The science behind amping, can someone explain?

No, impedance doesn't work that way.

The classic example is the Apogee Scintilla speaker. It has a 1.2 Ohm impedance. Easy to drive? Oh, hell no. The Scintilla overheats and literally melts amps not up to the task.

There are four factors to consider:

1. The amp's output power
2. The amp's output impedance
3. Headphone impedance
4. Headphone sensitivity

Impedance only tells you how well power transfers from the amp to the headphones. It's like connecting pipes of different diameters. Connect a 1" pipe to a 3" pipe and you're going to lose water pressure, right? It's a little more complicated than that, but you get the idea. Now, knowing that the hesdphones have, say, a 3" pipe going into them, that tells you nothing about the water pressure or volume of water going in. You need to know the diameter of the pipe coming out of the amp, the volume of water and water pressure coming out of the amp, and how much water the headphones require.

More practically, you want an output impedance lower than headphone impedance. Finding this out can be tricky since not all manufacturers will tell you, especially those who make OTL tube amps. Those almost always have a high output impedance. Sales literature will tell you that they work with "anything" but don't believe it. Tube amps with output transformers almost always have a low output impedance, like solid state.

The difference between output impedance and headphone impedance is called the Damping Factor. You want a high one. There's some argument (of course) about how much is enough. But keep it low, most agree on that.

However, even if you have a great damping factor, the amp's output power might not be enough to fully drive headphones. Throwing 250mW at a K-1000 doesn't work too well. You have to look at the output power, consider how that is modified by impedance (you can lose power with a bad impedance match) and take the power that gets through to see if there's enough considering the headphone's sensitivity.

These figures don't tell you everything.

First of all, the impedance is a complex value, there's areal part which is the resistance, and an imaginary part which is both the capacitance and the inductance. Summing it up to one number is an oversimplification. Capacitive and inductive behaviors are difficult to predict but the resistive part is easier. Usually, it's the resistive part that gets quoted, besides even the resistive part varies depending on the frequency, for example, the HD650 peaks at more than 600 ohms despite being rated at 300 ohms.

Sensitivity also varies according to frequency.

Besides what you should also pay attention to is the unit for the sensitivity, dB/mW or dB/V, they are not the same. Power = voltage squared / impedance. And you get 6 dB louder if you double voltage and 3 dB louder if you double power. For example I can tell you that the K701 is rated at 105 dB/V or 93 dB/mW. Compared that to the sensitivity of the Sonny MDR-Z1000 (108 dB/mW), and you see that the AKG is not a sensitive headphone).

PS: Does anyone know how sensitivity is measured for headphones? With speakers, it's usually at 1 m distance, what is it with headphone? If I want to compare the relative sensitivity of speaker transducers and headphone transducers, how should I proceed?
Edited by khaos974 - 7/10/11 at 10:48pm

I believe there are standards for headphone couplers - they have cavities in front of the mic that emulate the ear canal's acoustic filtering

they are always measured with something standing in for the head - you have to seal the ear cups, establish the same air volume, distance you would have with them on your head 

Thanks, so there's no direct formula to convert it to dB/W @1m,

There's a whole channel separation, slew rate, rise 'n fall time, etc. things going on.

Instead of using whatever headphone chip inside the iPod, you pull the Line signal and feed it into a dedicated box with a couple of AD8397's and a dedicated, well-engineered power system. Right there you get more isolation from whatever other things that are going on in that iPod.

There's also current and voltage stability things.

You gotta take these sensitivity specs with a grain of salt. It already has been pointed out that some manufacturers use dB/V instead of dB/mW, sometimes they don't even tell you what they chose.

And afaik, these specs are made by testing sensitivity with a single sine wave (1 kHz, sometimes 500 Hz).

This.

 

For example, the HD650s and K701s are rated at dB per volt, not milliwatt.  That would put their dB/mW (which you would need to compare to the ATs) ratings in the mid 90s.  I'm to lazy to do the math right now though...

Also too lazy to read a few posts above I see...

It sure is a shame that we're not always given both sensitivity ratings in dB/mV and efficiency ratings in dB/mW for every headphone (or speakers, minus the "m")...  Not to mention impedance curves (though we're lucky most established headphones have been measured)...

 

And if amp manufacturers would always state the gain, output impedance, maximum voltage (rms rather than swing, which is just annoying to have to convert), and maximum current output of their amps...

 

Well, I can dream of a world where manufacturers make it easier for consumers, can't I?

Edited by BlackbeardBen - 7/14/11 at 2:19am

Take a look at the manua of the Benchmark Dac 1, every manufacturer should do the same.

How did I miss that?  Oh well.  You didn't mention the Senns though, so it least it still serves a purpose...