Headphone Measurements Explained - Electrical Impedance and Phase

This plot shows the electrical impedance and phase plot for the Sennheiser HD 580.

Introduction
The fundamental DC resistance in a pair of headphones is primarily due to the length and thinness of the wires in the voice coil of the driver. The longer and/or thinner the wire, the more resistance it has. This resistance is a constant and will not change with the frequency of the applied signal.

In this article, we're primarily going to discuss the reactive nature of the headphone driver as an electrical load on the amplifier driving it, which is expressed as impedance and is essentially additive to the resistance of the voice coil. Impedance is somewhat like resistance in that it can be expressed in Ohms, but it's quite different in that it is "reactive" and the impedance in Ohms can change depending on the frequency applied. Here's how that happens.

Imagine a pendulum that swings at a rate of once per second or 1Hz (its natural resonant frequency). We now mount a motor on it and drive the motor with a 1Hz signal. Because this is the resonant frequency of the pendulum the motor doesn't have to do much work; it only needs to add enough energy to prevent the decay of the swinging motion.

Now imagine we try to send the motor a signal to drive the pendulum a little slower at 0.8Hz. In this case, the pendulum will always be fighting to go a little faster than the drive signal, and the amplifier driving the motor will have to resist being drug ahead to the faster natural rate of the pendulum. Remember, the motor is also an electrical generator, and the pendulum wanting to swing ahead of the drive signal will create its own reactive electrical motive force that the amplifier will have to damp in order to maintain the desired signal.

This is the fundamental difference between resistive and reactive loads: in resistive loads the impedance remains constant; in reactive loads, the load will "fight back" by producing back EMF (electro motive force) that will vary depending on the frequency.

Now imagine we try to drive the pendulum at 1.2Hz—faster than its natural resonant frequency. In this case, the pendulum will fight to slow down, and the amplifier will have to apply more voltage to overcome the pendulums effort to retard the drive signal.

Looking at the Sennheiser HD 580 electrical impedance and phase plot above, we can see the driver's primary resonance on the impedance plot (purple line) as a large peak centered at about 90Hz. This is analogous to the natural swinging rate of the pendulum discussed above.

You can also see the electrical phase, (blue line) starting at the left at 10Hz, slowly advancing in phase (rising on the plot; phase axis labels in degrees shown on right) more and more as it moves higher in frequency towards the resonance. This advancing phase is due to the driver resonance "pulling" the electrical signal towards resonance—similar to when the pendulum pulled towards resonance when we tried to drive it at a slower rate.

As we go through resonance at 90Hz and beyond, we see the phase swing through zero and go negative above resonance. This is due to the driver back EMF fighting against the drive signal and trying to retard it back toward the resonant frequency.

The bottom line here is that as we approach the resonant frequency of the driver from above or below, it fights harder and harder against the amplifier by generating its own counter EMF, making the impedance go higher as we near resonance. At resonance, the driver is most efficiently creating its own EMF, and therefor has its highest impedance to change. This is a little counter-intuitive as this is also the point at which the driving amplifier has the easiest job powering the driver, but remember, it's also the most difficult place for the amplifier to drive the driver away from, and therefore has the highest impedance.

In other words: There is a very close relationship between the impedance and phase plots...so close, that you usually don't need to bother looking at the phase plot as what information can be gleaned from this data is usually available in the impedance plot.

ELI the ICEman
This is a little mnemonic used in basic electronics education to help remember the relationship between voltage and current in a reactive system. The letter E is for voltage, and I is for current; the L is for inductive loads, and the C is for capacitive loads. The mnemonic reminds us that voltage leads current in inductive loads, and current leads voltage in capacitive loads.

In the HD 580 phase plot above (blue line) you can see that the electrical phase angle at 40Hz is advanced about 8 degrees. Because voltage is leading, in this case, we can say the amplifier is seeing an inductive load at 40Hz. At 200Hz, the electrical phase angle is about -7 degrees. Because the electrical signal is lagging behind, we can say the amplifier is seeing a capacitive load at 200Hz.

The voice coil itself is an inductor, but inductors of this size are relatively ineffectual at low frequencies, but can begin to exert its reactance as frequency gets higher. Turning our attention to the right hand side of the plot, we can see that both the impedance and phase angle start slowly rising as frequency gets higher and higher. This is the reactance of the voice coil acting as an inductor coming into play.

Virtually all voice coil (normally called dynamic) drivers will exhibit this slow inductive rise in the high frequencies. Planar magnetic headphones typically do not have coils but rather serpentine driver traces on their diaphragms. Since they are not a coil of wire they are not very inductive, and they do not exhibit this rise in impedance and phase at high frequencies. The one exception is the Oppo brand of planar magnetics, which have a circular pattern of diaphragm traces which do act as an inductor. As we will see later in this article, they do have this slowly rising impedance and phase at high frequencies.

Other Sources of Reactance Indicated in Impedance and Phase
As we've seen, the primary driver resonance creates back EMF that changes the impedance and phase characteristics measured. But there are other sources of resonance and reactivity of headphones that can be seen in the impedance and phase plots.

Many acoustic resonances in the headphone can exert acoustic back pressure on the driver, which will, in turn, be converted to an electrical back EMF which can be sensed in measurements. These can be high frequency resonances in the small areas near and within the driver, or they can be lower frequency resonances in the ear capsule behind the driver, and in the enclosed space between the driver and the ear.

Another source of reactance is the crossover networks of multiple balanced armature IEMs and in hybrid, dual-drive headphones.

Okay, let's take a closer look at some plots.

Impedance and Phase Plot Interpretation
Let's start with a well behaved, open acoustic headphone. I'll repost the HD 580 from the top of the page here:

Headphone101_InterpretingImpedanceResponse_Graph_SennHD600

In open headphone designs, the driver sees very little acoustic damping as it's essentially suspended in free air, which allows it to move without restriction. Almost all open headphones will show a primary driver resonance somewhere in the 60Hz to 150Hz range. The amplitude and narrowness (Q) of this peak can vary widely, however.

Also note that other than the resonant peak and slowly rising response in high frequencies there is very little other features on the plot. This is a good thing; it means that there are few other resonances in the headphone to disturb sonic performance. Also note that the distortion plot (THD+noise) shows very few features pointing to poor performance. It does, however, show rising distortion in the low frequencies in part related to the amplifier having to work hard to drive the load below its resonant frequency.

Sealed Headphones

Headphone101_InterpretingImpedanceResponse_Graph_FocalSpiritProfessional

Plots for the Focal Spirit Professional.

The Focal Spirit Professional shown above is a sealed headphone. In sealed headphones, acoustic damping can act to reduce or eliminate the primary driver resonance. Here we see that in the FSP. There does appear to be a resonance at 3.5kHz, but there is no increase in distortion at that frequency, so this resonance is likely by design. Looking at the FSP measurement data sheet, we can see that there is a rise in frequency response corresponding to this impedance peak. It's very likely this resonance was created to shape the frequency response to have a peak at 3.5kHz, which is desirable as described in the Harman Target Response curve.

Back EMF from Pad Bounce
Headphone101_InterpretingImpedanceResponse_Graph_SennHD449

Sennheiser HD 449, a low-cost, circumaural, sealed headphone.

"Pad Bounce" is a term I use to describe the phenomena of a resonance born from the springiness of the ear pads and enclosed air between the driver and ear. Many headphones have pad bounce, but inexpensive headphones using cheap, springy foam (not memory foam) are quite likely to exhibit the behavior.

In the frequency response plots of the Sennheiser HD 449 shown above, you can see some strong wiggles between 100Hz and 200Hz from a pad bounce resonance. Unusually, you can also see a coincident feature in the impedance and phase plots at about 170Hz. Essentially, the acoustic feedback from this pad bounce is impressing itself on the driver's movement and changing its impedance at the resonance. In my experience, pad bounce doesn't affect the listening experience much.

Planar Magnetic Headphones
As mentioned earlier, typically, planar magnetic headphones do not have a voice coil but rather a serpentine layout of traces on the diaphragm surface. As such, planar magnetic headphones are almost purely restive in nature, and have little reactive properties when driven.

Headphone101_InterpretingImpedanceResponse_Graph_LCD3A

Audeze LCD-3 planar magnetic headphone.

In the Audeze LCD-3 plot above, you can see that the impedance plot is nearly ruler flat at about 115 Ohms. This is typical of planar magnetic headphones.

You can also see a small but distinct feature at 5-6kHz on both plots. Because of its high frequency, this resonance is likely confined in a small space in the driver, somewhere close to the magnets and diaphragm. The thing to note here is that there is a corresponding distortion increase at this frequency.

Here's another LCD-3 plot.

Headphone101_InterpretingImpedanceResponse_Graph_LCD3B

In this plot, you can see the feature in the treble is now at 4kHz, and the corresponding peak in distortion has moved lower in frequency as well. It's interesting to note here that this feature on LCD series cans is much more apparent on models with the Fazor, with the notable exception of the LCD-4 which has a Fazor but no feature at this frequency.

My point here is that it is sometimes possible to relate features on the impedance and phase plots with spikes in distortion. It may or may not have audible effects, but I have to feel that it tends to indicate a design that could be improved upon.

Headphone101_InterpretingImpedanceResponse_Graph_OppoPM1

Oppo PM-1 planar magnetic with coiled traces.

The Oppo PM-1 shown above has coiled diaphragm traces as opposed to the serpentine pattern of most planar magnetic headphones. As such, it does behave a little like dynamic headphones with voice coils, which can be seen in the slowly rising impedance/phase response in the high frequencies as it begins to act like an inductor.

Also, you can see two resonant humps in the impedance at 250Hz and 400Hz. I was told by Oppo that these are the primary driver resonance peaks—one from the center area of the driver, and the other from around the edge area of the driver. Two corresponding peaks in distortion can also be observed.

Impedance Plots Give a Peak at Driver Design Quality
Though headphones are far too complex to closely diagnose problems from InnerFidelity impedance, phase, and distortion measurements, I do find they give a general sense of how well a driver is designed. As mentioned previously, excessive and rough bumps and wiggles in the 2-7kHz region may be evidence of poorly designed acoustics in the small spaces near and inside the driver assembly. The following plots show a clear relationship between rough spots in the impedance and phase plots at 2-7kHz and increases in distortion.

Headphone101_InterpretingImpedanceResponse_Graph_AKGK812

AKG K812.

Headphone101_InterpretingImpedanceResponse_Graph_UltrasoneHFi2400

Ultrasone HFi 2400.

Headphone101_InterpretingImpedanceResponse_Graph_UltrasonePro650

Ultrasone Pro 650.

Headphone101_InterpretingImpedanceResponse_Graph_TakstarPro80

Takstar Pro 80.

In all the above cases, I heard a significant roughness to the response likely due to acoustic problems in and around the driver.

Headphone101_InterpretingImpedanceResponse_Graph_CalHeadphoneSilverado

California Headphones Silverado.

Things are not always so simple however, the above California Headphones Silverado shows a very uneven impedance response, but no apparent relating peaks in distortion—though overall distortion is a bit high. In this case, a look at the entire measurement .pdf does show a significantly uneven frequency response, with feature that do coincide with impedance response features. This headphone simply has poorly designed acoustics broadly, and sounds quite colored with numerous internal resonances probably coming from a variety of sources.

Making the peak at 3.5kHz in IEMs with a resonance.
The concha bowl of your ear creates a resonance at about 3.5kHz that shows up on raw frequency response plots, and is needed for you to perceive the sound as flat through that range. When wearing regular headphones, this peak in response naturally happens because the sound is coming through the concha area in a way similar to normal sound.

But once an IEM is inserted into your ear canal, the concha is acoustically bypassed. IEM makers then need to find a way to artificially produce the peak at 3.5kHz. This is typically accomplished by designing the driver such that it has a natural resonance at 3.5kHz and will then therefore produce the desired peak in frequency response.

Headphone101_InterpretingImpedanceResponse_Graph_EtymoticER4PT

Etymotic ER4PT

The plot above shows the Etymotic ER4PT single balanced armature IEM. You can see there is a feature in the impedance plot in the 2-4kHz region indicating a resonance there. This resonance is designed to provide in increased frequency response, which you can see in the raw frequency response plots as a lovely gentle hump at about 3kHz. Many IEMs, both balanced armature and dynamic driver, will show a resonance in the impedance plot for this purpose. A nifty trick!

Non-Acoustic Sources of Impedance and Phase Response Features

Multiple Drivers - Variations in impedance can occur for reasons other than acoustic resonances. Headphones with multiple drivers will exhibit fluctuations in impedance both from the differing resonances of the various drivers, and from the reactive components (inductors and capacitors) of the cross-over components. Let's take a look at some multi-balanced armature driver IEMs.

Headphone101_InterpretingImpedanceResponse_Graph_VSonicVC1000

V-Sonic VC1000.

Headphone101_InterpretingImpedanceResponse_Graph_PhiatonPS200

Phiaton PS200.

The two sets of plots above are dual-balanced armature IEMs. You can see that the impedance plot is quite complex. I've stared for a long time at multi-BA IEMs and I can tell you that it's not readily apparent from the plots how many drivers are in the IEM. None the less, these are quite obviously more complex impedance plots than the Etymotic ER4PT single BA driver IEM shown above. How about 3 BA drivers?

Headphone101_InterpretingImpedanceResponse_Graph_SonyXBA3iP

Sony XBA 3iP.

Even though the Sony XBA 3iP has an additional driver, it's plots do not look more complex than the two dual BA IEMs above. I assume the complexity of multiple drivers and crossover components make it quite difficult to clearly determine the number of drivers from the impedance plots unless you're quite expert at IEM design.

It's also worth noting at this point that multi BA IEMs can have very large swings in impedance. For example, in the Sony XBA 3iP above, impedance can vary between 10 and 100 Ohms. This can be a big problem if your headphone amplifier has a high output impedance.

Let's say the output impedance of your amplifier is 10 Ohms. With the Sony XBA 3iP, the impedance below 1kHz is about 10 Ohms. That means half the amplifier's voltage will be dropped across the output impedance of the amp, with the other half of the voltage going to drive the headphones. At 8kHz the Sony has 100 Ohms impedance—ten times that of the output impedance of the amp. Now, only about 1/10th of the voltage will be dropped across the amplifiers output impedance, while the other 90% will be available to drive the headphones. In other words, with a high output impedance amp and low, but swinging impedance headphones, as the impedance of the headphone rises, the drive voltage to the headphones will rise. This causes the frequency response of the headphones to vary along with the impedance curve.

Bottom line: if you've got multi-balanced armature IEMs, make double-damned sure you've got a low output impedance amplifier to drive them or you'll end up with a colored listening experience.

Multiple drivers can also be found in regular sized headphones, and will exhibit similar features in their impedance and phase response.

Headphone101_InterpretingImpedanceResponse_Graph_FinalAudioPandoraHope4

Final Audio Pandora Hope 4.

The above plot of the Final Audio Pandora Hope 4 headphone is a hybrid dynamic/balanced armature headphone. I'm not aware of what components exactly are inside, but it's fairly obvious that something is going on 2-3kHz, likely the cross-over point of the headphone.

Other Oddities
And lastly, a couple of odd things you might see perusing InnerFidelity impedance response plots.

Other Components in Circuit - The Audeze SINE is a planar magnetic headphone, and as such ought to have a fairly flat impedance response. As you can see below, there's a significant feature at about 2.5kHz in the impedance/phase response, but no corresponding increase in distortion (in fact, distortion reduces there).

Headphone101_InterpretingImpedanceResponse_Graph_AudezeSine

Audeze SINE.

This feature comes from a small resonant circuit (an inductor and capacitor) used to surpress a peak that would otherwise appear in the frequency response. This small reactive circuit can clearly be seen in the impedance plot.

Active Circuits in Headphones - Many headphones have active electronic circuits in the headphone for bass enhancement or noise canceling. In this case, one often sees very high impedances as the incoming signal is no longer being applied directly to a driver, but is now seeing the input of an electronic circuit—which is often quite high.

Headphone101_InterpretingImpedanceResponse_Graph_BoseQC20

Bose Quiet Comfort 20.

The above shown Bose Quiet Comfort 20 is a noise canceling headphone with the electronics activated. The input impedance to these headphones is around 3000 Ohms in this mode. The impedance rise in the bass may be evidence of capacitive coupling on the input to the analog circuits.

COMMENTS
tony's picture

Applied Physics for audiophiles, phew, betcha you're catching everyone off-guard.

A nice break from my Studies of the Dead Sea Scrolls and the Foundations of Western Civilizations.

You even exampled the lovely HD 580. I'm impressed.

This is definitely my kind of place.

Full Marks for Tyll, thank you!

Tony in Michigan ( about to chain saw a wind downed Locust Tree )

ps. I wonder if you can detail the Impedance of Trump and the Voltage Hilary will need to overcome his momentum?

ultrabike's picture

Impedance is made up of both resistance and reactance. So it is reactance, not impedance, what changes as a function of frequency.

The fundamental difference between resitance and reactance is that reactance indicates the presence of an element that stores energy. Both resistance and reactance will "fight back" the driver.

I don't think one can claim "so close, that you usually don't need to bother looking at the phase plot as what information can be gleaned from this data is usually available in the impedance plot". For one, all of the plots above do not display frequency response phase, but magnitude of the frequency response, and I don't feel I can get frequency response behavior by just looking at the impedance plot. I may draw some tentative conclusions, but I would still bother looking at the frequency response phase plot (or CSD) if something doesn't seem to sound right. Second, as you mentioned towards the end or the article, there are a few "oddities" or exceptions to the rules. Probably because the model simplifies way to much.

There are all kinds of electromechanical driver models spread through out the web (free-air and sealed box). I understand those are perhaps a bit out of the scope of the goals of the article, which I think has a lot of valuable information. But more in-depth understanding may require more advanced books. The "EMF" theory stuff leaves way too much out IMO.

Just my no-body-cares 2-cents.

Josuah's picture

Like ultrabike, I also disagree that impedance and phase are so closely coupled that you can figure one out from the other. You may be familiar with the spiral plot of impedance and phase as an approximation of the difficultly an amplifier will face as a result of the load. Implying that one usually follows the other, which would directly influence the load characteristics seen by an amp, borders on irresponsible.

Also, looking for a link between THD and impedance and phase isn't good enough. You also need to look at it in conjunction with intermodulation distortion. This white paper by Robert Lee of Acoustic Zen has some information on this, under the "Impedance and Phase" section: Acoustic Zen white paper. There are also some research papers you can find via Google and Citeseer.

ultrabike's picture

I wouldn't say that things border on irresponsible.

I feel Tyll is doing his best to make some of this material accessible in layman's terms. This in many cases is very difficult.

I personally want to contribute to help folks better understand stuff as much as possible. I feel I fail way more than Tyll in doing so. And I don't understand many things either.

Josuah's picture

I hesitated to write that it borders on irresponsible, but in the end I decided to do so. Because I feel like it's one thing to gloss over complex details or to simplify some aspects to make it easier for the target audience, but it's another thing to present something that is incorrect and which those people will then take as truth.

A lot of people come to InnerFidelity and trust Tyll's reviews and articles about headphones and audio. And a lot of them only get exposure to technical details through articles like this. I think it is very bad if those people walk away with incorrect information and then start using that as the basis for their discussions elsewhere or for their understanding of audio and purchasing decisions.

It is difficult to provide technical articles that non-technical people can understand. But I think it is still important to make sure you are providing correct information. Even if it is simplified or glossed over.

tony's picture

Geez, since when has Consumer Audio had any source of reliable data?, all we've ever gotten was Sizzle Data.

Tyll makes an "Attempt" at explaining some of the Lexicon of this field, perhaps even a brave attempt.

We two owners of Esoteric Audio tried to explain phono cartridge cantilever compliance to our Turntable owners, my partner had a Phd., you could see peoples eyes tire and glaze over.

Anyone feeling like he should educate the vast group of headphone folks needs all the support we can give.

The fact that people who contemplate Physical relationships actually read this site is impressive to me.

Nice going to everyone, so far.

There's gonna be a test in the morning.

Tony in Michigan

printalert's picture

I like this..