ATH-R70x, 470 Ω: the $76 dongle against the desktop DAC, and why 16 dB decides it
The R70x needs 2.73 V — more than a 250 Ω DT 770 and more than an HD 650. A FiiO KA13 on phone power delivers 1.22 V and lands 7 dB short; a Topping DX3 Pro+ delivers 7.6 V and finishes 8.9 dB above target.
No and yes: the KA13 reaches 103.0 dB against a 110 dB target, the DX3 Pro+ reaches 118.9 dB. Same headphone, same music, 15.9 dB between the two sources.
The ATH-R70x is 470 Ω at 98 dB/mW, which is 101.3 dB/V; in this catalogue only the 97 dB/V HD 600 asks for more voltage. A 110 dB peak needs 2.73 V. That is only 15.85 mW and 5.81 mA: the R70x is not a power-hungry headphone at all, it is a voltage-hungry one, and the two failure modes look nothing alike. The KA13 delivers 1.216 V into 470 Ω, so it stops 7 dB short — the volume control at maximum, the sound thin rather than merely quiet. The DX3 Pro+ delivers 7.598 V and has 8.9 dB in hand.
Why 470 Ω is not the point. Audio-Technica themselves warn on the Japanese product page that some sources will not reach adequate level. The reason is the pair of numbers, not the impedance: an equally 470 Ω headphone rated 105 dB/mW would need 1.22 V and the KA13 would drive it exactly to target. Impedance alone predicts nothing; impedance plus sensitivity predicts everything.
The pearl: the KA13's advertised voltage is not the one you get. FiiO's own parameter table gives two figures for the same 3.5 mm jack. On phone power it is >5 mW + 5 mW into 300 Ω, from which V = √(0.005 × 300) = 1.22 V. In Desktop Mode — second USB-C port fed from a charger — the same jack does 19.5 mW into 300 Ω, about 2.4 V. Most shop listings quote 2.3 Vrms without mentioning which mode it belongs to. Even at the Desktop-Mode figure the R70x would still be about 1 dB short of the 110 dB target, so the mode is not what saves this pairing.
What we can check, for once. Both sources publish an output impedance: FiiO says <1.7 Ω, Topping says <0.1 Ω. Against 470 Ω that is a ratio of 276 and 4700, far past the 8 the 1/8 rule asks for, so tonal balance is safe on both — the failure of the KA13 here is purely a shortage of volts.