#### proton007

##### Headphoneus Supremus

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- Feb 9, 2012

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A lot of people ask this question in the other sections, so I thought this can be the thread to discuss it and hopefully it can act as a reference.

Headphones come in variety of Impedance (or *Nominal* Impedance values). Some manufacturers like Beyerdynamic have 2-3 different impedances for the same model, which they list for different sources.

So the question is, how to get the correct impedance for your source? And how to check which amp to get ?

I'll try to explain this as far as I know, please feel free to correct me!

**The Hydraulic Analogy for the simple minded:**

I think this analogy can help appreciate the need for an amplifier and establish a good basis for understanding the concepts ahead.

A voltage source is like a water pump, it creates pressure (voltage) that passes through pipes (Load). The amount of water that passes through the pipe per second, or the flow of water, is the Current. The narrower the pipe (Higher Impedance), the more pressure (Higher Voltage) you need to maintain the same amount of water flow (Same Current).

The reverse also applies; a wider pipe will need less pressure.

A headphone can be considered as a sprinkler. It utilizes the water given to it, and spreads it across the lawn (creates sound). We want the sprinkler to cover the lawn (get to a comfortable volume), too much and it'll wet the house, too little and its not enough.

The higher the number of holes the sprinkler has (low headphone impedance), the more water it needs, albeit at not so high pressure (needs more current than voltage). The lower the number of these holes (higher impedance), the more pressure it needs to sprinkle, but not so much water (needs more voltage than current).

So, some sprinklers (headphones) need more pressure (voltage), others need more water (current) to maintain the same spread. The ratio of this pressure or flow to the spread can be termed as the 'sensitivity' of the sprinkler (headphone). It depends on the design.

Sometimes, the pressure in the hose pipe (your audio source) isn't enough to run the sprinkler (headphone), so an additional pump is required, this would be an Amplifier.

The caveat here is that this additional pump (Amplifier) should supply additional water (current) and pressure (voltage), from its own water source (power supply),preciselybecause the hose pipe (source) doesn't have enough water (current) to supply at a specified pressure (voltage). Other taps in the house also need water you know!

Now, what this Amplifier does is this: it measures the pressure created by the hose pipe (audio source), and uses its own water source to add pressure and water flow to the sprinkler (amplifies current and voltage for the headphone). So, it adds more pressure and water in proportion to the pressure and water flow of the hose pipe. This is known as the 'Gain' of the amplifier.

Ideally, what we want is that the hose pipe (audio source) should not feed the pressure and water to the sprinkler, because otherwise it affects other taps in the house. Thats why we chose the amplifier to do that work from its own water source. BUT, the amplifier still needs to measure the pressure and flow of the hose pipe to add its own gain, so we connect a pipe whose' width (input impedance) is very very small (high impedance) on the input to the amplifier, so that its enough to measure the pressure and flow from the hose but not consume it.

Imagine the output stage of the amplifier like a pipe that connects to the sprinkler. We want this pipe's width (output impedance) to be as wide as possible (lowest impedance), so that the water flows unimpeded to the sprinkler (headphone).

If the flow of the water gets constricted here, the pressure at the sprinkler won't be enough, it won't sprinkle the water in a wider area (the headphone won't sound as loud), and this defeats the point of the amplifier.

Having a wide pipe here (lower output impedance) means that you can connect any sprinkler you want, because then the pipe of the pump is never a constraint in the flow of water, the sprinkler becomes the constraint, and based on its design, it can consume as much pressure and water it needs.

So, in the real world, how would you setup a sprinkler ? You would choose the sprinkler first. Then you would see if your hose pipe has enough pressure and flow, otherwise you'll need a pump (amplifier). This pump should have a very high 'input impedance' and a very low 'output impedance'.

**First of all, facts to establish before we go ahead:**

- A perfect/ideal Amp will produce a fixed voltage at a particular gain/volume setting, here we refer to it as Vsource (or
*Vs*) . - Voltages in terms of AC always use 'Vrms' to denote the mean voltage. Hence, Vload and Vsource are Vrms values.
- The gain used by amps is just a multiplier. It tells you how much is the original signal multiplied by. So for any gain G, Vout = G*Vin
- Amps have their own internal Impedance when seen from the output side, we call this 'source impedance' or '
*Zs*'. - A headphone will act as the load for this system, its 'load impedance' is '
*Zl*'. The voltage across this load is represented as '*Vl*'. - Headphones impedance as specified by manufacturer is only *nominal* impedance, but actually,it varies with the frequency of the signal. Some headphones can have as much as double this value at certain frequencies. We call this value 'load impedance' , or 'Zl'4) All headphones have a sensitivity rating, given in dB (Decibels) SPL/mW @ 500 Hz or 1kHz. For dB (Decibels) take a look at the links below. This denotes the "Sound Pressure Level" created by the diaphragm on 1mW power @ 500 or 1kHz signal. There is a rough relation between the SPL and loudness experienced by our ears (For more information: Loudness & Decibels). Note that some manufacturers reference the SPL to 1 Vrms instead of 1 mW, which makes the number look better.

Here's an impedance curve of a fairly popular headphone (HD650):

*Impedance vs Frequency*: The vertical line is the maximum impedance, while the horizontal line is the 'nominal' impedance.

Electrically, a source and load circuit can be represented by this diagram (taken from wikipedia):

As mentioned before,

*Vs*is the voltage produced by the amp, which is dissipated over its own impedance to the output (

*Zs*) and the load impedance (i.e. the headphone,

*Zl*). Zl and Zs are connected in series.

The effective voltage across the headphone is

*Vl*.

**Formulas:**

- Ohms Law: Vrms = Irms * Zl
- Average Power, or Pavg = (Vrms)^2 / Zl. Alternatively, Pavg = Irms * Vrms
- Vl = Vs * (Zl / (Zl + Zs)). Therefore, as Zs becomes smaller, the ratio Zl/(Zl + Zs) approaches 1.
- Total Impedance of two impedances connected in Series = Z1 + Z2
- Total Impedance of two impedances connected in Parallel = (Z1 * Z2)/( Z1 + Z2)

**From these formulas, we can make some deductions:**

- For the same Vrms to be produced, halving the Impedance doubles Pavg, and doubling the impedance halves Pavg. Hence, Pavg is inversely proportional to Zl (from point 2 above).
- If Pavg is increased, for the same Vrms, Irms needs to increase (from point 2 above).
- In order for Vl to be nearly the same as Vs, Zs needs to be much smaller than Zl, or Zs<<Zl (from point 3 above).
- This concept is known as Impedance Bridging, and it maximizes the efficiency of power delivered to the load. The point is to have all the Pavg delivered across the load. This can be achieved if most of the source's voltage is dissipated across the load. (Note, its efficiency of power delivery, not power efficiency itself!).
- Parallel connections reduces the overall impedance, and series adds them up.

Now, if you look at Amp specs you'll see the power specified at a certain min. and max. load impedance. For example, Fiio E9 has 1W (16Ω Loaded), 80mW（600Ω Loaded).

**So Average Power goes up with lower Load Impedance for the same Vrms. Is there a limit to an amp's power?**

Yes, all amps have a power limit, which means there's a Voltage and Current limit for every amp. The limit depends on the amp's design and power requirements. At the lowest impedance, the amp can run out of current to supply to the speaker. Generally, even before the limit is reached, there will be considerable increase in THD (Total Harmonic Distortion). Anything >1% is considered unacceptable by industry standards.

If the impedance is too high, a lot of voltage is needed to produce the desired power. This will cause amps to 'clip' once it hits the voltage limit.

**High or Low load Impedance?**:

Connecting a lot of high impedances in parallel will reduce the impedance. For instance, two 16 Ohms connected in parallel make up 8 Ohms, while two 600 Ohms make up 300 Ohms.

In relative terms the impedance is reduced by a factor of half in both the cases, but in absolute terms, by Ohms Law, for the same Vrms across both impedances the current requirements for 300 Ohms are easier than 8 Ohms (less by a factor of ~40).

Hence studio monitoring equipment has very high (>=600) Ohms impedance, so multiple headphones can be used without overloading the system. They can all be plugged in parallel.

Consider this as a rule of thumb, in order to achieve a certain power, for the headphone to be loud enough:

- A very high impedance causes the amp to reach its voltage limit before enough power can be delivered. There'll be clipping.

- A very low impedance causes the amp to reach its current limit before enough power can be delivered. There'll be distortion.

Hence, all amps will list the max and min impedance they can handle.

**Damping factor:**

Resonance is another issue concerning speakers, and too much of it can cause distortion. Since the speaker basically consists of a coil moving back and forth in an magnetic field, it will generate a back EMF, or back current by Faraday's Law. This induced current will restrict the coil movement, making it slower or less responsive.

Now looking from the speaker side, if the speaker generates a voltage, the amp is the load. If the load has lower resistance it'll allow more current to pass through, hence the back emf can be dissipated easily, controlling the unwanted oscillation at resonant frequency. This is known as a 'High Damping Factor'.

Most speakers have this happening near the lower frequency regions, so a High Damping means the Amp can control the speaker movement tightly.

But beware of damping marketing ploys. If amps have near zero output impedance, Damping is no longer a problem.

**In general, This means that high impedance headphones are better, right?**

*Then why do we recommend low impedance headphones for portable use?*

The answer is because portable sources, specifically batteries, are severely limited by the Vrms they can supply, and it is typically much less than the voltage that can be produced by an amp. A high impedance headphone will not sound loud enough because it needs higher Vrms.

Since there is a relationship between Power and SPL, the only way to increase power for portable devices is to increase current which is easier to do with lower impedances.

This also means that high impedance headphone will theoretically make your iPod battery last longer because it'll consume less current, but it won't be as loud as the earbuds.

Conversely, because low impedance headphones work at lower voltages, attaching this headphone to an improperly matched Amp can overdrive the headphone with high voltage, causing damage to the diaphragm. Not that much of an issue with headphone amps unless there's a design flaw, but if you plug in your headphones in the wrong output jack, this can happen.

**How do I know if I need an Amp? Will it be suitable for my headphones ?**

Generally, low impedance headphones are made for portable use, so an amp may not be required. But some people consider there are sonic benefits, so there's nothing against using one. Just use this to check:

To find out if the amp fits your requirements, I'll suggest to take a look at these key points:

- SPL / mW from your headphone manufacturer + the max impedance if possible(not nominal).

- Power specs from your amp manufacturer at different impedances.
- If possible, a graph of how the headphone impedance varies with the signal frequency. Some headphones can have wild variations here.

Use this formula to calculate the power needed:

- Power = Antilog ( (Desired SPL - SPL per mW)/ 10).
- Note that a 3dB increase in SPL will cause a 2x increase in Power. For reference, 85 dB is considered to be the limit where long term exposure can cause hearing damage.
- Use 85dB to calculate the
__average__power needed. Peaks in the music may be higher, as high as 110dB.

If your amp can supply this power, and the headphone impedance falls within the mum/Max load impedance the amp can drive, then go ahead and enjoy your amp.

Also, note that some headphones have higher impedance spikes than others (impedance variation with frequency, remember) as well and then you have the music itself where when certain dynamic passages will require higher transient peaks (higher voltage) here or there once in awhile requesting for more power. Hence its better not to push amps to their limit ( driving 600 Ohms with a portable amp may work, but it can also overload the amp due to its sensitivity and impedance characteristics).

How headphone impedance (vs frequency) affects sound.

In case of MP3 players, where output power is not specified, you can assume that the provided earbuds are already matched. Set the volume to a comfortable level, and now plug in your new headphones. If the volume sounds similar, your headphones are adequately powered.

**I've heard about using line out. What is that?**

A line out is a (supposedly) standardized form of signal when connecting audio devices, such that the internal amplifier of the device is bypassed. It stays at a Nominal Level, with Professional equipment at -4dBu and Consumer equipment fixed by some at -10dBu (not standard).

It can be useful in cases when you just want to send the signal over to another device for further processing/amplification, or record the signal.

It is always at a contstant Vrms (regardless of volume control), with the Source Impedance being somewhere around 100-200 Ohms( varies based on implementation).

There are two implications:

- You cannot use it to drive speakers/headphones directly (read: without an amp). There's impedance mismatch ( source is much higher than load ),meaning most of the voltage drops at the source, with an overall high current flow in the circuit dictated by the source. Not good!

- No volume control.

While its a common feature in receivers and sound cards, its not so common in media players. The iPod supports it through the dock or aftermarket line out cables.

**Ok, now I have an amp. Where do I control the volume (source or amp)? And what levels to keep?**

Most will suggest to keep the source at 100%, and use the amp for volume control. There's nothing wrong in that. But my suggestion is to adjust the source such that there is a bit of travel in the amp's volume control. It makes the control more intuitive, and allows for different headphones to be used. So, a 1 should sound like one (soft) and a 10 should be loud, with the comfortable level somewhere around 5-6.

You don't want to have ear blasting volume at just 5, its dangerous for someone caught unaware.

For amps with adjustable gain, you can factor in the gain as well.

Finally, to keep it simple, plug it in, take a listen and if you like what you hear then that's awesome. Enjoy the music!

*A few notes for those who want to dig deeper*:__Electrical__:

- Impedance is a complex (number) load, Z = R + jX, where R is 'resistance' and X is 'reactance', both of them represented in Ohms. This can also be written as Magnitude,|Z| and Phase θ.

- |Z| determines the voltage/current ratio, and θ determines the phase difference between voltage and current. Hence, the Power = VI statement does not hold at all points because of the phase difference. AC Power

- This means the headphone/speaker impedance curve will vary the power drawn by the headphone/speaker. The Real Power draw may be different from the Apparent Power draw. ( see AC Power above).

- Line out is not standardized. Pro and consumer gear targets different references and consumer gear has a tendency to be all over the place beyond that. Some line drivers can actually run some headphones, some cannot. There's no solid rule of thumb here (and it is not load invariant).

__Music Dynamic Range__:

- Determines the difference between the highest and lowest levels of the signal. Older Classical recordings can have a very high dynamic range (40 dB sometimes), so the average and peak power requirements of your amp will be vastly different. Modern/commercial music has a dynamic range of 2-3 dB (Loudness War), hence the average power requirements of the amp will be high.

__Sound Characteristics of the Amp__:

- "What you will hear" depends on the relationship between Zout and Zload and what the amplifier can actually do.
__If the amplifier can drive lots of volts into the load but has Zout__(e.g. a receiver or otherwise "large" amplifier, you could probably even count some amplifiers like the Beyerdynamic A1 in here since Zout is around 100ohms)__it will likely just mean attenuation or boost at various frequencies__,__if the amplifier cannot__(e.g. "line out" on a soundcard),__it will probably just mean roll-off__.__The former is perfectly okay, the latter is not__(the former means "coloration" or whatever else you like; the later is just things not behaving).

- Look at your amplifier's manual and find the sensitivity value for the input you are using. The value it gives is the input voltage required in order to produce maximum rated power when the volume control is set to maximum. If the input signal you are feeding to the amplifier is greater than the sensitivity value, then maximum output power will be produced before full volume on the control. Hence your amp will max out even before the dial is set to full.

More Links for information and concepts:

- Compression In Audio - Ever wondered why some music sounds flat and lifeless, even though it's loud?

More links on Damping:

http://sound.westhost.com/impedanc.htm

http://sound.westhost.com/project56.htm

http://sound.westhost.com/project70.htm

http://sound.westhost.com/z-effects.htm

Thanks to:

obobskivich, for his notes, corrections, and links.

stv014, for useful comments.

RexAeterna, for useful comments.