Choosing DAC/AMP (headphone source)

This post is a WIP. Check important facts.

Distortion

The THD+N should be inaudible. If the value is expressed in percentage in the specification, convert it into decibels. For a value $k$ in percent, the corresponding $a_k$ in dB can be calculated by:

$a_k = 20 \cdot log_{10}^{\frac{k}{100}}$

Conversely:

$k = 10^{\frac{a_k}{20}} \cdot 100$

Many calculators are available online, such as https://benchmarkmedia.com/blogs/calculators/thd-calculator and https://sengpielaudio.com/calculator-thd.htm.

Additionally, look for an inaudible noise floor.

Frequency response curve

The frequency response curve should be flat between 20-20kHz (for example, ±0.2dB). So that no frequency is exaggerated/masked.

Output impedance

Generally, the output impedance should be less than 1/8 of the headphone impedance. Two main problems can arise when the output impedance becomes high:

Frequency response coloration

The impedance of the headphone changes with frequency. When the output impedance is high, it creates frequency-dependent voltage division between the source and the headphone. This will change the frequency response curve of the headphone. This issue generally has an stronger effect on balanced armature headphones. Reference Audio Analyzer measured various headphones in this regard.

Reduced damping

When a sound stops, it should be damped. When the output impedance is high, the ability of the source to control the movement of the headphone driver is reduced, and the attenuation of stopped sounds takes longer. This results the headphone to sound ringing and boomy, especially the bass. This issue generally has an stronger effect on dynamic headphones.

Output power

Check the sound pressure level of the headphone and the output power of the source at the load equal to the impedance of the headphone. Calculate the max sound pressure level the headphone can reach using the source (formula ref: https://nwavguy.blogspot.com/2011/09/more-power.html). The output power should be able to drive the headphone to the desired sound level plus 24-30dB of headroom. The headroom is needed because while the average sound level (RMS/LUFS) is close to the desired level, some short peaks/bursts can take place (e.g., drums, vocal attacks), which keep the music vibrant and dynamic. Take hearing health into consideration when deciding the desired sound level. Two main problems can arise when the output power is too low:

Too quiet

If the source simply delivers too little output power, the headphone will sound too quiet even if you crank the volume all the way up.

Clipping

If the source does not have enough power to handle the peaks, clipping takes place and all sounds that require higher output get squashed into the highest output power. This is audible as harsh, gritty, or fizzy sound on the peaks.

Sample rate and bit depth don’t matter that much

44.1kHz/16 bit (aka CD quality) already covers the 20-20kHz human hearing range with around 96dB of dynamic range. A step up to 24 bit gives you around 144dB of dynamic range. At this point, the setup is probably bottlenecked by the output power of the source instead. Also, pay attention to the hearing health.

Hearing health

Ref: https://www.who.int/news-room/questions-and-answers/item/deafness-and-hearing-loss-safe-listening

The duration of safe listening time decreases rapidly as the sound intensity increases. Permanent damage can occur if you exceed the exposure limit. Consider adjusting the volume to a safe level. An table for reference is given below.

This is not medical advice. Consult a doctor if in doubt.

References

https://nwavguy.blogspot.com/2011/02/headphone-amp-impedance.html

https://nwavguy.blogspot.com/2011/02/headphone-impedance-explained.html

https://nwavguy.blogspot.com/2011/09/more-power.html

https://www.l7audiolab.com/

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