The Technical Capability of Headphones - Part 1

The reference comparison track is a pure 400 Hz sine wave. The second signal adds 4% third-order harmonic distortion and is just included to get you started so that you know what to listen for. This one should be obvious to your Grandma. Work your way down and see how low you can go. Given the right pair of headphones and a quiet listening environment, some of you should be able to hear the presence of the third harmonic even in the last of these tests, but most should find that 1% or even 0.5% distortion is easily audible. Would real music mask this effect? Perhaps. But it’s not for us to dictate what somebody else calls ‘real music’, and it would obviously be preferable not to have to rely on masking effects and psychoacoustics to sweep these errors under the carpet. Playing music at 100 dB, a 0.1% distortion ends up 60 dB below the fundamental, i.e., 40 dB, which is roughly the level of normal conversation. If we had a 0.001% (-100 dBFS) level of distortion at this same volume level, this would result in a 0 dB distortion amplitude, which would guarantee the distortion to always be completely inaudible without needing to rely on the pot-luck of masking effects. We don’t claim that any of the above levels of distortion would cause the bulk of the population to dislike a particular headphone – the masses are not that discerning, and even if they were it wouldn’t make distortion a leading-order effect on preference. However, all other things being equal, it could end up acting as a tie-breaker. Distortion that is obviously audible in some test scenario is enough to risk it being audible during actual music playback and this makes its measurement relevant and intrinsically interesting. The only safe solution in headphone design is to ensure distortion levels are sufficiently low that their audibility – in any situation – wouldn’t even be up for debate anymore. At modest (e.g., 70 dB) listening volumes, headphones such as the Beyerdynamic Xelento can already achieve this.

The prevalence of high levels of third-order harmonic distortion in balanced-armature drivers, along with their natural tendency to struggle with the generation of low frequencies and their greater sensitivity to seal-leakage effects can sometimes contribute to giving BA-based headphones a slightly lean and unnatural bass timbre, even if/when their frequency response graph appears to essentially match those of planar magnetic or dynamic driver IEMs. BA-based headphones also tend to suffer disproportionately from strong impedance variation with frequency. Despite these many reasons to avoid using BA drivers, there are some good reasons for OEMs to stick with them – use of multiple BA drivers can sometimes make a headphone easier to tune, they can give a bigger dynamic range, and they’re cheap and can offer larger profit margins.  

While a frequency-response graph typically covers the entire audible spectrum in a snapshot, actual music is comprised of a series of transients that contain only a limited subset of those frequencies at any given instant. A conventional FR graph couldn’t show even the largest of the distortion levels considered above.  Being generous and considering a healthy 5% level of distortion, we can sum an 80 dB and a 54 dB signal (5% of the fundamental amplitude) resulting in, even assuming perfect constructive interference, an increment of only 0.02 dB (continuing our generosity by rounding up to 2 decimal places). This very-audible effect would be completely imperceptible to the eye on any FR graph.

Most professional audiophile reviewers would never publicly admit that they couldn’t clearly hear the differences between one DAP and another, or between CD quality and hi-res audio. Yet the errors discussed above in terms of impulse response and harmonic distortion are far more significant than any errors in modern DAPs, or from any error resulting from only using a ‘low-res’ 44 kHz sample-rate. The real problem with the timing/phase and harmonic distortion errors discussed above is that they’re only the tip of the iceberg. There is, unfortunately, potential for much more easily-audible errors in actual music playback. Past attempts to address this have resulted in what we would term ‘traditional’ audio metrics, and are typically determined using test signals such as single sine waves, dual sine waves (testing for intermodulation distortion), square waves (testing frequencies up to Nyquist), triangle waves, full-spectrum white or pink noise, or program simulation noise, such as IEC 60268-1. Results are often presented as a single number, such as SINAD, which provides the ratio of the true signal amplitude to all sources of noise and distortion. It is important and relevant that SINAD include more than just harmonic distortion effects, because the inclusion of DACs and amps in modern Bluetooth headphones means all manner of distortions and errors could apply directly to headphone measurements. 

We have nothing against SINAD in its literal definition, but we question what tests are routinely used to define it. One of the most interesting and potentially relevant pieces of audio research in recent years is the development around the df-metric or histogram-median error by soundexpert.org. The significance is not so much the metric itself, but rather the work that has been done in highlighting how the accuracy of modern DACs and amplifiers varies so substantially with different input waveforms. A 1 kHz sinusoid has, unfortunately, become the de facto standard audio test signal, but much like the VW automobile tail-pipe emissions test, it has very little correlation with real-world performance. More complex waveforms (for example, actual music tracks) result in substantially higher errors, and the same is almost certainly true of every electro-mechanical system, including loudspeakers and headphones. The presence of sharp transients superimposed on lower-frequency waveforms causes a general detriment to reproduction accuracy; statistical errors from more complex waveforms (in particular, actual music) have far more relevance to the human listening experience. If we choose to define non-tonal, ‘technical’ error as the sum of all headphone errors, minus the effects of tonality (once the effect of the frequency-response shift has been subtracted out), then a test can be applied to the resulting headphone output, analogous to the nulling-error test applied to DACs and digital audio players using program simulation noise or actual music test vectors.  Watch this space for Part 2.