Impedance and amplifiers

 

It is variable, and depends on multiple factors. First, headphones have highly variable efficiency. Second, what is "enough power" depends largely on personal preferences and source material (e.g. classical music needs more peak power to sound as loud as pop music because of the lack of aggressive dynamic compression). Finally, the power the "unamplified" source you already have can output may also vary.

 

Quote:

 

Yes, see above. Other important factors are efficiency (sensitivity), and the linearity of the impedance curve. To calculate how loud a headphone can get without clipping (high distortion), you need to know the maximum power, and the efficiency (often specified in dB/mW). The power can be calculated from the impedance and either the maximum voltage, or the maximum current, whichever is reached first (V^2/R or I^2*R) - with a high impedance headphone, this is normally the voltage. The maximum voltage is also affected by the output impedance of the source: Vload = Vout * |Zload| / |Zload + Zout|. Note that these impedances can be frequency dependent, and result in a non-linear frequency response. Once you have the power value, you can calculate the sound pressure from it and the sensitivity.

A practical example: assume we have a source that can output 2 Vrms, has an output impedance of 100 Ohm, and feeds a 600 Ohm headphone that has 96 dB/mW efficiency. For simplicity, let's assume that both impedances are purely resistive for now, it is enough for a reasonable power estimate.

  Vload = 2 * 600 / (600 + 100) = 1.714 Vrms

  Pload = 1.714 * 1.714 / 600 = 4.90 mW

  SPL = 10 * log(4.9) / log(10) + 96 = 102.9 dB

Is that enough ? Well, it depends, but here is an article on what maximum levels one should generally aim for when choosing/building an amplifier.

For completeness, let's also calculate how the above example behaves in terms of frequency response. Assume that the minimum impedance of the headphone is 620 Ohm in the audio range, and the maximum is 740 Ohm, and the phase is zero (pure resistance) at both. The difference in the output level will be:

  20 * log((740 / (740 + 100)) / (620 / (620 + 100))) / log(10) = 0.20 dB

This is a minor change, and does not affect the sound much.

 

You can look for headphone data here. The sensitivities are specified in Vrms/90dB at this page, this changes the calculation as follows (assuming 0.4 Vrms at 90 dB):

  SPL = 20 * log(1.714 / 0.4) / log(10) + 90 = 102.6 dB

 

 

There are a number of practical benefits, some are due to historical reasons. Older sources, before iPods and other low voltage portable devices became common, often had high output impedance, but, being AC powered, did not have much difficulty outputting relatively high voltage. There is also an IEC standard from the 1990's that requires headphone outputs to have an impedance of 120 Ohm. This made high impedance headphones preferable, to improve power efficiency and damping factor.
One reason why some higher end headphones have hundreds of Ohms of impedance is using thinner wire in the voice coil (the resistance of a wire is proportional to its length and a material specific factor, and inversely proportional to the area of its cross-section). This makes the coil lighter, and the sound quality is slightly improved, as reduced moving mass allows the driver to respond faster to changes in the audio signal.

Another advantage of high impedance is that it makes the performance of the drivers less dependent on the output impedance of the amplifier. Keeping the ratio of the speaker/headphone impedance and the amplifier output impedance (the damping factor) as high as possible is generally preferred, as it improves the control over the drivers, dampens resonances, reduces frequency response variations that result from the drivers having frequency dependent impedance, and even reduces distortion. Therefore, with a 120 Ohm source, a 600 Ohm headphone (damping factor = 5) is better than a 24 Ohm headphone (damping factor = 0.2).

With a high output impedance source, there is no use making the impedance of the headphone lower than that of the source, since below that level the power output to the headphone will actually decrease. For example, with a source that outputs 2 Vrms through 120 Ohms, here is what the actual useful power output will be on various loads:

  - 16 Ohm: 3.46 mW

  - 32 Ohm: 5.54 mW

  - 64 Ohm: 7.56 mW

  - 120 Ohm: 8.33 mW

  - 250 Ohm: 7.30 mW

  - 600 Ohm: 4.63 mW

Outputs are sometimes AC coupled (i.e. the headphone is fed through a capacitor), this is needed if the output would otherwise have a large DC offset, and affects the bass response. The lower the impedance of the load, the more rolled off the bass will become. For example, the combination of a 100 uF capacitor and 16 Ohm load results in a bass roll-off with the -3 dB point at about 100 Hz. But with a 250 Ohm load the cutoff frequency moves down to about 6 Hz.

Amplifiers generally have worse distortion performace with low impedance loads. Common op-amps are usually not rated for loads below 600 Ohm - this does not mean that anything less will not work, but the distortion will increase. Good amplifiers for low impedance headphones have buffered outputs that can supply the higher required current with low distortion.

Finally, with a high impedance headphone, the signal to noise ratio may be better at the same output power, since doubling the output voltage with the volume control usually results in less than double noise voltage.

 

But the most important one of the above are probably the compatibility with high output impedance sources, and making the voice coil as light as possible (although there are also low impedance high end headphones now, so it may not actually be that important).

 

To follow on stv014's excellent reply - there is also a sound production reason for high impedance cans, and that is in a studio environment, it meant more headphones could be driven from a single amplifier or distribution point, without overloading the circuit. So you tended to see that on a lot of "studio" versions of headphones. Not relevant to most users, but interesting. 

Simply, because I'm not sure I understand the ins and outs very well, there ends up being a bit of an inverse relatinship. 

 

 

High impedance headphone:  requires more voltage but less current

Low impedance headphone:   requires less voltage but more current

 

Small battery portable devices have a hard time generating much voltage, but can push current (batteries are little current machines) through - so they pair better with Low impedance headphones). 

Desktop (especially tube) amps, are the other way around. They are high voltage devices - and you can add other high impedance headphones then without requiring a significant addition in current requirements. Broadcast headphones, for instance, can be as high as 2000 ohms, the upshot being that if you plug them into an active circuit, it doesn't affect other things on the circuit as much (plenty of voltage to go around) - no noticible drop in volume. But if you start plugging in speakers, or 24ohm headphones, each one is going to pull more current to get up to volume, and will cause a drop in available current to other devices (and if broadcasting, a noticeable drop in volume). 

 

That's my understanding anyway. 

 

Here is an example. 

 

For a headphone to receive 4 watts of electrical power (this is almost never the case, just a simple example) it can be driven by:

1. 1 Amp @ 4 Volts , or
2. 4 Amps @ 1 Volt.

therefore if 1 Volt draws 4 Amps of current the headphone has an impedance of:

Impedance = Voltage/Current (or Z = V/I)

therefore Z =1/4 Ohm. 

Based on Z=V/I, we can deduce that Case 1 will have an impedance of 4 Ohms, and Case 2 will have an impedance of 0.25 Ohms.

Again, this is just an example, headphone impedances are actually much higher.

 

So a high voltage system can take that 1 amp and really power it through pretty efficiently... but when you start adding in low impedance headphones, the required amperage (current) will go up, and that's harder on most amps to generate (and will create a lot of heat, among other things). 

 

Some general details here:

http://www.head-fi.org/a/headphone-impedance

Edited by liamstrain - 1/19/12 at 9:14am

 

R = resistance

Z = impedance

 

Both are the ratio of voltage and current, but impedance is a more general concept, and accounts for the possibility of the voltage and current being out of phase with an AC signal. Therefore, Z is actually a complex number, that has a real and imaginary component (or you can also view it as having a magnitude and phase, those are what you can see on the InnerFidelity impedance graphs - a phase of zero means pure resistance), and it can vary as a function of frequency. Resistance is the real part of impedance, a simple (ideal) resistor has only resistance. The imaginary part is called reactance (X), and depending on its sign, it is either inductive or capacitive. |Z| is the absolute value or magnitude, it equals to sqrt(R^2 + X^2).

For real, effective power that does actual work, only resistance is relevant. V^2/Z and I^2*Z are the apparent power (in VA), multiplying that by R/Z gives the real power (in W, V^2*R/Z^2 or simply I^2*R).

 

Higher impedance needs more voltage for the same power (which in turn depends on the efficiency for any given sound pressure, but not on the impedance), but less current.

 

Edited by stv014 - 1/19/12 at 9:32am

So I've been wondering, does the amount of impedance have anything to do with how a headphone sounds? Or rather, does that have anything to do with how a headphone sounds because of the way an amplifier's circuitry is? I mainly mean that since tube amps are more proper for higher impedance cans since they put out voltage, and since tube amps have a more inherently pleasing sound (in my opinion of course), does that ultimately make higher impedance cans sound better?

No, an engineer can make a high impedance version sound very close to the low impedance version or make it sound completely different, i.e. better or worse.
Btw, there's no point in generalizing everything as in the post above.

It's generalized statements like "high impedance headphones are hard to power" or "amp topology X sounds better" that are simply wrong. But the youngsters on the forum will pick up on them and spread them because they don't know better. Which is why I ask you to be a bit more specific, thanks.
Edited by xnor - 2/9/12 at 1:21am

No I'm trying to find why I'm enjoying my Crackhead tube amp so much (with Senn HD600)... The reason i'm curious about this topic is cause I sure as heck can't drive my LCD-2s with it, I'd have to get something far more expensive (as far as tube amps are concerned).

OTL amps put out a lot a voltage, but not a lot of current. The LCD-2 need a lot of current (but not a lot of voltage). With a tube amp, to drive big Orthos, you will need a "transformer coupled" amp (like the Bottlehead Smack). 

 

Ultimately the voicing of the headphone is more or less independent of the decision to go with high current/low voltage or low current/high voltage (though there may be some manufacturer trends when models is offered in different impedances). Orthos being the exception that they will always need more current, just by virtue of the type of driver. 

Edited by liamstrain - 2/9/12 at 10:22am

The Crackhead has an output impedance of 120 ohms. With the HD600's ~300 ohm impedance and large bump in the impedance curve the amp gives a boost of about 1.2 dB at 90-100 Hz, with the boost dropping along that curve. That extra bass and bass impact is giving you a warm coloration that you enjoy. That's in addition to any other colorations the amp adds on its own, like second order harmonics or frequency response variations.

 

You don't get that coloration with the LCD-2. You also get greatly reduced voltage because of the high output impedance vs. the LCD-2's low impedance, and you're probably introducing unwanted distortion and driver ringing (I've heard (I think from stv014) planars aren't affected as much as dynamics by electrical damping, I don't have the know-how to say for sure myself).

Not really.  Most of the new ones are that way but they don't have to be.  Plenty of the old Yamaha orthos were rated at 125 or 150 ohms and consequently don't need tons of current delivery but do need a fair bit of voltage and even work well from the Crack.  I have one as well as a Yamaha YH-3

 

All the new orthos are fairly insensitive anyway so the need plenty of voltage as well but physics dictates that such voltage also requires more current at their low impedances and the combination can more than some amps can handle.

Ah - thanks for the clarification, maverickronin. 

Thanks a bunch Liam/Head Injury. Makes sense