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Looking for a formula?! If an amp gives 100 mW into a 32 ohm headphone, then how many into a 70 ohm headphone? (for example)

Discussion in 'Sound Science' started by imackler, Apr 22, 2011.
  1. imackler
    Quite simply, I want to buy an amp for the HD25-1ii.
    But everyone I pm tells me their amp/source has more than enough juice! While they're probably all right, I'm trying to find some concrete grounds for comparing the output power of various amps into a 70 ohm headphone. But really, I want to know a formula that will help me do this for any impedance headphone, whether 32, 70, 80 or 300? Perhaps, there are too many variables to to this well, especially with some amps having different gains. But amp manufactures often list their mW at different ohms; some at 16, some at 32, some at 300. It's not standardized.
    Is there a formula that lets me figure out how many mW each gives at a certain impedance? In my case this time, its 70ohms. But I'm just as curious at 80 ohms, 300 ohms, etc.
    I don't know that this is actually valuable, for myself or anyone else. I'm not saying it sounds good. And I don't know what other variables I need to know. But I'm obsessed now, and I can't go back until I have an answer!
    Here are some of those I've compiled:
    UDAC and UDAC 2 (Portable Amp/Dac)
    Power output: 80mW @ 16-Ohm
    Fiio E5 (Portable Amp)
    Output Power: 100mW (32ohms ); 18mW (300ohms )
    Fiio E7 (Portable Amp/Dac)
    Output Power: 150mW (16Ω); 16mW (300Ω)
    Ibasso D2 (Portable Amp/Dac)
    Output powerUp to 100mW into 32 Ω
    Ibasso D4 (Portable Amp/Dac)
    Up to 230mW into 32 Ω
    Ibasso D6 (Portable Amp/Dac)
    Output power:Up to 650mW into 32Ω
    Soundmagic A10 (Portable Amp)
    Maximum Output Power :  70mW (33Ω)
    E11 (Portable Amp)
    57mW into 250Ohm (From quote from E11 Thread)
    Ibasso T3D
    120mW  (into 32? I'm guessing)
    Ibasso PB1 (Portable Amp)
    1400mW into 32Ω
    Ibasso PB2 (Portable Amp)
    Up to 2500mW into 32Ω
    Ibasso P4 (portable Amp)
    Output power: 600mW into 32
    NFB12 (Desktop Amp/Dac)
    3500mW/25 ohm
    1800mW/50 ohm
    900mW/100 ohm
    300mW/300 ohm
    150mW/600 ohm

    Yulong D100 (Desktop Amp/Dac)
    900mW at 32Ohm
    130mW at 300Ohm
    E9 (Desktop Amp)
    1000mW (16Ω)
     80mW (600Ω)
  2. rroseperry
  3. xnor
    Comparing the specs with the same load, e.g. x mW into 32 ohms, shouldn't be a problem.

    But you cannot simply deduce the output power into 600 ohms if all you've got is for example rated power into 32 ohms.
    The amps are all limited in output current and output voltage and depending on the load you approach those limits.

    Take a look at the D100 specs you posted:
    0.13 W into 300 ohms -> sqrt(39) volts, divide that by 32 ohms and the result is 1.219 W, the specs however say 0.9 W -> sqrt(28.8) volts.
    As the amp is loaded down with a more difficult load the voltage drops.
  4. imackler
    Thanks for the input! I was afraid it wasn't going to be that simple!
    Do you know of any good sources for those who want to read more on the basics of sound technology?
  5. rroseperry
    I asked Gary from Electric Avenues (he makes the PA2V2) about this awhile ago and this was his answer
    Any public library will have a good basic electronics text.
    And there's this book, which is supposed to be pretty complete, though I haven't read it.
  6. JamesMcProgger
    interesting read, I cant help you with the question, but I wanted to tell you to consider the Mni3. Its what I use with my HD25, and its a great amp
  7. monoethylene
    Actually in my opinion these are values to impress the reader. The standard reference in audio is 1mW into a 600 Ohm load which yields to a 0dBm level. Further I think these values are choosen by hazard. Correct me if I am wrong but the 32 Ohm level is normally connected with portable headphones. All in all you cannot conclude an amplification for 600 Ohm for example when you have the value of 32 Ohm. An Example is the Fiio E5:
    Fiio E5 (Portable Amp)

    Output Power: 100mW (32ohms ); 18mW (300ohms )


    Output voltage:


    1.79V @ 32 Ohm

    2.32V @ 300 Ohm


    Without the specs and without a proof it seems to me that there is an internal gain switch.


    Quite sure you can calculate the voltage for the different resistances but this wouldnt be an answer so far. 


    By chance I calculated the values of the 


    NFB12 (Desktop Amp/Dac)
    3500mW/25 ohm
    1800mW/50 ohm
    900mW/100 ohm
    300mW/300 ohm
    150mW/600 ohm


    and this would be an "ideal" amp. The voltage is always about 9.5V. So here you will have for the HD-25 1.29W :)

  8. xnor
    monoethylene, did you read my post? There is no 'internal gain switch' in the E5 afaik.

    What I forgot to mention in my previous post is output impedance. It also affects the amp's ability to transfer power to the load.
  9. tws1
    I recently tried the K701 with an AMB micro amp, just for fun.... Sounded great! Had to turn the volume up quite a bit, but certainly had enough power to get some really deep bass out of the K701. And reading posts from guys scoffing at the lack of power some amplifiers have, and the K701's are really hard to drive unless you have an insanely powerful amplifier, or their bass response will be terrible!....The AMB micro I tried uses a 9V battery..... The differences are incredibly small, no matter how big they seem from reading these forums.
    I think it is too hard to try and compare amps this way because they are all designed so differently. However, 100% of them will power the HD-25's. My iPhone did at the meet... Be more concerned with getting a cracking bargain, build quality, size, what the volume pot feels like, what the amp looks like! Certainly try to avoid working out how much power will be delivered, this isn't really a good representation of how good the amp is. You will notice the size and build quality a lot more, for example, than the 'mw' output into your '70ohm' headphones.
    On a side note, the HD-25's had a massive midbass hump compared to the K701's. Perhaps I just preferred the sound signature of AKG's, but I really didn't go for the physical fit and the sound signature of the Sennheisers. They look awesome, and look like I would love them, but I just didn't...
  10. monoethylene

    Yes, I did..
  11. BlackbeardBen

    Then I don't see what you don't understand?  This is very basic electrical engineering.
    An amplifier is going to have voltage swing limits and current supply limits - if it hits one of those limits at a given impedance (headphone + output impedance), the other limit doesn't come in to play.  For the E5, it's capable of about 2.32 V RMS (going off of your numbers there).  That's only 7.73 mA into 300 ohms.
    But at 32 ohms, if they're saying it's capable of 100 mW, it's at 1.79 V RMS as you've pointed out (or were in the specs).  Obviously that's less than the maximum voltage the amp is capable of (also, remember that audio is AC, so the V RMS we're using is Vpeak/sqrt(2)).
    Why is the voltage swing less for 32 ohms?  The amp can't supply enough current to push the full voltage swing into the low 32 ohm impedance - it's current limited.  You can run the numbers yourself if you'd like, but at 32 ohms it's at 55.9 mA of current.
    If it were to push the full 2.32 V RMS into 32 ohms, the amp's power supply would need to be able to supply 72.5 mA of current - obviously it can't do that.  If the combination of gain from your source and the amp (using the digital potentiometer on the E5) results in a voltage swing into a low-impedance load (headphone) that needs a current exceeding the power supply's capability, you'll get current clipping.
  12. monoethylene

    You are right!! I was too fast.. Got it today..
    BlackbeardBen likes this.

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