basic law for capacitors is:

Z = 1 / (2π f C)

where "Z" is the effective resistance of capacitor "C" at frequency "f". As you can see from this law, at high frequencies a capacitor has very little resistance and acts like a short circuit, or a short piece of wire. At very low frequencies, a capacitor has large resistance, and acts like an open circuit, which is almost like having no connection at all. In between low and high frequencies the capacitor has intermediate resistance, which is the effect we use to produce crossovers.