One Step Back

Pickups and microphones are known as transducers. They convert audio waves into electrical impluses. Sound is vibration in the air, and these transducers pick up this vibration and turn it into electrical energy. Electricical generators move a piece of metal into and out of a magnetic field, creating electricity. Transducers does the same thing, but since the piece of metal moves in a complex way (guitar string, ribbon in a microphone) the eletricity that gets created has a complex pattern as well.

A speaker is the opposite. A magnet and a piece of metal, only this time, the metal generates electricity, causing the magnet to vibrate. In fact, I've hooked up speakers as microphones! It's a very interesting sound to record and listen to.

I already knew all this, but the whole Ohms thing had me confused.

What are Ohms?

Ohms is a measure of resistance. You don't think of it, but substances conduct or resist electricity on a scale. Rubber isn't very conducive, copper is. This is why some premium cable are made out of silver and such - these substances conduct electricity better than others.

When the electricity passes into the speaker, some of it is 'resisted.' The ohms rating of the speaker is how much is resisted, and an indication of how much energy it takes to drive it - the higher the ohms rating,t he more difficult it is to drive.

An amplifier amplifies the electricial signal, causing the speaker to vibrate with greater force, otherwise the impulse would be barely audible. How much the amp drives is measured in watts. When an amp manufacturer gives it's wattage rating, it's always at a specific Ohm resistance. 100 watts @ 4 ohms, for example. When the resistance is 4 ohms, this amp will produce 100 watts. If that resistance changes, the amp will produce a different amount of watts.

This is the core concept to understand. We're used to things that have a strength independant of their surroundings. A flashlight produces light independant of how bright or dark it is. Since electricity usually travels in a loop, from a negative terminal to a positive one (which is why you have to hook up both halves of a battery) the elements in the loop affect the output. Alternating Current makes things even more complex, but I'm not going to address that here. These calculations are based on DC, but serve as good averages for AC as well.

How do I calculate Ohms - Series Wiring

If you connect your amp to one speaker, the ohms rating is equal to that speaker's ohms rating. An 8 ohms speaker

If you wire two or more speakers in series, you add the ohms rating together to get the total ohms. I know what series & parallel wiring is from grade school science. It's hard to describe without diagrams, so I'll keep my description minimal. You can refer to the diagrams in the articles from my bibliography if you need more help.

My grade school science book had the example of christmas lights. When you wire the lights in series, you connect the + terminal of one light to the - terminal of the next light. The elctricity flows through one light, and then on to the next. If any of the lights goes out, or any of the connections breaks, all of the lights go out. The connection is broken.

This increases the total resistance, reducing the total acoustical ouput. That is, because the electricity has to flow through each speaker one at a time, each speaker adds it's resistance to the whole. The formula is as follows:

Speaker A + Speaker B = Total Ohms Rating
8 Ohms + 8 Ohms = 16 Ohms

Two 8 Ohms speakers wired in series will have a total rating of 16 ohms.

How do I calculate Ohms - Parallel Wiring

Parallel wiring is something entirely different. If one of the Christmas lights goes out, none of the others goes out. Visually, this looks like a ladder, with each light in the center of a rung. Remove one of the rungs, and the electricity still flows to the next rung via the sides of the ladder.

This reduces the total resistance increasing the total output. That is, because electricity flows through all of the speakers simultaneously, each speaker added reduces the resistance of the chain. If you visualize all of the negative electrons on one side trying to get to the other, they'll have an easier time because there are so many possible paths for them to go by.

Resistance = (Speaker A x Speaker B) / (Speaker A + Speaker B)
Resistance = (8 Ohms x 8 Ohms) / (8 Ohms + 8 Ohms)
Resistance = 64 / 16
Resistance = 4 Ohms

Another calculation I've seen, which may be the same forumula stated a different way, or may be more accurate or less accurate is:

Resistance = 1 / (1/speaker 1 + 1/speaker 2)
Resistance = 1 / (1 / 8 Ohms + 1 / 8 Ohms)
Resistance = 1 / (2/8)
Resistance = 1 / .25
Resistance = 4 Ohms

How do I calculate Amplifier Output?

The calculation for figuring out how much is fairly straightforward, and pretty much what I would expect it to be. Since ohms measure resistance, the more ohms, the less output from the amplifier. Conversely, the less ohms, the more output from the amplifier.

Since the amp is rated at a specific amount of ohms (i.e 100 watts @ 4 ohms), a different amount of ohms will produce a different output. Two 8 ohms amps wire in series would cause the amp to produce 25 watts to each speaker.

Amplifier Output = Amplifier Watts x (Amplifier Rated at Ohms / Speaker Chain Ohms)
Amplifier Output = 100 watts x (4 ohms / 16 ohms)
25 watts = 100 watts x 1/4

Two 8 ohms speakers wired in parallel would cause the amplifer to produce 200 watts.

200 watts = 100 watts x (4 ohms / 2 ohms)

The amp produces 100 watts at 4 ohms. When the resistances is increased to 16 ohms, four times what it was rated, the amplifier produces one fourth as many watts.

You must be careful when wiring mutliple speakers together in a series or parallel chain because the amplifier may have trouble dealing with certain Ohms chain ratings, especially below 4 and above 16, and you must be sure that your speakers are capable of handling the wattage that they're receiving. Be sure to check the manaul for all of your equipment before doing any of this.

Conclusion

When combining speakers in a chain, you can do it in Series, Parallel, or even mix the two methods to ensure that the resistance is what you want it to be. With the right equipment you can use this to increase or reduce the output of any element in your chain.

In reading the calculations from various sources, I sort of skimmed over the complex math, but I know that there is complex math and these calculations are only approximations. Real World conditions may yield actual results that are somewhat different from these simplistic mathematical models. Speaker cabinets can even affect the Ohms rating of the speaker! Also, don't mix speakers, make sure all of the speakers in your chain have the same ohms rating. It would probably be a good idea to be sure they all have similar wattage ratings.

In other words, try this at home, but be extremely careful with the calculations and read the manual. Don't try anything too extreme like hooking up 18 speakers in a row, even if your speakers and amp say that they can handle what your calculations say because these calculations are only approximates and you could do serious damage to, well, a lot of things.

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