DT 770 Pro 32, 80 or 250 Ω on a Focusrite Vocaster Two: the version decides here
1.64 V from the Vocaster Two gives the 32 Ω version 5.2 dB of spare headroom, the 80 Ω version 1.3 dB, and leaves the 250 Ω version 3.7 dB short of the 110 dB peak target. Same driver, same 25.12 mW, three different answers.
On this interface the three DT 770 versions are not variations of one purchase. They are three different verdicts: +5.2 dB, +1.3 dB, and −3.7 dB.
beyerdynamic rates all three at 96 dB/mW. Converted with S_V = S_mW + 10·lg(1000/Z) that becomes 110.95, 106.97 and 102.02 dB/V. A 110 dB peak — 85 dB of listening plus 25 dB of crest factor — therefore needs 0.897 V, 1.418 V and 2.506 V. Focusrite publishes +6.5 dBu maximum output level for the Vocaster Two headphone amp, which is 1.64 V, so the three land at 115.2, 111.3 and 106.3 dB SPL.
All three need exactly 25.12 mW. The milliwatt does not know about impedance; what changes is the mix of volts and amps it is delivered in. The 32 Ω version pulls 28.02 mA at 0.897 V, the 250 Ω version 10.02 mA at 2.506 V. A small bus-powered headphone amp runs out of volts long before it runs out of milliamps, which is why the version that asks for less current is the one that fails here.
The pearl: Focusrite publishes two numbers for this output and they disagree. The user guide gives "+6.5 dBu maximum output level" and, separately, 8.5 mW into 270 Ω. That second figure works out to √(0.0085 × 270) = 1.515 V — 0.7 dB below the first. Read pessimistically the three become +4.6, +0.6 and −4.4 dB. The 250 Ω verdict does not change either way; the 80 Ω one slides from thin to almost nothing. When a maker publishes two figures for one output, the honest reading is the lower one, because it is the one measured under load.
What we cannot check. Focusrite does not publish the output impedance of the Vocaster headphone jacks. The 1/8 rule wants a source below 4 Ω for the 32 Ω version, 10 Ω for the 80 and 31.3 Ω for the 250 — and with no published figure there is nothing to compare against. The output impedance forms a divider with the headphone, and a divider only subtracts, so every level above is the optimistic end. Practical note: the DT 770 terminates in a 3.5 mm plug with a screw-on 6.35 mm adapter, and the Vocaster's headphone jacks are 1/4" — use the adapter that came in the box rather than a loose one.