Headphone & Amp Impedance

INTRO: The output Impedance of headphone sources is one of the most common reasons the same headphones can sound different depending on what they’re plugged into. This important parameter is rarely specified by manufactures but can make a huge difference in sound quality and headphone compatibility.

HEADPHONE IMPEDANCE MOVED: This article used to be about both output impedance and headphone impedance. But, in the interest of shorter articles, I’ve split them. So if you’re looking for info headphones, please see:

• Headphone Impedance Explained

THE SHORT VERSION: All you really need to know is most headphones work best when the output impedance is less than 1/8th the headphone impedance. So, for example, with 32 ohm Grados the output impedance can be, at most, 32/8 = 4 ohms. The Etymotic HF5s are 16 ohms so the max output impedance is 16/8 = 2 ohms. If you want to be assured a source will work well with just about any headphone, simply make sure the output impedance is under 2 ohms.

WHY DOES OUTPUT IMPEDANCE MATTER? It matters for at least three reasons:

• The greater the output impedance the greater the voltage drop with lower impedance loads. This drop can be large to enough to prevent driving low impedance headphones to sufficiently loud levels. A real world example is the Behringer UCA202 with a 50 ohm output impedance. It struggles with some 16 - 32 ohm headphones.
• Headphone impedance changes with frequency. If the output impedance is much above zero this means the voltage delivered to the headphones will also change with frequency. The greater the output impedance, the greater the frequency response deviations. Different headphones will interact in different, and typically unpredictable, ways with the source. Sometimes these variations can be large and plainly audible.
• As output impedance increases electrical damping is reduced. The bass performance of the headphones, as designed by the manufacture, may be audibly compromised if there’s insufficient damping. The bass might become more “boomy” and less controlled. The transient response becomes worse and the deep bass performance is compromised (the headphones will roll off sooner at low frequencies). A few, such as those who like a very warm “tube like” sound, might enjoy this sort of under damped bass. But it’s almost always less accurate compared to using a low impedance source.

THE 1/8th RULE: To minimize all three of the above problems, it’s only necessary to keep the output impedance less than 1/8th the headphone impedance. Or, put another way, just divide the headphone impedance by 8 to get the maximum output impedance without potential audible degradation.

IS THERE A STANDARD FOR OUTPUT IMPEDANCE? The only standard I’m aware of is IEC 61938 from 1996. It specifies an output impedance of 120 ohms. There are numerous reasons why this is standard is way out of data and a really bad idea. In a Stereophile article about headphones, they said of the 120 ohm standard:

“Whoever wrote that must live in a fantasy world.”

I have to agree with Stereophile. The 120 ohm standard might have been (barely!) tolerable before the iPod and other portable music sources became immensely popular, but it’s not any more. Most headphones are designed very differently today.

PSUEDO STANDARDS: A lot of professional gear has a 20 – 50 ohm headphone output impedance. I’m not aware of any that follows the 120 ohm IEC standard. Consumer gear tends to be in the range of 0 – 20 ohms and, with the exception of tube and certain other esoteric designs, most high-end audiophile headphone sources are well under 2 ohms.

THE iPOD INFLUENCE: Since the 120 ohm standard was published in 1996, music players advanced from lo-fi cassette tape and skipping portable CD players to the massive iPod craze. Apple helped take high quality audio portable and there are at least half a billion portable digital players in circulation not including phones. Nearly all portable music/media players now run from a single cell Li-Ion battery. These batteries only produce a bit over 3 volts which means you typically get less than 1 volt RMS of audio output driving typical headphones (sometimes much less). If you add 120 ohms to the output, and use typical portable headphones (nearly all of which are in the range of 16 –32 ohms) the headphones usually won’t play loud enough. And most of the battery power is wasted as heat in the 120 ohm resistor. Only a small fraction of the power makes it to the headphones. That’s a big problem in portable audio where getting the best battery life from ever smaller devices is critical. It’s much more efficient to deliver all the power to headphones.

HEADPHONE DESIGN: So what output impedance do headphone manufactures design for? As of 2009 well over 220 million iPods had been sold. The iPod, and similar portable players, are the 800 pound gorillas in the headphone market. So, not surprisingly, most manufactures started designing many or all of their headphones to work well with the iPod. That means they’re designed to work with an output impedance under 10 ohms. And higher-end full size cans are most often designed for sources that follow the 1/8th Rule or have a near zero output impedance. I’m not aware of any current audiophile headphones intended for home use designed to the ancient 120 ohm standard.

THE BEST HEADPHONES ARE DESIGNED FOR THE BEST SOURCES: If you do a quick survey of the most well reviewed high-end headphone amps and DACs, they nearly all have very low output impedances. Examples are products from Grace Designs, Benchmark Media, HeadAmp, HeadRoom, Violectric, etc. It only stands to reason that most high-end headphones are designed to be at their best with similar products. Some of the most highly regarded headphones have relatively low impedances including several models from Denon, AKG, Etymotic, Ultimate Ears, Westone, HiFiMAN and Audeze. All of these, as far as I know, were designed to be used with low (ideally near zero) impedance sources. I’ve also had a Sennheiser representative tell me they design their audiophile and portable headphones for zero ohm sources.

THE FREQUENCY RESPONSE PROBLEM: If the output impedance is more more than 1/8th the headphone impedance there will be variations in the frequency response. With some headphones, especially balanced armature or multi driver designs, these variations can be rather extreme. Here’s what 43 ohms of output impedance does to the Ultimate Ears SuperFi 5’s frequency response—a total, and very audible, variation of 12 dB:

 

10 OHM OUTPUT IMPEDANCE: Some might look at the above example and think it’s extreme with a 43 ohm source. But plenty of sources have around a 10 ohm output impedance. Here’s the same headphones with a 10 ohm source—there’s still a very audible 6 dB of variation. This sort of curve creates weaker bass, a “glaring” midrange emphasis, muted high frequencies, and odd phase characteristics due to the sharp “notch” at 10 khz that can alter spatial perceptions:

 

FULL SIZE SENNHEISERS: Here are the full size, higher impedance, Sennheiser HD590 cans with the same 10 ohm output impedance. Now the variation is only a bit over 1 dB above 20 hz. While 1 dB isn’t that much, it’s right in the most “boomy” bass region which is the last place most want any sort of emphasis:

 

DAMPING EXPLAINED: Any dynamic driver, in a speaker or headphone, moves back and forth with the music. That’s how it creates sound and they all have moving mass. The laws of physics say an object in motion tends to stay in motion. Damping is used to help avoid unwanted motion. Without going into too many details, if a speaker is under-damped, it keeps moving after it should have stopped. And if it’s over-damped (rare) its ability to accurately follow the signal is compromised—imagine a speaker trying to operate submersed in maple syrup. There are only two ways to damp a driver—mechanically and electrically.

BOUNCING CARS: Mechanical damping is much like the shock absorbers on a car. They add resistance so when you hit a bump the car doesn’t keep bouncing up and down long after the bump. But they also add harshness because they reduce the suspension’s ability to accurately follow the road. They’re a compromise—soft shocks give a softer but more bouncy ride and stiff shocks control the bouncing better but make the ride harsher. Mechanical damping is always a compromise.

ELECTRICAL IS BETTER: There’s a better option to control unwanted motion of headphone drivers and it’s called electrical damping. The voice coil and magnet of the driver work with the amplifier to control the motion of the driver. This kind of damping has fewer negative side effects and allows headphone designers to create headphones with less distortion and better sound. Just like a car suspension that can better follow the road, an optimally damped headphone driver can better follow the audio signal. But, and this is the critical part, electrical damping is only effective when the output impedance of the amplifier is much lower than the impedance of the headphones. If you plug 16 ohm headphones into an amp with a 50 ohm output impedance, there will be almost no electrical damping. That means when the driver is supposed to stop moving it might not. The headphone is more like a car with worn shock absorbers. If the 1/8th Rule is followed, however, there will be sufficient electrical damping.

A SPEAKER ANALOGY: Back in the day, before my time, speakers were mostly driven by amplifiers that used tubes instead of transistors. Tubes are high impedance devices that operate at high voltages so nearly all tube amps use output transformers. Without going into all the details, tube amps had widely varying output impedances that were often significant and violated the 1/8th Rule. Speaker manufactures couldn’t rely on amplifiers having a low enough impedance to provide much electrical damping. This compromised speaker design much like headphone design is compromised today if a headphone designer can’t rely on a low impedance source for proper electrical damping.

ACOUSTIC SUSPENSION: In the 1970’s the situation changed as solid state amplifiers became popular. Almost all solid state amps easily pass the 1/8th Rule. In fact, most pass a 1/50th Rule—their output impedance is generally below about 0.16 ohms—known as a damping factor of 50. Suddenly speaker manufactures were free to design better speakers that could take advantage of these much lower output impedances. And the first really good acoustic suspension sealed box speakers like the original AR's, Large Advents, etc. were developed. They had deeper and better bass than any of their tube-powered predecessors could manage from a similar box size. It was a big milestone in "hi-fi" to rely on lots of electrical damping from the amplifier. It’s too bad many headphone sources are 40+ years behind.

WHAT OUTPUT IMPEDANCE DOES MY SOURCE HAVE? Some manufactures make it clear they strive for a low output impedance (such as Benchmark), while others specify the actual output impedance of their products (such as Behringer does with the UCA202 at 50 ohms). And most, sadly, keep it a total mystery. Some product reviews, such as the ones on this blog, include measurements of the output impedance as it’s critical to the sound of the device with various different headphones.

WHY DO SO MANY SOURCES HAVE A HIGHER OUTPUT IMPEDANCE? The most common reasons are:

• Headphone Protection - More powerful sources with a low output impedance might be capable of delivering too much power into low impedance headphones. To help protect such headphones, some designers raise the output impedance. This is a compromise to try and have the amp adapt to the load used. But it comes at a big price with many headphones. A better solution is offering two gain options The low gain setting can lower the maximum output voltage when using low impedance headphones. And, in addition, active current limiting can be used so the source will automatically restrict the maximum output into lower impedance headphones even if the wrong gain setting is used. 
• To Be Different - Some manufactures raise the output impedance on purpose claiming it makes their source sound better. Sometimes “different sells” as it’s a way to differentiate the sound of their product from their competitors. But, in this case, the particular “different sound” you get is entirely dependent on which headphones are used. With some it might be an improvement and with others it’s more likely a big step backwards. The odds greatly favor degrading the sound.
• It’s Cheap – A higher output impedance is a band-aid for many inexpensive headphone sources. It’s a cheap way to achieve stability, a crude form of short circuit protection, and it can allow using an otherwise substandard op amp or output device that would be unable to drive 16 or even 32 ohm headphones directly. By adding some series resistance to the output all these things get “fixed” with a $0.01 part. But the cheap “fix” comes at a substantial price in the sound quality with many headphones.

EXCEPTIONS TO THE RULE: There are a few headphones supposedly designed for significantly higher output impedances. I do wonder if this might be more myth than reality these days in terms of audiophile and consumer headphones as I’m not aware for any specific examples. But it’s certainly possible. If so, using these headphones on a low impedance source might cause under-damped bass performance and a different frequency response than the manufacture intended. This might explain some of the “synergy” claims when certain headphones are mated with a certain source. But those “synergies” are entirely subjective—one man’s “bright and detailed” is another man’s “harsh”. The only way to get consistent performance is to use a low impedance source and follow the 1/8th Rule.

A CHEAP TEST: If you’re wondering if your current source is compromising the sound quality because of an unknown output impedance, consider buying the $19 FiiO E5 amp. It has a near zero ohm output impedance and has enough output for most many headphones under 100 ohms. If it obviously improves the sound, it’s likely your source has an output impedance that’s too high.

BOTTOM LINE: Unless you know your particular headphones sound better with a specific higher output impedance, it’s best to always use a source with an output impedance no higher than 1/8th the impedance of your headphones. Or, to make it even simpler, an output impedance of 2 ohms or less.

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TECH SECTION:

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IMPEDANCE VS RESISTANCE: These two terms are used somewhat interchangeably, but technically there are some significant differences. Electrical resistance is represented by the letter “R” and has the same value at all frequencies. Electrical impedance is more complex and its value typically changes with frequency. It’s represented by the letter “Z”. For the purposes of this article, the unit of measure for both is Ohms.

OUTPUT IMPEDANCE DIAGRAM: The diagram below shows the effect of output impedance. The blue circle on the left above represents a “perfect source”, the blue resistor (zig zag line) in the middle represents the output impedance. And the resistor on the right represents the load impedance (the headphones). If the output impedance is not zero, the voltage produced by the source will be reduced when a load is connected. The higher the output impedance, the greater the drop in voltage at the load. This drop is given by the formula: Load Voltage = Source Voltage * ( Zload / ( Zload + Zout) ). For more information see Wikipedia Voltage Divider.

VOLTAGE AND CURRENT: It’s important to have at least some understanding of voltage and current to understand impedance and this article. Voltage is analogous to water pressure (i.e. PSI) while current is analogous to the volume of water (i.e. gallons per minute). If you let water run out of the end of your garden hose with nothing attached you get a lot of flow (current) and can fill a bucket quickly but the pressure at the end of the hose is near zero. If you put a small nozzle on the hose the pressure (voltage) is much higher but volume of water is reduced (it takes longer to fill the same bucket). The two are typically inversely related. High pressure usually means low flow and visa versa. The same is true of voltage and current. The relationship between voltage, current, and resistance (and for the purposes of this article, impedance) is defined by Ohm’s Law. Substitute Z for R.

WHERE DOES THE 1/8th RULE COME FROM? The smallest audible difference most can hear is about 1 dB. For the output impedance to create a -1 dB change, you have antilog(-1/20) = 0.89. Using the divider formula from above, when the output impedance is 1/8 the load impedance you get 0.89 or a 1 dB drop. Headphone impedance can vary by a factor of 10 or more over the audio band. The SuperFi 5 is rated at 21 ohms but varies from 10 ohms to 90 ohms. So the 1/8 Rule gives a max output impedance of 2.6 ohms. Assuming a 1 volt source we get:

• Headphone Voltage at 21 Ohm Nominal Impedance = 21 (21+2.6) = 0.89 volts
• Headphone Voltage at 10 Ohm Minimal Impedance = 10 (10+2.6) = 0.79 volts
• Headphone Voltage at 90 Ohm Maximum Impedance = 90 (90+2.6) = 0.97 volts
• Frequency Response Variation = 20*LOG(.97/.89) = 0.75 dB (under the 1 dB goal)

MEASURING OUTPUT IMPEDANCE: As seen in the diagram above the output resistance forms a voltage divider. By measuring the output voltage with no load, and with a known load, you can calculate the output impedance. This online calculator makes it easy. The no load voltage is the “Input Voltage”, R2 is the known load resistance (don’t use headphones), the Output Voltage is the loaded voltage. Click Compute and R1 is the calculated output impedance. This can be done using a 60 hz sine wave file (Audacity can create such a file), a Digital Multi Meter (DMM), and a 15 – 33 ohm resistor. Most DMMs are only accurate around 60 hz. Play the 60 hz sine wave file and adjust the volume for about 0.5 volts. Then attach the resistor and note the new voltage. For example, 0.5 volts with no load, and 0.38 volts with a 33 ohm load gives an output impedance of about 10 ohms. The math is: Zout = (Rload * (Vnoload - Vload)) / Vload

REACTIVE LOADS: Few headphones represent a purely resistive load that’s constant over the audio band. Instead, they’re reactive loads and represent a complex impedance. Because of the capacitive and inductive elements in headphones their impedance changes with frequency. For example, here is the Super Fi 5’s impedance (yellow) and phase (white). The impedance is only 21 ohms below about 200 hz. Above 200 hz it climbs to nearly 90 ohms at 1200 hz and then drops down below 10 ohms at 10 Khz:

FULL SIZE CANS: Some are not interested in IEMs like the Super Fi 5’s so here the impedance and phase for the popular Sennheiser HD590. It still varies from about 95 ohms to nearly 200 ohms—a range of 2X:

THE MATH: Earlier a graph was shown demonstrating about 12 dB of frequency response variation for the SuperFi 5’s driven from a 43 ohm source. If we take their rated impedance of 21 ohms as the reference level, and assume a 1 volt source, the voltage at the headphones will be given by:

• Reference Level: 21 / (43 + 21) = 0.33 V and we’ll call that 0 dB.
• At their minimum impedance of about 9 ohms it’s 9 / (9 + 43) = 0.17 V = – 5.6 dB
• At their maximum impedance of 90 ohms it’s 90 / (90 + 43) = 0.68 V = +6.2 dB
• Total Variation = 6.2 + 5.6 = 11.8 dB

DAMPING LEVELS: The damping of a headphone driver, as explained earlier, is either entirely mechanical damping (Qms) or a combination of electrical (Qes) and mechanical damping. The total damping is known as Qts. How these parameters interact at low frequencies is explained by Thiele Small modeling. Damping can be generalized into three categories:

• Critically Damped (Qts = 0.7) - This is widely considered ideal as it provides the deepest bass extension without any frequency response variations or excessive "ringing" (uncontrolled driver motion). The bass from a critically damped driver is often described as “tight”, “quick”, and “clean”. Q of 0.7 gives what most consider the ideal transient response.
• Over-Damped (Qts < 0.7) - This keeps even tighter control over the driver but at the expense of less deep bass (the response rolls off sooner). So manufactures rarely intentionally over damp their products.
• Under-Damped (Qts > 0.7) - This trades off some low bass extension for a peak at higher bass frequencies. The driver is also no longer well controlled and exhibits excessive "ringing" (i.e. it doesn't stop soon enough when the audio signal stops). Under-damping creates frequency response variations, less deep bass, poor transient response and an upper bass peak. Under-damping is a cheap way to provide the illusion of more bass at the expense of the quality of the bass. It's frequently used in cheap headphones and speakers to provide "fake bass". Under –damped headphones/speakers are frequently described as having "boomy" or "sloppy" bass. If your headphones were designed for electrical damping, and you use them with a source impedance greater than 1/8th their impedance, you will get under-damped bass.

TYPES OF DAMPING: There are three ways to damp the driver and control resonance:

• Electrical Damping – This is known is Qes and it’s something like regenerative braking on on hybrid or electric car. When you hit the brakes, the electric motor slows the car by turning into a generator and sending the energy back to the battery. A driver in a headphone (or speaker) can do the same thing. But as the output impedance of the amplifier goes up, the braking effect is greatly diminished—hence the 1/8th Rule.
• Mechanical Damping – This is known as Qms and, as explained earlier, it’s more like the shock absorbers on a car. As you add mechanical damping to a driver, it resists the musical signal driving it, and becomes more non-linear. This increases the distortion and degrades the sound quality.
• Enclosure Damping – The enclosure can provide damping but this usually requires either a sealed enclosure, one with a tuned port, or one with a controlled restriction. Many of the best headphones, however, usually are open backed. This largely eliminates the headphone designer’s option of using the enclosure to provide damping as is done with speakers.

EAR CUP LOADING: For headphones that form a fairly consistent seal, such a fully circumaural over the ear headphones with earpads that fit snuggly against the head, the designer can somewhat rely on the “enclosure” formed by the ear cup to possibly provide some damping. But the shape of heads, ears, type of hair, headphone positioning, eyeglasses and other factors make it highly variable. And this option isn’t available at all for all the supra-aural (on the ear) headphones. Here are two graphs of the Sennheiser HD650 impedance. Note the open air bass resonance peaks at about 530 ohms but drops to 500 ohms on a simulated head. This is due to damping provided by the ear cup enclosure and the ear pad.

FINAL WORDS: Hopefully I’ve made it clear the only way to get consistent performance between headphones and their source is to follow the 1/8th Rule. While some may prefer the sound using a higher output impedance, that’s very specific to each particular headphone, the particular output impedance, and the person’s own subjective tastes. Ideally a new standard should be developed and manufactures should be encouraged to design headphone sources with an output impedance below 2 ohms.