Edit (8/24/2023): Check out Sterling’s summary:
Announcement of The Element has reminded us that output power is widely misunderstood. Most confusion can be resolved by understanding that Volume sets Power.
In the world of audio, Power is the amount of energy that an amplifier can deliver into a specific load (ohms), at a specific frequency (Hz), for a specific duration (seconds), with a specific threshold of noise and distortion. And as we’ll explain, a speaker or headphone needs only enough power to reach your desired listening volume. Listening volume is set by your personal preferences and the efficiency of the driver. Onto the math:
Power in wattage is formally defined as:
P = V2/Z
- V = Signal Voltage, in Volts Root Mean Square (VRMS)
- Z = Impedance of the load, technically consisting of Z = (R + jX). For amplifier measurements, the reactive portion X is assumed to be 0, so Z = R. The value of R is specified by the headphone manufacturer in ohms, Ω.
Signal Voltage, V, is determined by the source strength and amplifier gain. Thus:
V = Gain*Vsource
Gain is set by the amplifier. Many models feature multiple gain levels that you are able able to physically select. Vsource is simply the strength of the DAC or audio player with unit VRMS.
Minimum power in milliwatts (mW) required to reach a specific Sound Pressure Level (dBSPL) is:
Pmin = 10(x-η)/10
- x = Your desired listening volume in dBSPL
- η = Efficiency of the headphone, in dB/mW
Next, it’s key to understand that an audio source generates only as much voltage as you select with the volume control (digital or analog), and that volume is only as strong as the particular music you’re playing. Low listening volume means Vsource is small, and high volume means Vsource is big.
From these equations, one can see that power is a function of volume. Output voltage is dictated by the strength of the input signal (from DAC or external device), which is then multiplied by the amplifier’s gain. More voltage means more volume, which means more output power.
As a purely hypothetical example, a 2.1VRMS DAC operating at 100% volume, playing music recorded at full scale, connected to an amplifier with gain of 4.7 also at 100% volume, into a 32 ohm headphone would yield P = (4.7*2.1)(4.7*2.1)/32 = 3.044W = 3044 mW. But, thermal and current (mA) limitations mean that an amplifier will be driven into distortion at some threshold, and that threshold depends on operating frequency and how long the amplifier has been subjected to the test. This is why we must conduct real world measurements and define test criteria.
Power Test Criteria
Standard audio Power measurements are taken at 1kHz with a maximum THD+N of <= 1%. Well, 1% distortion is rather obvious, and unacceptable for high fidelity listening. We set stricter standards.
JDS Labs conducts all Maximum Output Power tests into purely resistive loads at 1kHz, while maintaining THD+N <= 0.005% for a continuous duration of at least 45 minutes. Peak Output Power is the same as Maximum Output Power, but restricted to a duration of 10 seconds, still maintaining THD+N <= 0.005%.
Headphone Power Requirements
You do not need to crunch numbers to determine suitability of an amp for your headphones. Simply find the impedance (ohms) and sensitivity (dB/mW) specifications of your headphones, then refer to our SPL Chart:
Most users are satisfied when their headphones can reach 110dB. If you listen to quiet recordings or demand extreme volumes, look at the 115dB column. If an amplifier’s output power exceeds this number at your headphone’s rated impedance, it’s sufficiently powerful.
Since an amplifier only generates as much power as you set by listening volume, there is absolutely no concern of a headphone amplifier being too powerful for a set of headphones or IEMs. You can only damage headphones when you intentionally turn volume so high that the sound distorts. Your ears will let you know when this point has been reached.
That said, an amplifier can have excessive gain. O2+ODAC and The Element both ship with low gain of 1.0x (unity) for low volume listening, and a higher gain for achieving maximum volume/power. Use low gain for most listening. Switch to high gain only when you’re unable to reach desired listening volumes at low gain.
Audio specifications and output power have been thoroughly covered over the past century. Should you have further interest, we recommend the following articles: