As a headphone is essentially a miniature loudspeaker, it shouldn’t be surprising that the interactions between headphones and headphone amplifiers are very similar to those between loudspeakers and power amplifiers. Many of us have hopefully developed a pretty good knack for selecting appropriate amplification for our loudspeakers and vice versa, but how confident are we in our abilities to do this for our headphones?
There are many design variables that affect the performance and perceived synergy of such pairings – not to mention our own individual sonic proclivities – so we cannot simply reduce things to a few quantifiable specifications. There are however three attributes that play an important role in the matchmaking process and are often responsible for explaining some of the sonic differences heard between various headphone and amplifier combinations. I discuss each of these in turn in a trio of articles on output power, gain and output impedance.
Let’s explore output power first, the fundamental attribute of any audio amplifier designed to drive a transducer. Ohm’s law shows that if we know any two electrical parameters of a DC circuit, we can calculate the third:
It is important to make clear from the outset that Ohm’s law holds true for DC circuits and can only be used for AC circuits if the load (R) is purely resistive. Audio signals are AC, and headphones are reactive loads (that is they have inductance and capacitance properties), which means the relationship between power and load as shown in the above diagram is not a simple one of proportion. This means we can only use the above equations to approximate an amplifier’s output behaviour into a reactive load. It is important to bear these limitations in mind when we model a headphone’s power requirements and headphone amp’s power delivery capabilities, and accept that there will always be a margin of error in our predictions. We mustn’t be discouraged by this however, since a somewhat inaccurate prediction is still more instructive than none at all.
Most manufacturers publish at least two specifications for their headphones: nominal impedance expressed in Ohms,and sensitivity expressed either in dB/mW or dB/Vrms. While dB/mW is still the most commonly published, many manufacturers are now shifting to the dB/ Vrms standard. Either rating can be used to estimate the drive requirements of an amplifier, however the dB/Vrms rating is more tangible and intuitive since it is voltage that determines the loudness of a signal. dB/mW can be converted to dB/Vrms and vice versa using an online converter or the following formulae, where Z is impedance:
There are also online calculators that use Ohm’s law to give us the predictions we require in a matter of seconds. The following two relationships are also very useful to remember: doubling or halving the power increases or decreases the SPL by 3dB; doubling or halving the voltage increases or decreases the SPL by 6dB.
Headphone sensitivity is most often measured at 1kHz and thus may not be an accurate reflection of a headphone’s average SPL output over its entire frequency range. If a headphone exhibits a peak in its amplitude response at 1kHz then its rated sensitivity may be higher than its full-spectrum average, if the headphone has a dip in its response at 1kHz then its rating may be lower than its average. Such variations are however unlikely to be large enough to significantly skew our calculations.
I have included below the estimated voltage, current and power requirements of a selection of audiophile headphones to demonstrate how these vary with rated sensitivity and nominal impedance. For headphones whose sensitivity is published in dB/mW, I have also included the dB/Vrms conversion. (Please note that the Listening Loudness classifications were set by DigiZoid, The Ear does not encourage listening to music at potentially harmful SPLs.)
A headphone amplifier that provides enough output for transient peaks up to 110dB, some 25dB higher than what is accepted to be the maximum sustained safe level of 85dB, ought to satisfy the SPL requirements of listeners wishing to reproduce live concert dynamics in privacy. It very much depends of course on the genre of music being enjoyed. Audiophile masterings of jazz and classical music tend to have wide dynamic range, and will require far more headroom than mainstream popular music that’s often a victim of the “loudness wars” and has peaks of just a few dB above sustained average levels. Readers can therefore adjust their thresholds upwards or downwards according to their typical listening levels and preferred music styles.
The Beyerdynamic DT880 headphone is an instructive example to begin as there are three versions available, each with a different nominal impedance:
It is evident that all three DT880 models share the same power sensitivity but vary significantly in their voltage sensitivity. Consistent with V = √(PxR) and I = √(P/R), we see that the low impedance DT880 requires less voltage and more current to produce a given SPL, while the high impedance DT880 requires more voltage and less current. There is more than a four times difference in voltage sensitivity and current draw between the 32Ω and 600Ω models in the above example.
This relationship is important because not all amplifiers are capable of delivering plentiful supplies of both. A portable audio player can deliver lots of current into a headphone, but its voltage swing is limited by the battery’s potential and can often be less than 1Vrms. An output transformerless (OTL) vacuum tube amplifier on the other hand lacks the means to transform the high voltage, low current signal from its tubes into the lower voltage, higher current signals needed to drive low impedance headphones.
An amplifier delivers a voltage that corresponds to the level of the music at that instant in time. The load then draws a current from the amplifier, the size of which corresponds to the resistance of the load. Clipping is a form of waveform distortion that occurs when an amplifier is asked to deliver an output voltage or current beyond its maximum capability. The maximum voltage an amplifier can swing determines the maximum theoretical signal output level, beyond which it is ‘clipped’, producing harmonic distortion.
As the requested output voltage is increased further, the severity and thus audibility of the clipping increases as THD levels escalate. Amplifiers employing vacuum tubes in their outputs tend to clip in a ‘soft’ manner, where peaks are squashed instead of being abruptly chopped off. This form of clipping produces more low-order harmonic distortion, which is perceived to be less offensive to the ear than the ‘hard’ clipping by solid state output transistors that produces more high-order harmonic distortion.
It is important to emphasise that voltage and current are inextricably linked, i.e. there must be enough current available to sustain a given voltage into a given load, otherwise the amplifier will drop the output voltage back to that of the maximum sustainable current and clip the signal. This is why it is useful where possible to estimate your headphone’s voltage sensitivity and current draw and compare these against the voltage and current delivery capabilities of your headphone amp.
Predicted voltage, current and power requirements of some popular audiophile headphones:
** In-ear monitors (IEMs) are typically far more efficient than on- and over-ear designs and thus have much lower power requirements.
With a few exceptions, the above tables illustrate that dB/Vrms sensitivity tends to reduce as nominal impedance increases, and that high impedance headphones require more voltage and less current to reach a desired SPL while low impedance headphones require less voltage and more current, as was demonstrated earlier by the Beyerdynamic DT880 example.
So, how does this affect the choice of appropriate amplification? Let’s use the Arcam rHead Class A headphone amplifier as an example, as its manufacturer has helpfully published both the output power and voltage into three different loads. The rHead specifies 2,000mW into 16Ω (5.7Vrms), 1,100mW into 32Ω (6.0Vrms), and 130mW into 300Ω (6.5Vrms). As the rHead is rated for use with headphones between 16Ω and 600Ω, we could extrapolate the above drops in power and increases in voltage and predict it will output around 70mW and 6.8Vrms into 600Ω.
Using I = P/V, I = V/R orI = √(P/R), we can expect the rHead to deliver approximately 355mA into 16Ω, 186mA into 32Ω, 21mA into 300Ω and 11mA into 600Ω. Based on these predictions, this amplifier should supply enough voltage and current to drive all of the headphones listed above, with the exception of the Audeze LCD-4 and HiFi Man HE-6, to levels of at least 110dB before the output clips.
Portable audio players often have much lower output voltages of between 0.5Vrms and 1Vrms, reducing the maximum achievable SPL of any headphone to, at best, its dB/Vrms sensitivity rating or, at worst, 6dB lower than this (recall that doubling or halving the voltage means a 6dB change in SPL). This is where the choice of pairing becomes far more critical, since it moves more headphones into the underpowered category.
The above conclusions make assumptions not only about the amplifier’s drive behaviour into different loads, but also about the headphone’s behaviour when driven. A headphone’s impedance and phase angle can vary with frequency. Voltage remains constant across a headphone’s impedance curve while current draw varies (assuming the amplifier is an ideal voltage source with zero output impedance). In theory, using a headphone’s minimum impedance instead of its nominal impedance will more accurately predict the maximum current it will draw from the amplifier to achieve the desired SPL.
Manufacturers rarely publish frequency response and impedance curves for their headphones (there are however a small number of enthusiast websites that do measure and publish these variables). Fortunately, unlike many loudspeakers, the relative difference between nominal and minimum impedance in traditional dynamic driver headphone designs is usually insignificant, and it is negligible in planars as these behave much more like resistive loads. In multi-driver, balanced armature in-ear monitors (IEMs) the swings are often vast, though this is largely offset by the tendency of IEMs to have very high sensitivity and lower current requirements to begin with. Using the nominal impedance as a substitute for minimum impedance is therefore generally fine for estimating headphones’ current draw.
If manufacturers were however to publish both the voltage and current capabilities of their headphone amplifiers into various loads, this would improve the accuracy of our estimations and allow us to assess with greater confidence an amp’s ability to drive a particular headphone to a given SPL. In reality, we are lucky if we are told more than simply the output power into two representative loads. Short of contacting the designer to request more information, those of us whose headphone’s impedance lies between or beyond these representative loads can only guesstimate the amplifier’s behaviour into our particular load.
Our predictions should of course serve merely as a guide, it is always sensible to test them with auditions and avoid discounting potential headphone and headphone amp pairings based on specifications alone! During such auditions it is often useful to set the output louder than your typical playback level and listen out for characteristics such as a hardening or compressing of the sound, disappointing low frequency reproduction (low frequencies are often the first to suffer as they require the most power to faithfully reproduce), or the presence of any other undesirable distortions, as these can often be clues to insufficient power.