Consider the following: high-quality modern electroacoustic transducers (speakers or headphones) can achieve distortion figures in the ballpark of 0.1% (-60 dB), and this applies to really good units.
Now, imagine two DAC/AMP combos that deliver 0.01% (-80 dB) and 0.0001% (-120 dB) distortion to these high-class speakers with 0.1% distortion.
Right away, there is a catch regarding the difference we can expect from both systems. Harmonic distortions from different components in an audio chain do not simply add linearly in a straightforward way (e.g., -80 dB + -60 dB does not directly result in a single combined dB value). In most real-world scenarios, the phase of the distortion components is not perfectly aligned, so we treat them as uncorrelated signals and combine their power (not amplitude). However, let's imagine an absolute worst-case scenario and assume that harmonics are perfectly in phase, so we add distortion amplitudes directly.
For -80 dB playback system:
Convert dB to Amplitude:
And here we have it, folks - hardly any improvement of only 0.82 dB.
What's worse - the real-world number will be even lower.
Now, imagine two DAC/AMP combos that deliver 0.01% (-80 dB) and 0.0001% (-120 dB) distortion to these high-class speakers with 0.1% distortion.
Right away, there is a catch regarding the difference we can expect from both systems. Harmonic distortions from different components in an audio chain do not simply add linearly in a straightforward way (e.g., -80 dB + -60 dB does not directly result in a single combined dB value). In most real-world scenarios, the phase of the distortion components is not perfectly aligned, so we treat them as uncorrelated signals and combine their power (not amplitude). However, let's imagine an absolute worst-case scenario and assume that harmonics are perfectly in phase, so we add distortion amplitudes directly.
For -80 dB playback system:
Convert dB to Amplitude:
- DAC/AMP: -80 dB = 10^(-80/20) = 0.0001
- Speakers: -60 dB = 10^(-60/20) = 0.001
- Total amplitude = 0.0001 + 0.001 = 0.0011
- dB level = 20 * log10(0.0011) = -59.17 dB
- DAC/AMP: -120 dB = 10^(-120/20) = 0.000001
- Total amplitude = 0.000001 + 0.001 = 0.001001.
- dB level = 20 * log10(0.001001) = -59.99 dB.
And here we have it, folks - hardly any improvement of only 0.82 dB.
What's worse - the real-world number will be even lower.
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