Calculating dB with my Ultrasone Pro 650 and Nuforce uDac-2

The uDAC-2 can do 2.2 Vrms into 150 ohms. Its output impedance lowers that for low impedance headphones, but 75 ohms won't be too affected. I'm just going to guess 2 Vrms because I don't know enough about the math to come to a real conclusion.

2 Vrms into 75 ohms is 53 mW. With 95 dB/mW sensitivity, that's a maximum of about 112 dB.

It's very hard to translate that into sound pressure at half volume, though. Every song is different, some quieter than others. Your headphone has its own frequency response too, and some frequencies will be louder than others. And I don't know how the uDAC's volume knob changes the volume, as in if a half turn on the knob is half of max volume or not.

Best thing to do is to get an SPL meter from Radioshack or something. Another thing you could try is have someone talk to you from a few feet away. The Pro 650 is closed back and has some isolation which will complicate that. Maybe have them talk at a volume that sounds like conversation level with the headphones on but without music playing. Have them keep talking at that volume after you turn the music on. You should still be able to hear them, even if you can't make out all the words.

Quote:

Originally Posted by Tilpo 


Actually 2Vrms is more than the headphones will actually get.
They should only get a measly 1.47V, which means they will get 14mW of power. This correlates to 107dB Calculations (Click to show)

Voltage over the load is given by: V=Vin * Zload / (Zload + Zoutput)
V = 2.2 * 150 / (150 + 75) = 1.47V
Power is given by: P = V^2 / Z
P = 1.47^2/150 = 14.4mW
The difference in volume relative to 1mW can be found by 10*log(P), where P is in milliwatts.
10*log(14.4) = 11.5dB
Relative to the standard sound pressure of reference (20uPa) this is 11.5dB + 95dB = ~107dB

Normally output impedance of an amp should be less than 1/8th of the impedance of the headphone. Not only because of sheer maximum volume, but also because the impedance of headphone is not constant at all frequencies.

Where are you getting 75 for Zoutput? Unless I'm misunderstanding, I think you're using the wrong numbers. Shouldn't you do 75 (the headphones) for Zload and 6 (which is the uDAC's output impedance) for Zoutput? Assuming 2.2 Vrms, that would give you

2.2 * 75 / (75 + 6) = 2.04 Vrms

Thanks for the calculation though, that'll be helpful.

I know how to calculate power.

For a very rough ballpark estimate...

(1) create a 200 Hz sine wave or whatever in Audacity or similar program, and play it

(2) adjust the volume until it's about how loud you normally listen

(3) unplug the headphones and plug a male/male cable into the output of the uDac-2 (don't change the volume setting)

(4) grab a multimeter (a cheap one is under $10 honestly, everyone should have one)

(5) measure the (AC) voltage between left or right channel and ground while this is playing; that is, between the tip or ring, and the sleeve

That should give you an idea of the output voltage V_unloaded.  When loaded with 75 ohms, given that the source has 6 ohms output impedance, you'll get V_headphones = 75 / (75 + 6) * V_unloaded output to the headphones.  Then you can do a simple calculation as above to figure out how loud that should translate to, based on the sensitivity of the headphones.

With real music, a cheap multimeter will not be accurate because of a number of reasons including the limited bandwidth, the slow speed, and the output waveform not being like a sine wave (so the rms voltage is not 1/sqrt(2) of the peak, unlike for sine wave).

As I understand it, the uDAC is so badly designed that it actually starts clipping within the volume control range, so the maximum volume calculations might be a bit off if that isn't taken into account.