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Confused about headphone impedance
I have a guitar multi effects that has a headphone out with 47Ω
I want a budget somewhat neutral headphone to use with it and I am getting confused with the answers I found so far.
The AKG K240 mk2 (55Ω) seems to be a popular choice with people who own another multi effects (HX Stomp) with a different impedance (I think it's 12Ω).
This headphone is within my budget, but it seems too close to the 47 output of my multifx.
Will I have a problem with this?
I read somewhere that the headphone impedance should be much bigger than the output impedance, but another text I read somewhere explained that they should match closely.
I'm really confused about this.
Impedance is a little bit of a tricky concept. The best analogy I have seen is imagine thin string, one end tied to a chain, making one long length. Move the string up and down to create a wave in the string. What happens when it meets the chain? What if the overall length was all string - or all chain - instead?
In electricity, that energy has to go somewhere; when there's an impedance mismatch, the energy is typically reflected back to the source.
For audio equipment, you typically want to match impedances: this allows the energy from the source to flow to the destination unimpeded.
However - there is an exception. Sort of. If equipment is impedance matched but power-mismatched (ie, headphones can accept 5w but output from an amp is 200w), all that 200w is going to flow to headphones only able to handle 5w and blow them up.
Avoid this situation by using power-matched and impedance-matched equipment.
47:55 should be a reasonable mismatch. Those headphones don't have a single impedance, anyways. See here: https://reference-audio-analyzer.pro/en/report/hp/akg-k-240-mk2.php#gsc.tab=0
Gotcha. But does this happen with headphone outputs? Are there headphone outputs with this much power?
Anyway, the AKG K240 should be a safe choice in my case? According to that link it can go from 55 to 200 and the average is 87.
Generally speaking, no good dedicated headphone output should do or even be capable of that "blow them up" effect unless they are faulty or you are pairing some extraordinarily sensitive IEMs with an amp . Even the most high end headphone outputs should be pushing single digit watts or less, so I'd be more concerned with making sure you don't damage your ears. In the rare cases that you'd consider connecting headphones to a more powerful source like a speaker output, you'd use a resistor to severely limit the power.
As to your question, I think you may be mistaken about what impedance matching means for headphones. It does not mean they should be the same number. The source (amp output) impedance should ideally be lower than the headphone impedance (the rule of thumb I see thrown around is generally a 1:8 or 1:10 ratio). If they are too close or the headphone is higher than the amp, it can lead to some coloration of the sound. That doesn't mean they won't work, it just means that the sound you're hearing may not be exactly how it should, which is obviously important for audio work.
I'm not any sort of audio engineer, I just like headphones so don't take my word as gospel. Please look around at other sources , but here are a few links from a quick web search that may do a better job explaining than I can.
https://www.lewitt-audio.com/blog/impedance-in-headphones
https://north-america.beyerdynamic.com/blog/what-impedance-should-i-choose-for-my-headphones/
According to those links, the headphone being 8~10 higher shouldn't be the ideal?
So for the 47 headphone output of my multifx I would need at least a 400 ohms headphone? This seems a lot. Is there any budget options for this?
47 Ohms is really high impedance for a headphone output and atypical now days, but yes, and this is why Sennheiser and Beyerdynamic make 300-600 ohm headphones for studio use. As an example, my headphone amp has an output impedance of 0.1 Ohm.
Impedance just means you need an amp. Higher impedance means your headphones is effectively seen as a larger load from the point of view of a power supply, ergo you need an active amp.
But why they say you need a headphone with at least 8 times the impedance of the source's output?
The problem is that impedance varies with frequency, you want your headphones to have an (electrically) flat response, and the headphones and amplifier make a voltage divider.
Suppose the amplifier and your headphones are each nominally 50Ω output, but they vary by ± 20% over the audio band. Also suppose for simple math that the amplifier outputs about 1V.
If the impedance of the headphones and amplifier were both exactly the nominal rating, the amplifier would output 1V and the headphones would see 1*50/(50+50) = 0.5V of that.
However, if at (say) 1kHz the headphones are really 60Ω and the amplifier is really 40Ω, then the headphones will instead see 60/(60+40) = 0.6V. If the situation reverses at another frequency, then the headphones will see 40/(40+60)=0.4V. Some frequencies will be 20% louder than they should be, and others 20% quieter.
Now, if instead the output amplifier has low impedance (say 5Ω), the situation is much nicer. The headphones will nominally see 1*50/(50+5) = 0.91V, and at the extremes they might see 1*60/(60+4) = 0.938V and 1*40/(40+6) = 0.870V. The fluctuation is within ±5%, simply because the amplifier output has lower impedance.
There's nothing special about an 8:1 ratio, but it's a reasonable balance balance between noticeable reduction of distortion and technical feasibility at a modest cost.
Thanks! That cleared things up. The 8:1 is more of a safe number to go by.
The output is 47 in my case, so I think a headphone with 250 or more should be fine.
I believe you're most likely thinking of the maximum power transfer theorem, where the concept of impedance matching is a real "strategy".