Originally Posted by MrMateoHead
stv - Can you help me understand how to read into certain specs then, because I have been going nuts trying to figure out what honest power outputs are of a variety of sources.
Well, the following simple equations show the relation between power (P), voltage (V), current (I), and resistance (R). Impedance (Z) is similar to resistance in that it is the ratio of voltage and current, but it is for AC signals and depends on the frequency, and can be a complex number if the voltage and current are not in phase. For now, to keep things simple, you can ignore the difference between resistance and impedance.
R = V / I
P = V * I = V * V / R = I * I * R
The voltage (and also current) of an AC signal can also be expressed as RMS (root mean square, the equivalent DC level that would produce the same amount of power on average), peak (the maximum absolute difference from the 0 level), and peak to peak (the difference between the maximum and minimum level). Usually, when not specified otherwise, an AC voltage is meant as the RMS voltage of a sine wave. Here is how to convert between these:
Vp-p = 2 * Vpeak = 2.8284 * Vrms
So, once you know the maximum RMS voltage or current, you can calculate the power as shown above. For high impedance headphones, the maximum output is usually voltage limited, but with some amplifiers and low impedance loads, it can also become current limited. Another factor to take into account is the output impedance of the amplifier, which, if not insignificant compared to that of the load, can reduce the voltage and thus also the power as shown below:
V = Vout * R / (R + Rout)
In the best case, you can find a graph like this for your device:
If one is available, just find the voltage where the distortion starts to rise steeply for the load impedance nearest to whatever you intend to use. So, for example, the FiiO E10 is capable of a maximum of ~1.5 Vrms output driving a 32 Ω headphone.
Unfortunately, the manufacturers rarely release such graphs, so you have to calculate the maximum output from whatever limited information is available. It is safe to assume that if an amplifier is capable of outputting a certain voltage into a known impedance, then it can also output at least as much (and often more) into a higher impedance. On the other hand, if the power/voltage is only specified for a high impedance, then it is not guaranteed at all that the same voltage will also be available when driving a low impedance load, because of the total (open loop) output impedance and possibly current limiting. You can actually see this on the graph above.
For the TPA6120A2, assuming the usual +/- 12 Volt power supply (~10 Volt peak ~= 7 Vrms output) and 10 Ω output impedance, here are some simple example power calculations:
16 Ω: V = 7 * 16 / (16 + 10) = 4.31 Vrms, P = 4.31 * 4.31 / 16 = 1.16 W
32 Ω: V = 7 * 32 / (32 + 10) = 5.33 Vrms, P = 5.33 * 5.33 / 32 = 0.89 W
600 Ω: V = 7 * 600 / (600 + 10) = 6.89 Vrms, P = 6.89 * 6.89 / 600 = 0.079 W
To convert the calculated power or voltage to maximum sound pressure level (SPL), you need to know the sensitivity of the headphones. This is usually specified in dB at either 1 mW power, or 1 Vrms voltage. At innerfidelity.com, you can also find measurements that show the amount of voltage and power needed for 90 dB SPL. Use one of the following formulas:
SPL = 10 * log10(P * 1000) + [dB/mW]
SPL = 20 * log10(V) + [dB/Vrms]
SPL = 10 * log10((P * 1000) / [mW/90 dB]) + 90
SPL = 20 * log10(V / [Vrms/90 dB]) + 90
It depends on personal preferences and the dynamic range of the music how much is enough, but if you get less than 100 dB, that is likely underpowered, while 120 dB is more than enough for basically everyone, and 110 dB is a reasonable target for most.
Originally Posted by MrMateoHead
The Schiit Asgard is a known 1 watt amplifier, but specs "1 volt RMS" at .1% THD or something like that, 8-600 ohms.
That is a different type of specification, it is the total harmonic distortion (THD) at the specified output voltage. Basically, it quantifies (in a rather limited way) the sound quality, rather than the maximum power output.
Edited by stv014 - 10/29/12 at 11:24am