Connecting Loudspeakers to Amplifiers

By | October 27, 2015

Note: Some amplifiers will be very unhappy if you max them out without an appropriate load – and inappropriate could mean open-circuit, short-circuit or just too high or too low.

This article covers the basics of connecting loudspeakers to amplifiers – in this case I am thinking of solid-state guitar amplifiers which are generally going to have class-AB output and be directly coupled to full-range loudspeaker drivers. Vacuum tube (valve) amps and high-impedance (70V/100V line) systems with transformer-coupled outputs are not covered by this article.

Generally, a passive loudspeaker is a box with one or more drivers (which could be sub-woofers, woofers, midrange squakers or tweeters), a crossover network, baffles and tuning (e.g. reflex port, horn) and acoustic absorption – or some combination thereof. However, for this article, when we talk about a loudspeaker, think of a 12″ full-range guitar driver.

Ohms Law and the electrical Power Law

Ohms Law tells us that voltage is equal to current multiplied by resistance. This is written V = I.R  or sometimes E = I.R

The electrical power law tells us that power is equal to voltage multiplied by current. This is written P = V.I

Using a little algebra we can show the following relationships:

Connecting resistors in series and parallel

For resistors in series, add the resistances together.

For resistors in parallel, the math is a little more complex but for loudspeakers, we don’t usually need to use it:

Note that for two identical resistors in series, the resistance is doubled – and in parallel, the resistance is halved.

Here are a couple of tricks: Firstly, when we are considering just two resistors in parallel, we can use this formula:

Secondly, when we are paralleling resistors of the same value, we can use this formula:

where n is the number of resistors and R is the resistance of each individual resistor.

Loudspeaker Impedance

The specified impedance of a loudspeaker is a nominal value. The actual impedance of a loudspeaker is frequency-dependent and a nominal 8 Ohm loudspeaker will have a minimum impedance of about 8 Ohms. Mostly the impedance will be considerably higher. Here’s a typical curve of a 12″ guitar speaker in free air:

Note that the impedance is shown. If you take a multimeter and measure the d.c. resistance of the loudspeaker coil you will likely get a reading of about 6.5 Ohms.

Loudspeaker Power Handling

Loudspeakers are current-driven devices. For dynamic loudspeakers, the loudspeaker cone moves as a result of magnetic interaction between the voice coil (an electromagnet) and the permanent magnet surrounding the coil.

The amount of power the loudspeaker can handle is directly related to the average current flowing in the voice coil. As loudspeakers are super inefficient at converting electricity into sound, most of the energy from the power amplifier is dissipated in the voice coil as heat. There is a limit to how quickly the driver can dissipate heat to the surroundings so, if the average rate of heat generation is higher than the average rate of heat dissipation, the average temperature in the voice coil will rise. As the temperature rises, the copper winding which forms the voice coil increases in resistance and thus current and power dissipation are reduced. This effect is called thermal power compression and effectively places an upper limit on the average power dissipation of a loudspeaker voice coil. I have heard it say that the practical limit of power dissipation for an individual driver is as low as 200W RMS. Therefore, if you’re buying a loudspeaker with a continuous power rating in excess of 200W RMS, expect the driver to have a substantial size and excellent thermal management. If it doesn’t, the manufacturer is lying to you.

One upshot of the above is that it is better to have two or more drivers operating at moderate power than one driver operating at high power.

Matching Amplifier Power to Loudspeaker Power

Before we get into detail, we must stress that we are talking about continuous RMS power at less than 1% total harmonic distortion (THD). Anything other than continuous RMS power (e.g. Peak Music Power Output or PMPO) is irrelevant drivel; any specification that boasts a power of (say) 600W @ 10% THD is extremely suspect.

There are four schools of thought regarding matching amplifier power to loudspeaker handling capability:

Firstly there is the make-the-amp-bigger-than-the-speakers argument. The thinking is that if the amplifier clips, the extra high-frequency energy from the clipping distortion will take out the speaker, so it’s best to have an amplifier with plenty of headroom to avoid clipping. However, if you turn the amp up, the normal undistorted signal will happily burn out the loudspeaker voice coil.

Secondly, there is the make-the-speakers-bigger-than-the amp argument. The thinking here is that if the amp does go into clipping, the loudspeaker drivers will be able to handle it. However, loudspeakers are big, heavy and expensive – why would you spend the extra money on bigger speakers and then not be able to get the most out of them? You’re almost bound to drive the amps into clipping, have a distorted sound, and regularly blow tweeters.

Thirdly, there is the follow-the-manufacturer’s-recommendation argument. But does this mean the amplifier manufacturer or the loudspeaker manufacturer?

The answer is, you should follow the recommendation of the loudspeaker manufacturer. If the amplifier is of good design and reputable manufacture then (for the purposes of this argument) its performance will be essentially identical to any other amplifier with the same specifications.

In the absence of a manufacturer’s recommendation, you should approximately match the RMS amplifier power output with the RMS loudspeaker power handling. This means that you’re getting the most out of the amplifier/speaker combination and if you’re getting clipping, you are definitely running the system too hard.

Fourthly, in modern professional PA systems, the loudspeaker manufacturer models the characteristics of the speaker for use in a Digital Signal Processor (DSP) located before the power amplifier in the signal chain. The DSP analyses the incoming audio and tailors it to get the best from the speaker. This is also true of high-end active loudspeakers – typically, they will be bi- or tri-amped and the DSP will manage crossover, phase delay, etc. to give flat frequency response and ensure that the speaker is not overloaded long term.

Voltage, Current and Power Amplification

In audio, we generally talk about pre-amplifiers vs power amplifiers and we need to understand the basic difference between the two. Setting aside the notion that the pre-amp usually has input switching and tone controls etc, the main idea is that a pre-amplifier is essentially a voltage amplifier and a power amplifier is essentially a current amplifier. Usually, a power amplifier has both voltage and a current gain (hence power amplifier), but the current gain is about 1000 times the voltage gain.

E.g. consider a 1V signal into a 100W power amplifier. Let’s say the amplifier has an input impedance of 10k Ohms and will deliver 100W into an 8 Ohm load for a 1 V input.

So the input current is 1V/10,000 Ohms = 0.1 mA.

From the equations above, we calculate the output voltage is 28V and the output current is 3.5A.

So the voltage gain is 28V/1V = 28 and the current gain is 3.5A/0.0001A = 35,000.

It is important to note however, that the gain-structure of an audio system is focused on specifying, measuring and metering the voltage and – because of this – a power amplifier will be designed for a flat frequency response with respect to  voltage. Furthermore, despite the fact that a loudspeaker is a current-driven device, the loudspeaker designer also aims for a flat sound pressure level (SPL) with respect to applied voltage (within the nominal frequency response, natch) and lets the current take care of itself (remember that the impedance curve of the loudspeaker driver is anything-other-than-flat. See above).

Conceptually, an amplifier does not take the input signal and stretch it to make it bigger. Rather it takes the input signal and creates a bigger copy of it by modulating the voltage of a power supply. The output can nominally be modulated from zero to a little less than the rail voltage. If the amplifier is capable of delivering 100W into 8 Ohms, the rail voltage must be at least sqrt(P.R) = 28.3V. In practice, we need some headroom, so the rails will probably sit at forty-something volts. At 40V you get 20.log(40/28.3) = 3dB headroom at full power.

At 100W into an 8 Ohm load, the current is 3.5A. This means that the power supply must be able to deliver 3.5A at 28.3V across the frequency range. So, we might design the power supply to give up to 5A at 40V to give ourselves voltage and current headroom. Now 40 x 5 = 200W – we have made the power supply twice as powerful as the nominal output power of the amplifier.

What happens if we put a 4 Ohm speaker on this amplifier? Well for the same nominal maximum voltage (28.3V) the current demand would be double (7A) and, since the power supply will only deliver 5A, this would not work.  At a maximum current of 3.5A, the maximum voltage is 3.5A x 4 Ohms  = 14V and the maximum power is 50W.

So the amplifier design is optimised for a particular loudspeaker impedance and if you put a different impedance load on the amplifier, you will get a lower maximum power – because you either don’t have enough current or you don’t have enough voltage.

Multiple Speakers on One Amplifier Channel

In terms of making multi-speaker cabs for guitar amplifiers, we need to consider the impedance and the power handling of the drivers. To make things easy, we should try and use identical drivers. There are good sound-quality reasons for this which we won’t address here. The main thing is that if the speakers are the same, they will all dissipate the same power and this makes the calculations easier. For our purposes, we can assume that the nominal impedance of each driver is a simple resistance and we can use the serial/parallel equations above.

A Note on Valve (Vacuum Tube) Amplifiers.

For a solid-state amplifier, if we don’t impedance match the speakers to the amplifier all it means is that we can’t get the most out of the amplifier – the amplifier does not inherently care what load it sees. However tube amplifiers are almost always transformer-coupled at the output and it is important to impedance match the loudspeaker to the appropriate tapping on the output transformer. If you have an impedance mismatch, the quiescent operating point of your output tubes will change and this will be detrimental to the life of the tubes and probably cause the output transformer to fail in time.

4 Ohms, 8 Ohms, 16 Ohms

The following table shows the net resistance value of two identical drivers connected in series and parallel:

It is clear that you can make 8 Ohms out of two 4 Ohm speakers in series or two 16 Ohm speakers in parallel. It does not matter which you choose (two 4 Ohm or two 16 Ohm) when purchasing drivers. When it comes to four-driver cabinets, there are three ways you can wire your speakers. Assuming you use four identical drivers of resistance R, connecting them in series will give 4R; in parallel R/4; or in series-parallel R.

Clearly series-parallel is useful as you can buy four 8 Ohm 100W drivers, wire them up series-parallel and get an 8 Ohm 400W loudspeaker cabinet.