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# calculating the amp you need. Example with the AKG Q701

Hi Guys,

This is my first post here, I've been thinking about buying the AKG Q701 but I got really confused in the amping needs for this headphones, all threads are full of 200+USD recommendations that I'm just not going to spend without a real reason behind it. So I started a real research in amps-headphones matching.

I'm an electronic engineer, so I understand how an amp affects an electric signal, and it affects it in such a deterministic way (mathematical), it does not have an effect on the "openess" and the "sonic" performance of the headphones, it just make your source strong enought to drive your headphones. So for those who feel like poets when talking about amping: I really would like them to understand the science behind it before giving their opinions without understanding everything.

To calculate the amp you need there are some things that you need to know before selecting it:

1. desired volume level in dBSPL (decibels of sound pressure level).

2. headphone sensitivity in SPL/mW (milliWatt): it means the amount of sound level that your headphones produce with 1mW of input power

3. Headphones impedance: I won't explain what impedance means electrically, I will just say is a relation between voltage and current in a circuit with a determined impedance (mostly constant).

1. volume: The sound level you would like should be between 105dB and 115dB depending on the compression level of the music you hear. If you want audiophile sounds at levels that will harm your ears if you leave it like that for enough time may be you would choose 115dB, but for me, just a guy that loves listening music during long periods of time I think 112dB SPL is enough.

2. headphones sensitivity: for the AKG Q701 there are two ways in which I found the sensitivity of them. one was 105SPL/V (the same as 105dB/V) and other one was 93dB/mw. Actually you need the latter to make the calculations easier. The first one is just a trick of AKG to inflate this phones sensitivity and make them more buyable.

3. Headphones impedance: this data is easy to get, for the AKG Q701 the impedance is 62 ohms

Now lets get to the real calculations. The volume level you selected is the amount of sound pressure you would like to have in your ears when listening music, taking in mind that you will use the less compressed music you already have (lets say flac classical music). So your mission is to make your amp+headphones sound that hard in your ears without having distortion. The equation behind it is:

dBSPL (desired volume in dB) = headphones sensitivity (in dB) + 10*Log(max power of your source-amp in mW)

From here you will want to calculate the maximum power of your amp so that you can go out and search for it while you understand why did you choose that amp. For my case and the AKG Q701 the equation should look like this:

112dB (volume) = 93dB/mW +10*Log(power of the amp you need in mW)

so if you solve for the power you get:

power of the amp = 10^((112-93)/10)=79.43mW

So we've already found the power you need from your amp, but it is not enough information to select an amp. since P(power)=V(volts)*I(current) you could achieve this power (80mW in my case) with a lot of current and low Voltage or with a lot of Voltage and low current, but real amps have limitations on this variables. For this reason we need to specify the maximum amount of power that we are going to need from the amp but taking in mind the impedance at which this power is delivered.

In less words we are going to need data from our amp and it would be:

1. maximum power at some impedances (i.e 100mW @16ohms)

2. amp output impedance: just make sure that your amp has an output impedance so that the relation between your headphones impedance and this output impedance is more than 10. For example, as the AKG Q701 has an impedance of 62 ohms, you must choose and amp with an output impedance of 6.2 ohms or less. This output impedance is no a big restriction since in general an amp has an output impedance of less than 3 ohms.

with that in mind the cheapest (and actually more than necessary) amplifier that I could see in the market was the shiit magni. It throws an excesive 1000mW at 50 ohms (so at 62ohms it will be more than 200mW that is the limit for the AKG) and it has an output impedance of 1ohm so it won't be a problem either.

The only issue I found it that it does not have a perfectly constant frecuency response, but I'll just let it happen like that since i don't have any more money.

Fellow C/EE here. NEEDS MOAR POWER ERMAHGERD. I have a table that does this as well, but it just uses the '3dB needs twice the power' approximation. If you wanted to hear why people buy amps that have mega overhead for what they need, check out the sound science forum. I don't have an opinion on the subject... I just look for something that meets my input/ouput requirements, a good pairing reputation, from a good brand. My AGD NFB-28 will do ~1.25W SE or 7W balanced into my LCD-2.2F, which is about 124 dB and 132 dB respectively... I haven't tried it balanced yet but will once I make the cable. I'm not sure if I expect to hear a difference.

Oh, and btw, welcome to Head-Fi! Best first post I've seen in quite some time!

And check out the O2 amp as well. The 'O' means 'objective' as in 'science, math, computers'!

Edited by jodgey4 - 6/20/14 at 8:58pm
There are some other variables to consider, though. Like the distortion at the rated output power for the amp. Also the impedance curve of the headphone.
But great post, the most important stuff is covered!
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