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# Speaker Impedance, Power Handling and Wiring

The speaker ohm rating is an indication of the speaker's AC impedance, which varies with the frequency of the input signal. This variation of the speaker's impedance can be seen on the speaker's spec sheet impedance curve. This is why the spec sheet indicates this speaker to have an 8 ohm "nominal impedance."

Most of the speakers are available in alternative ohm ratings (usually 4, 8 an 16 ohm versions). This variety allows for more flexibility in matching the overall equivalent impedance of your speaker(s) to the output impedance of the amplifier. It is important that the output impedance of your amplifier matches the overall equivalent impedance of your speaker(s) for maximum power transfer and so that you do not damage the amplifier.

When using more than one speaker with your amp the equivalent overall impedance changes depending on how the speakers are wired. You can wire multiple speakers "in series," "in parallel" or in a combination of the two wiring configurations ("series/parallel").

Speakers also have a wattage rating which indicates how much power from the amp they can handle before being damaged. When you use multiple speakers, the output power from the amplifier will be distributed among the speakers. We recommend using speakers with the same ohm rating in multi-speaker cabinets so that the power is evenly distributed to each speaker. (For guitar amplification, we recommend choosing a speaker rated for at least twice the maxiumum power it could experience from the amp).

## Example 1: Single Speaker Wiring

In example 1, we have a 50W amp with an 8 ohm output impedance. It has been matched to one 8 ohm speaker.

Since there is only one speaker, it could experience the entire 50W from the amplifier.

**In this case we recommend choosing an 8 ohm speaker with a rated power of at least 100W.**

## Example 2: Series Wiring

When multiple speakers are wired in series, the sum of the impedance ratings of of the speakers should equal the output impedance of the amplifier.

~z_{\text{equivalent}}~ = Equivalent Overall Impedance

~z_n~ = Impedance of speaker ~n~

$$z_{\text{equivalent}} = z_1 + z_2 + \ldots + z_n$$In example 2, we have a 50W amp with an 8 ohm output impedance. To determine the speaker values, we need to solve using the equivalent impedance formula.

$$z_{\text{equivalent}} = z_1 + z_2 + \ldots + z_n$$$$z_{\text{equivalent}} = 8Ω$$$$8Ω = z_1 + z_2$$Since we know ~z_1 = z_2~, we can simplify:

$$8Ω = z_{\text{speaker}} + z_{\text{speaker}}$$$$8Ω = 2 \times z_{\text{speaker}}$$$$\frac{8Ω}{2} = z_{\text{speaker}}$$$$z_{\text{speaker}} = 4Ω$$Since there are two speakers, each speaker could experience 25W (half of the output power from the amp).

**In this case we recommend choosing two 4 ohm speakers with rated power of at least 50W each.**

## Example 3: Parallel Wiring

When multiple speakers are wired in parallel, things are a little more complicated as the overall impedance of the parallel circuit will be less than the individual speaker impedance ratings as shown in the following formula.

~z_{\text{equivalent}}~ = Equivalent Overall Impedance

~z_n~ = Impedance of speaker ~n~

$$z_{\text{equivalent}} = \frac{1}{\frac{1}{z_1} + \frac{1}{z_2} + \ldots + \frac{1}{z_n}}$$In example 3, we have a 50W amp with an 8 ohm output impedance. To determine the speaker values, we need to solve using the equivalent impedance formula.

$$z_{\text{equivalent}} = \frac{1}{\frac{1}{z_1} + \frac{1}{z_2} + \ldots + \frac{1}{z_n}}$$$$z_{\text{equivalent}} = 8Ω$$$$8Ω = \frac{1}{\frac{1}{z_1} + \frac{1}{z_2}}$$Since we know ~z_1 = z_2~, we can simplify:

$$8Ω = \frac{1}{\frac{1}{z_{\text{speaker}}} + \frac{1}{z_{\text{speaker}}}}$$$$8Ω = \frac{1}{\frac{2}{z_{\text{speaker}}}}$$$$8Ω = \frac{z_{\text{speaker}}}{2}$$$$z_{\text{speaker}} = 16Ω$$Since there are two speakers, each speaker could experience 25W (half the output power from the amp).

**In this case we recommend choosing two 16 ohm speakers with rated power of at least 50W each.**

## Example 4: Series/Parallel Wiring

When multiple speakers are wired in a series/parallel configuration, things become even more complicated. First,the equivalent impedance needs to be determined for all speakers wired in series using the same formula as in Example 2 above. Once this is done, then the overall circuit impedance rating of the circuit can be calculated using the parallel circuit formula in Example 3 above.

In example 4, we have a 50W amp with an 8 ohm output impedance. To determine the impedance of the speakers, we will have to solve using both the perallel formula and the series formula for equivalent impedance.

Because the top two speakers are wired in parallel with the bottom two speakers, we can express the formula for equivalent impedance using the parallel impedance formula as follows:

$$z_{\text{equivalent}} = \frac{1}{\frac{1}{z_1} + \frac{1}{z_2} + \ldots + \frac{1}{z_n}}$$$$z_{\text{equivalent}} = \frac{1}{\frac{1}{z_{\text{top}}} + \frac{1}{z_{\text{bottom}}}}$$Where ~z_{\text{top}}~ is the equivalent impedance of the top two speakers and ~z_{\text{bottom}}~ is the equivalent impedance of the bottom two speakers.

So in order to solve this formula, we need to determine the impedance for the top and the bottom sets of speakers. Each of these two sets of speakers is wired in series, so we can use the equivalent series impedance formula to solve.

$$z_{\text{equivalent}} = z_1 + z_2 + \ldots + z_n$$$$z_{\text{top}} = z_1 + z_2$$Because all speakers have the same impedance, we know that ~z_1 = z_2~ and we can simplify further:

$$z_{\text{top}} = z_{\text{speaker}} + z_{\text{speaker}}$$$$z_{\text{top}} = 2 \times z_{\text{speaker}}$$Because all speakers are the same value, we know also that:

$$z_{\text{bottom}} = 2 \times z_{\text{speaker}}$$So we can also see that ~z_{\text{top}} = z_{\text{bottom}}~

Plugging these equations into our original formula for ~z_{\text{equivalent}}~, we can see how to calculate:

$$z_{\text{equivalent}} = \frac{1}{\frac{1}{z_1} + \frac{1}{z_2} + \ldots + \frac{1}{z_n}}$$$$z_{\text{equivalent}} = \frac{1}{\frac{1}{z_{\text{top}}} + \frac{1}{z_{\text{bottom}}}}$$$$z_{\text{equivalent}} = \frac{1}{\frac{1}{2 \times z_{\text{speaker}}} + \frac{1}{2 \times z_{\text{speaker}}}}$$$$z_{\text{equivalent}} = \frac{1}{\frac{1}{2 \times z_{\text{speaker}}} + \frac{1}{2 \times z_{\text{speaker}}}}$$$$z_{\text{equivalent}} = \frac{1}{\frac{2}{2 \times z_{\text{speaker}}}}$$$$z_{\text{equivalent}} = \frac{1}{\frac{1}{z_{\text{speaker}}}}$$$$z_{\text{equivalent}} = z_{\text{speaker}}$$So after all that work, we can see that the equivalent impedance of this series/parallel circuit is just equal to the impedance of the speaker. Because we know the output impedance of the amplifier is 8Ω, we can easily see that

$$z_{\text{speaker}} = 8Ω$$Since there are four speakers, each speaker could experience 12.5 W (one fourth of the output power from the amp).

**In this case we recommend choosing four 8 ohm speakers with rated power of at least 25W each.**

For this configuration, it is easiest to calculate the equivalent overall impedance in two steps.

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By Kurt Prange (BSEE), Sales Engineer for Antique Electronic Supply - based in Tempe, AZ. Kurt began playing guitar at the age of nine in Kalamazoo, Michigan. He is a guitar DIY'er and tube amplifier designer who enjoys helping other musicians along in the endless pursuit of tone.

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