Regardless of the power restrictions, since the impedance of few headphones does not vary with frequency, significant voltage division from a relatively high output impedance may well lead to significant changes in the measured frequency response. To ensure without knowing the frequency dependency of the impedance that the range of those changes remains within a given level difference, the ratio of the output impedance to the minimum impedance of the headphone has to be at most the voltage amplitude ratio corresponding to the desired maximum level difference less one:
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If both the minimum and the maximum impedance are known, the ratio of the output impedance to the minimum impedance must be at most the voltage amplitude ratio corresponding to the desired maximum level difference less one divided by one less the product of the voltage amplitude ratio corresponding to the desired maximum level difference and the ratio of minimum impedance to the maximum impedance:
View attachment 114135
For a range of at most 1 dB, the output impedance must thus be at most 12.20 % of the headphones' minimum impedance, while for a range of at most 0.5 dB, the output impedance must be at most 5.925 % of the headphones' minimum impedance and for a range of at most 0.1 dB, the output impedance must be at most 1.1579 % of the headphones' minimum impedance.
Correspondingly, for a 24 ohm output impedance, the minimum impedance required to ensure a range of at most 1 dB is 197 ohm, while for a range of 0.5 dB it is 405 ohm and for a range of 0.1 dB it is 2073 ohm. In contrast, for a 0.1 ohm output impedance, the same required minimum impedances are 0.820 ohm, 1.688 ohm and 8.636 ohm, respectively, making the effects of voltage division probably negligible for nearly all headphones.
Assuming that the maximum impedance of the headphone is only twice the minimum impedance, only lessens the requirements by about a factor of one half. For a range of at most 1 dB, the output impedance must thus be at most 27.80 % of the headphones' minimum impedance, while for a range of at most 0.5 dB, the output impedance must be at most 12.60 % of the headphones' minimum impedance and for a range of at most 0.1 dB, the output impedance must be at most 2.343 % of the headphones' minimum impedance.
Starting from the formula for voltage division, the derivations are fairly straightforward and for any finite output impedance and any frequency dependent headphone impedance, the denominator in the second equation is always positive.