More Power?

INTRO: 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.

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.

DIFFICULT 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: 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.

TESTING 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.

TESTING 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:

• Sennheiser HD600: Sound pressure level (SPL) 97 dB (SPL) at 1 mW, 300 ohms
• Sennheiser HD650 - Sound pressure level (SPL) 103 dB (1 Vrms), 300 ohms
• Ultimate Ears TripleFi 10 - Sensitivity: 117 dB SPL/mW, 1 kHz, 32 ohms
• HiFiMAN HE-5LE - Sensitivity: 87.5 dB, 1 mW, 38 ohms
• Ultrasone Edition 10 – Sound Pressure Level 99 dB (useless spec!), 32 ohms

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.

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TECH SECTION (math ahead)

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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 “10^x” (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 / V_90db )
• 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:

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:

• Headphone Amps Explained
• All About Gain 
• Noise And Dynamic Range