**This is a guide on how to match the different parts of a sound system to optimize output efficiency. We will cover two main areas: amplifiers and speakers.**

I don't want to make this subject too complex but it is. We must get into some technical background on this subject. I guess I could just tell you how to get more volume but the technical stuff is important. If you understand the concepts you will be better able to apply them to your specific situation. To understand how this all works we must first understand the way people perceive sound.
Sound level is measured in terms of decibels (dB). Volume is referred to as sound pressure level (SPL). In tests, the average person can detect a 3dB change in volume. 3dB is just enough difference that you can barely tell the volume has changed. A 10 dB change in SPL is perceived as twice as loud. With that in mind we can move on to what is required in terms of power (measured in watts) for an amp to create a 3dB change.

**Amplifier output** - It takes 2 times the power from an amp to change the volume 3dB. In other words if an amp is producing 1 watt of power it needs to increase to 2 watts of power to make a 3dB change. This is a ratio of 2:1. By the same token if the amp is producing 50 watts of power it will need to increase to 100 watts to produce a 3dB change. 100 watts would take 200 watts for that same change.

How much power would it take to Increase the SPL 10dB? It will take 10 times the power to increase the SPL by 10dB! In other words, if your amp was producing 50 watts of power you would need to increase it to 500 watts to achieve a 10dB increase. (fig A&B) As you can see it takes a lot of power to get a small increase in volume.

**fig.A**
To determine the change in dB from one amount of wattage to another use this formula:

dB = 10 x log (P1 /P0)

P1 =desired watts

P0 = starting watts

**Example :**

dB =10 x log (2/1)

dB =10 x log 2

dB =10 x .301

dB =3.01

dB = aprox. 3

You will need a log chart or a scientific calculator to determine the log.

**fig.B**

Here is a chart you can use to find out how much power it will take to achieve a specific dB increase. (Red text is the most useful)

**Example:**
If you start with 50 watts how many watts would it take to make a 3dB change in SPL?

50 watts x 2.0 = 3db (change in SPL)

100 watts = to make a 3db change

**Number of Speakers** is a factor that effects volume. This concept is not as simple as it first appears. If we double the number of speakers we will increase the SPL by 3dB. Here is an example. If you have a 50 watt amp with one 12" speaker and you add another 12" speaker you will get the magic 3dB increase. You would have the same SPL as a 100 watt amp with one 12" speaker. To get the next 3dB increase we need to double the speakers again so we would need four 12" speakers. Having 4 speakers will give us a 6dB increase in SPL compared to 1 speaker. Sounds like the same system as the power ratio above doesn't it. Here is were the complex part comes in. If we double the 4 speakers to 8 speakers you would think that there would be a 9dB increase in SPL compared to one speaker, right? Nope. What we get is only a 6dB increase compared to one speaker. Huh? We have now introduced a new factor to this equation...Phase Cancellation. (fig C) In short the distance between the speakers causes the sound to reach your ears, from some of the speakers, at a different time . This has the effect of canceling some of the sound. So...More speakers are better up to a point.

**Speaker efficiency** also plays a role in the optimizing of SPL. How well a speaker can convert electrical energy into mechanical energy is called speaker efficiency. If you look at the specification sheet of a speaker it will contain information of this type. It is described as, "Output measured at one watt - at one meter", and then a dB value is given. What this means is a one watt signal is played through the speaker and then its SPL is measured at a distance from the speaker of one meter. Because we know about the 3dB increase concept described above we can compare the SPL of different speakers to determine which one can produce the most SPL. The larger the SPL number the more efficient and louder the speaker will be. It will usually be less expensive to get a more efficient speaker(s), than a larger power amp, to produce the same or greater SPL.

**Matching speaker impedance to the amplifier** is important in optimizing output power and in protecting the amplifier from damage. Amplifiers are designed to produce a certain amount of wattage based on the amount of resistance that the speaker(s) provide. The resistance to an AC current in speakers is referred to as impedance. Impedance is measured in ohms and is represented by the letter Z. If you look on the back of an amp where the speaker connection is you may see something like - 100 watts into 8 ohms ~ 175 watts into 4 ohms ~ 4 ohm minimum. What this means is if you have speaker(s) with a TOTAL impedance (referred to as load in this application) of 8 ohms connected to the amp, the amp can produce 100 watts. If the total load is 4 ohms the amp can produce 175 watts. It is not recommended that you have less than a 4 ohm load connected to the amp. Please note that if you have less than a 4 ohm load, in this example, amplifier damage can occur due to excessive heat build-up in the amp.

How do we know what the total load will be? Lets look at how the impedance changes when we wire speakers together. A pair of speakers can be wired together in two different ways: in series or in parallel. (fig. D) Depending upon the way the speakers are wired will effect their total impedance. See the formulas in (fig. E) In series wiring all the values are simply added together. The parallel wiring formula is more complex especially if the values are not the same.

In sound systems it is not recommended that you mix speakers with different impedances. If all the speakers have the same value then here is a shortcut to the parallel formula: Take the impedance of one speaker and divide by the number of speakers. Another rule-of-thumb in parallel systems is that the total impedance will always be less than the smallest impedance.

Now that we know how to calculate total impedance lets apply it to the amplifier example above. It is important to note that the jacks on the back of most amps that allow more than one speaker to be connected, per channel, are wired in parallel! Our example is a mono amplifier. If it were a stereo amp then each channel would be treated separately. We can connect one 8 ohm speaker and get 100 watt capability from the amp, one 4 ohm speaker and get 175 watt capability, or two 8 ohm speakers (in parallel 8/2=4) and also get 175 watt capability. If we connected two 4 ohm speakers however, we would get a 2 ohm load (4/2=2 ohms) and possible damage of the amp could occur.

Final notes regarding sound systems. Use the proper kind of wire to hook up the speakers. See About Cables. When wiring multiple speakers to an amp it is best to wire each speaker directly to the amp and not in a daisy chain fashion. (fig. F) This will improve the ability of the amp to control the speaker movement. This control is known as dampening factor. But that's another topic!