Ohms, Amps and Speakers
I posted a question to The Bottom Line, a bass player's mailing list, about how to calculate Ohms with multiple speakers. After receiving 10 very gracious explanations, this is my understanding of it. Correct me if I'm wrong.
One Step Back
Guitar pickups and microphones are known as transducers, meaning they convert sound waves into electrical impulses. Sound is vibration in the air, and these transducers pick up this vibration and turn it into electrical energy. Electrician generators move a piece of metal into and out of a magnetic field, creating electricity. Transducers do the same thing, but since the piece of metal moves in a complex way (guitar string, ribbon in a microphone) the electricity 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 - silver & other expensive materials - they conduct electricity better than others.
When the electricity passes into the speaker, some of it is resisted. The ohms rating of the speaker is a measure of how much electricity is resisted by the speaker, and an indication of how much energy it takes to drive it - the higher the ohms rating, the more difficult it is to drive.
An amplifier amplifies the electrical signal, causing the speaker to vibrate with greater force, otherwise the impulse would be barely audible (think of the size of a microphone vs. the size of a speaker). How much the amp drives the speaker 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 independent of their surroundings. A flashlight produces light independent 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.
If you're still confused, think of water in a hose. The larger the hose, the less pressure is produced at the end of the hose, even though the same amount of water is flowing through it.
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 would have a rating of 8 ohms.
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 electricity 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 output. 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 formula stated a different way, or may be more accurate or less accurate is:
Resistance = 1 / (1/Speaker A + 1/Speaker B)
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 speakers wire in series (16 ohms total) 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)
Amplifier Output = 100 watts x 1/4
Amplifier Output = 25 watts
An amplifier designed to put out 100 watts into 8 ohms will put out 200 watts into 4 ohms. Two 8 ohms speakers wired in parallel (4 ohms total) would cause the amplifier to produce 200 watts.
200 watts = 100 watts x (8 ohms / 4 ohms)
The amp produces 100 watts at 4 ohms. When the resistance 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 multiple 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 manual for all of your equipment before doing any of this.
The limiting factor, from what I hear, is the power supply. If the power supply isn't designed to handle a 2 Ohm load, you may fry your amp. In fact, it takes a very special amp to work below 4 Ohms. Again, check the manual, call the manufacturer, don't just start wiring things into a 1 Ohm load hoping to get 4 times the power out of your amp.
Mike Faithfull informs me of another possible problem: You could also destroy a transistor in the output stage by demanding it to supply more current (into the extra-low resistance load) than it is rated for (this is probably a more common failure than the power supply!)
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.
Thanks To the folks at The Bottom Line: (in no particular order, just the order I found the names when it came time to copy/paste them here)
Wade T. Shelton
page first created on Sunday, May 05, 2002
© Mark Wieczorek