Headphones

I am no engineer but what I understand is that impedance is exactly electrical resistance but more or less for a term for AC circuits/analogue devices.

Both inputs and outputs of a device has an impedance.

The impedance of a headphone denotes proportionally the maximum amplitude of a fixed signal that is transmitted to the headphones.

The amplitude of a signal relates to the power and thus volume.

Eg a device with 30mOhm of impedance will be significantly louder than a 39kOhm headphone given that the signal and amplifiers are the same.

Different amplifiers have different ranges of gain. The higher the maximum gain the more the amplifier can “amplify” a signal. I think on data sheets they will make it simple and just state what ranges of impedance an amp is rated for.

It's kind of hard to explain in a useful way if you're not familiar with the fundamentals of electronics.

When an amp applies a voltage across a headphone, a current flows through it that is proportional to the voltage, and inversely proportional to impedance (aka resistance for DC signals). This is Ohm's law.

But by itself, impedance does not tell you very much, it's just one of the variables you need to plug in to figure out the amplifier requirements. It needs to be combined with the sensitivity of a headphone, which is most commonly specified as the sound pressure level you get when you feed a headphone 1 milliwatt of power, or less commonly, the sound pressure you get when you feed a headphone a 1 volt. If you know how much power (current x voltage) your amp can deliver into a given impedance, then you can calculate how loud it will get.

Impedance in layman's terms is how difficult it is to drive a set of headphones, rated in ohm. The more ohm it's rated for, the more volume you need to crank to get the same level of sound. IEMs/earbuds tend to be around 16-40 ohm, perfectly easy to drive with anything. Headphones tend to start from 32 up to 600 ohm. A quick & dirty guide would be up to 70-80 ohm, you can use your phone, laptop, cheapo dedicated audio player (DAP). Beyond that you'd want a dedicated amplifier (expesive DAPs tend to have powerful amp in it).

That's not all though, because there's also sensitivity, measured in dB SPL/mW. Sometimes db SPL/mV which I honestly still don't understand that much. But, the rule of thumb is; the smaller the number in dB SPL/mW, the harder it is too drive. With the "ideal" sensitivity at 100 dB SPL/mW. Can go +/- 10. Sometimes -20.

High impedance headphones were originated from around 1970s when manufacturers can finally make good sounding headphones, but the high price meant they were only viable for studio monitoring application. There are many entwined audio gears in a studio that by the time it reaches the headphones plug, there was gonna be a lot of static noise in the headphones. High impedance will filter out that noise.

The high impedance = good sounding headphones paradigm today still pretty much comes from that 1970s principle. To filter out static noises that might be in the DAC and amplifier. But these days, you can get good sounding headphones with a much lower impedance.

Think of your audio system like a car. Your car's engine needs to provide a certain amount of power to keep it moving down the road, and more power to overcome its inertia and start moving, or accelerate.

Any time energy is transferred between parts in your car, that implies friction. The total friction of the parts in your car is analogous to electrical resistance. But it's not the only thing the car has to overcome. There's things like the wind, the terrain, the gear you're in, etc.

The total of all these components, weighted against each other, is the total factor by which the effort of your engine is being held back. Its impedance, in other words.

If you shift a car into a high gear without letting it gain enough momentum, it'll bog; the efficiency of the whole system will go down. You may not completely come to a stop, and you may recover eventually if the engine is simply allowed to work a bit too hard for a bit, but you don't really want to do it this way.

Similarly, headphones with high electrical impedance *can* run on output sources not rated to handle this impedance. But their performance will be reduced, they won't sound as good, because the signal is too weak, everything has to stumble around to keep up. The typical solution to this is to raise the volume, but then you're left with reduced dynamic range. In general, too little power to a pair of headphones makes them sound dull, dark, or muddy.

Modern headphones are generally pretty low-impedance. This is because the specifics of their design is simply more efficient. Unless a pair of headphones specifically tells you its impedance, you don't generally need to worry about it.

My mother has a PhD in advanced mathematics, so here goes...

Like your mother. Ok, this will be really really shallow but you'll get the idea. I'll throw in a bonus after.

💻 This is your music source (ipod, phone, pc etc..)

⚡ This is the signal (electricity that carries the music)

🎧 These are your headphones (signal goes to these)

So 💻 -----> ⚡ -----> 🎧

The signal carries the music from your ipod to your headphones but because of physics, there are factors that make it harder for the signal to reach the headphones easily. That's impedance. The resistance that makes it harder for ⚡ to get from 💻 to 🎧. If the impedance is higher then it's harder for the signal to get to your headphones, so you need something to help boost the signal like a more powerful amplifier.

So: High impedance headphones = you need a good amplifier to get the most out of your headphones

  Low impedance headphones = a basic should be 
  enough to drive your headphones well

Now the bonus: Sensitivity is another factor that tells you how much power you need for your headphones to be driven but think of it as the opposite

So if your headphones are highly sensitive then it can "hear" the signal better, even if the signal is weaker.

I tried not to use metaphors so I hope this helps. There's more to it, much more, but this will get you by till you're ready to take a deeper dive

Now go to bed. It's late ,😘

Hi Mom! Please turn off The Price Is Right so that I can explain speaker impedance to you. You need to learn why those new speakers which you got for Dad and which you hooked up yourself burned up Dad's amplifier.
Resistance is how hard it is for direct current (DC) to pass through a wire. The DC voltage doesn't matter since the DC resistance will always be the same for a wire. For DC voltage, the impedance is also equal to the resistance. The same is true for direct current (DC) passing through a speaker even though the speaker has a magnet and a voice coil. The measured resistance will be constant, and the impedance will be equal to the resistance.
Things get more complicated when alternating current (AC) is used instead of direct current (DC). Another variable is the frequency of the AC. If you pass a very low frequency (perhaps 1 or 2 Hz) AC through the speaker, the impedance will still be almost exactly equal to the measured DC resistance of the speaker. If you pass progressively higher frequencies of AC through the speaker, then the impedance will rise or fall in comparison to the speaker's measured DC resistance. Why the impedance rises and falls depends on the mechanical design of the speaker. You can create a graph of the rise and fall of the impedance versus the frequency of the alternating current (AC).
For example, let's say that you have an 8 Ohm speaker. The measured DC resistance usually will be noticeably less than 8 Ohms, yet the DC resistance will always be constant. Yet when you send AC through the speaker, the impedance at various frequencies can rise above 8 Ohms or drop below 8 Ohms. In other words, the graph of the speaker's AC impedance versus the frequency will be a wavy line when measured at AC frequencies from 20 Hz to 20,000 Hz. How wavy the line is will depend on the mechanical design of the speaker.
The DC resistance of a speaker is always constant. Think of impedance as being the equivalent the DC resistance of the speaker for AC current at a specific frequency. If the AC frequency is increased or decreased, then the equivalent DC resistance of the speaker can either increase or decrease.
We now have a wavy line for the speaker's measured AC impedance versus frequency. What is the average impedance of the speaker for AC frequencies from 20 Hz to 20,000 Hz? It is the average of the wavy line. The average of the wavy line is the impedance rating for the speaker. If the average of the wavy line is 8 Ohms, then the speaker gets a stamp which says "8 Ohm" on the back of the speaker's magnet. As I mentioned, the average AC impedance of the speaker usually is a good bit higher than the measured DC resistance of the speaker. And as I mentioned, the actual AC impedance of the speaker can be higher or less than the average AC impedance, depending on the frequency of the alternating current (AC).
Mom, you burned up Dad's amplifier since you hooked up the additional pair of speakers into the B channel of his amplifier. The minimum combined impedance for the A and B channels of Dad's amplifier is 4 Ohms. Dad's original speakers have a rated impedance of 4 Ohms. When you hooked up this new set of 4 Ohm speakers to the B channel, the combined impedance of both pairs of speakers became only 2 Ohms. This combined impedance was too low, and this is how you burned up Dad's amplifier since the combined pairs of speakers drew way too much current from Dad's amplifier.
Hey Mom, don't worry. I can replace the burned up output transistors on Dad's amplifier with new transistors from either Mouser or DigiKey since nothing else in Dad's amplifier was burned up.
Mom, it seems that you now understand about impedance. Impedance is simply the resistance at a particular alternating current frequency. Cool. You seem to totally get it.
Lets look at some other stuff inside Dad's amplifier. Do you see these things which look like little cans inside Dad's amplifier? Those are capacitors. Do you see these coiled wire things? Those are chokes. Do you see these things with three legs coming out of them? Those are transistors. Transistors are like the pedals and the control column and yolk in a passenger airliner. Movements of these by the pilot get greatly amplified in order to move the huge control surfaces on the wings and the tail of the airliner. In other words, transistors amplify small signals in order to turn the signal into much greater signals. Hey Mom, how cool is that? The power assisted brakes in your car do the same thing when you press the brake pedal. The power assisted steering in your car also does the same thing. You can think of both systems in your car as being the mechanical equivalents of transistors! This kind of signal amplification stuff has been around since the 1920s.
Yes Mom, transistors simply amplify things. Let's look again at those capacitors which look like tiny cans and look at those chokes which look like small coils of wire around small magnets.
Now things get even more fun. All capacitors totally block DC current, yet will pass AC current. How much AC current flows through a capacitor depends of the capacitance of the capacitor (basically the physical size of the capacitor) and on the AC frequency! Cool, isn't it? All chokes and coils pass DC current, yet progressively block AC current at progressively higher frequencies! Again, the physical size of the choke, and whether or not the choke has an internal magnet, determines how progressively the choke blocks higher frequencies. More cool stuff, isn't it?
Now lets think about Dad's 3-way speakers. In a nutshell, capacitors and chokes are used to limit what range of frequencies go to each speaker in a 2-way or 3-way speaker system. The combination of chokes and capacitors in a speaker are usually mounted on a crossover board inside the speaker.
Dad really loves his expensive IEMs. Amazingly, miniature crossover boards are used in Dad's expensive multi-driver IEMs to send specific frequency ranges to the specific drivers. This is very similar to how crossover boards are used in Dad's speakers to control what frequency ranges are sent to each speaker in Dad's 3-way speakers. Now that is really cool, isn't it? I think that it is really amazing that many expensive IEMs truly implement resistance (R) and choke (L) and capacitor (C) or RLC crossover boards inside these tiny IEMs.
Hey Mom, do you remember a few years ago when your cat Precious decided to use one of the midrange speakers on Dad's favorite speakers as a scratching post and that Precious destroyed that midrange speaker. Do you remember that Dad replaced that speaker with a generic speaker which had the correct stamped impedance and power rating? And do you remember that this replacement speaker sounded muddy at frequencies around 600 Hz? The reason that this replacement speaker sounded muddy around this frequency which was in the crossover range in Dad's 3-way speakers is that this replacement speaker's impedance around the crossover range was significantly different than the original speaker. This resulted in a significant phase shift for the replacement speaker versus the original speaker. In other words, the replacement speaker's sound, moving out of sync due to the phase shift, was somewhat cancelling the sound from the woofer.
Mom, I need to teach you more about phase shift and how varying impedance affects phase shift. Yet at least you now have an understanding about impedance and some understanding about other stuff such as capacitors, chokes and transistors.

Water analogy is the best.

Impedance (actually resistance) would be the thickness of the pipe. Straw - high impedance. River - low impedance. Voltage would be the difference in pressure between the two ends of the hose. Current would be the speed of water.l. Power (watts) how much water actually makes through, either because it is fast or because the pipe is thick.

Sensitivity however is not quite as you describe it. Once you pump "water" through it, it shows how much useful work will be done. It could be almost useless and that is low sensitivity. Or a small amount of water makes a lot of music, because the machine is efficient, that is high sensitivity. Low sensitivity is good because it is noise resistant. High sensitivity is good because low power is needed.

I said resistance, because we were simplifying to a constant stream of water in one direction (DC), but the music signal is not. Music is AC, it is water going back and forth, wobbling. Turns out if it does that, the "pipe" behaves differently depending on frequency. So impedance us resistance under one particular frequency. In audio it is 1kHz. It is not enough to fully explain the property of the headphones, just an approximation. Different headphones with the same impedance at 1kHz can have a different impedance when low bass is played.

Tube amp is a good device to generate a huge differences in pressure to push your straw, but quickly run out of water. Solid states usually just generate an infinite amount of water to power river headphones, but normally with low difference in pressure.

If you are interested, capacitor is a rubber cap preventing water in the middle of the pipe. It can be stretched one way up to a certain point. If the water is not actually going anywhere, but wobbles back and forth, it wobbles too mostly unnoticeable. So it removes DC from AC.

The inductor is a wheel in the pipe. It spins using inertia. It takes work to speed it up and to slow it down. It removes AC from DC.

Linear power supply is like a water tank. You pour messy sprinkles of water on the top, but a constant stream of water comes out at the bottom.

Simple. Ohm's Law. Just 3 letters: V=IR.

Electrical impedance is like resistance but with AC electrical current (flows back and forth, which is what creates vibrations in headphones to generate sound) instead of DC current (flows in one direction). Electrical impedance can be different for lower frequencies (e.g. headphone bass) and higher ones (e.g. headphone treble).

Headphone/earphone makers account for this when designing gear. If an amplifier has a high output impedance, it adds impedance, potentially skewing the ratio and, thus, the sound. That's why you generally want low amplifier output impedance, though some headphones can sound better with high.

Hi mom, don't worry about it, I'll do it.

Super thankful for everyone contributing here! It’s a bit of a complex concept but I feel I have a closer idea now! And thank you to those who have tried the approach of being my dear children for a while! 🤣😜

Someone mentioned earlier of the existence of an online headphones power calculator, which I’m finding quite useful!

I will be in the seek of headphones soon (mostly to connect to my iPhone via the lightning jack adapter, as I use a vintage amp on my desk and that one won’t be an issue), so trying to figure out the right impedance-sensitivity balance I should be aiming for to try and avoid getting a DAC/amp.

Nwavguys old blog describes it pretty well: https://nwavguy.blogspot.com/2011/02/headphone-amp-impedance.html?m=1#:~:text=Headphone%20impedance%20can%20vary%20by,output%20impedance%20of%202.6%20ohms.

I got a degree in electrical engineering a long time ago, but I forgot most of the analog stuff. I will give it a crack though.

When you draw diagrams of circuits, there are lots of different symbols that you can use to generalize it. Impedance is usually an inductor. We don't need to think too much about magnetism right now so lets just look at the formula.

Z = jwL

We don't need to care too much about the j or L right now, but notice that it is proportional to w, which is the angular frequency. This means the resistance of an inductor changes with frequency.

If I have a headphone which had an impedance of 8 ohms to 12 ohms across the frequencies that I care about then I might say they have an impedance of about 10 ohms. If I have a headphone with has an impedance of 27 ohms to 33 ohms I might say it has an impedance of about 30 ohms.

This might get weird if I have a headphone with an impedance of 8 ohms to 30 ohms across my targeted frequencies. It might be hard to control the sound if the impedance changes so much across the frequencies. Why does the ohms matter?

V = IR

For a set power source which is V, if the R which is measured in ohms goes up, such as with my 30 ohm headphones, the current which is I must go down. If the R goes down such as with my 10 ohm headphones, the current goes up. Generally low impedance headphones might sound louder, or that if you have a very high impedance set, it would be very quiet unless you have more power.

You probably would not want to plug very low impedance headphones into a super powerful source because it would draw a huge amount of current and might cook something.

You might think this means low impedance is always better, because you can just turn the volume down, but this might not be the case. When the impedance is very low, changes across the frequencies and the impact from other parts of the system factor in higher.

It may in some cases be better to inflate all of the numbers to reduce the impact of certain parts of the equation. Bigger numbers may also mean that component variability +- may have a smaller impact on production. The downside is your power source needs to drive much higher numbers.

In short, low impedance headphones are easier to power, but depending on quality control and other factors, they might have the potential for more artifacts such as noise, weird frequency changes, or unit variability or other such things.

I will touch slightly on electromagnetism which is more confusing. When electrons move, they produce magnetic fields, and this is how most drivers work afaik. If you can control a magnet electrically, then you can make it move around according to the signal, which generates the air pressure that you hear. Very generally, the problem is that interactions can make the system non-ideal due to response times. So depending on the design, you may have the air pressure being generated not quite like the signal you sent. This probably is part of why some headphones don't sound good. Impedance can be a factor, but it's probably more of an issue of design and components, including material choice, weight, thickness etc. becoming much more complicated.