All About Gain

INTRO: For those interested in headphone amps, gain is an important topic. Here are the essentials about gain with lots of links to more information. In addition to this introduction explaining gain, there are later sections on:

• Excess Gain
• Gain Calculations
• Gain Details

RELATED ARTICLES: The following may be useful understanding how gain fits into the bigger picture:

• Headphone Amps Explained
• Amplifier Power Requirements
• Noise And Dynamic Range

WHAT IS GAIN? Put simply, gain is the maximum amount an amplifier can increase a signal. In the world of headphones, it's usually voltage gain. The diagram above shows a source with a weak output made 3 times stronger by an amplifier. Applying gain to a signal doesn’t normally change the dynamic range, it just makes everything louder. Other ways to specify gain, such as power and current, are rarely used for headphone gear.

YACA (Yet Another Car Analogy): The relationship between gain, volume, and maximum power can be confusing to some. Using car analogies might help:

• Gain Is Like The Gear Selection - When a car is in its lowest gear its top speed is limited to a fairly low value but it can climb steep hills. It's somewhat the same with a headphone amp set to low gain. Think of a gain switch as 1st, 2nd, and 3rd gear on a car's transmission. Different gears are used for different driving conditions.
• Volume is like the Throttle (Accelerator) - The volume control adjusts the overall power to the headphones much like the throttle in a car adjusts the power to the wheels.
• Maximum Power is like Top Speed - Most cars are capable of going faster than most people need. While a car might have a top speed of 100 MPH, in first gear, it might only do 40 MPH. So gain can be used as a way to limit maximum output and better match the output to a given pair of headphones. The difference between the top speed and the highest speed limit is somewhat analogous to excess gain.

WHY DOES GAIN MATTER? If you don't have enough gain, your headphones probably won’t get loud enough. If you have too much gain, you will be forced to use only a small portion of the volume control's range, there may be increased channel balance problems, more noise, more distortion, and you could even damage your headphones more easily. Most any amp will perform worse at higher gain settings so you want to use the least amount of gain that gets the job done.

GAIN AND VOLUME ARE IMPLEMENTED DIFFERENTLY: Turning down the volume is not the same as lowering the maximum gain (with a few rare exceptions). A race car doesn't turn into a family car if you never use more than half throttle. Certain compromises were made in the race car that make it less suitable for family car duty even if you try to drive it slowly. The same is true with a high gain amp. It's important to not have much more gain than you really need.

GAIN CAN BE USED TO LIMIT MAXIMUM POWER: If you have some fairly efficient headphones that are as loud as you would ever want with only 0.7 volts of audio. But you have a high-end desktop headphone amp that can put out 10 times as much (7 volts). By reducing the gain, even if you accidentally turn the volume all the way up, you can limit the maximum power to your headphones. This can help prevent hearing damage and even headphone damage. It also also allows using much more of the volume control's range making volume adjustments easier and more accurate.

GAIN CAN CHANGE WITH DIFFERENT HEADPHONE LOADS: If an amp doesn’t have an output impedance below 2 ohms the gain will change with different loads. The higher the output impedance, the more dramatic the change. For example, an amp with a 120 ohm output impedance with 5X gain at no load, will have only 3.5X gain with 300 ohm headphones and only 0.6X gain with 16 ohm headphones. This is another reason it’s important to know the output impedance.

GAIN CANNOT CORRECT FOR A LACK OF MAXIMUM POWER: If your headphones need 5 volts but your amp is only good for 2 volts cranking up the gain won't help any and will just make the amp clip sooner. Clipping is what happens when an amp runs out of power. The rest of this article assumes your amp is capable of enough power for your headphones. For more on this topic see: More Power?

 

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GAIN DETAILS

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HOW IS GAIN EXPRESSED? Gain is usually expressed as a factor (ratio), such as 4X, or in decibels (dB) such as 12 dB. In this case, 4X is the same as 12 dB and simply means with the volume control set to maximum, the output voltage of the amplifier will be four times higher than the input voltage. If you put 1 volt in you will get 4 volts out (assuming you don't exceed the maximum output capability). I show how to convert from ratios to dB and back in the Gain Calculations section below.

WHAT ARE TYPICAL GAINS? Headphone amps that have just a single fixed gain typically range from 2X (6 dB) to 5X (14 dB). For amps with two gain settings, low gain might be 2X to 3X and high gain 5X to 8X. Some amps have three or more gain options while others allow changing internal jumpers or resistors to set the gain.

A ROUGH GUIDELINE: If you want to skip the more technical details, the table below offers some idea of what gain will be usable with various headphones and sources:

Headphones	Portable	USB DAC	HOME	< Source
IEM 100 - 115 dB/mW 16 - 32 ohms	1X/0 dB	1X/0 dB	1X/0 dB
Sensitive Low Impedance Full Size Grado, Denon, Etc.	2X/6 dB	1X/0 dB	1X/0 dB
Average Full Size HD5xx/600/650 100 - 300 ohm	5X/14 dB	3X/10 dB	2X/6 dB
High Impedance Full size 300 - 600 ohm	10X/20 dB	5X/14 dB	3X/10 dB

DO I NEED AN AMP AT ALL? If your headphones already get plenty loud enough, and you're happy with the sound, odds are you don't need an amp. But if they don't get loud enough, an amp may be required. The table above shows several combinations where the gain is listed as 1X which implies no amp is required. But you might still want to use an amp to lower the output impedance of your source. For example, the iPod Touch 3G has a 7 ohm output impedance. With balanced armature IEM headphones this causes audible problems. See: Output Impedance. So while the IEMs don't need any more voltage they can still benefit from a lower output impedance. Some amps, like the O2, can be easily configured for 1X gain and improve the sound of higher impedance sources. For more on headphone amps in general, see: Headphone Amps Explained

 

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EXCESS GAIN

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EXCESS GAIN: If your amp has just enough gain for your headphones to hit the desired level at full volume with a 0 dBFS signal it's sort of like having a car with a top speed equal to the highest speed limit in your area. There might be times when you want to go even faster. But how much extra do you need? The amount of volume control range above where a 0 dBFS signal clips is considered “excess gain”. Here are some points to consider:

• Excess Gain Is A Tradeoff - As described above in Why Does Gain Matter, too much gain has negative side effects. So it's a tradeoff between those side effects and how much excess gain you want.
• Excess Gain Is Only Useful For Quiet Tracks - Most properly recorded digital music is designed to hit, or get within 1 dB of, 0 dBFS. If your amp has excess gain, using full volume with normal tracks will cause the amp to clip (badly distort) and may even damage your headphones. But, without excess gain, rare quiet tracks may not be loud enough even with the volume at 100%. One solution is having a reasonable amount of excess gain. Another solution is to normalize quiet tracks to 0 dBFS using Audacity or other software. This simply raises the levels so the loudest portion of the track is at 0 dBFS. Yet another solution is to use ReplayGain which helps equalize all tracks to roughly the same perceived volume. 
• ReplayGain (volume leveling) - If you use something like ReplayGain nearly all of your music should play at a consistent subjective level. ReplayGain is essentially like having someone automatically adjust the volume for each track (or CD). The default target loudness of 89 dB leaves 14 dB of headroom between the average volume and 0 dBFS. For the most compressed pop music this means the peak levels will be as much as 6 dB below 0 dBFS, while dynamic music will get much closer to, or even hit, 0 dBFS. If you use ReplayGain, or something similar, for volume leveling, you may want up to 6 dB of excess gain to allow for the overall volume reduction ReplayGain applies to some tracks. For more on average volume see: More Power?
• Dynamic Range – It’s important to note that neither the gain of an amplifier, nor ReplayGain, normally changes the dynamic range of music. Gain changes normally apply equally to the softest and loudest portions of the signal (music). To change the dynamic range you have to apply compression, limiting, (or dynamic range expansion).
• Clipping vs Maximum SPL – Some amps have plenty of power and your headphones, or ears, will give up before the amp does when dialing up excess gain on a recording that already hits 0 dBFS. But, in some circumstances (especially with low sensitivity headphones), the amp might run out of power first. If you want to be assured your amp will never clip, just work backwards from the amp’s maximum output into your headphone impedance to determine the gain. If your amp maxes out at 7 volts, and your source is 2 volts, set the gain to 3.5X and the amp will never clip even at full volume with a worst case recording.  See: More Power?
• 9 dB Excess Gain Is A Reasonable Maximum - I would aim for at least 3 dB of extra gain but somewhere around 9 dB the negative side effects already mentioned start to outweigh the advantages. A few might want to go as high as 12 dB but only if they've used something like ReplayGain to normalize their music library to a lower than normal average volume or have other unusual requirements.
• The Math – 3 dB of extra gain means multiplying the minimum gain by 1.4 and for 6 dB multiply by 2, and for 9 dB multiply by 2.8.

THE CHANNEL BALANCE PROBLEM: Devices with conventional volume controls may have audible channel imbalance at very low volumes. It's extremely difficult to manufacture volume control potentiometers that maintain tight channel balance below about -40 dB (referenced to full volume). Having too much excess gain forces using only the lower portion of the volume control's range with normal recordings. If your amp has 10 dB of excess gain, for example, -40 dB below 0 dBFS on the volume control is -50 dB below full volume. The channel balance error will likely be much greater and more audible. Some products get around this problem by using digitally controlled electronic volume controls that can maintain better channel balance at low settings but these can add distortion and often controlled by up/down buttons rather than a simple knob. Stepped precision attenuators are another solution but are expensive and sometimes their step size is too great.

 

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GAIN CALCULATIONS

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HOW DO YOU CONVERT FROM Gain Ratio X TO dB? The math requires using a function known as base 10 logarithm (LOG on a calculator). But you can also just use an online dB calculator:

• Online dB Calculator
• Gain in dB = 20 * LOG₁₀ ( Gain Factor ) [i.e. 20 * LOG₁₀ ( 4 ) = 12 dB]
• Gain Factor = ANTILOG₁₀ ( Gain in dB / 20 ) [i.e. ANTILOG₁₀ ( 12 / 20 ) = 4X]

HOW MUCH GAIN DO I NEED? This comes down to only three things:

• How much voltage your headphones need
• How much output your source has
• How much excess gain you want.

HEADPHONE REQUIREMENTS: For a given pair of headphones, the More Power? article helps determine what your headphones need. This is related to the sensitivity and impedance of your headphones which vary widely. The most efficient IEMs only need about 0.1 volts to play loudly, Sennheiser HD600s need about 2.3 volts and Beyer DT880-600s need about 6 volts or 60 times more than the IEMs.

SOURCE OUTPUT LEVEL: Sources have a maximum output level. It's the output voltage at 0 dBFS (the loudest digital music can get) and at full volume (if the source has a volume control). Sources can be roughly divided into the follow categories (all voltages are Vrms):

• Portable Players - Most of these have a maximum output of 0.5 - 1.0 volts from either their headphone jacks or LOD (Line Output Dock) connectors. The iPod Touch is 0.5 volts from the LOD.
• USB Powered DACs - Most of these have a maximum output of 1.5 volts or less.
• Normal Home Audio Gear - The Redbook standard for any home equipment that plays digital audio is 2 volts. Some go slightly higher up to 2.5 volts. There are also a few USB powered DACs that can manage similar voltages (such as the HRT Music Streamer II).
• Unusual (rare) Home Sources - A few companies, arguably unwisely, have decided to go well above the established standard and output more than 2.5 volts. But I'm not aware of any that go above 3.3 volts unless they have a volume control.
• Balanced Outputs - These can be misleading because balanced outputs normally have twice the output of unbalanced outputs. A 4 volt balanced output, used with an unbalanced adapter or cable, is really only 2 volts.
• Unknown Sources – See DIY Gain Measurements below.

CALCULATING THE REQUIRED GAIN: Once you've figured out the above three requirements, it's fairly easy to calculate the gain you need. Just follow these steps (examples are given for the HD600's driven from an iPod LOD with 3 dB excess gain):

• Calculate Minimum Gain: Gain Factor = Vout / Vin [i.e. 2.3Vout with 0.5V Vin = 2.3/0.5 = 4.6X]
• Convert To dB: Minimum Gain in dB = 20*LOG( Gain Factor ) [i.e. 20*LOG(4.6) = 13.2 dB]
• Add Excess Gain: Final Gain in dB = Minimum Gain + Excess Gain [i.e. 13.2 + 3 = 16.2 dB]
• The result is 16.2 dB (6.5X) of gain for the example case.
• You can also multiply 4.6X by 1.4 to get 6.5X (1.4 is 3 dB excess gain as a ratio)
• If you know the output impedance multiply by (Zload + Zout) / Zload

INPUT OVERLOAD: Also be aware that many devices, especially portable ones, have inputs that can be overloaded by certain sources. Because the Redbook standard is 2 volts, a lot of devices are designed to only handle about 2.1 volts such as the FiiO E9 desktop amp. And the portable FiiO E7 overloads at about 1.2 volts on the input because it was designed for use with portable players which are generally under 1 volt. Sometimes the input overload point may depend on the gain settings. So check the documentation for a given amp--especially if you plan to use home sources with a portable amp, or sources with more than 2 volts of output.

RESISTOR VALUES: Some amplifiers let you set the gain by changing resistor values. The diagram to the right shows a typical non-inverting amplifier stage. The gain is given by 1 + 1000/500 = 3. For all the math, see Wikipedia Gain and Wikipedia Amplifiers. Some amplifiers may have multiple gain stages, in which case you have to multiply the gain of each stage together. So an amp with a 2X and 3X stage has a total gain of 6X.

DIY GAIN MEASUREMENTS: If you have a decent DMM (multimeter) that can measure x.xx volts AC (i.e. 0.01 volt resolution) you can play back a 60hz 0 dBFS sine wave and measure the output of your source in Vrms. You can create the file with Audacity. Ideally the voltage should be measured using a “Y” cable with your source connected to the amplifier. You can then also (carefully so not to cause short circuits) measure the output of your amplifier. Don’t connect your headphone as they could be damaged. And don’t try higher frequencies as most meters are not accurate much above 60 hz. Vout/Vin = Gain

BOTTOM LINE: Gain is important. There's a definite sweet spot for most headphones and sources. The closer an amp comes to having the ideal gain, the better overall performance you will get.

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

Sennheiser HD 650

REFERENCE CLASS? Sennheiser bills the HD 650 as “Reference Class”. For anyone writing reviews having solid references is important. That’s partly why I bought a Benchmark DAC 1 Pre. While my Denon AH-D2000s are respected in some circles, they’re not all that well known which reduces their usefulness as a reference. A few months ago I added a much more popular headphone to my collection: The Sennheiser HD 650. After dozens of hours of listening to a wide range of music I’m rather impressed but, I have to admit, they’re a bit of an acquired taste.

CHOICES: I wanted headphones revealing and accurate enough to expose subtle differences among different gear. They also needed to be compatible with typical headphone amps which rules out Stax and other electrostatics. References get more respect when they’re well known and well regarded. That eliminated the more obscure contenders like the Audeze LCD-2. And I wanted something that was not only revealing but I’d also enjoy listening to for hours on end. That ruled out ruthlessly analytical headphones like the AKG K701 and uncomfortable ones like the popular Audio Technicas. I ended up narrowing my choice to the Beyer DT880 and the Sennheiser HD 600/650/800. The DT880s, while quite nice, suffer from some of the same problems as my DT770s. That left the trio from Sennheiser.

THREE FLAGSHIPS: It’s hard to dispute the popularity of Sennheiser’s top headphones but there are endless debates on the internet about the relative merits of the HD 600, HD 650 and HD 800. Chronologically, the HD 600 was originally the top of the class (based on the discontinued but immensely popular HD 580). Then the HD 650 was added as a new flagship. And, most recently, Sennheiser went over the top with the HD 800. To make things more complicated, near as I can tell, not all HD 600s and HD 650s sound the same. Sennheiser has apparently made various production changes along the way. Some even claim HD 600 drivers have been used in HD 650s and visa versa. See the Tech Section for some further evidence. Perhaps the 600s and 650s had more obvious differences in the past, but listening carefully to the current crop, they’re three peas from the same pod. Published measurements back that up.

MAKING A CHOICE: I ultimately chose the HD 650 over the HD 600 because, to my ears, it’s the more pleasant of the two for extended listening with typical source material. And the HD 800, while generally more impressive, it’s hard to justify the roughly three times higher price. The 600 and 650 are already approaching the point of diminishing returns.

BASICS: The HD 650s are full size circumaural (around-the-ear) headphones with an open back. They don’t provide much isolation from the outside world, and the outside world may hear whatever you’re listening to. And the HD 650’s earcups are tilted in a way that makes wearing the headphones “backwards” immediately apparently if you accidentally put them on wrong. You also get a nice hinged permanent storage box with a foam insert.

SENNHEISER PRICING POLICIES: The street price for the HD 650 has gone up with Sennheiser cracking down on dealers excessively discounting their products. They’re now refusing warranty work unless you can prove you purchased from an authorized dealer. And authorized dealers are restricted to what’s known as MAP—a Minimum Advertised Price. The MAP appears to be around $500 while the MSRP (list price) is $650. If you find a price much lower than $450 it’s probably either for reconditioned headphones or it’s not an authorized dealer. If you don’t care about the warranty, there are better deals to be found although even used prices have gone up. Be cautious, however, of possible counterfits—especially for the HD600. Chinese HD600 fakes may also explain some of the larger than life differences some claim between the 600 and 650.

COMFORT: If you read my DT770 review, you know I’m big on headphone comfort. A lot of headphones sit more on the ears rather than over them. And even headphones that sit over the ears can still be uncomfortable because they’re too heavy, have a poor headband design, get sweaty, etc. The 650s are relatively light and have breathable velour covered earpads to combat any sweat problems. Likewise the headband pads seem to work well over the long haul. The 650s, as delivered, had a bit more clamping pressure than I’d prefer. Sennheiser increased the force over the HD 600 supposedly in the interest of better sound. But to my head, after a few hours, they became somewhat uncomfortable. But there’s a fix…

PRESSURE TWEAK: Wanting a bit less head squeezing, I very carefully bent each of the metal portions of the headband (one at a time) just enough to lessen the pressure a bit. And now they’re very comfortable although still not quite a match for the even lighter HD 590s. If you try this, be extremely careful not to put much pressure on the plastic portion of the headband or earcup supports as the plastic can break. The foam in the earpads also seems “break in” and soften making them more comfortable with time. I didn’t notice a huge change in the sound, but if you press lightly while listening to simulate the tighter clamping you can hear some subtle differences. So I’d try the 650s “as is” first. And if they’re uncomfortable, only then consider trying to bend them.

CABLE & PLUG: The HD650 uses a split “Y” style replaceable cable. It’s a 4 wire cable to better isolate the left and right drivers. Other headphones, like the HD590, share a common conductor in a 3 wire cable. Some prefer “side entry” like the 590 and DT770 but that only works well if it’s on the side your source is. The cable on the 650 is notably higher quality, softer, and less microphonic than the thinner and stiffer cable on the 600. If you like to spend money on snake oil (see Subjective Debate) there are several third party cables available. Unlike nearly every other headphone I own, the HD 650 has a 1/4” large plug and comes with a pigtail adapter for use with 3.5mm mini jacks.

AESTHETICS & BUILD QUALITY: I’m not much into bling and tend to emphasize function over form. For example, it’s frustrating when products are compromised in the interest of looking better or different—like the flat keyed “island” keyboard pioneered by Apple that slows down typing. And the new HD 598 with its Pimp My Ride treatment is less comfortable than the older HD 590 it replaces. But, that said, I have to point out the HD 650s don’t look and feel like $500 headphones. They’re almost entirely plastic, the glossy somewhat mottled paint looks tacky, “Sennheiser” is cheaply silkscreened onto the headband in giant letters, and the HD 650 badges are seriously cheesy. Mine were made in Ireland and whoever painted them probably had a few too many pints at lunch. As a point of reference, the AKG K701 and Denon AH-D2000 both cost less but use higher quality materials and seem more high-end.

DRIVER BREAK IN: A few readers challenged the idea of breaking in my Beyer DT770s as being audiophile myth. So with the HD650 I decided to see if I could measure a change. I tested them right out of the box and again after 48 hours of break in. There was a small but measureable change in the bass resonance. I don’t know if it’s audible but at least the concept has some basis in objective reality. See the Tech Section for more.

INITIAL SUBJECTIVE IMPRESSIONS: I thought the HD 650 had a pleasant honesty and openness upon first listen but otherwise it didn’t make a strong first impression. To me, they’re warm, mellow, and rather laid back. It’s neither sterile and analytical like say the best Etymotics, nor exciting and enhanced like the Beyer DT770 or some of the Ultrasones. But there’s more going on than is initially obvious. And, in some ways, I think the HD 650’s main strength lies in what’s missing from what you hear. Here’s the best analogy I can think of…

POLARIZED SUNGLASSES (seriously!): Have you ever compared regular and polarized sunglasses while driving a car or out on a lake? The polarized variety dramatically cut glare and reflections. The best sunglasses remove more of what you don’t want (glare) letting you see more of what you do want. In harsh conditions, they actually enhance your vision. Believe it or not, that describes what I like most about the Sennheiser HD 650. They seem to remove glare, sibilance, harshness and other obvious flaws that are so common in many (especially pop) recordings and somehow reveal more of the music. At first, the lack of harshness can leave music sounding a bit lifeless in comparison to other headphones. But, for me, much of what’s missing usually turns out to be unwanted anyway. And once you’ve adjusted, it translates into an amazing lack of long term listening fatigue. I find myself hearing things I never noticed before.

LONG TERM LISTENING: I’ve spent hours at a time listening to the HD 650s driven from my Benchmark DAC1 Pre on all sorts of music and they’re really easy to live with. After listening to them for an hour, switching to any other headphone sounds just plain wrong. That’s partly human nature and how our brains work. But the interesting thing is the reverse isn’t nearly as true. Listening to the Beyer DT770 for an hour and then switching to the 650, instead of sounding wrong, the 650s might sound a bit dull in comparison but their strengths are immediately apparent. There’s an honesty to the 650’s sound my brain seems to immediately recognize and latch onto. And, after just a few minutes with the 650, I have no desire to go back to the Beyer.

COMPROMISES: Using yet another car analogy, on a brand new glass smooth road even a hardcore sports car can deliver a fairly smooth ride. But on more typical roads that are worn, patched, potholed, etc. a big luxury car delivers a much smoother ride. You can’t have razor sharp handling and an ultra plush ride. It might not be as exciting, but if you want to cover 500 miles of choppy worn freeway, most would consider a good luxury car the more pleasant choice. The Sennheiser HD 650 is the Mercedes S Class of headphones. The big Mercedes makes bad roads seem better than they really are while still delivering an accurate and precise driving experience and the 650 does the same with typical flawed recordings. Few roads are glass smooth and most music is is not very well recorded, mixed and mastered. Both are a great solution to a very common problem. But a Mercedes S Class isn’t a Porsche 911. And, on the right roads, the Porsche can put a bigger smile on a car enthusiast’s face. But stuck in traffic or spending hours on the freeway the Mercedes is the better choice. The same is true here. For the best recordings there are more exciting headphones than the HD 650. But in the real world, with a large variety of typically recorded music, the 650 is hard to beat if you like an honest, relatively accurate sound.

THE FLAWED TUBE ANALOGY: Some have said the 650’s sound is “tube like” but I can only partly agree and it’s a critical distinction. Some tube gear has a similar “warm” sound often caused by the frequency response of the output transformers and/or a higher output impedance. But tube gear also typically has much higher distortion (euphonic or otherwise) and that distortion, if anything, masks details in the music along with the flaws. The 650 does the opposite and isn’t masking anything with added grunge. It has extremely low distortion and reveals more detail in the music.

A HINT OF OBJECTIVITY: I used my failed attempt at a poor man’s fake measurement “head” (a box with an embedded microphone) to level match the headphones using pink noise driving two at a time from essentially identical sources with a near zero output impedance. In short, I tried to level the playing field as much as possible. I listened to the same track on the 650 and the comparison headphone, switching back and forth as necessary, noted the differences, and moved on to the next track and repeated the process for a total of five very different pieces of music. Rinse, lather and repeat for the other headphones and you have at least a relatively fair subjective comparison.

SENNHEISER HD 590 vs HD 650: The HD 590 was my previous open-backed reference headphone. The HD 650 is slightly less efficient needing a few dB more volume. The first few times I swapped back and forth the 590 seemed a bit more “alive” due to a brighter high-end and an increased “presence” through part of  the midrange. The 650 sounded a bit boring in comparison. But focusing on some female vocals I quickly decided the midrange on the 650 is much closer to what a female voice is supposed to sound like. And then I noticed the 590’s brighter high end is mostly added harshness in the high frequencies rather than actual HF content from the recording. The HD590 shares this trait with the Beyer DT770 but it’s less obvious without a proper reference like the 650. The bass is very similar between the two headphones on most recordings. But if there’s really deep bass down low the HD 650 does a better job. And the 650 is more open and spacious—which is saying quite a bit as the 590 is no slouch in that area. The 650 ultimately comes across as more honest, with a vastly better midrange, and significantly less fatiguing. But the 590 is still the most comfortable headphone I own being lighter than the 650. Sennheiser has gone backwards in the comfort department.

DENON AH-D2000 vs HD 650: The Denons are my closed back reference and are significantly more sensitive (efficient) than the HD 650. The D2000 has a more forward and intimate sound than the 650. Instead of sitting 10 rows back, it’s like you’re on stage and the musicians have huddled around you. It’s a different perspective but it’s otherwise tough to fault the Denons when listening to clean recordings. I’d say the Denon’s lower midrange and upper bass is subjectively more accurate than the 650. Like the 590, the Denon is brighter in the highs but it’s a cleaner sort of bright. But it’s still a double edged sword and, in my opinion, the Achilles heel of the Denon. On less than ideal source material the D2000 shines a relentless spotlight on high frequency flaws. The sound is more strident and can become fatiguing much quicker. The lower bass is a bit more exciting on the Denon while the upper bass is more accurate but its overall similar to the 650. So, for me, it mainly comes down to the Denon’s slightly “cooler” midrange, brighter highs, more intimate soundstage and much less forgiving nature. On clean source material they’re both very pleasing headphones in their own ways. For evaluating gear and recordings, I think the Denons are the better choice. But for enjoying typical mass produced music, the Sennheisers get my vote for their ability to smooth over the rough edges. The Denons are also significantly less comfortable because they rest more on, rather than over, the ear with their oddly shaped ear pads. They’re also heavier.

BEYERDYNAMIC DT770 PRO 80 vs HD 650: The sensitivity is close but the HD 650 is slightly more power hungry. Much like with the 590, a quick switch with the DT770 makes the 650 seem flat and boring. The punchy deep bass and “enhanced” highs of the Beyer provides an even greater contrast. And, while there’s some initial appeal to the Beyer’s lively sound, the emphasized highs mean much greater fatigue. The highs suffer from the same problem as the HD590’s only worse. It’s mostly a fake sense of detail and, to my ears, is more distortion than music. The Beyer’s upper midrange isn’t nearly as natural as the 650’s. And when I listen to the 650 for a while and go back to the DT770 its like viewing an oversaturated photo that’s been heavily tweaked in Photoshop. Some might like the enhancements, but I find myself preferring the more realistic original. I will confess, on certain music, I do enjoy the DT770’s pyrotechnic deep bass. And, when driven from a low impedance source, I think the 770’s upper bass and lower midrange are probably more accurate than the 650’s. Subjectively, the 770’s bass emphasis is much lower down the spectrum avoiding the “warm” bias of the HD 650. In terms of soundstage and openness the 770 is at least in the same league but not as transparent. Without the exaggerated thump, sizzle, and grunge, the 650 is easily more revealing. I notice many more subtle details in recordings than with the DT770. The comfort is very similar.

SENNHEISER SIBLINGS: I don’t own the HD 600 or HD 800 but I did get to spend some time with each and compare them to the HD 650. There are probably a million words already written on the 600 vs 650--complicated by the fact Sennheiser has apparently changed both along the way—but here’s my two cents worth along with an HD 800 comparison:

HD 650 vs HD 600: To my ears, the current HD 600 has noticeably less deep bass, a slightly “cooler” balance through the midrange, and a bit more sparkle (and perhaps a bit of harshness) in the highs. But the difference is not nearly as dramatic as many have argued. More significant to me, on less than pristine source material, the HD 650 is more forgiving with significantly less listening fatigue. I also prefer the slight increase in bass although, ideally, I wish the emphasis was confined to the deepest bass more like with the DT770. Despite their more forgiving nature, the 650 doesn’t give up much in the way of resolution or detail over the 600—everything is still there, it’s just presented in a slightly warmer and more flattering way. In terms of pure accuracy, however, the 600 is probably the winner. If I only listened to audiophile recordings I probably would have chosen the cheaper HD 600 instead. The comfort is the same as my headband tweaked 650.

HD 650 vs HD 800: To me, the HD 800’s highs sound more like the the HD 600 while the deep bass sounds more like the HD 650. So, in some ways, it’s the best of both. The 800 is also better made and has a much higher bling-factor for those who care about such things. The 800 seems even more revealing than the 600 while the angled drivers and larger earcup volume contribute to a more spacious sound. For an ultimate reference headphone, the 800 easily wins and I would love to own a pair. But if I have to choose just one for listening to typical real world music, I think the 650 is a better compromise. Comfort is close, but to my head the esoteric 800 is actually a bit less comfortable.

SOURCE REQUIREMENTS: The HD 650 has a high impedance (300 ohms) and needs more voltage than most portable devices and PC headphone outputs can provide. Generally you need about 2 volts RMS (5.7 volts peak-to-peak) for wide dynamic range music at realistic levels. PC and portable audio gear is typically limited to around 1 volt or less with many managing only about 0.5 volts. So you might need a headphone amp. While the 650 may deserve better, even the $20 FiiO E5 can manage about 1.3 volts which might be enough for many tastes. The FiiO E9 can do a great job with the 650 as its 10 ohm output impedance is relatively insignificant compared to 650’s 300 ohms and the E9 has a very healthy 7 volts of output. For more, see my blog articles on amps and impedance.

CAUTIONS:  If you prefer a more exciting and/or a brighter sound, the 650 might not be a great choice. Serious thump and sizzle fans are even more likely to be disappointed. And if you’re looking to reveal flaws (say for mixing work) the 650 is probably too forgiving and polite. The HD 650 needs more than an iPod to play loud enough for most tastes. The Denon D2000 is much more efficient and easier for most gear to drive. Also remember the 650 has a large 1/4 inch plug and requires a bulky adapter to use with portable gear.

MEASUREMENTS: See the Tech Section for an impedance plot and a few other details. But, lacking an artificial head, I don’t have a way to measure full size headphones properly. So I present measurements from HeadRoom instead.

FIRST CLASS:

• Very low listening fatigue
• Makes marginal recordings much more enjoyable
• Detailed and revealing sound
• Relatively accurate (leaning towards warmth)
• Very comfortable

ECONOMY:

• Might be too laid back for some tastes
• Some excitement lost with the best recordings
• Aesthetics and build quality don’t match the price
• Relatively expensive
• May need a dedicated headphone amp

BOTTOM LINE: If a lack of audible fatigue with nearly all music and physical comfort are important, the HD 650 should be on your short list of headphones under $500. If you listen to them, give yourself some time to adjust as it’s easy to confuse a lack of high frequency distortion with a lack of high frequency musical content. Once acclimated, my ears often hear more of the music with the 650 but that wasn’t immediately obvious on the first listen. Their ability to improve the sound of typical recordings is, in my opinion, their greatest strength. But just like a luxury car’s smooth ride comes with a price, the HD 650 is probably not quite as much fun as some other headphones, including the Denon AH-D2000, on pristine source material. I’m ultimately in this hobby for the music. And I don’t want to be restricted to the very limited selection of audiophile-grade recordings to thoroughly enjoy an expensive pair of headphones. So I value the HD 650’s ability to make vast quantities of margin recordings more enjoyable without masking musical details. But as an ultimate reference headphone, I think it falls a bit short.

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TECH SECTION:

SPECS: The Sennheiser provide specs are:

• Impedance : 300 ohms
• Cable: 3 Meters (10 feet) with 1/4” plug
• Sensitivity/Efficiency: 103 dB at 1 V RMS
• THD: 0.05%
• Weight: 9.2 oz (260 grams)
• Frequency Response: 10 – 39,500 hz (darn, I was hoping for 40,000 hz!)

IMPEDANCE & PHASE ON SIMULATED HEAD: Here’s the impedance and phase on my “simulated head” which is really just a head-sized multi-layer damped box with a microphone embedded in one side. In this case, it’s just closing off the earcup and you can see the bass resonance is around 90 hz. The minimum impedance is a bit above 300 ohms and peaks around 500 ohms. As proof something is going on over the years with Sennheiser making changes, HeadRoom measured a peak of about 450 ohms lower down at 70 hz. Some of the difference could be due to HeadRoom using a true HATS (head) but even wearing the HD 650 on my own head and running the plot it looked a lot like it does here so I suspect there have been changes to the drivers:

BREAK IN: To see if there are measurable differences before and after break-in I made several measurements when the 650 was new right out of the box. And then I ran them at moderately loud volume for 48 hours and repeated the measurements. I went so far as to leave them undisturbed on my “simulated head” the entire time. I also rechecked the measurements in open air and with them on my head and the difference was consistent. The bass resonance shifted slightly lower by a few hertz and that’s what you might expect as the driver’s suspension loosens up a bit. Imagine a new pair of shoes being stiff and after you’ve worn them for a while they break-in and flex easier. That’s roughly what’s likely going on here. That said, the difference in resonance frequency is so slight it’s hard to imagine it’s audible. But it’s possible other characteristics, like distortion, also improve with break-in. Collectively all the changes together could be audible. And it’s very possible other headphones, with different driver designs and suspensions, would show much bigger changes after break-in:

DRIVE REQUIREMENTS: I used an oscilloscope with a very fast update rate to capture peak signal values playing various music while listening to the headphones. As mentioned in the main article above, I think most people would be very satisfied with about 2 volts RMS of drive capability (5.7 volts peak-to-peak). This exceeds what you can get from typical 3.7 volt Li-Ion battery powered gear, or 5 volt USB/PC powered audio devices. The FiiO E5 and E7 use a DC-DC charge pump to generate a negative power supply rail to increase their output but still manage only around 1.3 volts RMS which is likely enough for typical compressed pop music, but might clip on wide dynamic range music like classical or audiophile jazz recordings. The HD 650 ideally deserves an amp with a proper split power supply like the FiiO E9 or even a good dual battery Cmoy. But it will need enough gain to get up to at least 2 volts from whatever your source can manage (typically at least 4X or about 12 dB).

HEADROOM FREQUENCY MEASUREMENTS: The Frequency Plots at HeadRoom show the HD650 has extremely low distortion and very similar frequency response to the HD600 and HD800 and even the Denon D2000. But you can see about 5 dB of enhanced bass compared to the HD600 and a significant dip above 10 Khz. A lot of the bumps and dips from 2 khz to 10 Khz are related to reflections and standing waves in the earcup. In my tests, just moving the headphones around slightly can make a big difference in this range. The brain seems to largely filter these reflections out while the measurement microphone cannot. So it’s best to draw an imaginary line through those peaks and valleys yielding an average trend. If you do that, you can see the Denon D2000 is probably the most accurate of the 4 headphones shown in the link followed by the HD800.

HEADROOM DISTORTION PLOT: Headroom’s Harmonic Distortion Spectrum is a bit odd in how the frequency axis is scaled. But it shows, for a low frequency signal, the distortion is below –90 dB which is an amazing result as that’s about 0.003%! I’ve seen similarly low distortion measurements of the 650 elsewhere. This is lower distortion than many amplifiers and helps bust the myth that headphones always have far more distortion than electronics. Some proponents of tube gear, singled ended amps, and zero feedback amps, like to believe the relatively high distortion of their amp is OK because headphones always distortion even more. But it’s far from true.

HEADROOM SQUARE WAVE: The 500 hz Square Wave Response shows typical overshoot and subsequent ringing but is a fairly decent result. If you draw an averaged line through the ringing, the square wave is fairly flat which implies accurate midrange frequency response. For comparison purposes, see the popular Grado SR 80. The Grado looks much less like a square wave.

AN EQ EXPERIMENT: I tried using highly configurable parametric EQ to tweak my Denon D2000s to be similarly forgiving and I failed. When I filter out equivalent amounts of sibilance and harshness with the Denons, more of the music is gone and the result sounds veiled and artificial. The HD 650, to my ears, somehow works more like polarized sunglasses. They largely remove what I don’t want while revealing more of what’s left. It’s not just a simple frequency response difference. My objective side wants to pin down what’s going on but I don’t have a full explanation besides the HD 650’s lack of distortion.

MEASUREMENT SUMMARY: As with speakers, headphone measurements only tell part of the story. In this case they show you may well need an amp to properly drive the HD 650, they share frequency characteristics with the HD 800/600 and have very low distortion. They also help validate claims Sennheiser has changed the design over the years. And, just barely, I’ve shown a measurable difference before and after break-in. But I can’t fully explain their ability to improve poor recordings with little loss of detail. I might do better if I had a proper artificial head and conducted more acoustic measurements comparing the HD 650 to say the Denon D2000. But, for now, I’m happy to just enjoy the HD 650.