Wanted to add some math/info for pairing these with the Schiit Midgard in particular.
Iāll split the info into two sections:
- What the Tungsten needs at a certain volume
- What the Midgard can provide at a given impedance
Section 1:
We know from the store page that the Tungsten has a sensitivity of 78 dB/mW and 155 ohms impedance.
If we assume an average listening level of 80 dB (what I listen at) and a crest factor of 30 dB (enough for most genres of music) we want to see what the Tungsten needs to produce 110 dB.
We can get this from the calculator:
Section 2:
Disclaimer: The correct way to do this is to use an audio analyzer like the AP x555b with a 155 ohm load on the Midgard and see what we get. Below, weāre seeing what the math gets us as an estimate
The Schiit Midgard provides 3200 mW into 50 Ohms
and 750 mW into 300 ohms.
Using the values for Current and Voltage above, we can see that voltage ranges from 12.6V to 15V and Current ranges from 0.25A to 0.05A.
Iām not an electrical engineer but using Amps and Impedance to calculate Voltage and Power gives some nonsensical results (155 ohms and a current of 0.25 A gives a value of 9 watts which doesnāt make sense as that is higher than the power outputted at a lower impedance). Given that Voltage induces current and not the other way around, weāll use the voltage values from above (12.6 V at 50 ohms to 15V at 300 ohms) to see what we get at 155 ohms.
At 12.65 V @ 155 ohms:
At 15 V @ 155 ohms:
So we can estimate that the Midgard puts out roughly 1 ~ 1.45 W into 155 Ohms. We can call this value P1
Now, as Oratory1990 explained to me (but this also seems to be standard EE knowledge), the change in sound pressure caused by changing the power from P0 to P1 is calculated as 10*log10(P1/P0) where P0 is 1mW and P1 is the power output at a given impedance.
In Oratoryās words āIf you know the power sensitivity (in dB/mW) and you want to know how much sound pressure the headphone is producing at an input of X mW, you calculate the difference in level caused by changing the power from 1 mW to X mW, and then you add this difference to the sensitivity.ā
As we calculated above, P1 in our case ranges from 1000mW to 1450 mW.
So we get the following values:
@ 1000mW: 10 * log10 (1000/1) = 29.9 dB
@ 1450 mW: 10 * log10(1450/1) = 31.6 dB
Given the Tungstenās sensitivity of 78 dB/mW we get the following:
@ 1000mW: 78 dB/mW + 29.9 dB = 107.9 dB
@ 1450 mW: 78 dB/mW + 31.6 dB = 109.6 dB
What this tells us is that the Schiit Midgard produces between 107.9 dB to 109.6 dB on the Modhouse Tungsten at max settings. This is just shy of the 110 dB target we were aiming for.
TL;DR: If you listen at an SPL of 80 dB on average, the Schiit Midgard should be good enough to power the Tungsten for most genres of music (assuming the crest factor in your music is <= 30 dB).
