In live sound, the terms resistance and impedance crop up with the regularity of a pre-privatisation number nine bus, but what do they mean and why do they matter? Paul White explains.

Loudspeakers, amplifiers, microphones, mixing consoles — even cables — exhibit electrical resistance and electrical impedance. Once you start connecting different pieces of equipment together, they both rear their ugly heads. If the impedance match isn't correct, you could end up with signal loss, distortion, excess noise — you could even damage something. Fortunately, the concept is reasonably simple, as are the rules for matching.

Electrical resistance is simply a means of describing a circuit's opposition to DC current flowing through it; the higher the resistance of a circuit, the more voltage you need to push a given current through it. Copper cable has a low electrical resistance, hence current flows through it easily, whereas something like plastic has a much higher electrical resistance and it's very difficult to get current to flow through it. Materials with very high resistances, such as rubber, are known as insulators.

Resistance is measured in Ohms. A simple formula known as Ohms Law establishes the relationship between current, voltage, and resistance. If you know any two of these parameters, you can easily calculate the third using the formula

RESISTANCE EQUALS IMPEDANCE

Knowing how to calculate resistance in a DC circuit is fine in theory, but in audio, we're dealing with alternating currents right up to 20kHz or beyond — the upper threshold of human hearing. At these frequencies, circuitry ceases to behave as a pure resistor and instead is said to exhibit an impedance. Think of impedance as being AC resistance and you won't go far wrong.

Impedance is also measured in Ohms. In a purely resistive circuit, resistance and impedance are the same thing, but in a circuit that has electrical capacitance and inductance as well as resistance, things start to get more complicated. For example, a circuit which presents a capacitive load will fall in impedance as the frequency rises, so you can't just quote a single figure and expect it to always apply. However, impedance is also useful, because using capacitors, resistors, and inductors, we can construct circuits that offer a higher impedance to some frequencies and a lower impedance to others. We call these circuits filters, and they are used to build devices such as equalisers and crossovers.

In the case of audio equipment, it is desirable to keep the impedance reasonably constant over the entire audio range, although this isn't always possible. For example, loudspeaker impedance varies with frequency. When the speaker is in a cabinet, the acoustic loading affects the electrical impedance. This latter point isn't always appreciated, so go by the impedance marked on the speaker cabinet, not the ratings of the drivers inside. The same is true of horn-loaded loudspeakers — a 4 Ohm driver might actually present an impedance closer to 8 Ohms when driving into a horn flair.

INPUT IMPEDANCE

Input impedance is related to how much current the input terminals of a device draw from the device feeding it — the lower the impedance, the more current is required. If a circuit needs more current than the circuit feeding it can provide, you have a mismatch. The input impedance of a circuit is determined by the electrical components used in that circuit. When we're dealing with line-level audio signal, or signals from microphones, it is necessary to make sure that the receiving device demands less current than the maximum the source device can supply, otherwise signal loss and distortion will result. In mechanical terms, a mismatch of this kind is exactly the same thing as trying to operate a machine from a motor that isn't powerful enough to turn it.

Output impedance is a measure of how much current an output can supply — the lower the output impedance, the more current the unit can supply. It stands to reason then that to pass a signal from one piece of equipment to another, the output impedance of the source must be equal to, or lower than the input impedance of the source.

If the aim is to transfer the maximum power from one device to another, the optimum matching conditions occur when a circuit with a given output impedance is feeding an input which has exactly the same value input impedance. Exact matching is important in any circuit where we're concerned with transferring the maximum amount of power from one circuit to another, for example, an amplifier driving a loudspeaker. I like to describe impedance matching as being the electrical equivalent of a gearbox — to make the most efficient use of an engine, you have to choose an appropriate gear ratio.

When dealing with line-level audio signals, we're not concerned about transferring lots of energy — we are more concerned with transferring the signal voltage from one piece of equipment to another with as little loss as possible. To achieve this, it's usual for the source impedance (the output impedance of the equipment providing the signal) to be significantly lower than the load impedance it feeds (the device accepting the signal). A factor of around five or ten times lower is not uncommon. Not only does this prevent the source signal from being unduly loaded, it also enables a single source to drive multiple loads simultaneously if required.

Note that a simple splitter lead may be used to feed one output into two or more inputs, but you can't do the same in reverse. You can't join two outputs to feed one input; for that you need a mixer.

The mic input stage of a typical mixing console has an impedance of around 1kOhm, while a typical low impedance dynamic microphone will have an impedance of between 150 and 200 Ohms (or thereabouts). This obviously provides a good match. Similarly, most pro audio line-level equipment has an input impedance of several tens of kOhms — 47kOhms is a common figure — whereas output impedances tend to be made as low as possible so that long cables can be driven without significant loss. Budget equipment, such as effects units, will typically have an output impedance of 10kOhms or less, while professional equipment may have an output impedance of only a few tens of Ohms.

BASIC RULES OF MATCHING

When connecting amplifiers to loudspeakers, the output impedance of the amplifier should be equal to the impedance of the loudspeaker cabinet to which it is connected. If more than one cabinet is connected to the same amplifier, then the combined impedance must still be the same as the amplifier's output impedance.

Note: Amplifiers are designed to take into account any variation in speaker impedances, so you can treat the impedance figures on the spec sheets at face value when it comes to matching speakers and amplifiers.

If the amplifier's rated output impedance is lower than that of the speaker, the system will still work, but because the matching (electronic gear ratio) is incorrect, the amplifier will deliver less than the optimum power to the speakers. As a general rule, doubling the speaker impedance halves the power delivered to the speaker. Conversely, if the speaker impedance is lower than the rated output impedance of the amplifier, the amplifier will attempt to deliver more current than it was designed to do. Depending on the magnitude of the mismatch in this scenario, either the amplifier will overheat, or the protection circuity will step in and shut it down.

When connecting mic or line-level audio equipment, the source impedance should be significantly lower than the load impedance, ideally by a factor of five or more. If the load impedance is lower than the source impedance, the signal level will drop and there may also be audible distortion.

Note: Never run valve amplifiers without a speaker connected as damage may result. Solid-state amps usually — but not always — survive this treatment.

When using cables in excess of 10 metres, use low impedance sources to avoid signal degradation caused by cable impedance and external interference. Balanced systems offer greater immunity to interference than unbalanced systems, and on very long cable runs, on-stage line drivers may be required.

With very high impedance sources such as electric guitar, keep the cable length as short as is practical and choose a cable designed for guitar use.

SUMMARY

Impedance matching is important, but thanks to the degree of standardisation that has been adopted by our industry, you can safely assume that the majority of line-level equipment will work together without too many problems. However, correct speaker/amplifier matching is important. In a situation where you may be using a different number of cabinets depending on the size of gig, and where one amplifier may be required to drive more than one speaker cabinet, it is important that the amplifier and combined speaker impedances are the same (more on this subject in the near future).