Power, Impedance and Matching Amps to Speakers

An amplifier and a loudspeaker are an electrical pair before they are a musical one. The amplifier produces a voltage, the speaker decides how much current that voltage pulls out of it, and the product of the two is the power that becomes heat and sound. Every wiring choice you make on a stage — one cabinet or two, this channel or bridged — is a decision about that number, whether or not you did the arithmetic.

The usual assumption is that an amplifier hands out its rated wattage the way a tap hands out water, and that a box marked 8 ohms is an 8-ohm thing. Neither holds. The amplifier delivers whatever power the load draws at the voltage it is holding, and the 8 is a label stretched over a curve that moves with frequency. The gap between those two sentences is where dead tweeters and amplifiers that mute mid-song come from.

Ohm's Law Is Simple, the Load Is Not

Ohm's law says current equals voltage divided by opposition to current, and in a speaker circuit that opposition is impedance — symbol Z, measured in ohms. Power is voltage times current, so substituting one into the other gives three forms worth having in your head: P = E × I, P = E² ÷ Z, and P = I² × Z. Put 32 volts RMS across an 8-ohm cabinet and all three agree. Current is 32 ÷ 8 = 4 amperes, and power is 1,024 ÷ 8 = 128 watts, which is also 4² × 8, and also 32 × 4.

What makes that useful is that a modern power amplifier behaves very nearly as a voltage source: for a given input it holds the same output voltage regardless of what is hanging off the terminals. Halve the impedance and the voltage stays where it was, so the current doubles and the power doubles with it. Those same 32 volts into a 4-ohm load draw 8 amperes and deliver 256 watts — twice the output for no change at the desk, which sounds like a bargain and is actually the bill arriving.

Resistance and impedance are not two words for one thing. A multimeter pushes direct current through the voice coil and reads plain copper resistance, typically five to six ohms on a driver sold as 8. Music is alternating current, and an alternating signal also has to fight the coil's inductance and the driver's own mechanical resonance, neither of which holds still as the frequency changes. Impedance is that sum — resistance plus the frequency-dependent terms — and it behaves as a curve rather than as a number. It runs high where the driver resonates, high again in the top octaves where inductance takes over, and lowest somewhere in between. That low point is what the nameplate approximates, and it approximates from above, so the real minimum sits under the printed figure.

Every Cabinet You Parallel Makes the Load Harder

Hang two cabinets off one amplifier output and you have almost certainly wired them in parallel, because that is how the link jack on the back of a box is connected internally. Parallel impedances combine as the reciprocal of the sum of the reciprocals — 1 ÷ Z = 1 ÷ Z₁ + 1 ÷ Z₂ + … — and the answer is always lower than the smallest box in the chain. Two 8-ohm tops on one channel make 4 ohms. Four 8-ohm wedges daisy-chained on a monitor send make 2. A 16-ohm wedge alongside an 8-ohm one lands at 5.33 ohms.

Series wiring does the opposite and simply adds, so two 8-ohm boxes in series present 16 ohms and the amplifier, holding the same voltage, delivers half what it would into one of them. You will rarely meet it on a stage, and the reason is that a series chain has no redundancy — lose one coil to an open circuit and every box on that run goes quiet with it. The combination is the case that earns its keep: four 8-ohm boxes wired as two series pairs, and those pairs then paralleled, come back to 8 ohms and let a single channel feed all four.

Every amplifier states a minimum load, commonly 4 ohms per channel and 2 on many current class-D designs, and bridging doubles that figure because each half of the amplifier then sees half the load. Going under it is undramatic at first, which is the trap. Current climbs past what the supply and output devices were built for, heat follows, and the protection circuits begin making decisions: rails fold back, the output current-limits, a thermal cut-out mutes the channel, or on an unprotected design the output stage simply fails. Current limiting flattens the waveform, so what you hear first is distortion nobody asked for. Remember too that the nominal number hides the dip — a pair of 8-ohm cabinets is labelled 4 ohms, and somewhere in its range it measures under 4, which is the reading your amplifier actually has to survive.

A Power Rating Is a Sentence, and Most of It Gets Left Off

A loudspeaker's power handling usually arrives as three numbers, and they describe three different questions. Continuous — the AES figure on a professional driver's sheet, measured with band-limited noise over hours rather than seconds — is the long-term heat the voice coil survives. Program is conventionally twice that and peak four times, and both describe shorter windows rather than sturdier construction. A single number with no method attached tells you nothing, because you cannot tell which of the three you are holding.

Amplifier ratings leave out more, and which condition goes missing is never an accident. Peak rather than continuous, one channel driven rather than both, a single 1kHz tone rather than the full audio band, distortion left unstated: each of those inflates the headline without changing anything inside the box. A wattage only means something next to another wattage when all four conditions travel with it — the load it was measured into, whether both channels were working, the bandwidth, and the distortion it held.

The load-dependence is the part worth deriving for yourself, because it is where the arithmetic and the carton disagree honestly. An amplifier holding 300 watts into 8 ohms is swinging about 49 volts, and 49 volts across 4 ohms comes out at 600 watts on the same equation you started this article with. Real units of that size land nearer 500. Nothing is being concealed: the supply cannot hold its rails up while the current doubles, so the voltage sags and takes the power with it. It is the amplifier claiming a clean doubling into half the impedance that should make you ask which conditions moved.

Clipping Does Not Send DC Anywhere

The most repeated explanation for blown speakers is that an underpowered amplifier clips and sends DC to the driver. An amplifier that has not failed puts out alternating current, and a clipped waveform is a distorted alternating waveform, not a direct one. The real mechanism is duller and worse. Clipping raises average power for a given peak: flatten a sine until it approaches a square and its RMS voltage rises by a factor of √2, which is double the power — the +3dB the decibel lesson attaches to a doubling — and it is sustained rather than momentary.

Voice coils fail from heat. A coil is thin wire wound on a former and held with adhesive, so what it survives is a property of those materials rather than of the music. Ordinary constructions start letting go somewhere between 150 and 180°C — the high-temperature parts used in professional drivers hold on to around 300. Clipping attacks that from two directions at once. It squashes the crest factor so average power climbs steeply, and the harmonics it manufactures land above the crossover point in a passive two-way, where the high-frequency driver sits with a fraction of the woofer's wire, mass and cooling. That driver goes first, which is why an abused rig loses its top end rather than its bottom. Mechanical failure from over-excursion is the other route, and it belongs to the loudspeakers lesson rather than this one.

The honest version of the claim, then, is that a small amplifier harms nothing by being small; it harms a driver when you push it into hard clipping chasing a level it cannot make cleanly. A large amplifier will cook the same coil quite happily, and without the warning distortion first. Manufacturers accordingly disagree about how much amplifier to specify, and the disagreement is genuine rather than careless. Published guidance runs from matching the speaker's continuous rating exactly, for a rig where nothing can stop the amplifier clipping, through 1.6 to 2.5 times it for ordinary use. Where a limiter is doing the stopping it opens up to 2 to 4 times — 3 to 6dB of headroom. Your place in that range is set by the material: quiet and dynamic at the bottom, loud and already compressed at the top.

Watts Buy Decibels at a Punishing Exchange Rate

Sensitivity is the number that turns watts into loudness. It is the SPL a cabinet produces one metre away, on axis, driven by one watt. Take a box rated 97dB at 1 watt and 1 metre, and feed it 500 watts. Five hundred watts is 10 × log₁₀(500) = 27dB above one watt, so the paper ceiling is 97 + 27, about 124dB at a metre — and eight metres out, three doublings of distance later, the six-per-doubling loss of a free field has taken roughly 18 of those decibels back.

Try to make it louder and the exchange rate bites. Doubling to 1,000 watts buys 3dB. Reaching the ten-times-power mark that most listeners would call twice as loud needs 5,000 watts, which is a different amplifier and a different power distro. Sensitivity is the far cheaper lever: a cabinet rated 91dB rather than 97 needs four times the power, close to 2,000 watts, to arrive at the same 124, because 6dB is two doublings of power.

Two things keep that ceiling on paper. The cabinet has to survive 500 watts continuously, and coils lose efficiency as they heat, so the figure decays over a set rather than holding. The other catch is in the specification itself: sensitivity is increasingly quoted at 2.83 volts rather than one watt, and 2.83 volts is one watt only into 8 ohms. Into a 4-ohm box it is two watts, so the quoted number arrives 3dB flattered. Subtract three before you weigh it against an 8-ohm rival.

What to Work Out Before You Plug Anything In

• Add the load up before the show — parallel totals are the reciprocal of the sum of the reciprocals, and the result is always lower than the smallest cabinet on that channel.
• Leave margin under the stated minimum — a nominal 4-ohm pair measures under 4 somewhere in its range, and that dip is what wakes the protection circuits.
• Read the whole power rating — load, both channels driven, bandwidth, distortion. A figure missing any of those cannot be compared with one that has them.
• Size the amplifier above the speaker's continuous rating — 1.6 to 2.5 times it for normal use, and up to four times only when a limiter is holding the amplifier out of clipping.
• Treat distortion at the desk as an alarm, not a texture — clipping doubles average power and pushes harmonics into the driver least able to shed the heat.
• Shop for sensitivity before you shop for watts — 6dB more sensitive does the work of four times the amplifier, with no extra current and no extra heat.
• Convert 2.83-volt sensitivity figures first — into a 4-ohm cabinet that reference is two watts, so the printed number is 3dB optimistic against an 8-ohm box.
• Never bridge into the stereo minimum — bridged mode doubles the lowest load the amplifier can face, so a 2-ohm-capable unit needs 4 ohms in bridge.