Estimating Headphone Volume

Discussion in 'Audiophiles: Headphones, Earphones, etc.' started by tinyman392, Dec 17, 2011.

Page 9 of 12

  1. cryphakon Active Member

    Member Since:
    Mar 18, 2012
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    iPad 2 (Black)
    For future reference here are the trident specs to calculate volume:

    Type: Open Air Dynamic (6.8mm)
    Sound Pressure Sensitivity: 93 +/-3dB (1,000Hz/mw)
    Frequency Response: 20Hz-20 KHz
    Impedance: 16ohm +/-15% (DC)
    Rate Input: 2mW
    Max Input: 10mW
    cryphakon, Jul 28, 2012
    #81

  2. Pixovate New Member

    Member Since:
    Jan 18, 2013
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    1
    Hey! I found your post really interesting and would love to use the calculations. How did you find the maximum voltage output? I tried looking it up with other phones but I can't find it?

    Thanks! :D
    Pixovate, Jan 18, 2013
    #82

  3. yksn New Member

    Member Since:
    Feb 23, 2013
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    Most of the formulas and tools in this thread are wrong..

    For example the volume control is neither linear nor squared. It's logarithmic.
    Headphone drivers are not in a parallel circuit. Usually there is a single driver per channel, nothing in parallel at all.
    Mixing actual and maximum output voltage in the power formula makes no sense.
    SPL is usually specified in dB SPL, not Pa.
    Multiplaying sensitivity with anything shows a complete lack of understanding what's going on...

    Check the corresponding thread on head-fi in the sound science forum.

    How could this misinformation be spread over a year without anyone noticing??
    yksn, Feb 23, 2013
    #83

  4. GadgetOrgy Well-Known Member

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    How are sure this is wrong? I am not expert on this, but are you like an audio engineer or something? If this is wrong then I suggest finding some sources to disprove this.
    GadgetOrgy, Feb 23, 2013
    #84

  5. yksn New Member

    Member Since:
    Feb 23, 2013
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    Most is very basic stuff. A look at some Wikipedia articles should be enough.

    Volume control:
    http://phys.org/news80304823.html
    but the formula in #1 uses squared volume percentage, e.g. 50% = -12 dB when it should be roughly -30 dB
    That's a huge difference!

    Power:
    P = V * V / R = V * I
    but the formula in #1 uses two different voltages.

    Impedance is specified as nominal impedance per channel. No need to calculate anything in parallel.

    Sound pressure and sensitivity is usually specified as dB SPL, not Pa.
    Some manufacturers provide sensitivity using 1 V, others using 1 mW. I don't think this is even mentioned in the first post, but again can make huge differences.

    Decibels are added, not multiplied.

    Give me a headphone and its specs and your iPod's volume and I will post an example of how it's properly calculated. (maybe include a well known track you're listening to at the given volume so I can include the RMS amplitude of that..)
    yksn, Feb 23, 2013
    #85

  6. tinyman392 Super Moderator

    Member Since:
    Jul 10, 2008
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    5G iPod touch
    As stated, there were assumptions made about the output of the iPod with each volume increment. That said, it may be logarithmic, but no guarantees on that.

    dB SPL is a rating for pressure. Guess what that's measured in? Pa, thank Mr. Pascal for our units of pressure. dB is simply a logarithmic scale for Pa (we can always directly convert back and forth). All measurements are made in a linear scale, so we get Pa (on a linear scale), not dB (on a logarithmic scale). We then convert over. My calculations can only calculate Pa, so we do need conversions, which is the last step. Again, dB SPL is a logarithmic scale for Pa. dB is Pa on a non-linear scale.

    I just looked over the calculations I did, but never multiplied dB, nor did I add. I just used the equation to convert from Pa to dB. I also did multiply the same voltage as well. The voltage multiplied is the (now incorrectly defined) output voltage based on the estimated voltage curve. No other voltages are multiplied. We use volume output (percentage) as a function of the max voltage output (of my iPod) to get the output voltage.

    So, right now, I thank you for the corrections about the volume percent incrementation being related logarithmically, I'll update that when the time comes. I'll look over the non-parallel impedance as well.
    tinyman392, Feb 23, 2013
    #86

  7. SilverShip Well-Known Member

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    Sep 5, 2012
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    iPad 2 (White)
    What about just measuring it by using a sound level meter at the earphone speakers?
    SilverShip, Feb 23, 2013
    #87

  8. tinyman392 Super Moderator

    Member Since:
    Jul 10, 2008
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    The sound level meter can't do it too well because it can't emulate the seal that is created between your head and pads (or ears and tips). There are tools to do that, but most involve a dummy head :p
    tinyman392, Feb 23, 2013
    #88

  9. yksn New Member

    Member Since:
    Feb 23, 2013
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    iPhone 4S (Black)
    The article I linked to that shows how the volume control works was posted in 2006.

    No, as I wrote sound pressure is usually measured in decibels, yes referenced to 20 uPa, hence dB SPL. Converting to Pa is a pointless exercise.
    Some manufacturers just write dB because it's clear that we're talking about sound pressure.

    You calculate the sound pressure produced by the headphone as:
    SPL (Pa) = Sensitivity * Power
    Sensitivity is measured in dB SPL, power in watts, how do you end up with Pa after a multiplication? It doesn't make any sense.

    ---

    Here's a simple example how it should be done:
    HP: Sennheiser PX 100
    Sensitivity: 114 dB SPL/V

    Player with 1.11 V max output with volume set to 100% (-0 dB).

    V = 1.11 * 10^(-0/20) = 1.11 [V]
    SPL = 114 + 20*log10(1.11 / 1) = 115 [dB SPL]

    That's it. Subtract the RMS amplitude of the track you're listening to to get the actual SPL.

    ---

    In case the manufacturer specifies sensitivity in dB SPL/mW, let's say 99 dB SPL/mW for a 32 ohm headphone:

    S = 99 + 10*log10(1 / (32 * 0.001)) = 114 [dB SPL] for 1 V of input


    Of course you can also stick with dB SPL/mW and go the power route:

    SPL = S + 10*log10(P/0,001)

    Using the numbers from above:
    P = V * V / R = 1.21 / 32 = 0.0378125 [W]
    SPL = 99 + 10*log10(0.0378125/0,001) = 115 [dB SPL]

    ---

    Your tool calculates (1.11 V output, full volume)
    for 114 dB SPL (/V): 113 dB SPL
    for 99 dB SPL (/mW): 112 dB SPL

    so it's completely off.
    yksn, Feb 23, 2013
    #89

  10. tinyman392 Super Moderator

    Member Since:
    Jul 10, 2008
    Message Count:
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    Device:
    5G iPod touch
    My tool is used to do a rough estimation, I never gave error bounds for it. You say it's completely off, I don't think it's too far off. Your calculations are more accurate than mine, and let's assume it's the actual output (I don't doubt it).

    So, let's calculate relative errros.

    For 114 SPL you get 115 output (max). For 99 SPL, you get 115. OK, I'll accept that. My tool generates 113 and 112 respectively. Let's calculate error for both instances.

    (Act - Cal) / Act
    (115 - 113) / 115 = 1.7 % error

    (115 - 112) / 115 = 2.6 % error

    I never claimed my calculations to be 100% accurate. Much of it was based on estimating the voltage curve of the iPod in relation to the volume selected (error 1). The second was a poor assumption on my part that it was wired in parallel (error 2). So yes, there are errors. How close are the numbers? They're a few percent off in the cases supplied. My program was to create a rough estimation, it did just that.

    _____

    Now, tell me exactly how this function below equates to SPL

    SPL = SPL dB Rating + 20*log10(V / 1) = dB SPL

    Forgive me for not just seeing it, maybe show a short proof of it?
    tinyman392, Feb 23, 2013
    #90
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