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Headphones sensitivity, impedance, required V/I/P, amplifier gain

Discussion in 'Sound Science' started by xnor, Jun 15, 2013.
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  1. xnor
    The following table is based on measurements, not manufacturer specs.
     
    Target SPL is 110 dB SPL.
    The source is assumed to output 2 V. The amp is assumed to be a voltage source (0 ohm output impedance).
    Voltage, current, power are RMS figures.
     
    What do the columns mean?
    S@1V is the sensitivity with 1 V, 500 Hz sine wave input in dB SPL.
    Z is the impedance at 500 Hz in Ω.
    Voltage is the required voltage to reach the target SPL.
    Current is the required current to reach the target SPL in milliamperes.
    Power is the required power to reach the target SPL in milliwatts.
    Gain is the gain the headphone amplifier theoretically needs to reach the target SPL without excess gain. If needed you can add a few dB excess gain (suggestion: 3 to 9 dB).
    Notes:
    1. 1 kHz: the measurement was done at 1 kHz instead of 500 Hz
    2. specs: based on specifications provided by the manufacturer, not independent measurements
    3. nc: noise canceling enabled
     
     
    There is no guarantee that the data is 100% correct. The sensitivity of some headphones can vary as much as +/- 3 dB (some manufacturers even specify this explicitly).
     
     
    ManufacturerModelS@1V [dB SPL]Z [Ω]Voltage [V]Current [mA]Power [mW]Gain [dB]Notes
    AKGK240 Studio103642.23934.9878.3111 
    AKGK271 MK II106651.58524.38338.644-2 
    AKGK272 HD11065115.38515.385-6 
    AKGK550115350.56216.0679.035-11 
    AKGK601991313.54827.08596.1015 
    AKGK701105651.77827.35848.65-1 
    AudezeLCD-2108451.25927.97635.22-4 
    AudezeLCD-3102482.51252.331131.4492 
    Audio TechnicaATH-AD700113350.70820.22714.32-9 
    Audio TechnicaATH-AD900114370.63117.05310.76-10 
    Audio TechnicaATH-AD900X114380.63116.60410.477-101kHz, specs
    Audio TechnicaATH-ANC7B1183050.3981.3050.52-14nc
    Audio TechnicaATH-ANC91091001.12211.2212.589-5nc
    Audio TechnicaATH-M50115380.56214.7988.322-11 
    Beats by Dr. Dre Pro117180.44724.81611.085-13 
    Beats by Dr. Dre Studio1212160.2821.3050.368-17nc
    BeyerdynamicCustom One Pro116180.50127.84413.955-12 
    BeyerdynamicDT770 Pro982513.98115.86163.14361kHz
    BeyerdynamicDT770-32111320.89127.85224.823-7 
    BeyerdynamicDT770-6001005573.1625.67717.9534 
    BeyerdynamicT1997503.5484.73116.7865 
    BeyerdynamicT5p116410.50112.2246.127-12 
    BeyerdynamicT7011038012.6322.632-6 
    BeyerdynamicT901023082.5128.15520.4862 
    BoseAE2112360.79422.06517.527-8 
    BoseQC1511348000.7080.1470.104-9nc
    Bowers & WilkinsP5117270.44716.5447.39-13 
    DenonAD-D2000115250.56222.49412.649-11 
    DenonAH-D1001112310.79425.62320.353-8 
    DenonAH-D7000114250.63125.23815.924-10 
    DenonAH-D7100108301.25941.96452.83-4 
    Fischer AudioFA-003117750.4475.9562.66-13 
    FostexT50RP107541.41326.15836.949-3 
    FostexT7113800.7088.8496.265-9 
    FostexTH900108251.25950.35763.396-4 
    Grado LabsSR60i to 325i111340.89126.21323.363-7 
    HifimanHE-4906310158.731587.30214 
    HifimanHE-500102342.51273.879185.5762 
    HifimanHE-6894311.22260.9352927.73415 
    HifimanRe0118600.3986.6352.641-14 
    KRK SystemsKNS640011034129.41229.412-6 
    KRK SystemsKNS8400106351.58545.28371.768-2 
    SennheiserAmperior113220.70832.17922.781-9 
    SennheiserCX880120340.3169.3012.941-16 
    SennheiserHD202119340.35510.4363.703-15 
    SennheiserHD280 Pro114730.6318.6435.454-10 
    SennheiserHD555/595114720.6318.7635.529-10 
    SennheiserHD558/598112700.79411.3489.014-8 
    SennheiserHD6001053221.7785.5239.821-1 
    SennheiserHD6501043331.9955.99211.9550 
    SennheiserHD7001051991.7788.93615.891-1 
    SennheiserHD8001034302.2395.20611.6561 
    SennheiserIE800125180.1789.8791.757-21 
    SennheiserPX100 II114340.63118.55811.709-10 
    SennheiserPX200 II115380.56214.7988.322-111kHz
    ShureSE215126180.1588.8051.395-22 
    ShureSE535133360.0711.9670.139-29 
    ShureSRH1440107381.41337.17252.507-3 
    ShureSRH1840102662.51238.05995.62 
    ShureSRH440116410.50112.2246.127-12 
    ShureSRH750113390.70818.15212.851-9 
    ShureSRH840116440.50111.3915.709-12 
    ShureSRH940113400.70817.69912.53-9 
    SkullcandyAviator118360.39811.0594.402-14 
    SkullcandyCrusher114320.63119.71712.441-101kHz, specs
    SkullcandyMix Master119200.35517.7416.295-15 
    Sol RepublicTracks118600.3986.6352.641-141kHz
    SomicMH463106451.58535.2255.82-21kHz, specs
    SonyMDR-MA900111150.89159.41752.955-7 
    SonyMDR-XB1000115270.56220.82711.712-11 
    SonyMDR-XB500123430.2245.2061.166-19 
    SonyMDR-XB700115280.56220.08411.294-11 
    SuperluxHD668b108611.25920.63825.982-4 
    SuperluxHD66911062116.12916.129-6 
    TakstarHI2050104601.99533.25466.35101kHz, specs
    UltrasoneEdition 8115340.56216.5399.301-11 
    UltrasoneHFI580115360.56215.6218.784-11 
    UltrasoneHFI680115750.5627.4984.216-11 
    UltrasoneHFI780116400.50112.536.28-12 
    UltrasonePro550117650.4476.8723.07-13 
    UltrasonePRO750114410.63115.3899.71-10 
    UltrasonePRO900108431.25929.27736.858-4 
    V-ModaCrossfade M100115360.56215.6218.784-11 
    YamahaPRO 300116580.5018.6414.331-12 

     
     
     
    Some have raised concerns with 110 dB SPL being too loud. Well, that is just the absolute highest SPL you can reach with a full-scale 500 Hz tone and the volume set to max.
    Music has a higher crest factor than sine tones, which means that the RMS value will be much lower.
     
    The following graphic shows a volume control with a 15A taper pot as found in many heapdhone amps. Ideal range should be somewhere between 10 and 2 o'clock.
    The inner labels show the attenuation of the pot at each full hour. So 110 becomes 95 dB SPL at 12 o'clock.
    The outer blue/red labels show the overall perceived SPL of an uncompressed classical track and a heavily compressed metal track respectively. Loudness was calculated using an EBU R128 compliant scanner.
     
    Obviously, you can really hurt your hearing if you listen to highly compressed music and turn up the volume. With less compressed music overall levels will be a lower but there can still be very loud passages or short peaks in SPL.
     
    So turn the volume down - better be safe than sorry. Don't rely on calculations only. Use a sound level meter.
     
     
     
    volctrl.png
     
     
    Please let me know if you find that some values are completely off or want some headphones added.
     
    anetode, miceblue, kalston and 6 others like this.
  2. HalidePisces
    Audio Technica ATH-AD700
    Sony MDR-MA900

    For fun, you could do a "marketing headphone" (Beats, SOL Republic, etc.).
     
  3. Steve Eddy
    Quote:
     
    RMS I presume?
     
    se
     
  4. xnor
    Yes, 2 Vrms.
     
    Obviously the target SPL with that gain is only reached with a full-scale 500 Hz tone. But depending on the frequency response the headphone will produce a couple dB more at other frequencies.
     
  5. xnor
    Added some more headphones. SOL Republic Tracks has a terrible dip at 400 Hz, which is the only headphone so far that has such a problem near 500 Hz, so I chose 1 kHz instead.
     
  6. Greenleaf7
    Thanks for the added information. I have a question regarding how the calculations work. Take for instance the Beyerdynamic T1, which is rated at 600 ohms. Why did you base the calculations on a 730 ohm impedance?
     
  7. 00940
    I might be wrong but... looks like the value in mA are based on the RMS voltage. They should be based on the peak voltage.
     
  8. xnor
    @Greenleaf7: That's because manufacturers provide nominal impedance in the specs. That number is just an approximation anyway.
     
    The measurements of T1's I've seen never reach 600 Ohm. The minimum at 2 to 4 kHz is somewhere around 630 Ohm. It has a very broad impedance peak at about 80 Hz, so the impedance at 500 Hz is higher.
     
  9. xnor
    @00949: Numbers are based on RMS power. P = Vrms^2 / R = Vrms * Irms.
     
  10. 00940
    Irms is almost never used, datasheets and specification sheets usually use Ipeak and that's what is assumed when giving values in mA. If you use it, you should specify it (as you did for V).
     
  11. xnor
    Added some more headphones, added manufacturer column.
     
    Interestingly, with just 3 dB excess gain more than 70% of the headphones listed require no more than unity gain (0 dB).
     
    Even with a 1 V source like an iPod the SE535 would be fine with 20 to 14 dB of attenuation due to their high efficiency.
     
    And to the DIYers and reviewers: If you have a DAP or amp that is free of hiss with the SE535 it is very likely going to be fine with any other earphone or headphone.
     
  12. xnor
    As we know, ideally the volume control pot should spend most of its time between 10 and 2 o'clock.
     
    Assuming the pot ranges from 7:00 to 17:00 and has a 15A resistance taper we get an attenuation of about 22 to 9 dB at those positions.
    With the 110 dB SPL target and no excess gain that results in 88 dB to 101 dB SPL with the 500 Hz full-scale tone.
     
    Using an EBU R-128 loudness scanner I looked at some completely uncompressed classical / hypercompressed metal tracks.
    The perceived overall loudness of those tracks, which may have soft and loud passages, is up to 20 dB / 6 dB quieter compared to a full-scale 500 Hz tone.
     
     
    What does this all mean?
     
    Example:
    110 dB SPL target with a 2 V source as used in #1
    Sennheiser HD800 => amp with 0 dB gain
    no excess gain
     
    1) volume control at 10 o'clock
    perceived overall loudness:
    a) classical recording: 68 dB SPL
    b) compressed track: 82 dB SPL
     
    2) volume control at 2 o'clock
    perceived overall loudness:
    a) classical recording: 81 dB SPL
    b) compressed track: 95 dB SPL
     
    3) volume control at max
    perceived overall loudness:
    a) classical recording: 90 dB SPL
    b) compressed track: 104 dB SPL
     
     
    (EBU R128 uses Loudness Units instead of dB but I used plain old decibels to avoid [even more] confusion.)
     
     
    edit: will have to do some measurements to see how big the error is using a 500 Hz tone as reference
     
  13. ab initio
    Couple quick thoughts
     
    1) First and foremost, thank you for this reference! 
    [​IMG]
    This is extremely helpful (see below) and *should* be linked to very very often in the future.
     
    2) If you are from an english-speaking country:
    Code:
     sed '/[0-9]\,/s/\,/./g'
     I spent 20 minutes trying to figure out how the heck the HE-6s needed 3 kW to reach 110 dB!!!
    I knew they were inefficient, but I didn't think they were that bad! [​IMG]
     
    4) there is no number 3.
     
    5) This data is super helpful for guiding people who are considering new headphones or amplifiers and are unsure whether or not their amp-cans combination will work. If they have cans A and are considering cans B, they can compare the sensitivities, current requirements, and voltage requirements and weigh the differences against their amp's capability to source that current and voltage. 
     
    6) I think 110 dB is a little bit high for a reference loudness, especially since 90dB is the typical threshold for hearing damage. Because this data is especially useful for guiding newer enthusiast in their search for headphone nirvana, I think it's a little dangerous to give the impression that they should be listening at 110dB SPL with any regularity. Perhaps you could put a disclaimer in the original post warning against prolonged exposure to  >= 110 dB. Of course I'm just picking nits here.
     
     
    +1 rep
     
    Cheers!
     
  14. KamijoIsMyHero
    Quote:
     
    why? I never heard of this ideal placement for a volume pot
     
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