copyright 1998 by rick chinn. all rights reserved.

headphones, mixers and headphone amplifiers

this article started as a stream of email between myself and rich marcolini. it all started innocently enough when rich asked the following question via the churchsoundcheck listserv:

what headphones do you recommend for live mixing (praise and rock)?

what headphones do you recommend for a drum monitor mix?

- I would like to be able to turn them up really loud if necessary (~1 Watt?)
- Durable
- Hopefully not too expensive

--------------------------------

headphone choice

my preference is the sony mdr-v6 or mdr7506. why? you can make them very loud using the headphone amp found in most consoles. they sound good. perhaps they're not the most accurate phones made, but i've learned to use them as a reference. they are a bit bright sounding, and you just have to recognize this. the seal could be better, but you can turn them up somewhat to compensate.

they may or may not work for a drum monitor mix. it is drummer dependent. they do get loud enough. you may not want a pair of phones that seals well for the drummer. it will help if he can still hear his ambient sound, and the phones won't have to work as hard.

in a pair of headphones, one-watt really doesn't mean anything other than the headphones are capable of dissipating one watt of power without self-destructing. it really has nothing to do with how loud the headphones can get.

what determines loudness?

If you're driving the headphones from a console headphone output, this is usually limited to +/- 15V signal swing internally (power supply limitation). This says that if you want loud headphones, you should ensure that the headphone impedance is less than 150-ohms. The Sony phones, at 63 ohms, work **very** well in this situation.

two things determine loudness: first is the basic sensitivity of the ear speakers used. second is how much power your headphone jack can deliver to the ear speakers. higher impedance phones limit the amount of power delivered by the headphone jack (ohms law).

akg phones sound very good, but typically their impedance rating is 240 ohms or higher. akg may have 'seen the light' and lowered it, but if you're going to run the phones from the console's headdphone jack, (a recent check at a dealer said that they haven't seen the light.) you need to aware of this.

try before you buy!

to get a pair of phones really loud, you have to know something about the circuit that is driving the phones.

let's use the mackie headphone amp since i'm familiar with it. the mackie headphone amplifier uses two halves of a 4560 ic opamps in parallel, with 120 ohm resistors from each opamp output to the phones jack. it take 4 opamps to drive a pair of stereo phones in this situation.

since the 120 ohm resistors each source current to the jack individually but are driven by the same signal, you can consider them to be connected in parallel. so, this means that the headphone amplifier has an output impedance of 60 ohms.

if you plug in lower impedance phones, you get less voltage across the phones (load) because you're creating a voltage divider based on the output impedance of the phones amp and the impedance of the load. classic impedance matching theory tells us that you get maximum power transfer when the source impedance equals the load impedance.

so, from a power transfer standpoint, the sony phones are ideal. i know from experience that each opamp in a 4560 ic will deliver +22 dbu into its load, within reason.

changing +22 dBu into volts: v = .775 * 10 ^^ (22/20) = 9.75V

we're going to lose signal into the load because the headphone impedance is a substantial fraction of the source impedance. how much will we lose?

loss = 1 + Rs/Rload = 1 + 60/63 = 1.9524

divide the output voltage of the headphone amp by this figure to see what actually gets to the headphones:

9.75 / 1.9524 = 4.99V. Call it 5 V.

so, you can see that by matching impedances, you lost half of the signal right off. now, how much power is that into the ear speaker?

P = E^^2 / R = (5 * 5) / 63 = 396.8 mw

headphone sensitivity is spec'd as x db at 1mw input. so, how many db is this number above 1mw?

dB = 10 * log10(396.8) = 25.99 dB. call it 26 dB.

now, what is the sensitivity of the mdr-v6 headphone? 106 db @ 1mw according to the sony spec sheet (that comes with the phones). so, how loud are the phones with 5v across them?

106 dB + 26 dB = 132 dB.

now, in fairness, you probably ought to drop the number by 10 db, so let's call it 122 db with 10 db allowance for peaks.

now, let's look at the akg 'phones. they're 600 ohms, and 88 db/mw. first the loss,:

1 + (60/600) = 1.1

so the 9.75 v output turns into 8.86v. what power is that?

p = (8.86^2)/600 = 131mW.

how many db above 1mw is that?

dB = 10 * log10(131) = 21.17 dB

so how loud does that make the k240m phones?

88 dB + 21.17 dB = 109 dB.

taking the 10 db peak allowance, that's only 98 db. you can see why these phones aren't considered loud. if you have a power amp that can develop some serious voltage across these phones, you can make them bark. but you're not going to be able to do this with the headhphone amp built into a console.

so, let's see...just how much power? using the sony's as a starting point, let's see what it takes to develop 132 db peak spl with the k240m phones. 132 db is 44 db louder than the phones are at 1mw. so, i've got to deliver 44 db more power. what's that amount to? turning 44 db back into a power ratio:

10 ^^ (44/10) = 25119.

so this means that i have to deliver 25119 * 1mw into the phones in order to get them to 132 db, so this works out to be 25w (which you and i know the akg phones won't take, even on a bet!).

now, this is 25w into 600 ohms, and most power amps that we can buy are rated into a 8-ohm load, so what is the 8-ohm power rating needed?

V = sqrt(P*R) = sqrt(600*25) = 122.47 volts.

now this same voltage into an 8-ohm load will give us the 8-ohm power rating needed:

p = e^^2 / r = (122.47^^2)/8 = 1875 watts!

now the good news is that the amplifier could drive 600/8 pairs of phones.

conclusion

as you can see, if you are dealing with a headphone amplifier that is voltage limited, you're best off with lower impedance headphones that also have high sensitivity. the walkman style headphone fills this bill well.

if you have a moderate-to-large (75w up) power amp for your headphone system, then you can drive phones like the akg k240 to reasonable levels. but getting these phones loud enough to launch them takes a truly prodigious power amplifier.

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