Is the iFi audio ZEN DAC 3 loud enough for the AKG K240 Studio?
Both are rated 104 dB/V, so both need 1.995 V for a 110 dB peak — a $69 semi-open and a $480 flagship, five times apart in impedance. What differs is current: 36.28 mA against 6.65 mA.
Same voltage, same verdict, different bill in current. K240 Studio: 114.2 dB, 4.2 dB spare. HD 660S2: 114.3 dB, 4.3 dB spare.
AKG publishes 104 dB SPL/V for the 55 Ω K240 Studio; Sennheiser publishes 104 dB at 1 Vrms for the 300 Ω HD 660S2. Both are already per volt, so nothing needs converting and the requirement is identical: V = 10^((110 − 104)/20) = 1.995 V. iFi does not publish a voltage for the ZEN DAC 3 either, only power — >18 mW into 600 Ω single-ended — from which V = √(0.018 × 600) = 3.29 V. That covers both headphones with room to spare.
Where the five-to-one impedance difference actually shows up. At the same 1.995 V the K240 draws 36.28 mA and 72.38 mW; the HD 660S2 draws 6.65 mA and 13.27 mW. The cheap semi-open asks its source for five and a half times the power of the flagship, and every «high impedance is hard to drive» rule of thumb has it backwards on this pair. It matters when the source runs out of current rather than volts — battery dongles and phone jacks — but never for a mains-fed desktop DAC.
The pearl: the 0.1 dB gap is the output impedance, and it is the only reason the two results differ at all. iFi publishes ≤1 Ω for the headphone section. That 1 Ω forms a divider: the 55 Ω K240 keeps 3.231 V of the 3.29 V (a loss of 0.16 dB), the 300 Ω HD 660S2 keeps 3.279 V (0.03 dB). So the low-impedance headphone is very slightly the more penalised — the exact opposite of the folk rule, and the whole visible difference between 4.2 dB and 4.3 dB.
Damping: checkable, and fine. 55 Ω against 1 Ω is a ratio of 55, 300 Ω against 1 Ω is 300, both far above the 8 the 1/8 rule asks. Note that iFi's figure is «≤1 Ω», an upper bound rather than a measurement, so we record the bound and the conclusion holds at the worst end of it. Also note that the K240 name is shared by three electrically unrelated headphones — the current 55 Ω Studio, the 600 Ω Monitor and the old Sextett. Only the 55 Ω version is on this page.