Pixel 10 + Hidizs S9 Pro Plus + DT 700 Pro X: one impedance instead of three
48 Ω at a stated 100 dB SPL (1 mW / 500 Hz) works out to 113.19 dB/V and needs 0.693 V. The dongle's 2.1 V reaches 119.6 dB — 9.6 dB of headroom from a phone. The unit in beyerdynamic's own line is what makes the number readable.
The DT 700 Pro X is beyerdynamic's answer to the impedance-version problem: one 48 Ω model instead of three. On a phone dongle that turns out to be the right answer.
The sensitivity line reads 100 dB SPL (1 mW / 500 Hz), so at 48 Ω the conversion gives 113.19 dB/V and a 110 dB peak needs 0.693 V, 14.43 mA, 10.00 mW. The Hidizs S9 Pro Plus Martha reaches 2.1 V on its 3.5 mm output, which puts the chain at 119.6 dB SPL — 9.6 dB of headroom, comfortable, from a device that hangs off a phone by a short cable.
The pearl: that 2.1 V is derived, not printed. Hidizs publishes 138 mW + 138 mW into 32 Ω for the single-ended port; √(0.138 × 32) = 2.10 V. Derived-from-published is not the same as published, and it carries an assumption — that the amplifier holds the same voltage into 48 Ω as into 32 Ω. Here that assumption is cheap, because the requirement of 0.693 V sits three times below the ceiling; the same assumption would be worth arguing about if we were computing a 300 Ω headphone at the edge of the range. Always check how far you are from the edge before deciding how much a derived number matters.
Why the unit on the beyerdynamic sheet matters beyond this page. The DT 700 and DT 900 PRO X sheets are the only place in beyerdynamic's documentation where the sensitivity scale is spelled out. The classic DT 770 sheets print "Nominal SPL 96 dB" with no unit at all — and it is the PRO X line that tells you those are per milliwatt too. One product's spec sheet is the key to another's.
What we cannot check. Hidizs does not publish an output impedance. The 1/8 rule wants below 6 Ω for a 48 Ω headphone, and there is nothing to compare against, so 119.6 dB is computed without divider loss and is the optimistic end. On power: the Pixel 10's USB-C port supplies 4.5 W; our record for the dongle carries 2.5 W, but Hidizs publishes no consumption figure, so that is the USB 2.0 bus default recorded as a ceiling rather than a measurement. The 4.4 mm balanced port would give more than 2.1 V; no figure for it is published in the source we cite, so we do not compute it.