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Objective Reviews & Commentary - An Engineer's Perspective

September 2, 2011

More Power?

volume knob mikael altemarkINTRO: While the plugs on most headphones are compatible with the jacks on most gear that doesn’t mean the two will play nice together. Headphones vary widely in their power and drive requirements and some sources are far more capable than others. Mismatches are common. If you’re not satisfied with what you have now, or you’re shopping for new gear, this article might be worth checking out. (photo: Mikael Altemark).

THE PROBLEM: Put simply, a lot of headphones are not well suited for a lot of sources and vice-versa. There’s more involved than just using headphones with the right impedance. One of the most important things to consider is the sensitivity (efficiency) of the headphones.

THE EASY WAY (ROUGH ESTIMATE): If the sensitivity of your headphones is listed in dB/mW you can get a rough idea how much amplifier power is needed with the following table. To use the table, find your headphone’s sensitivity in the left column (use the next lowest number if it’s between two numbers). Then look at the numbers in the next 3 columns. Most should use a peak SPL of 110 dB (the middle column). But if you don’t like loud music, or listen to mostly pop music, you might be happy with 105 dB. If you like it really loud, or listen to a lot of audiophile recordings, use 115 dB.  For example, the Sennheiser HD600 is 97 dB/mW so it requires 20 mW to hit peaks of 110 dB. The tricky part is your source needs to produce at least that much power at the impedance of your headphones and some manufactures don’t do a good job specifying power output. More on that in the Tech Section. You can also use the table in reverse to look up a source’s output power and see how that might match up to different headphones.

dB/mW 105 110 115 < Peak SPL
85 100.0 316.2 1000.0  
88 50.1 158.5 501.2  
91 25.1 79.4 251.2  
94 12.6 39.8 125.9  
97 6.3 20.0 63.1  
100 3.2 10.0 31.6  
103 1.6 5.0 15.8  
106 0.8 2.5 7.9  
109 0.4 1.3 4.0  
112 0.2 0.6 2.0  
115 0.1 0.3 1.0  
118 0.1 0.2 0.5  

SPECIFICATIONS DO MATTER: If you ask a lot of the audiophile manufactures why they don’t offer more complete specs for their products they often counter with something like: “specs don’t really matter”. But in this case they very much do matter. Headphones playing loudly enough with a particular source isn’t magic or something that can only be determined by trial and error. It’s entirely determined by a few numbers and some relatively simple math. It’s not like all headphone sources work well with nearly any headphones. It’s very much the opposite—compatibility problems are widespread. So the next time you hear “specs don’t matter” consider that person either mis-informed or they’re intentionally trying to mislead you.

MAXIMUM POWER vs GAIN: A headphone amp needs both enough maximum power and also enough gain to reach that power level with a given source. Sources vary widely in their output. An iPod Touch line output (LOD) only produces a maximum of 0.5 volts while most home gear has at least four times more output. So just because your amp has enough power you also need to make sure it has enough gain. See: All About Gain

POWER REQUIREMENTS vs POWER HANDLING: There’s often a big difference the amount of power headphones need to play loudly enough versus the maximum power the manufacture claims they can handle. When you see a specification that says something like “Maximum Power: 200 mW” that doesn’t mean you need, or even want, 200 mW. It only means if you use much more than 200 mW you might damage the headphones.

FIVE FACTORS: If you want know everything that goes into determining headphone and source compatibility there are five things to consider:

  • Type Of Music (average volume) – Music varies widely in its average volume. Heavily compressed pop music has a much higher volume than say an audiophile jazz recording.
  • Desired Maximum Output – This is simply the maximum perceived volume someone wants to listen at. It varies from person to person but it can be estimated fairly accurately several different ways.
  • Headphone Sensitivity – This is how loud the headphones will play for a given power or voltage level (from the specs or professional measurements).
  • Headphone Impedance – This makes a big difference in the next item and is necessary for some conversions. This is nearly always in the headphone specs.
  • Source Maximum Output – This is how much power the source can produce which varies depending on the impedance of the headphones. This is often poorly specified but it is measured in proper product reviews with full measurements. You can sometimes make assumptions from what specs are provided.

Lady Gaga Just Dance Exactly As Ripped From The CD

AVERAGE (RMS) VOLUME: Music varies widely in average volume (also known as “RMS volume”) which roughly equates to the perceived loudness of the music. Somewhere around the early 90’s the “loudness wars” started. Recording engineers starting using more and more compression (which boosts the soft parts of music) so their mix sounded louder than other mixes. As a result, over the last two decades, the average volume of pop music has slowly risen dramatically. With digital recordings the loudest anything can be is 0 dBFS where the “FS” means Full Scale. This sets the maximum peak levels on the recording. Average volume is measured in dB below 0 dBFS and here’s a rough guide:

  • Highly Compressed Pop (see pic above right): –6 dB to –9 dB
  • Well Recorded Pop: –9 dB to –12 dB
  • Well Recorded Acoustic/Jazz: –12 dB to –18 dB
  • Wide Dynamic Range Classical: –18 dB to –30 dB

WHAT’S RMS? RMS is just a geeky way to, for the purposes of this discussion, describe the average level of a waveform. It’s roughly 1/3 the peak-to-peak value of a sine wave. For something as complex as music, the RMS value is much more complicated but still can be calculated by software analysis and measured by more sophisticated instruments.

WHY AVERAGE VOLUME MATTERS: If you include the extremes there’s a range of roughly 24 dB in average volume between different kinds of music. How much is 24 dB? If we take highly compressed pop recording and play it at given average volume a highly dynamic classical recording might require 250 times more peak power! This isn’t strictly a fair comparison as if you really tried to play the classic recording at that level you would likely be reaching for the volume control during the louder parts. But it illustrates how important the source material is in determining peak power requirements.

audacity flim and the bbs - new americaDIFFICULT MUSIC: The most challenging music is where the average volume is always relatively low prompting you to turn up the volume but there are very brief transients that are far higher in level. This is most common in audiophile recordings where very little or no compression is used and there are Sforzando (brief loud) notes in the music. This is very different than say symphonic classical music that builds up to fairly high sustained average levels  (i.e. crescendos) that will have you turning down the volume. Brief loud transients add impact to the music without making it seem much louder. Worst case, these brief transients can be 20+ dB above the average level requiring around 100 times more power than the average level. Compare the Flim and the BB’s – New America track in Audacity to the Lada Gaga – Just Dance track (the two screen shots above). Even during the “loud” part of New America the average level (light blue portion) is still relatively low.

clipping fiio vs o2 scope traceCLIPPING: When the source doesn’t have enough voltage and/or current to meet the peak demands of the music it clips off the peaks. Studies have shown it may go unnoticed if it’s infrequent and mild. But if it happens often, or a single event is severe, it tends to be plainly audible as a harsh “grunge”. It’s the number one cause of plainly audible distortion in everything from cell phones to car stereos. In the waveform shown to the right the yellow trace is properly reproduced while the green trace is from a less capable amp and you can see what happens to the peaks in the music—they’re “clipped” off as if someone took scissors to the music.

DESIRED MAXIMUM VOLUME: So how loud is “loud enough”? To establish the upper end of subjective tastes, studies show the threshold of pain starts around 120 dB SPL. It seems reasonable to use that as the absolute upper limit. 120 dB SPL is also the level at which even short term exposure can cause permanent hearing impairment. Studies have shown even sustained average levels above 85 dB SPL can cause hearing damage. For more on these thresholds see Sound Pressure Levels. The research indicates the average maximum level should be at least 85 dB, and with classical music, that puts the peak level up to 30 dB higher at a worst case 115 dB). For more typical music peak levels of 110 dB SPL are more reasonable.

LIVE MUSIC: If you monitor sound pressure levels during live performances, rock concerts typically average 110 dB with peaks of 115 dB to 120 dB. Classical performances typically have peaks hitting 110 dB and a much lower average level of around 90 dB or less.

hd650-pop-music-max-SPLTESTING THE THEORY WITH POP MUSIC: I used my non-fatiguing HD650 headphones plugged into my O2 amplifier, and played several different selections of fairly well recorded pop music at levels as loud as I would ever want to listen—likely into hearing damage territory for any sort of sustained or cumulative listening. The HD650 needed about 1.7 – 1.8 Vrms which works about to about 107 dB SPL. The oscilloscope screenshot to the right (click for larger) shows the music and the the horizontal dashed lines are the peak-to-peak value (about 4.8V). Notice the marked peak isn’t all that far above the rest of the music. For this kind of music, and my subjective idea of what’s “too loud”, I’m close to the 110 dB SPL guideline established above. So far the guideline is holding up well.

hd650-highly-dynamic-music-max-SPLTESTING WITH FLIM & THE BB’s: Next I repeated the above test but this time using the same Flim & the BB’s – New America track shown earlier. I set the volume to where the loudest parts of the track were about at my limit of still being “comfortable”. Now the peaks hit 5.1 volts in one direction or about 10.2 volt peak-to-peak (the sample in this case is about 9 V p-p). That’s about 3.2 – 3.6 Vrms which is about 114 dB from the HD650’s on the peaks. This at the limit of or beyond what most portable amps can manage (the O2 being a notable exception). This correlates well with the 115 dB rule of thumb for highly dynamic music. So, working backwards from the threshold of pain and hearing loss you get 105 – 115 dB. Using live performance levels you get 105 – 115 dB. And testing using my own music, ears, and headphones, I get 107 – 114 dB SPL. So, all things considered, 110 dB SPL seems like a good target if you want to pick just one number. Add 5 dB for really wide dynamic range music at live levels and subtract 5 dB if you listen to mostly Lady Gaga or don’t like it very loud.

HEADPHONE SENSITIVITY: Headphones need widely different amounts of power to play at the same loudness. How loud they get with a given amount of power is their Sensitivity or Efficiency. This number is properly specified as either dB SPL per milliwatt (1/1000 of a watt) or as dB SPL per volt. The older international standard used the milliwatt method and the newer method uses voltage. But sometimes manufactures don’t specify either in their specs—such as Ultrasone in the list below. The list shows a range of 87 dB to 117 dB at the same 1 mW of power. That’s 30 dB and, believe it or not, the HiFiMAN headphones need 1000 times more power to play at the same level as the TripleFi 10s!  Some examples:

HEADPHONE IMPEDANCE: The impedance is listed at the end of the specs for each of the above headphones. It’s important to know the impedance if you want to convert between watts and volts—to say compare the HD600 to the HD650’s sensitivity. It’s also essential to estimate how much output a given source will have using a particular pair of headphones. Impedance is specified in ohms (Ω).

SOURCE MAXIMUM OUTPUT: This is where things often get vague. A lot of sources, including portable players, headphone DACs, and headphone amps, have incomplete output power specifications. The output power of any device is very dependent on the impedance of the headphones (known as the “load”). Power is a function of voltage and current. And, unfortunately, different sources have differing maximum amounts of both. Some, like Apple, keep it all a secret while others, like Sony, specify a useless value. The output impedance of the source (which is rarely specified) also alters the maximum power into different loads. So without complete specs it can be difficult to estimate. Here are some typical examples:

  • Apple iPod Touch – Power not specified, output impedance not specified
  • Sony NWZS545 – Audio Power Output: 5mW + 5mW (useless!), output impedance not specified
  • NuForce uDAC-2 - Power output: 80mW x 2 @ 16-Ohm, output impedance not specified
  • FiiO E7 – Output power: 150mW (16 Ohm); 16mW (300 Ohm), output impedance not specified
  • FiiO E9 - Output power: 1W (16Ω); 80mW (600Ω), output impedance not specified
  • Leckerton UHA-4 - 20mW 16 ohms, 40mW 32 ohms, 50mW 100 ohms, 15mW 300 ohms, output impedance 0.4 ohms

HEADROOM: The 105 – 115 dB guideline established above works fairly well without any extra headroom. But audio purists might want to add another 25% – 100% (1 – 3 dB) more power for a bit of extra headroom so the amp is even less likely to clip any peaks.

SUMMARY: The table at the start of this article can be used to get in the ball park and I’ve tried to explain how average volume and preferences also make a big difference. The more technically inclined may want to keep reading and learn how to calculate volume levels, convert between different specs, and more.


TECH SECTION (math ahead)


PERFECT SOURCES: As shown earlier, headphone and source specifications range from non-existent to fairly complete. Some headphone sources behave as a perfect voltage source. That means they will always produce the same output voltage no matter what reasonable load you connect. Even a headphone amp such as the $20 FiiO E5 can produce the same 1.2 Vrms into any load from 16 ohms (about as low as headphones go) to 600 ohms (the common upper limit). As long as you don’t need more than 1.2 V, it does a pretty good imitation of a perfect voltage source. This is because it has a low output impedance and enough current to drive 16 ohm loads without current limiting. With such a source the max power output is given by:

  • P = (Vmax * Vmax) / Headphone Impedance

POWER EXAMPLES: For low impedance sources that have ample current available, such as the FiiO E5, here’s the same amp with 3 different headphones, note the widely different power outputs:

  • HD600 (300 ohms) & FiiO E5 – (1.2 * 1.2)/300 = 4.8 mW
  • Beyer DT770 (80 ohms) & FiiO E5 - (1.2 * 1.2)/80 = 18 mW
  • TripleFi 10 (32 ohms) & FiiO E5 - (1.2 * 1.2)/32 = 45 mW

IMPERFECT SOURCES: In this case “imperfect” doesn’t necessarily mean bad, but several factors can limit the output of a given source. Any source can only manage so much voltage even with no load at all. It’s limited by the internal power supply voltage, and with most portable battery powered gear, is often relatively low. Most iPods can only manage about 0.5 – 1.0 Vrms maximum voltage, the FiiO E7 1.2 Vrms and the Leckerton UHA-4 about 2.2 Vrms into the highest impedance headphones (600 ohms). As the impedance drops, instead of the voltage staying the same, the voltage also may drop. This can be due to a significant output impedance and/or reaching the internal current limits (current limiting).

OUTPUT IMPEDANCE: Headphone sources have output impedances ranging from less than 1 ohm to 120 ohms or more. As the output impedance gets within about 1/8th of the headphone impedance it starts to significantly decrease the output available. The output impedance creates a voltage divider with the headphones.  It’s no longer close to being a perfect source as explained above. If an amp has a 50 ohm output impedance, and you plug in 50 ohm headphones, only one quarter as much power is delivered to the headphones compared with a zero ohm output impedance.

CURRENT LIMITING: Look at the specs for the Leckerton UHA-4 above. It puts out 50 mW at 100 ohms and that works out to 2.2 Vrms. If it could manage the same 2.2 Vrms into 16 ohms it should put out (2.2 * 2.2)/16 = 302 mW. but Leckerton only lists 20 mW. It has an output impedance of only 0.4 ohms so that’s not the problem. So what’s going on? The answer is some sources run out of current as the load impedance drops below some value. That’s what’s happening with the UHA-4. It just doesn’t have the beans to maintain the same voltage into loads much below 100 ohms. If a manufacture doesn’t specify the power output over a wide range of impedances it’s impossible to predict this behavior. Some might be tempted to argue that low impedance headphones are much more sensitive and need less power so this doesn’t matter, but that’s not always true. The HiFiMAN headphones above, many of the AKG models, and others, have low impedances and relatively low sensitivities. And they would be a poor match with something like the Leckerton.

CONNECTING THE DOTS: If a company doesn’t specify the power output around your headphone impedance you’re forced to try one of the following:

  • Power Specified At A Lower Impedance – In this case you want to figure out the voltage at the lower impedance and use that instead. The math is V = SquareRoot( Power in Watts * Impedance ). So for the FiiO E7, for example, it’s SquareRoot ( 0.15 * 16 )  = 1.5 Vrms.
  • Power Specified At A Higher Impedance – It’s impossible to accurately predict a source’s behavior into impedances lower than specified when you don’t know the output impedance or maximum current. The Leckerton UHA-4 example above shows how it goes wrong with current limiting. And the E9 shows how it goes wrong due to its higher (10 ohm) output impedance. The E9’s 80 mW into 600 ohms gives: SquareRoot ( 0.080 * 600 ) = 6.9 Vrms which should yield 3 watts at 16 ohms, but the E9 only manages 1 watt or 4 Vrms because a lot of power is lost due to the 10 ohm output impedance. A very rough estimate can be obtained by calculating the voltage at the next higher impedance, and then dividing that value by four to calculate power at lower impedances.
  • To Many Unknowns If you don’t know a device’s output into an impedance at least as low as your headphones, I would strongly suggesting choosing a different source with better specified output power (or voltage). Generally manufactures that don’t offer complete specs likely are trying to hide something or they many not even know themselves. Their potential customers should not be forced to guess if their gear will meet their needs. A better specified product is a much safer investment.

BRINGING IT ALL TOGETHER: If your eyes haven’t glazed over yet, it’s time to bring all of the above together. That involves converting between volts, power and decibels.

LOGARITHMS: Don’t panic, but the math involved requires a button that might not be on your calculator usually labeled “LOG” (base 10 logarithms are known as LOG10 in spreadsheets) and the inverse usually labeled “10x” (base 10 antilog or POWER(10,value) in spreadsheets). There are some online logarithm calculators that can also help with the math.

CALCULATE SPL FROM POWER: If you have a given source, and want to know how loud your headphones will get, you need to know the sensitivity of your headphones in dB/mW and the output power of the source in mW at the headphone impedance. Here’s the equation and the the FiiO E5 driving the HD600s (from above):

  • dBSPL = Sensitivity in dB/mW + 10 * LOG ( Pmax in mW)
  • 97 + 10 * LOG ( 5.6 ) = 103.8 peak dB SPL for HD600 & FiiO E5

CALCULATE SPL FROM VOLTAGE: If you know the voltage of your source at your headphone impedance, and your headphones sensitivity is rated at 1 volt, you can calculate the maximum output using the FiiO E5 and the HD650:

  • dB SPL = Sensitivity in dB/volt + 20 * LOG ( Vmax)
  • 103 + 20 * LOG ( 1.2 ) = 104.6 peak dB SPL for HD650 & FiiO E5

HOW LOUD WILL IT BE? The rule of thumb established above is 110 dB SPL for peak levels with a reasonable range of 105 – 115 dB depending on music and preferences. The E5 obviously falls a bit short with either the HD600 or the HD650 but it might still get loud enough for some tastes—especially with heavily compressed pop music with a high average volume. So let’s work the numbers the other way and see how much power the same headphones ideally need.

CALCULATE POWER FROM SPL: Using the HD600, rated in dB/mW you get:

  • Power in mW = Antilog ( ( Desired SPL - SPL at 1 mW ) / 10 )
  • Antilog ( ( 110 - 97 ) / 10 ) = 20 mW for HD600 to hit 110 dB SPL peak
  • Antilog ( ( 115 - 97 ) / 10 ) = 63 mW for HD600 to hit 115 dB SPL peak

CALCULATE VOLTAGE FROM SPL: As above except for the HD650 rates in volts we get:

  • Voltage RMS = Antilog ( ( Desired SPL – SPL at 1Vrms) /20 )
  • Antilog ( ( 110 – 103) / 20 ) = 2.2 Vrms for HD650 to hit 110 dB SPL peak
  • Antilog ( ( 115 – 103) / 20 ) = 4.0 Vrms for HD650 to hit 115 dB SPL peak

TO CONVERT FROM OTHER SPECS: Sometimes you might find things specified a bit differently. InnerFidelity, for example, measures headphones at the voltage required for 90 dB SPL. Here are some conversions:

  • 90 dB Voltage to SPL at 1 Volt: SPL at 1 Volt = 90 + 20 * LOG ( 1 / V90db )
  • Voltage to Power : Power in Watts = ( V * V ) / Impedance
  • Power to Voltage: Voltage = SquareRoot ( Power * Impedance )
  • Decibels from Two Voltages: dB = 20 * LOG ( V1 / V2 )
  • Decibels from Two Powers: dB = 10 * LOG ( P1 / P2 )
  • Volts p-p To Volts RMS: Vrms = Vp-p * 0.354
  • Vrms to Vp-p: Vp-p = Vrms * 2.83

DOING IT RIGHT: The best manufactures specify a device’s power output at several impedances—including the extremes of 16 and 600 ohms. The Leckerton example earlier is one example and another is Violectric’s Specification Page. The best measurements do the same thing. Here, for example, is the output of the O2 amplifier vs THD into several loads. You can see the distortion remains very low until the amp reaches clipping and then the distortion quickly goes nearly vertical and off the top of the graph. The 1% THD point is the generally accepted level for maximum output. The O2 has current limiting to help avoid damaging low impedance headphones. That’s why the 15 ohm and 33 ohm output voltages are lower. But you’ll notice at 80, 150 and 600 ohms the voltages are almost identical at about 7.3 Vrms because the output impedance is very low and the O2 is behaving essentially as a perfect voltage source:

O2 V11 AC Both Ch 1 Khz 10mV  THD N vs Output Left to Right 15 33 80 150 600 Ohms comments

MEASURING MAXIMUM OUTPUT: To measure output power correctly specialized equipment is required. RMAA has no concept of absolute levels (such as voltage) and it can’t plot output vs THD as seen above so it’s not very helpful. It’s also easy to damage a soundcard’s input which typically have a maximum input of 2 Vrms or less. You can make a very crude measurement using an oscilloscope with a known load resistance (don’t use headphones) and increasing the level until barely visible clipping is observed. Ideally the test is done with a 60 hz sine wave and a DMM used to read the RMS voltage (most DMMs are only accurate around 60 hz and not at higher frequencies). You can also read the peak-to-peak voltage from the scope but that’s less accurate. Tests should be brief (only a few seconds at full power) into lower impedance loads as sustained sine wave testing can exceed the thermal limits of many devices. Without a scope or distortion/audio analyzer it’s very difficult to get accurate output measurements.

BOTTOM LINE: Hopefully, especially for the more technically (or at least mathematically) inclined, this article sheds a bit more light on power output and volume levels. Once you get past the math, the main hurdle is incomplete specifications. The best remedy for shoddy specs is to simply spend your money on products from companies that are not afraid to publish detailed specs. The others will eventually get the message.

OTHER RESOURCES: These may also be useful:

64 comments:

  1. Use reaplaygain! (needs to be mentioned I think)

    ReplyDelete
  2. Thanks Satellite. Replay Gain doesn't change the power requirements but it does help avoid having to adjust the volume between different tracks or CDs. It works to try and level out the perceived average volume which is a big help--especially with long playlists.

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  3. Isn't ReplayGain or Dialnorm (objective wise) really doing Dynamic range compression?

    Correct me if I'm wrong, my understanding of this article is how to best match source gear to output listening equipment. This running both at optimal efficiency.

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  4. Max theoretical dynamic range of 16 bit signal is 96 dB. If we put noise floor of CD to human threshold level (at 1 kHz) then we need only 96 dB SPL. :) We can add 10 dB so the noise foor is little audible and even in that cause we need only 106 dB SPL. :)

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  5. It's kind of ridiculous how much I see people write "power" and mean something other than power. Unfortunately this kind of article cannot be linked to, where such people tend to congregate.

    There's some kind of pervasive misunderstanding about needing a more powerful amp. One headphone amplifier may sound better or different than another for any number of reasons, but that doesn't have to do with the max output power rating if the original amplifier had enough power for the headphones being driven.

    re: perfect sources.

    Nobody can count the number of fields where "perfect" describes a certain ideal behavior in one technical sense and does not imply the colloquial meaning of the word. This has been an item of confusion when researchers talk to sponsors providing funding (e.g. we've come up with a perfect ____, but...)

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  6. Is there a reason why companies like Apple, Sony, etc do not release the output impedance of their products? is it because the vast majority of consumers do not care or know what output impedance is, or what do you think is the reason?

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  7. The ReplayGain I know about uses a tag in the header of the music file to set the playback volume for that track (or CD). It's not changing the dynamic range it's simply trying to adjust the volume for you so all your tracks play at a similar volume.

    The whole point of ReplayGain is it doesn't alter the actual music data in any way (including dynamic range). If it did, and it the files used lossy compression (i.e. MP3 or AAC), it would have to decode the music, alter it, and re-encode it resulting in additional losses and degradation.

    There might be some software out there that does alter dynamic range, but in my opinion that wouldn't be very desirable unless it was just a second copy of the music for some specific application (like a portable player) and you left the original unaltered.

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  8. Exactly right NwAvGuy. Additionally, it can prevent clipping by reducing the volume to a level so that the highest peaks never clip.
    MP3 files, for example, commonly are compressed to have peaks above the magic 0 dBFS.

    Btw, does the O2 go up to eleven?

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  9. @anon The "clipping prevention" in ReplayGain is a bit misleading. The loudest signal you can have in a digital music file is 0 dBFS. Any playback chain (assuming you don't add gain anywhere above 100%/0 dB) should be able to play a 0 dBFS signal with no clipping (the NuForce uDAC-2 is a rare exception).

    And some recordings are clipped when they're mastered. If you look at the files with Audacity you can see peaks lopped off by hard clipping. This sort of clipping cannot be "undone" by ReplayGain. You can use software like iZotope's RX to try and "reconstruct" the clipped areas much like using Photoshop to fix problems with a picture. But, just like with Photoshop, you introduce new artifacts in doing so (and if it's a lossy format you have to re-encode it as well). That sort of "reconstructive surgery" is something entirely different than ReplayGain.

    AFAIK, the "clipping prevention" in ReplayGain simply means it won't try to boost the volume of a weak track above 0 dBFS. It will only boost the track so the loudest part of the track is right at 0 dBFS even if that falls short of your selected average volume target. It's not fixing anything, it's just avoiding creating a new problem at the expense of the track still being subjectively quieter than most of your other tracks.

    @Christian, I don't know why so many manufactures are so vague with their specs. I think sometimes it's what happens when you put very "artsy" and "creative" marketing types in charge of the website content. They typically want to emphasize other things and personally may not understand specs. So they just leave most of them out. It's sad.

    @Alexander, the 96 dB/16 bit argument doesn't work because it has nothing to do with what a human perceives as "loud". The background noise in even a quiet room is around 35 - 45 dB which invalidates the 96 dB number. I've shown three different ways in the article that all support 105 - 115 dB SPL and provided reference links for them. I would suggest reading up on dB SPL, etc. if you want to know more.

    @Mike, Thanks for your comments. Yes, the phrase "power" is often misunderstood which is partly why I wrote this article. The phrase "perfect voltage source" is an engineering term. It's used in modeling circuits and, because it exists only in theory, it's entirely valid--sort of like math functions that extend to infinity.

    PS - Sorry for the odd order of response, Blogger seems to be having some issues with the comment approval process.

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  10. @NwAvGuy, lossy encoding can in fact cause a signal to go beyond 0dBFS due to it operating in the frequency domain. Such clipping can induce artifacts in the sound beyond the compression itself. RG's clipping prevention ensures that the playback volume does not cause these peaks to clip.

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  11. Now that amps have been covered nicely, how about enlightening us about digital to analog conversion? Specifically upsampling (before D-A conversion), oversampling and non-oversampling DACs, sample rate conversion...

    PS: Great articles, too bad I already knew about everything covered in this one.

    Cheers,
    Julian

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  12. Anon, do you have a reference on the sort of clipping you're talking about? I'm not aware of how lossy encoding creates clipping unless it's a really poor CODEC. I've done extensive testing with the LAME MP3 CODEC, for example, and I've never see it create clipping. If AAC does so, shame on Apple. I'm also not aware of how ReplayGain can "undo" any clipping that already is present in a digital music file.

    Julian, you might want to see my CDs Are So 1980s article which covers digital formats. I do plan to publish more articles on the digital side of things in the future. I'm just one guy doing this stuff in my spare time. I'm glad you already understood everything in this article but, in my experience, that makes you somewhat rare. Few seem to know the math to calculate dB SPL with a given source and pair of headphones. And some still have their heads wedged deep in the sand chanting "specs don't matter."

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  13. I've transcoded CD audio with LAME mp3 and other codecs plenty of times and gotten ReplayGain in foobar2000 to report that the track peak for the lossy version was over 1 (so over 0 dBFS). This can happen even if nothing in the original was at 0 dBFS.

    The lossy file contains magnitude information for different frequencies, that hopefully follows the original signal closely. When reconstructing this information back to PCM, some values can exceed 0 dBFS if there is some error in the lossy representation (and there is since it's lossy). i.e. the original plus the error signal is greater than 0 dBFS. So there can be clipping if you take the lossy information at face value, even if the original does not clip.

    I think the easiest test would be to take some dynamic range compressed pop music (with 0 dBFS peaks everywhere), drop the whole thing down by 0.1 dB in Audacity, save the reduced-amplitude version, and then convert the reduced-amplitude version to a lossy format. I'm sure you will get a lot of 0 dBFS values or higher as a result. (Arguably those values in the original are already clipped, so this isn't a great example, but you get the point hopefully.)

    Also as a related subject, see this:
    http://en.wikipedia.org/wiki/MP3Gain

    ReplyDelete
  14. About one year ago, I was looking for a DAC/Amp combo for my triple.fi 10. Turned out that the first device I bought used a TPA6120 with the usual 10 Ohm output impedance. I really noticed how specs do matter. (This device featured a selectable 192 kHz upsampling function, that's why I'd like to see whether upsampling makes a measurable difference.)

    Regarding the clipping from lossy encoding: That should be easy to unterstand. Imagine a perfect (e.g. infinite frequency bandwidth) square wave at 0 dBFS. Now remove all frequencies above a certain threshold. This will give you some overshoot and oscillation, especially at the edges.

    So, encoding to a lossy format doesn't clip the music by making it louder. It doesn't per se add distortion But if it is decoded, those removed frequencies slightly alter the apmlitudes. And those altered amplitudes result in clipping and extra distortion, if they go above 0 dBFS.

    Replay Gain saves the peak amplitudes (decoding seems to be done in 32 bit float, which can go higher than 0 dBFS) and uses that peak information the prevent clipping. However, most of the tracks that go above 0 dBFS are so loud that they have a highly negative Replay Gain value anyway and the extra clipping protection is not needed.

    E.g. peak amplitude 1.13422 (+1.1 dBFS), but Replay Gain value is -10 dB. Peak would then be at -8.9 dBFS, whether clipping prevention is enabled or not.

    ReplyDelete
  15. Lame does create clipped samples just like (m)any other mp3 codecs, but that's part of the psychoacoustic modeling. In other words, those peaks are rarely an audible problem.

    ReplyDelete
  16. I'm still having weird issues with Blogger and comments. But thanks Mike, Anon, and Julian for your explanations.

    There's also a controversial form of clipping known as "intersample clipping" that some say can occur during poor mastering. A/D and D/A designers apparently deal with the issue somewhat differently which can lead to problems--especially with heavily compressed pop recordings. It's too bad the digital medium is essentially being abused as part of the "loudness wars".

    I plan to do a future article dedicated to "Gain" and all of this will be better discussed there. We're getting way off topic for this article.

    ReplyDelete
  17. Just a quick amendment for the section on output impedance, where you give an example of a 50 ohm output impedance feeding a 50 ohm headphone.
    Half the voltage is lost, but three-quarters of the power is lost (not half the power)

    Ian

    ReplyDelete
  18. Thanks Ian. We're both right. Half the amp's total output power, at the combined total impedance, is wasted in the resistor. But you're correct the headphones see only one quarter the power compared a zero ohm output impedance. I'll revise that.

    ReplyDelete
  19. Crest Factor can be used to describe the peak-to-average power ratio (compression/loudness) of music signals. It may also be used to influence mastering and or broadcasting engineers ;)
    To measure the crest factor in real time of audio signals. Freeware. http://www.tolvan.com/crest

    ReplyDelete
  20. Hey man, I'd really like to know something about MP3Gain:

    Does it provide more headroom?

    When I had an iPod, I cannot use those EQ settings because they were additive, so the bass boost is more like a bass clip. However, after "changing" all my tracks from 96dB-ish to 89dB by using MP3Gain, such EQ no longer clips.

    Same thing with my PCM-D50 recorder. Before using MP3Gain, songs sounded harsh ans the bass was not very satisfying. After using MP3Gain, again down from 96dB-ish to 89dB, the harshness was gone and it sounded more transparent. Although I tell you, this is all subjective and I cannot prove it. But the whole clipping issue on the iPod was not subjective. Clip is clip.

    So here's the thing. Are the amplification circuits in my DAPs trying to go beyond their gain because the input level (unchanged 96dB files) was too high? I assume so because similar effects (clipping) have been personally obtained by daisy-chaining amps. If so, what MP3Gain does is basically to lower the average output level (volts, I assume) of these files, right? Still, it shouldn't make music sound "less harsh"...

    Also seriously, very very nice articles. Pure truth. It's a good thing we have a real engineer here.

    Ex-3602 of Head-Fi. Now banned at my own request.

    ReplyDelete
  21. How MP3Gain works in terms of "headroom" would depend on the player. MP3Gain lowers playback levels on many recordings. The actual bits in the file, however, are not changed and may still hit 0 dBFS. So it depends on how and where in the playback process your DAP applies the EQ and gain.

    Many players use "smart EQ" that's all done in the digital domain (DSP) and it won't allow "digital clipping" (known as overflow to DSP geeks). When you turn on "Bass Boost" on an iPod the average volume drops to create enough "headroom" to allow boosting the bass. With other players, the amount of bass boost you get starts to taper off at higher volume settings until you get to max volume and there's zero bass boost.

    Because DAPs have digital volume controls the DSP knows the volume, it knows the EQ settings, and it literally can "do the math" to make sure the player doesn't clip with a 0 dBFS signal at any frequency even with EQ applied. I think the Rockbox firmware guys have some write ups on how they did their EQ that might explain some of this further.

    There are two kinds of clipping in a DAP--digital clipping (trying to go over 0 dBFS before the DAC--i.e. DSP overflow) and analog clipping after the DAC. Many DAPs, including most iPods, give you a few dB of excess gain with the volume control allowing you to push the DAP into analog clipping at max volume. ReplayGain may drop the average level far enough with most recordings to keep many DAPs from clipping even at max volume.

    This is a complex topic as there are lots of variables and differences between hardware and even PC software and operating systems.

    ReplyDelete
  22. AAC stands for Advanced Audio Coding and has nothing to do with Apple :) In fact, I praise Apple for popularising it as it's FAR better than outdated mp3 on all levels. There's a good reason why the International Standards Organisation replaced mp3 with AAC in it's audio layer in MPEG-2!!! Yes, that long ago, the latest MPEG standard is MPEG-4. mp3 creates much more artifacts than AAC, easily observed via spectrogram measurements vs say a lossless source file. Great article as always :)

    ReplyDelete
  23. Thanks for all the great info. I hate to pile on the list because I know people have been lining up to ask you to test various equipment. But I was wondering if you had plans to test the headphone output on any popular AVR receivers (say like an Onkyo 706)? Curious because I routinely see folks dismissing the output from receivers as second rate at best. But with my 32-Ohm headphones, it sounds quite good. Just wondering if I'm missing something.

    ReplyDelete
  24. Mark, it would be interesting to test AV receivers, but I fear they probably differ widely. Some likely still use large value resistors from the speaker level outputs which results in an unacceptably high output impedance. Others probably use a cheap op amp or headphone chip amp. Neither will match the performance of a proper headphone amp. Some higher-end receivers might include a higher quality headphone output but I suspect they would mention it in their marketing materials if they did.

    It's hard enough to keep up with Apple iPods which are all implement differently and change every year let alone the 100+ popular AV receivers that also change every year. I have several AV receivers I could test, but even the newest is no longer available. But I'll put it on the list... :)

    ReplyDelete
  25. I haven't tried it myself, but vintage receivers with headphone outputs that are padded down via resistors from the speaker taps are supposed to be pretty good for planar magnetics since they have flat impedance curves so the FR won't change and don't seem to have much back EMF since so much of their driver damping is done mechanically so they apparently don't require much in the way of damping factor.

    It also helps that even the "weak" ones can put out tons of power by headphone standards if you swap the resistors.

    ReplyDelete
  26. I recently contacted Koss, asking them for max. power handling capacity of Koss Porta Pro(60Ohms ,101dB SPL, Distortion & max. power handling capacity - Top secret). The reply was”There are no guidelines for the maximum power handling capacity of a stereophone.” Hmm. (And I recalled your blog about “more power”).Can you “guesstimate” the power handling capacities of these headphones or still better a practically tested spec. chart of most popular headphones (The ones in your stable will also do) ? (No hurry, I know you are busy right now with O2-desktop ver.)

    ReplyDelete
  27. Soundshui, you bring up a good point. I should add this to the article but there's a big difference between maximum power handling and power requirements. The first number is usually in reference to what the headphone can survive without damage and Koss has a point. It can be difficult to define as it can be made up of thermal limits, peak power limits, excursion limits, etc.

    But you have what you need. You can use the 101 dB SPL (assuming 1 mW) and 60 ohms to figure out how much power you need for a given maximum listening level. The short answer is not that much.

    ReplyDelete
  28. I am using the PortaPros with a Behringer UCA202 as a DAC/Headphone Amp combo at work. It works very well. It sounds very clean with plenty of volume.

    ReplyDelete
  29. Hello nwav, I recently read something interesting on head-fi and I have a couple of questions to clarify. Sorry if this sounds like a silly question :P

    Someone wrote that "Loud SPL does not equal maximised performance."

    So let's say that I've got a low impedance (suitable for portable DAPs), high sensitivity headphones, a portable DAP that measures well and a desktop amp that measures well.

    The usual argument here is that the desktop amp will provide more "juice" to the headphones and as a result the source>amp>headphone set-up will sound better than the source>headphone set-up as the desktop amp maximises the driver performance. Would you say that this is true? Or is the difference between the two set-ups a result of the different sound characteristics of the amps?

    Assuming both set-ups are volume matched and that both the desktop amp and the DAP's amp will not clip at high volume.

    ReplyDelete
  30. @Jon, I'm not sure what the "Loud SPL" statement is supposed to mean, but the "more juice" argument is false if neither amp clips AND both have a suitably low output impedance. I suspect that perception is from using say a portable with a 10 ohm output impedance and a desktop amp at 0.5 ohms. In that case the desktop amp might have an advantage with some headphones that might wrongly be attributed to "more juice".

    From what I've seen the reverse is at least as likely. There are lots of desktop amps with output impedance that violates the Z/8 guideline. And, because it's more efficient (and helps battery life), there are lots of portables with very low output impedance.

    Of course other things can affect the sound quality like frequency response, distortion, etc. But assuming all those measure sufficiently well, it will nearly always come down to output impedance if neither amp clips. And if the output impedance of both is under Z/8, they should sound very similar.

    See my Output Impedance article if you haven't already.

    ReplyDelete
  31. Hey nwav,

    Thanks for the explanation and the link to the Output Impedance article. From what I understand, the output impedance of a certain amp should be much lower than the headphone's impedance (x/8).

    i.e A transparent amp will have close to 0 output impedance while amps that have their own sound characteristics (warm/clinical/musical) generally have very high output impedance. Technically this is bad for headphones because of underdamping/overdamping leads to a change in frequency response.

    Right?

    ReplyDelete
  32. Jon, it's not quite that black a white. For example my idea of "musical" is "accurate". That means the amp doesn't have a sound of its own and lets you appreciate the music without the amp getting in the way. But you're correct about the headphone impedance divided by 8. Higher impedances lead to changes in frequency response and underdamping. The degree to which both happen depends on various other factors.

    ReplyDelete
  33. Oh I see.

    Keep up the good work on your articles.

    By the way do you frequent any audio forums?

    I'd love to stalk and read some of the stuff that you post.

    pce.

    ReplyDelete
  34. Hi NwA,

    Loot the RMAA of Fiio e11 (Iphone 4 and Triple Fi load)
    http://www.markuskraus.com/RMAA/iPhone4_E11.htm

    Good no?

    ReplyDelete
  35. @Rafael, Some of those tests make me wonder if the TripleFi was really used as a load. The crosstalk, in particular, seems too good to be true considering the E11 uses the same problem-causing virtual ground IC as the AMB Mini3 and the impedance of the Triple Fi's is relatively low. I may get the chance to test the E11 someday but right now, I'm more interested in the E10 which uses the same output op amp and includes a hi-res capable DAC for around the same price as the E11.

    Also, the E11 cannot be used and charged at the same time or run from AC power. It can only be used on battery power which makes it a very poor desktop amp.

    ReplyDelete
  36. dBSPL = Sensitivity in dB/mW + 10 * LOG ( Pmax in mW)

    97 + 10 * LOG ( 5.6 ) = 103.8 peak dB SPL for HD600 & FiiO E5

    ----

    Is it me, or is this wrong? 97 + 10 * log (5.6) = ~104.4

    I think you just mixed up what the power was (you had previously calculated 4.8, and if you use 4.8 it does work out to 103.8 as you listed.

    ReplyDelete
  37. Thanks for catching the error.

    ReplyDelete
  38. Hi NwAvGuy,

    I have a few questions regarding source power requirements:

    1) Is the sensitivity/efficiency of full size dynamic headphones typically constant from low to high frequencies?

    2) As you mentioned in the headphone impedance article, the impedance of the headphone can change depending on the frequency. So taking the Senn HD280 as an example, would it be "safer" to calculate power requirements using its 160 Ohm peak impedance @ 75Hz, instead of the 64 Ohm impedance @ 1kHz?

    3) Relating the two questions above, is it possible that if the source power is chosen to satisfy loudness requirements using the manufacturer's specified sensitivity and nominal impedance @ 1kHz, you can end up having enough power and hence loudness for 1kHz, but due to some combination of variable sensitivity and/or headphone impedance, that the bass frequencies don't have enough power/loudness? (This is assuming the source is otherwise properly chosen, e.g. output impedance < 8x headphone impedance, etc.)

    Thanks!

    ReplyDelete
  39. Hi NwAvGuy,

    Considering what you stated about headphone impedance varying with frequency, would it be "safer" to calculate the source's required output power at the maximum headphone impedance, instead of the nominal 1kHz value?

    For example: With the Sennheiser HD280, your graph indicates the maximum impedance is 160 Ohms @ 75Hz. Should I choose a source that can deliver the required power at 160 Ohms instead of the nominal 64 Ohms?

    Thank you very much!

    ReplyDelete
  40. @hlin599, The sensitivity and impedance are not constant. Ideally it's measured with broadband pink noise which takes into account what you mention. Otherwise, you have to do the best you can with whatever data you have.

    If you want to be conservative, and know the maximum impedance, you can use that value for calculating required power. But be sure to use the minimum or nominal impedance for the "1/8th" rule in calculating the amp's output impedance.

    Also, while some manufactures specify impedance at 1 Khz it's often more of an "average". Etymotic and Ultimate Ears, for example, don't follow the 1 Khz method as with B.A. IEMs the impedance at 1 Khz can be far off what's "nominal".

    ReplyDelete
  41. Hi NwAvGuy,

    I have read your extensive review on the E9. I would like to know if it would be a good match for the AKG K701.

    The input impedance is 62Ohms and sensitivity is
    105dB SPL/V. Based on the 1/8 rule you discussed, does it mean this pair would not work?

    Of course there are other variables like you stated above, but I am not really sure how this pair would work.

    Thanks!

    ReplyDelete
  42. @anon, I think the E9 is marginal for the K701 because of the 1/8th rule and I'm also not impressed with the low frequency distortion. You could certainly do worse than the E9, but you can also do better for around the same price--i.e. the O2.

    ReplyDelete
  43. Ah, the O2. I would gladly get this if it is available in the market without the diy stuff. I hope it goes into production in the future.

    But for now, I am thinking of pairing e10+e9 for the k701. Would this make some improvement over e9 alone or e10 would do better due to its lower ouput impedance? I have no idea if e10 theoretically has enough power to drive the k701s as everyone just seems to say that portable amps could not drive them without specifying why. Some numbers on this could really help.

    ReplyDelete
  44. If the E10 is like the E11 (they use the same output op amp) it won't have enough power for the K701. The E11 can only manage around 2 Vrms or less into the K701 and the distortion is relatively high. Just like the Mini3 it's based on, the E11 doesn't do well with lower impedance headphones that need much over 0.5 volts. I'm not sure if the E10 will be much better but I'll be testing one once they're available from the usual dealers in the USA.

    ReplyDelete
  45. When looking for an inexpensive amp to drive K701s, the E9 would definitely be fairly high on my list. That, or maybe the Pro-Ject Head-Box II (I don't think these are available outside Europe - it's a single-supply '2068 + BD139/140 AB buffer design running on +15V with a somewhat highish gain and output impedance, but nice build quality, costs a little less than the E9 here).

    K701s aren't particularly picky about output impedance, their impedance only varies between about 60 and 75 ohms in the 20 Hz .. 10 kHz range. With a 1 dB deviation rule, that means anything with 47 ohms or less should be fine. By contrast, a HD598 with its widely varying impedance (60..280 ohms) would need 10 ohms or less.

    What K701s do need is a good amount of clean power. A TPA6120A2 isn't exactly super happy with them but should still do a good job. Otherwise one would have to upgrade the budget and get something like a Lake People G93 (if an LM1876 won't cut it, I don't know what will), or go DIY.

    BTW, it looks like amplifier recommendations for loudspeakers aim for a SPL of at least 100 dB @ 1 m... and ordinary hi-fi listening distances are bigger than that. Many acclaimed hi-fi and studio speakers will hit <~105 dB max (>=100 Hz). We headphone guys are one spoiled bunch!

    In fact, it seems like a good idea to keep an ear on listening levels. Inexperienced listeners in particular may find that the volume they've chosen is rather on the high side compared to speaker playback. I'm sure nobody wants to contract hearing damage from their hobby. Learning to listen to typical warning signs should be high on the list of priorities. If your hearing is not amused, it will definitely complain (and sometimes it's too late then).

    (I bet there are a number of people with semi-shot hearing who have gotten into headphones precisely for their high undistorted levels.)

    ReplyDelete
    Replies
    1. I have a Pro-ject Headbox 2 which is problematic with my AKG 702.
      Why ? Very recessed from lower mid range down, easily bettered by
      a Denon 1912 receiver head phone output, right next to it. A Pioneer
      VSX 518 is also vastly better in bass and midrange. These are both supposedly resistor outputs, Denon going for opamps in the next model up.
      These are reputed to be poor quality headphone outputs, but they got the orchestral sound right on the 702's. Maybe slightly boomy ( to me ) bass, but 702's can do with a bit of that.
      By contrast to the Project, a Perreaux SXH2, 1 ohm output impedance,
      ( designer told me personally, not in printed specs ) is fine.
      The tone with the Headbox is simply too light, very smooth highs, excessively smooth, and palid intonation overall.
      I think it may be a matter of bass roll off with a low impedance can, on the Project. Capacitors in the wrong place maybe, a fence post could hear that the Project/AKG combination is lacking. The Project is much better with my HD650's.

      Delete
    2. The cheap Pro-ject Headbox, from what I know, does use a capacitor coupled output. Any headphone amp that runs on a single DC "wall" supply generally either uses capacitor coupled outputs, or a Virtual Ground. Either can cause audible problems--especially with low impedance headphones.

      A proper headphone amp needs dual ("split" or "bipolar") power supplies like the O2 uses. That eliminates the need for capacitor coupled outputs and virtual grounds.

      Any output impedance much above 1 or 2 ohms can also cause audible problems. See Sonic Advantages of Low Impedance Headphone Amps and Headphone Amp Impedance.

      Delete
  46. Great article. I am indeed running into the peak power problem with my V-Can amp driving AKG K601 headphones. I first noticed the problem when playing a software piano, live. I sometimes experience clipping at the "attacks" of the piano. (the moment the hammers strike the strings). If my calculations are correct, the V-Can is clipping at about 113dB SPL. (3.2V RMS into 120 ohms, sensitivity 102dB/V, and there is a 2dB increase at the particular frequency I tested at, according to the detailed frequency response curve of the K601)

    This article has given me some reassurance that I do not have unusually high expectations in sound level.

    It is obvious to me that the O2 would easily solve my problem.

    Greg.

    ReplyDelete
  47. (minor correction to last - the K601 sensitivity is actually 101dB/V)

    ReplyDelete
  48. Of course, the SPL I am experiencing when playing piano depends on the frequencies present at the time. So, there was no point in consulting the frequency response graph to determine the SPL that happened to conincide with the sine wave test signal I used. The purpose of the test signal is simply to determine the maximum voltage that the amp is capable of, when loaded with the headphones.

    One thing that would be interesting would be play the piano when it it just reaching the point of clipping, recording the performance, and then re-play the performance with the headphones connected to equipment that could not only measure raw SPL, but also do "perceived loudness" calculations, to get a feel for the actual perceived loudness for a human. This may be very different to the simple peak SPL. Alternatively, knowing the frequency response of the headphones, it may be possible to simply run the recording file through a perceived loudness analyzer. This may not be quite as accurate, though, if the transient response of the headphones comes into play. \Greg.

    ReplyDelete
  49. Does anyone have a link to the formula for calculating the perceptual change in loudness, for a given change in SPL? So far, the best I've found is the table here: http://www.sengpielaudio.com/TableOfSoundPressureLevels.htm but that's just in 3dB increments. \Greg.

    ReplyDelete
  50. Hi, thanks for the great article.

    I was wondering, if it's not specified weather a headphone's sensitivity is for 1 mW or 1 volt, is it safe to assume it's one of the two? or could it be for some other amount of power or voltage?

    Thanks

    ReplyDelete
    Replies
    1. Generally if it's not specified it's likely at 1 mW. As another guide, the 1V values are generally 10+ dB higher. The relationship between the two depends on the headphone's impedance.

      Delete
    2. Nevermind... I just found out that most listeners will set their average level at 69 dB in quiet environments, so my math was probably fine. Now I know I don't need 110 dB SPL!

      Delete
  51. Hi there,

    I know this has probably been asked already, but is there a direct way to convert dB/V to dB/mW, in terms of headphone efficiency (sensitivity)?

    Thank you!

    ReplyDelete
    Replies
    1. The two are related by the impedance of the headphones. To convert from dB/mW to dB/V you add 20*LOG(1/SQRT(0.001*Z)). So for 32 ohm headphones (Z=32), that works out to adding about 15 dB. So if a pair of 32 ohm headphones are rated at 90 dB/mW they're 105 dB/V. To go the other way, you subtract the value you get from the above equation.

      The difference drops with increasing impedance. For 600 ohm headphones, it's only about a 4.4 dB difference. I should make a table and put it in the article.

      Delete
    2. Very cool, thanks for the equation!

      Delete
    3. Oh wow. Using your equation, the ER-4P has an efficiency of a mere 86 dB/mW! With 27 ohms of impedance this has got to be a huge current-eater.

      ...Might want to grab something with higher impedance and higher efficiency.

      Delete
    4. The ER-4P is rated at 102 dB SPL at only 0.1 Vrms. That's 122 dB at 1V. So it's plenty efficient. A typical 0.5 Vrms portable will drive it to 116 dB which is above the 115 dB SPL target.

      Delete
    5. I didn't see NwAvGuy's answer at first, so I came up with this:
      Sensitivity in dB/mW = dBV - (10 * log(1000 / Z))

      Delete
    6. Hi, A simple xl based h/p power calculator can be found over here www.apexhifi.com/specs.html

      Delete
  52. Geez, I didn't look carefully. Thanks for the correction!
    Was sorta thinking, wow not a K701 again!

    ReplyDelete
  53. So, NwAvGuy, I've got an Auzentech Forte with an NJM4580 op amp for the headphone amplifier (don't know if that is important). It's been difficult getting any solid answer on Head-Fi (where everyone has their own opinion or repeat what someone else said), so I'm wondering if you can tell me if this card can drive the beyer DT 880 (250 ohm) or AKG Q701 properly? Would I be right in assuming that since the Q701 consumes 3 times the power of my AD700, I should expect to turn my volume up to about 3 times what it is now for the same SPL?

    Also, is there a difference between maintaining the right volume and reaching the headphones' "full potential" as Head-Fi likes to call it?

    ReplyDelete
    Replies
    1. It's impossible to say without knowing the power supply voltages supplying the NJM4580 if the DT880 would work. The Q701 will not be a good match as the 4580 can't supply enough current even if it can supply enough voltage. The volume control position isn't linear so you can't really predict anything from that.

      Delete

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