Power is Volume

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:

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.

Too 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.

Further Reading

Audio specifications and output power have been thoroughly covered over the past century. Should you have further interest, we recommend the following articles:

20 thoughts on “Power is Volume

  1. Can I ask what headphones do you test with and any headphones you recommend (sorry if it is a naive question but want to know your opinion on the top headphones)

    1. Hi Rohit: We conduct formal benchmarks with a Prism dScope Series III audio analyzer, using physical “dummy” loads (no headphones). You can find more information under True Performance Design.

      Listening to headphones is also important during development. We use a diverse collection. A few of these include:

      • Etymotic ER4S/ER4P
      • Sennheiser HD-600, HD-650, HD-280 Pro
      • Grado SR-60i
      • Beyerdynamic DT-880 Pro 250 ohm
      • Fischer Audio FA-011
      • AKG Q-701
      • Audeze LCD-XC

      Keep in mind there is no perfect headphone, and the shape of your head and ears creates a unique experience. Therefore, it’s best to evaluate as many sets as possible and choose the headphones that appeal to you. Innerfidelity.com and Headfonia.com maintain popular lists of recommendations. Good luck!

  2. Would the element work well with the Beyerdynamics T51i headphones (impedance of 32 ohms)? I’m considering pre-ordering one of these.

  3. How does output power of an amp relate to the volume knob?
    e.g. I have a FiiO E12 amp and I can barely use the volume knob at all for listenable volume levels and they claim to have a 0 dB gain. Because of this, I don’t use it at all unless I do amp-amp A/B tests.

    On the contrary, the Objective 2 has more power output I think, yet I can use much more of the volume knob with unity gain, and at much more listenable volume levels.

    Also, how would one predict the volume level of an amp if you don’t know the gain?
    e.g. If I get an Element, which outputs 1.1 Wmax-continuous at 32Ω (far too much for me), how will I know how much of the volume knob I can use?

    1. @miceblue: Volume knob position is dictated by gain and the potentiometer taper (or stepped attenuator or digital attenuation).

      You can see tapers here:
      http://www.alphapotentiometers.net/html/taper_curves.html

      O2 and The Element use a ’15A’ taper. Many amps use a more aggressive ‘3B’ taper, so that volume increases rapidly at low levels, and slowly at high levels. Our ears expect logarithmic volume increases, and 15A is fairly close.

      Output volume = V = Gain*Vsource

      The attenuation taper dictates how quickly volume changes. You could predict knob position using an equation defined for the taper. Good luck!

  4. On your details page for the Element you mention that you have smart logic eliminating turn of/off pops. I was wondering if you could elaborate on how to did this? I’ve always struggled in my own designs on how to eliminate DC offset. I know I can either put a cap in the signal path on the output or have a high pass filter set to filter at 5 Hz but that can cause attenuation issues.

    1. Fullinator: Latching and non-latching relays! This method eliminates negative audio circuitry impacts (no DC offset, no filtration, no added output-Z).

      We’re considering releasing a series of DIY modules. While Element uses a microcontroller for relay logic, a 555 timer is equally effective.

  5. Would it be a overkill to drive a 32 Ohm T5p with this DAC?
    I mean, can I really turn up the volume, or should I turn up the volume just a few millimeters, thus, it is not extremely loud?

    1. @Frank: Which DAC? As long as audio is clean to your ears, it’s reasonable to use any volume position that you prefer. A more powerful amp becomes a necessity when you’re unable to reach desired volumes cleanly.

  6. Does the O2 amplifier produce as much power at 1.0 gain as the Element amplifier does at 1.0 gain? I am using the HIFIMAN 400i and I’d like to get an amp that produces the bigger soundstage, hence I’m looking for something that’s powerful at the lowest gain setting. Currently I’m using the Fiio E12 and I’m not completely satisfied. At low gain, it’s loud enough but it feels like the sound is a little thin. At high gain (16db) it has more “oomph” but it feels like I’m listening something that’s closer to a closed-headphone.

    Thanks.

    1. Daniel: Yes, both O2+ODAC and Element have a 2.10VRMS DAC, meaning power into 35 ohms is voltage limited at 1.0x gain.
      P = 2.1*2.1/35 = 126mW

      1. I thought that power came from the Amp and not the DAC.

        Also, when you mention the maximum output of the amp at various ohms, that refers to when the gain switch is at the highest setting, correct?

        I mean I’m sure the sound that I’d get from any of your amps would make for a pleasurable listening experience. Just when I recent played a CD on my parents old (20yrs+) Technics stereo system and plugged my headphones in the the headphone jack, I was blown away by how enveloping was the sound that came from my He-400i.

        I guess i can’t expect that kind of power from a portable/transportable amplifier.

        1. Daniel: Check the top of the article again. Output power depends on gain and source voltage. The DAC is the source voltage. Both O2+ODAC and The Element can produce more voltage than their DAC, but you asked specifically about power at 1.0x gain (meaning current buffering only–no voltage gain).

          Also realize that these DACs can only produce 2.1VRMS into a high-impedance, line-level input. Performance plummets into a headphone load, so output power would be nowhere near that of the amp+DAC together.

          Yes, maximum output power is measured at an amplifier’s highest gain position.

  7. I am thinking hard on purchasing a pair of Audeze LCD-3 this summer. From every fourm I read they need power to have them sound at their best. Can please tell me if the element would work? I am living in the UK .

  8. This is such a handy resource. There is quite a lot of misconception surrounding power needed to drive headphones to listenable levels (and beyond). I have linked this several places to dispel myths that abound. Keep up the good work, John!

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