## hooking up speaker cabinets

How do I connect my speakercabinets to my amp without overloading it and setting it to fire? It is a question that not only musicians (when they build massive amp stacks for their electric guitar or bass) but also music lovers in general (when expanding their expensive stereo) often have to ask themselves. This article gives a short lesson on electricity and explains the difference between series and parallel, how wattage and ohmage are connected to eachother and how to calculate them.

impedance

Most readers will probably already have suffered through a lesson on the theories behind electricity in high school but were probably with their minds somewhere else. So let’s refresh some things.

The flow of electrons through an electric circuit which we call electricity, can be easily compared with water flowing through a hose. This electrical current is measured in amperes. At the end of your garden hose is usually a gun. When you are doing nothing, it will retain water, thus logically pressure occurs just before the gun. With electric current, this pressure is called voltage and stopping the water is similar to a speaker not being connected: there is pressure (voltage) but no (electric) current.

You can now vary this pressure by setting up the gun in different ways, so every time a certain amount of water leaves the hose. In an electrical circuit the gun, which transforms the continuous water flow into a useable water spray, a mass, something that works on electric power and that has a resistance or impedance, both measured in ohms (abbreviated as the Greek letter omega, or Ω).

A resistance is always constant and can therefore be found with direct current (DC), impedance on the other hand varies depending on the frequency and is therefore applicable to alternating current (AC). The signal from an amplifier to a speaker is always an alternating signal. That’s why from now on we will speak of impedance when we mean a resistance to the flow.

In other words, a speaker is a mass and thus an impedance, which in fact just shows how hard the amplifier will have to work to move the speaker. If the resistance in the speakers is too low, the amplifier will have to work harder and you risk overloading it. If the speakers’ resistance is too high on the other hand, your amplifier won’t be able to deliver it’s full power to the speaker. That’s why impedance is really important. Typical impedances for speakers are 4, 8 and 16 ohms.

The flow of electrons through an electric circuit which we call electricity, can be easily compared with water flowing through a hose. This electrical current is measured in amperes. At the end of your garden hose is usually a gun. When you are doing nothing, it will retain water, thus logically pressure occurs just before the gun. With electric current, this pressure is called voltage and stopping the water is similar to a speaker not being connected: there is pressure (voltage) but no (electric) current.

You can now vary this pressure by setting up the gun in different ways, so every time a certain amount of water leaves the hose. In an electrical circuit the gun, which transforms the continuous water flow into a useable water spray, a mass, something that works on electric power and that has a resistance or impedance, both measured in ohms (abbreviated as the Greek letter omega, or Ω).

A resistance is always constant and can therefore be found with direct current (DC), impedance on the other hand varies depending on the frequency and is therefore applicable to alternating current (AC). The signal from an amplifier to a speaker is always an alternating signal. That’s why from now on we will speak of impedance when we mean a resistance to the flow.

In other words, a speaker is a mass and thus an impedance, which in fact just shows how hard the amplifier will have to work to move the speaker. If the resistance in the speakers is too low, the amplifier will have to work harder and you risk overloading it. If the speakers’ resistance is too high on the other hand, your amplifier won’t be able to deliver it’s full power to the speaker. That’s why impedance is really important. Typical impedances for speakers are 4, 8 and 16 ohms.

one speaker

Most (valve) amplifiers indicate themselves how much power (the wattage, usually indicated on the front of the amp) they send to their speakers at a certain impedance (in ohms, usually indicated at the speaker jack on the back). Remember that power is inversely proportional to impedance. If a 200 watt amp sends out 8 ohms to a mass, for example, he will have to produce about 350 watts at 4 ohms. This means that it must generate more power than what is was intended for, which will soon result in a loud bang and a plume of smoke... So if you connect your amplifier to a cabinet, it’s simple: find a cabinet with preferably the same (for best performance) or else definitely a higher (although this will give a lower output) impedance.

To know how many watts you effectively use with a particular set up, this formula is sufficient: effective use = (amplifier impedance / total speaker impedance) x amplifier wattage. For example, if your amp can push 800 watts at 2 ohms and you connect it to a speaker with 8 ohm impedance, the effective use is (2 / 8) x 800 = 200 watts, which is far below the capability of your amplifier.

If you divide the effective use by the ‘ideal’ use you get a percentage that indicates how efficiently the amp is being used. Both ‘under’- and ‘overfeeding’ of cabinets is bad for the speakers. There may already be slight damage when the efficiency ratio passes beyond the limits of fifty to one hundred fifteen percent. On the other hand, speakers and cabinets are usually rated on their Root Main Square (RMS), the average value during prolonged use which is well below the peak power. For example, if a cabinet has a capacity of 150 watts, it probably can handle an amp of 200 watts because the peak power is some thirty or forty percent higher (around 195 to 210 watts). Of course, this is not really safe...

The wattage of your speakers is also important for the total radiated power. If the speakers in one cabinet all can handle equal power, their total power is the power of one speaker x the number of speakers, for example, 50 watts x 4 speakers = 200 watts total power. If the speakers have different values they all receive the same power from the amplifier so the lowest values are used for calculation. For example, a cabinet with two 50 watt and two 25 watt speakers has a total capacity of 25 x 4 = 100 watts.

To know how many watts you effectively use with a particular set up, this formula is sufficient: effective use = (amplifier impedance / total speaker impedance) x amplifier wattage. For example, if your amp can push 800 watts at 2 ohms and you connect it to a speaker with 8 ohm impedance, the effective use is (2 / 8) x 800 = 200 watts, which is far below the capability of your amplifier.

If you divide the effective use by the ‘ideal’ use you get a percentage that indicates how efficiently the amp is being used. Both ‘under’- and ‘overfeeding’ of cabinets is bad for the speakers. There may already be slight damage when the efficiency ratio passes beyond the limits of fifty to one hundred fifteen percent. On the other hand, speakers and cabinets are usually rated on their Root Main Square (RMS), the average value during prolonged use which is well below the peak power. For example, if a cabinet has a capacity of 150 watts, it probably can handle an amp of 200 watts because the peak power is some thirty or forty percent higher (around 195 to 210 watts). Of course, this is not really safe...

The wattage of your speakers is also important for the total radiated power. If the speakers in one cabinet all can handle equal power, their total power is the power of one speaker x the number of speakers, for example, 50 watts x 4 speakers = 200 watts total power. If the speakers have different values they all receive the same power from the amplifier so the lowest values are used for calculation. For example, a cabinet with two 50 watt and two 25 watt speakers has a total capacity of 25 x 4 = 100 watts.

two or more speakers

When connecting two or more speakers to an amplifier there are two possibilities: in series (the speakers are connected to each other) or parallel (each speaker has its own output signal of the amplifier). Series means that the minus of the amplifier is connected to the positive terminal of the first speaker, the minus of the first speaker to the positive of the second speakers and so on until the minus of the last speaker is connected to the positive terminal of the amplifier. Parallel means that every negative terminal of each speaker is connected to the minus of the amplifier and every positive terminal of each speaker to the positive terminal of the amp.

A ‘reversely’ connected speaker (with the minus of the speaker connected tot the positive terminal of the amplifier or vice versa) will not result in any damages. However, the speaker will move forward when all the rest goes backwards and vice versa, eliminating certain frequencies. So maybe it’s not such a good idea after all...

A ‘reversely’ connected speaker (with the minus of the speaker connected tot the positive terminal of the amplifier or vice versa) will not result in any damages. However, the speaker will move forward when all the rest goes backwards and vice versa, eliminating certain frequencies. So maybe it’s not such a good idea after all...

series

When speakers are connected in series to an amplifier, you just have to add their individual impedances to know the total impedance. For example, connecting two 8 ohm speakers to our amplifier of 800 watts at 2 ohms, you get an actual wattage of (2 / 16) x 800 = 100 watts.

Series connections are almost never used in amplifier - speaker connections, for the simple reason that the impedance gets so big that too little effective power remains. Speakercables are always parallel, so if you connect a cable from your amp to the first cabinet and one from the first to second cabinet, it still is a parallel connection.

Series connections are almost never used in amplifier - speaker connections, for the simple reason that the impedance gets so big that too little effective power remains. Speakercables are always parallel, so if you connect a cable from your amp to the first cabinet and one from the first to second cabinet, it still is a parallel connection.

parallel with equal impedance

Speakers are usually connected in parallel with amplifiers and that’s where all problems start. Impedance is an odd little beast. If we continue with our example but now connect two 8 ohm speakers in parallel instead of in series to our amp, the total impedance is not 8 ohms x 2 speakers = 16 ohm as you might expect. The correct formula, which of course applies only if the impedances of the cabinets are all equal, is total impedance = impedance of one speaker / total number of speakers, which in our example would be 8 / 2 = 4 ohms. The effective output of our 800 watts at 2 ohms amplifier connected to two 8 ohm speakers in parallel now becomes (2 / 4) x 800 = 400 watts. In other words, when connecting to our amp an extra speaker in parallel, we double our effective wattage. However, when connecting that same extra speaker in series, we halve the actual wattage. To get our 100% power of 800 watts we have to connect four speakers in parallel.

Now what happens if we connect a fifth speaker of 8 ohm to our amplifier? The total speaker impedance will be 8 / 5 = 1.6 ohms, the effective use (2 / 1.6) x 800 = 1000 watts. In other words, the total impedance is decreased and we risk overload our amp and eventually set it to fire... So remember to never, NEVER connect a speaker or speaker combination to your amplifier with a total impedance that is lower than the one which is specified on your amp. In other words, the impedance shown on your amp should always be preferably EQUAL and otherwise certainly HIGHER than the impedance of your speaker cabinet(s).

Now what happens if we connect a fifth speaker of 8 ohm to our amplifier? The total speaker impedance will be 8 / 5 = 1.6 ohms, the effective use (2 / 1.6) x 800 = 1000 watts. In other words, the total impedance is decreased and we risk overload our amp and eventually set it to fire... So remember to never, NEVER connect a speaker or speaker combination to your amplifier with a total impedance that is lower than the one which is specified on your amp. In other words, the impedance shown on your amp should always be preferably EQUAL and otherwise certainly HIGHER than the impedance of your speaker cabinet(s).

parallel with different impedances

Now what if I would like to connect an 8 ohm cabinet and a 4 ohm cabinet to that same 800 watts at 2 ohms amplifier? In this series would not be a problem: 8 + 4 = 12 ohm total speaker impedance, which gives an actual output of a meager (2 / 12) x 800 = 133.33 watts. The formula for the total speaker impedance for the same configuration in parallel is as follows: (impedance speaker 1 x impedance speaker 2) / (impedance speaker 1 + impedance speaker 2). In our example this would be (8 x 4) / (8 + 4) = 32 / 12 = 2.67 ohms. As the total speaker impedance must always be lower than that of the amplifier, it is not a good idea to connect these speakers in parallel to your amp. If you got more than two speakers, each with different impedances, the formula becomes one divided by the sum of the reciprocals of the impedances. If you got for example a speaker 4, 8 and 16 ohms, then the total impedance would be

1 / (1 / 4 + 1 / 8 + 1 / 16) = 1 / (0,25 + 0,125 + 0,0625) = 1 / 0,4375 = 2,29 ohms or

1 / (4 / 16 + 2 / 16 + 1 / 16) = 1 / (7/16) = 16 / 7 = 2,29 ohms.

Two 4 ohm speakers in parallel have a total impedance of 4Ω / 2 = 2 ohms. Two 8 ohm speakers in parallel have a total impedance of 8Ω / 2 = 4 ohms. So we can see a Y-ohm speaker as two speakers of 2Y ohms. In other words, a simpler way of calculating is to look at the 4 ohm cabinet as two 8 ohm cabinets. Then we can apply our previous formula: impedance of one cabinet / number of cabinets = 8 ohms / 3 = 2,67 ohm cabinets. This also means that if you see a speaker output jack that says ‘minimum 4Ω load’, you can attach not only one 4 ohm speaker but also two of 8 ohm.

1 / (1 / 4 + 1 / 8 + 1 / 16) = 1 / (0,25 + 0,125 + 0,0625) = 1 / 0,4375 = 2,29 ohms or

1 / (4 / 16 + 2 / 16 + 1 / 16) = 1 / (7/16) = 16 / 7 = 2,29 ohms.

Two 4 ohm speakers in parallel have a total impedance of 4Ω / 2 = 2 ohms. Two 8 ohm speakers in parallel have a total impedance of 8Ω / 2 = 4 ohms. So we can see a Y-ohm speaker as two speakers of 2Y ohms. In other words, a simpler way of calculating is to look at the 4 ohm cabinet as two 8 ohm cabinets. Then we can apply our previous formula: impedance of one cabinet / number of cabinets = 8 ohms / 3 = 2,67 ohm cabinets. This also means that if you see a speaker output jack that says ‘minimum 4Ω load’, you can attach not only one 4 ohm speaker but also two of 8 ohm.

© Wouter Adriaensen, 2010