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frequency response graphs (or curves) - compensating with graphic equalizer settings

Discussion in 'Headphones (full-size)' started by curlysue, Aug 15, 2014.
  1. curlysue
    For the last few days I have been struggling with how good and how poor headphones sound.
    I have been listening to a variety of music with a small variety of headphones with MSRP of (approx) less than $180.
    Specifically (in alphabetical order), I have been listening to . . .
    JVC HA-RX700
    Senal Sound SMH-500
    Sennheiser HD 558
    Superlux HD668B
    Superlux HD681
    According to their respective manufacturers, these cans include the following specs (copied from respective website, packaging or box) . . .
    JVC HA-RX700 . . . . . . . . .  Sensitivity 105dB/1mW . . . . . . . . . . . . . . . . Impedance 48 ohms
    Senal Sound SMH-500 . . . . Sensitivity 101 dB +/- 3 dB (@ 1 kHz/mW) . . . . Impedance 58 ohms @ 1 kHz
    Sennheiser HD 558 . . . . . .  SPL 112 dB (1 kHz/1 Vrms) . . . . . . . . . . . . . . Impedance 50 ohms
    UPDATING initial posting of Sennheiser HD 558 specs to also read . . .
    Sennheiser HD 558 . . . . . .  SPL 99 dB (1 kHz/1mW) . . . . . . . . . . . . . . Impedance 50 ohms
    Superlux HD668B . . . . . . .  Sensitivity 98dB (SPL/1mW) . . . . . . . . . . . . . Impedance 56 ohms
    Superlux HD681 . . . . . . . .  Sensitivity 98dB SPL/mW . . . . . . . . . . . . . . . Impedance 32 ohms
    While I understand these (and other) manufacturers manipulate Sensitivity or SPL ratings to enhance product marketing, I do not understand how to quantify the differing units.  For example, while I understand dB/1mW represents decibels per one milliwatt, I do not understand how "dB/1mW" compares to "1 kHz/1 Vrms" or "1 kHz/mW" or "dB/mW." 
    I have read many threads regarding an industry standard for Sensitivity and other specifications.  I have also read volumes of reviews at this website and other websites whom claim to test headphones (using a variety of components) and present Frequency Response graphs or curves.  Unfortunately, similar to the manufacturers, these websites do not use identical components to test the headphones they choose, and their Frequency Response graphs are often (if not always) different, and the units associated with the Frequency Response graphs vertical axis differ as well (e.g. Amplitude (dB), Amplitude (dBr), Relative Response in dB, dB V/V (smoothed 1/3 oct), etc).
    I may be wrong, but I believe dBr means dB Relative or Relative dB . . . and if so, they ARE the same.  But then there's dB V/V . . . where the vertical axis range is -50.0 to 0.0 incremented at 5.0 through this range.  I have no idea how to relate dBr to V/V . . . particularly when dBr graphs vertical axis has a midpoint of zero, 0, and then positive dB above, with negative dB below - a majority of the graphs I found use this standard. 
    Ideally, for my analysis, I would love a single website that has Frequency Response graphs (or curves) for each of the above headphones, but that is not the case.  If it were, then I would assume any idiosyncrasies would be consistent throughout the testing and that, relatively speaking, any errors would be consistent from one manufacturer to the next - but I've probably said too much there. 
    For my analysis, what I have done thus far is measure the amplitudes associated with 30, 60, 120, 250, 500, 1K, 2K, 4K, 8K and 16K Hz.  Next, for each FR graph using the respective amplitudes (ignoring the dBr or V/V units), I normalized all frequencies to 1K Hz . . . meaning, I zeroed 1K and then added or subtracted the differences between it and the other frequencies.  Using photoshop software, given the graphs available (online and or from the manufacturer) I believe my measurements are very accurate and consistent within logarithmic scales.
    Using a DAC amplifier with digital graphic equalizer (with dB fine tuning to more than 0.1 dB per frequency) and an MP3 player with digital graphic equalizer (with dB fine tuning to 0.1 dB per frequency), I conducted my tests. 
    Conducting my listening tests, I chose the Senal SMH-500 as my benchmark - both for listening and quantifying amplitudes across the frequencies noted above. Next, I documented the graphic equalizer (G.E.) dB setting for each frequency noted above.  Then, for each frequency, I added the G.E. dB to the "Relative Response in dB" values obtained measuring the dB amplitudes (described above). 
    The resulting (addition) dB value, per frequency, was then used as a baseline for each of the other headphone manufacturers (noted above).  For example . . . at 2K, using the SMH-500 graph, I measured an amplitude of approx 115.62 dB and 110.00 at 1K . . . normalizing to zero, I used an amplitude of 5.62 dB for 2K . . . and at 2K the G.E. setting was 3.30 dB . . . 5.62 plus 3.30 yields 8.92 dB for 2K. 
    Using 8.92 dB for 2K as a baseline, and the measurements for each of the headphones (noted above), I adjusted the G.E. settings to compensate for higher or lower amplitudes obtained from the respective manufacturers FR graphs.  For example, at 2K, using the HD668B graph, I measured an amplitude of approx -0.15 dB, and after normalizing 1K to zero, the resulting amplitude measured appox 2.08 dB at 2K.  Using the SMH-500 benchmark value of 8.92 dB for 2K, I set the G.E. at 6.84 dB for HD668B.  This same approach was implemented across each of the frequencies noted above.  In essence, regardless of impedance (which primarily effected volume levels), I wanted to ensure each headphone was producing the same approx SPL at each of the frequencies noted above. 
    While my methods may be exceedingly elementary, and perphaps unscientific, I must say the results have been stunning and surprising.  In short, I am astounded by how similar these cans sound when their output dB's are supplemented (as described above) using a G.E.  I should add that the audio quality does vary when compared to the Senal cans . . . JVC and Superlux - very little, Sennheiser - not terribly significant (no surprise given the MSRP is nearly 3X the other cans).  For me, in this instance, quality of sound represents how my ears perceive each note or how a chord runs in or bleeds out, along with clarity and smoothness, and where subtle notes or riffs can be heard with one pair of cans, but not the other(s). 
    For critical listening, audio quality is very important to me.  But for day to day listening, I have to say I am astonished by how G.E. settings manage to create such similarity between each set of cans.  My tests included FLAC and 320 kbps CBC rips of a variety of artists I enjoy listening to and tracks I know well.
    I know there are other specifications to quantify, but at this time I am happy with what I have achieved thus far.  That said, I would like to get a better understanding of how to correctly quantify the units "dB/1mW" an "1 kHz/1 Vrms" and "1 kHz/mW." 
    Has anyone here quantified frequency response curves in the manner I described, implemented and tested?
    Thanks in advance for your comments.

    P.S. For those interest in the FR graphs I used, below you will find links for three of them:
    Senal SMH-500 . . . http://i60.tinypic.com/2a7dgsz.jpg
    Sennheiser HD 558 . . . http://i62.tinypic.com/34doqiq.jpg
    Superlux HD668B . . . http://i61.tinypic.com/2r70ig6.jpg
    P.S.S.  How cool is this - I just received an email from my boss where he has been corresponding with Sennheiser regarding their specifications . . .
    Good Morning NAME REMOVED,
    Thank you for contacting Sennheiser Technical Support. My German colleagues said that it was one hundred (100) mW.
    NOTE: These headphones are 50 Ohm headphones and hence designed to work off a much less powerful audio signal. These models were specifically designed for use with less powerful audio devices (like portable devices) and portable inline amps.
    If you are looking for something that will handle a strong signal then you should consider the HD 650 which are 300 Ohms and will handle 500 mW max nominal continuous input power.
    Have a great day.
    . . . and the 50 Ohm headphones referenced in the above email are Sennheiser HD 558 - which apparently are good to only 100 mW.  After learning from MindsMirror (noted below) THAT makes me want to re-evaluate my interest for Sennheiser HD 558 cans.  100mW?  Really?!?!  WOW . . . that has got to be an industry low for entry level audiophile cans . . . 100mW . . . they MUST be joking.

  2. MindsMirror
    The unit of sensitivity is always dB SPL. The measurement is taken in two different ways, from a 1KHz sine wave at 1mW, or a 1KHz sine wave at 1V RMS. Of the headphones you listed, the Sennheiser is measured at 1V RMS, the others are all measured at 1mW. The different manufacturers just have different ways of writing this.
    To covert from volts to watts, use Ohm's law for power.
    P = V^2/R
    The impedance of the Senheiser is 50 Ohms, voltage is 1V, so power is 20mW.
    20x power is about 13dB, so the sensitivity of the Sennheiser is 99dB @ 1mW.
  3. curlysue
    First, thank you so very much for your reply MindsMirror.  :)
    Thank you as well for the additional info regarding Ohm's Law as it applies here, and for the 20x power education.  I would like to know how to specifically calculate the result ending with 99dB @ 1mW.  I suspect it involves logarithms . . . something like 20Log(something) where Log is base 10 (maybe) . . . but no doubt something I can work out using my HP15C calculator.  I will look to the Internet to find this equation and to learn how to properly execute it. 
    Not to pick on Sennheiser, but if I were Sennheiser I would be embarrassed to promote an SPL of 112 dB when, in fact, the more widely used unit of mW or 1mW results in a value nearly 11% less.  If you ask me, it borders on misinformation to those of us not as well versed in power calculations or dB's and Logrithms, etc. 
    Now, given your help, MindsMirror, I am able to assess each headphone based on dB at 1mW which allows me to view Sennheiser in a slightly different light. 
    Thanks again!
    CurlySue  :)
  4. curlysue
    FIRST LESSON LEARNED . . . inspired y, dated 15 August 2014 at 11:19am . . . calculation confirmed after reviewing A PRACTICAL GUIDE TO dB CALCULATIONS by Chuck McGregor in September 1999 . . . as follows:
    Sennheiser HD 558 specifications state . . .
    Sennheiser HD 558 . . . SPL 112 dB (1 kHz/1 Vrms) . . . 50 Ohms
    . . . and the other manufacturers (as listed in my original post) state their SPL ratings per mW. 
    As MindsMirror reply states, Power = Volts (squared) divided by Ohms, derived from V = I x R and P = V x I . . . where V is Volts, I is Amps, and P is Power (in Watts, milliwatts, etc).
    Given 1Vrms across a 50 Ohm load, P = 20mW . . . and I am calling this value "watt 2"
    Because the other manufacturers state their SPL ratings at 1mW . . . I am calling this value "watt 1"
    To determine the dB drop from "watt 2" to "watt 1" we use the following equation . . .
    dB  = 10 x Log (watt 1 divided by watt 2)
         = 10 x Log ( 1 divided by 20 )
         = 10 x Log ( 0.5 )
         = -13.0103
         = -13.0 truncating (not rounding) the remaining decimal places
    Therefore, while HD 558 supposedly create 112 dB at 1kHz/1Vrms . . . at 1kHz/1mW they create 13.0 dB less . . . 112 dB - 13 dB = 99 dB (as MindsMirror's reply states). 
    Sennheiser HD 558 . . . SPL 112 dB (1 kHz/1 Vrms) . . . at 50 Ohms . . . is equivalent to . . . Sennheiser HD 558 . . . SPL 99 dB (1 kHz/1mW) . . . at 50 ohms
    And now I fully understand his reply . . . and herein thank him again.
    Accordingly, I have updated my original post to reflect my new knowledge.
    Thanks again, MindsMirror 
  5. MindsMirror
    I'm not sure why that 100mW number would have any affect on your interest in the headphones. At 100mW the headphones would produce 119dB of noise in your ears, which according to Wikipedia is almost loud enough to be at risk for instantaneous hearing loss. Why would you want it to handle more?
  6. curlysue
    I liken my preference to electrical power emergency backup systems for super computer facilities - where sizing a UPS (uninterruptible power suppy) in 100s or 1000s of KVA and or Engine-Generator Set in 100s or 1000s of KW is not based soley on maximum continuous load - where industry standards rarely (if ever) size a UPS or EGS to exceed 80% of its maximum rated continuous load. 
    I guess I've also become biased by other manufacturers specs where (using the headphone specified in my initial post) they are all greater than 300mW . . .
    JVC HA-RX700 . . . Max. Input Capacity . . . 1500mW(IEC)
    SMH-500 . . . Maximum Input Power . . . 1000mW
    Superlux HD681 . . . Max. Power . . . 300mW
    Superlux HD681 . . . Max. Power . . . 300mW
    . . . 100mW seems quite light in comparison.  Though I thoroughly understand your point - given my new understanding of dB and I suppose I should have calculated the dB at 100mW before showing my ignorance, which you exposed. 
    While I doubt we are paying much for the additional 200mW to 900mW to 1400mW(IEC) for the other cans, given your perspective (as referenced your reply, according to Wikipedia) what is your perspective on other Sennheiser cans . . . for example HD 650, HD 700, and HD 800?
    Looking at Sennheiser HD 650 specs, I find . . . Max. Nominal Continuous Input Power . . . 500 mW as per EN 60-268-7 . . . Characteristic sound pressure level (at 1 kHz) . . . 102 dB (1 Vrms) . . . Nominal impedance . . . 300 Ohms . . . given your perspective and my new knowledge (courtesy of you sharing your knowledge), 1 Vrms translates to 3.33mW . . . using 10 x Log ( 1 divided by 3.33 ) yields . . . if my calculations are correct, HD 650's Characteristic sound pressure level (at 1 kHz) . . . less than 97 dB (1mW) . . . and at 500mW the SPL would exceed 123 dB (over twice the power compared to your figure of 119dB at 100mW for HD 558's) and at 100mW the SPL would exceed 116 dB - seems the additional 400mW is wasted dB headroom.
    Seems Sennheiser is not discouraged by Wikipedia and if I interpret your critique correctly it seems they have designed OVERKILL in their MSRP $500 HD 650.  I'd like to think they designed HD 650's with additional capacity for a reason, but (given my boss' correspondence with them) not so in their MSRP $180 HD 558. 
    Then there are HD 700, where given Sennheiser's specs, at 500mW their SPL would also exceed 123 dB.  Given Wikipedia's perspective, the added capacity seems a complete waste of power capacity or an MSRP of $750 that's padded with excessive SPL.
    Same results for HD 800 . . . at 500mW they would exceed 123 dB.  Seems folks are all paying (a percentage) of the $1500 MSRP for added capacity that would be over two times louder than what may be loud enough to be at risk for instantaneous hearing loss. 
    Within their 500-series, presuming their maximum input power is also 100mW (do not have supporting documentation), then Sennheiser HD 518 SPL would be 115 dB . . . and Sennheiser HD 598 would be identical to HD 558 at 119 dB.   
    And given Sennheiser Momentum specs, including 200mW capacity at 18 Ohms, their SPL would exceed 120 dB.  Why 200mW when at 100mW these cans would still deliver over 117 dB given Sennheiser's specs (if my calculations are on the money).
    I guess it simply seems reasonable to desire the additional capacity, MindsMirror . . . their other cans provide it - as does Sennheiser's non-500-series cans. 
    Just my two cents.
  7. MindsMirror
    I just think that the power rating is not that important. For someone just listening to a pair of headphones, it might as well be an arbitrary number. I have only listened to the HD 800. They sounded great, so my perspective is that they are great headphones. I think you are paying more for the engineering and materials that go into making them sound better, not for their ability to handle more power.
  8. mtliu
    I'm going to revive an old thread to say that I've tried doing this, and the results were less than satisfactory. Inner Fidelity publishes a lot of graphs for many cans. I've used these and tried to compensate with eq, only to find very sibilant and honky sounding results. 

    There are some boxes that can be used for room sound calibration - stick a RTA reference mic into these boxes, hit a button - and the EQ automatically adjusts for frequency response of the room. More sophisticated boxes do this for multiple mic positions in the room.

    This is the kind of setup needed in order to do this accurately for cans - except none exists right now. There is no way to stick a reference mic in your specific head - then generate the calibration impulses. The closest thing would be to have Innerfidelity lend you their setup - which is one of a kind and is not available to be lent out.

    The other large part of the puzzle is that specifications and frequency response graphs do not tell the whole story. If they did, we could just tell how a set of cans sounds by looking at these numbers and graphs - without needing to audition first. If this were the case, head-fi would not exist in it's current form  - since a large number of members here value subjective descriptions over numbers and graphs. The numbers and graphs are definately useful - but it tells less than half of the story. They are certainly not useful as a direct measurement tool for indicating how to adjust a graphic eq to get a different sound signature.

    Things like this have also been tried with microphones - attempting to make a cheap $30 dynamic mic sound like a top of the line $2000 condenser mic. While Eq certainly will change the sound of a mic, what these graphs can't do - is measure the difference in things that these graphs do not measure, such as harmonics. The total harmonic distorion spec is also of limited value because it is just a number rather than a detailed report of which harmonics are present. This is also the reason why tube amps might spec worse than a solid state amp sound better to some people. These modelling transformations only offer very limited results as of now.

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