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Impedance, sensitivity, and whether you need an amp

By Maria Caspar. Published . 6 min read

Impedance is the specification people quote and it is not the one that decides whether a phone can drive a pair of headphones. Sensitivity is. A 300 ohm headphone with a high sensitivity can be easier to run from a laptop than a 32 ohm one with a low sensitivity, because what a small source runs out of first is voltage, and impedance on its own tells you nothing about how much voltage a given loudness needs. Two numbers decide it, and half the industry publishes the second one in a unit that cannot be compared across models.

What impedance actually describes

Impedance is the opposition the driver presents to an alternating signal, in ohms. The single figure on the box is a nominal value, not a constant: as Sound on Sound puts it, "impedance varies with frequency for most headphones", often by a large factor around the driver's resonance, and multi-driver designs with crossovers vary more than single-driver ones.

Higher impedance means less current is drawn at a given voltage. That is the whole mechanism, and it cuts both ways. Benchmark Media's application note states both directions plainly: "Low-impedance headphones can deliver more power from the small voltage swing that is available from battery-operated devices", but "the low impedance demands high current from the headphone amplifier", while "High-impedance headphones are easier to drive than low-impedance headphones because they usually draw less current from the headphone amplifier for a given loudness."

Read that carefully, because it inverts the usual advice. High impedance is not inherently hard to drive. It is hard to drive when the source cannot swing enough voltage, which is a different failure and a much more specific one.

The two sensitivity units, and why they do not compare

Sensitivity says how loud the headphone gets for a given input. There are two conventions and they answer different questions.

Benchmark describes the split: sensitivity "is often expressed as dB SPL at 1 mW (acoustic output as a function of input power)", whereas "Sennheiser specifies sensitivity in terms of dB SPL at 1 Vrms (acoustic output as a function of input voltage)".

Power sensitivity, dB per milliwatt, is the one that misleads. Your source does not deliver milliwatts, it delivers volts, and how many volts a milliwatt requires depends entirely on impedance. Two headphones with an identical dB/mW figure need completely different voltages if their impedances differ.

Converting between them needs the impedance, and Benchmark gives the formula:

power_sensitivity + 20*LOG(SQRT(1000/R)) = voltage_sensitivity

with the worked case that a Sennheiser HD 650 at 107 dB SPL per milliwatt and 300 ohms becomes 112 dB SPL at 1 Vrms.

Two sensitivity units, and the impedance between them The two conventions for quoting headphone sensitivity and the conversion between them. Power sensitivity is decibels of sound pressure per milliwatt and answers a question your source does not ask, because a source delivers volts rather than milliwatts. Voltage sensitivity is decibels per volt and is directly usable. Converting from one to the other requires the headphone's impedance, using the formula power sensitivity plus twenty times the log of the square root of one thousand divided by resistance. For a Sennheiser HD 650 at 300 ohms, 107 decibels per milliwatt becomes 112 decibels at one volt. power sensitivity dB SPL at 1 mW not comparable across models + 20 log of sqrt(1000/R) needs the impedance voltage sensitivity dB SPL at 1 V directly usable worked example, Sennheiser HD 650 at 300 ohms 107 dB per mW becomes 112 dB at 1 V Your source delivers volts, not milliwatts. Two headphones with the same figure per milliwatt need different voltages if their impedances differ. Published numbers also move between revisions: Sennheiser's current HD 650 page states 103 dB at 1 V, not 112. So never compare two models unless both are quoted in the same unit under the same reference condition.
The same headphone quoted in two units, and why the conversion needs the impedance.

A caution about that number. Sennheiser's current HD 650 page publishes "300 Ω" impedance and an SPL of 103 dB at 1 V, not 112. Published figures move between revisions and measurement conditions, so treat any single sensitivity number as approximate and never compare two models unless both are quoted in the same unit under the same reference. The arithmetic below is worth more than any one datasheet line.

Run the number on your own pair

The useful question is not "does this need an amp" but "what voltage does my listening level need, and can the source produce it". With a voltage sensitivity the calculation is one step, because SPL rises 20 dB per tenfold increase in voltage.

Take the Sennheiser HD 600, published at "300 Ω" and "97 dB (1 V)". For an undistorted peak of 110 dB, which is loud, you need 13 dB above the 1 volt reference. That is ten to the power of 13 over 20, so about 4.5 volts. Into 300 ohms that is 15 milliamps and roughly 67 milliwatts. The current is trivial; the 4.5 volts is not, and it is far more than a phone jack or most dongles will swing.

The HD 650, published at 103 dB at 1 V, needs only 7 dB above the reference for the same 110 dB peak, about 2.2 volts. Same impedance, same family, and a materially easier load, entirely because of the sensitivity figure.

That is the calculation. Target level minus the sensitivity at 1 volt, divided by 20, as a power of ten, gives the volts you need. If you only have a dB/mW figure, convert it with Benchmark's formula first.

Volts needed for the same loudness, same impedance Two Sennheiser headphones of identical 300 ohm impedance, showing the voltage each needs for an undistorted 110 decibel peak. The HD 600 is published at 97 decibels for one volt, so it needs 13 decibels more, which is about 4.5 volts, drawing 15 milliamps and roughly 67 milliwatts. The HD 650 is published at 103 decibels for one volt, so it needs only 7 decibels more, about 2.2 volts. Identical impedance, and one is twice the voltage of the other, which is why impedance alone does not tell you how hard a headphone is to drive. volts required for an undistorted 110 dB peak. Both headphones are 300 ohms. HD 600, 97 dB at 1 V 4.5 V, which is 13 dB above the reference 15 mA, 67 mW HD 650, 103 dB at 1 V 2.2 V, 7 dB above 1 volt reference The method: target level minus the sensitivity at 1 V, divided by 20, as a power of ten, gives the volts you need. The current is trivial in both cases. Voltage swing is what a phone or a dongle runs out of first. Same impedance, same manufacturer, same driver family, and twice the voltage. Sensitivity is doing all the work here. If you only have a figure per milliwatt, convert it first, because that conversion needs the impedance.
Volts required to reach a 110 decibel peak, for two headphones of identical impedance.

An unlabelled sensitivity figure is unusable

Beyerdynamic publishes the DT 990 PRO with a "Nominal sound pressure level: 96 dB" and offers it in "80 ohms" and "250 ohms". The DT 770 PRO carries the same 96 dB and comes in "32 ohms", "80 ohms" and "250 ohms".

Ninety six decibels of what? A milliwatt and a volt give answers that differ by tens of decibels at 250 ohms, and the page does not resolve it. Worse, the same 96 dB is printed against impedance variants spanning 32 to 250 ohms, which cannot be true in both units simultaneously.

This is not a criticism of the headphones, which are fine. It is the practical reason the specification argument is unresolvable from marketing pages: you frequently cannot tell which quantity was measured. When the unit is not stated, the number cannot be used for the calculation above, and the honest move is to find a measurement from someone who states their method.

Output impedance, and the tone change nobody mentions

The amplifier's own output impedance forms a voltage divider with the headphone's. Because the headphone's impedance varies with frequency, that divider attenuates unevenly, which is an equalisation you did not ask for. Sound on Sound describes exactly this: with an amp of non-negligible output impedance "you get a form of equalisation on top of your headphone's native frequency response", and demonstrates it on a Shure SE535 as a "very audible 7.5dB" deviation between a 1 ohm and a 50 ohm source.

Note which headphone that happened to. The SE535 is a low impedance multi-driver in-ear, the type most likely to be plugged into a phone, and the type whose impedance curve swings most. High impedance headphones are the ones that shrug this off, since a few ohms of source against 300 ohms of load is a rounding error.

Well-designed amplifiers make the divider irrelevant by having almost no output impedance. Benchmark's HPA2 "has an output impedance of about 0.1 Ohms", which the note explains "provides a high damping factor".

There was an attempt to standardise the opposite approach. Sound on Sound records that "The most popular standard was IEC 61938, which was introduced in 1996 and specified that an amplifier's headphone output should have a source impedance of 120Ω", the idea being that headphones could then be designed against a known source. It was not adopted, so a modern low output impedance is the safer default because it changes the response of whatever you plug in by the least.

Output impedance as unrequested equalisation The amplifier's output impedance and the headphone's impedance form a voltage divider. Because the headphone's impedance varies with frequency, that divider attenuates unevenly, which acts as an equaliser laid on top of the headphone's native response. Measured on a Shure SE535, a low impedance multi-driver in-ear, the difference between a one ohm source and a fifty ohm source is a very audible 7.5 decibels. A high impedance headphone barely notices, because a few ohms against 300 ohms is a rounding error. Well designed amplifiers avoid the problem by having almost no output impedance, such as the Benchmark HPA2 at about 0.1 ohms. amplifier output impedance voltage divider attenuates unevenly headphone impedance varies with frequency measured deviation on a Shure SE535, a low impedance multi-driver in-ear 1 ohm source reference response 50 ohm source 7.5 dB deviation, described as very audible The headphones most likely to be plugged into a phone are the ones whose impedance swings most, so they suffer this worst. A 250 or 300 ohm headphone shrugs it off: a few ohms of source against 300 ohms of load changes almost nothing. IEC 61938 proposed standardising on a 120 ohm source in 1996 and was not adopted. A very low output impedance is the safer default.
How amplifier output impedance turns a varying headphone impedance into unrequested equalisation.

What to check, in order

Find a sensitivity figure with its unit stated. If it is per volt, use it. If it is per milliwatt, convert it with the impedance. If the unit is unstated, treat the specification as missing.

Work out the volts your listening level needs. Compare that against what the source can actually swing, which is the specification laptop and dongle makers are least likely to publish and the one that decides the outcome.

Prefer a source with output impedance well under the headphone's, which matters most for low impedance multi-driver in-ears and barely at all for 250 or 300 ohm designs.

Then be honest about the answer. A separate amplifier is genuinely required for a narrow class: high impedance and low voltage sensitivity together, of which the HD 600 at 4.5 volts for a loud peak is the textbook case. For efficient in-ears and most consumer headphones the phone already produces more voltage than the level needs, and an amplifier adds nothing but a lower output impedance, which is worth having for the response flatness and not for the volume.

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