Impedance, sensitivity and amplification: do your headphones need an amp?

Two numbers, two questions

The spec sheet of a pair of wired headphones gives two values that describe its relationship with the device driving it.

• Impedance, in ohms (Ω): the resistance the headphones put up against the current. It ranges from 16 Ω for earbuds to 600 Ω for some studio headphones. It tells you in what form the headphones want their energy: a lot of current if it's low, a lot of voltage if it's high.
• Sensitivity, in decibels: the sound level produced for a given amount of energy. It tells you how much energy is needed.

Very sensitive 300 Ω headphones can play loud from a phone; low-sensitivity 30 Ω headphones can stay timid on the same device. Hence the mistake of looking only at the ohms.

The trap of the two sensitivity units

Sensitivity is expressed in two ways, and manufacturers don't always say which one they're using:

• in dB/mW: the sound level for one milliwatt of power;
• in dB/V: the sound level for one volt of signal.

The two figures can't be compared with each other. You convert from one to the other using the impedance Z:

dB/V = dB/mW + 10 × log₁₀(1000 ÷ Z)

For 32 Ω headphones, the gap is 15 dB; for 300 Ω, it's 5 dB. So headphones rated at "100 dB" tell you nothing until you know the unit. Because headphone outputs behave like voltage sources, the dB/V figure is the more telling one: it says directly what you'll get from a given device.

Doing the math for your headphones

You need a target: to listen comfortably to dynamic music, the peaks have to be able to reach about 110 dB, even if the average level stays well below that (fortunately for your ears). The voltage required is calculated like this:

voltage (V) = 10 ^ ((110 − sensitivity in dB/V) ÷ 20)

On the other side, what do sources deliver? A phone's USB-C to 3.5 mm adapter supplies between 0.5 and 1 volt; a laptop's headphone jack, 1 to 2 volts; an audio interface or a desktop amplifier, from 3 to more than 10 volts.

The conclusion can be read straight off the table. With a 1-volt adapter, the 300 Ω headphones top out at 97 dB on peaks: they work, you hear music, but with no headroom. The loud passages are squashed, and the sound comes across as flat, as if it "never takes off." That is exactly the situation in which an amplifier changes what you hear.

What an amplifier does, and doesn't do

A headphone amplifier supplies the voltage and the current the source doesn't have. If your headphones are short on level or distort on the peaks, the gain is obvious. If they were already playing loud enough, and cleanly, the amplifier will add neither detail nor "musicality": a good amplifier is transparent by definition.

The DAC (digital-to-analog converter) is a separate matter: it turns digital data into an electrical signal. The one in a recent phone or computer is generally beyond reproach to the ear. You replace a DAC when the output hisses, crackles or lacks power, not to gain resolution.

The one-eighth rule

Every headphone output has an impedance of its own, known as its output impedance. If it is too high relative to that of the headphones, two flaws appear: the bass loses its grip, and the frequency response gets bent out of shape.

The second effect mainly concerns headphones whose impedance varies widely with frequency, notably in-ear monitors with several balanced armature drivers: plugged into an ill-suited output, they literally change signature. The practical rule is simple:

The output impedance of the source should not exceed one-eighth of the impedance of the headphones.

For 16 Ω earbuds, that means an output of 2 Ω at most. Phone adapters and modern amplifiers do far better; it's old hi-fi systems and some tube amps, with outputs of 100 Ω or more, that cause problems.

Why do high-impedance headphones still exist?

In a studio, a single amplifier once drove several pairs of headphones in parallel: high impedances kept it from being overloaded. A voice coil wound from thinner, longer wire also lightens the moving assembly (coil and diaphragm), which benefits precision. Finally, high-impedance headphones are largely immune to the electronic hiss of the source. Many studio models come in several versions (32, 80, 250 Ω): the lowest for portable use, the highest for a fixed workstation.

Sources and references

1. IEC 60268-7 — Sound system equipment: headphones and earphones
2. IEC 61938 — Multimedia systems: guide to the recommended characteristics of analogue interfaces