Headphone & Amp Impedance Questions? Find the answers here!

Discussion in 'Sound Science' started by proton007, Apr 25, 2012.
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  1. proton007
    Hi all,

    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.
     

    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):
     
    graphCompare.png
     
    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):
    Source_and_load_circuit_Z.png
     
    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:
     
    1. A very high impedance causes the amp to reach its voltage limit before enough power can be delivered. There'll be clipping.
     
    1. 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:
    1. SPL / mW from your headphone manufacturer + the max impedance if possible(not nominal).
     
    1. Power specs from your amp manufacturer at different impedances.
    2. 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:
     
    1. Power = Antilog ( (Desired SPL - SPL per mW)/ 10).
    2. 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.
    3. 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:
     
    1. 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!
     
    1. 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:
     
    1. 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.
     
    1. |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
     
    1. 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).
     
    1. 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:
     
    1. 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:
    1.  "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).
     
    1. 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:
     
     
     
     
    1. Is Sound an Illusion? - An interesting discussion about our perception of sound
    1. Clipping Behaviour - One of the lesser known effects of amplifier clipping, and the damage it can do.
     
    1. Impedance - What does it really mean?  A general discussion on impedance, damping, etc.
     
    1. Phase Angle Vs. Transistor Dissipation - A simplified approach to understanding Safe Operating Area
     
    1. Valves & Amplifiers - Information about valves, myths, etc.
     
    1. The Truth About Cables, Interconnects and Audio in General (MUST READ)
     
    1. More Truth About Cables
     
    1. Cable Impedance - Characteristic impedance, high capacitance designs and amp stability
     
    1. Compression In Audio - Ever wondered why some music sounds flat and lifeless, even though it's loud?
    1. dB: What is a decibel?
     
    1. Amplifier Sensitivity, Decibels, and You!
     
    1. Impedance Matching and Bridging, and how it affects your sound.
     
    1. Headphone Tips and Tricks
     
    1. Noise - Auditory Effects
     
    1. Pimp your sound card! How to get more bass under a heavy headphone load

    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.
     
  2. firev1
    I stand here give the another perspective. I feel that not all studios prefers high impedance headphones, I have seen many many studios(by videos, pictures) use relatively low impedance phones and some mastering engineers also use low impedance Denons DX000 series for their work(with good results I may add), though I concede to the fact that this may not apply to every studio. Examples of such headphones are Fostex T20rp which I have seen used in a few pop studio environments, MDR-CD900st is extremely popular in Japanese studios, D2000 once by a mastering engineer(take a look at positive feedback), the Shure 840s and DT770PRO80OHM are very popular in my school's(polytechnic) diploma courses in music. 
     
    Another point I would like to address is the use of low impedance headphones in portable audio. Although generally indeed low impedance seems to be preferred in portable audio, that is also because manufacturers have no way to address the problem of getting high sensitivity AND high impedance at the same time IMO. With high sensitivity and impedance, headphones can be driven nicely without problems associated with low damping factor(overall higher noise/distortion and frequency response screwups).
     
    As for another reason why beyerdynamic has so many different models for the same headphone, I believe it is done to balance the drive ability with amp impedance issues(generally a studio engineer may want a 600ohm, while maybe someone working on field may want a 250ohm/pro 80ohm) the benefits of course with 600ohm is more control of the driver due to increased damping factor thus lower distortion. 
     
    All that I said has been said before many many times already but I hope I'm adding meat and not rubbish in this discussion. 
     
  3. proton007
     
    Quote:
     
    Well, there's no official rule against this, and low impedance can certainly be used, but the effect will be seen if multiple headphones are connected in parallel.
    I hope we can get someone who works in studios to give an input on this. 
     
    Quote:
     
    AFAIK, there's no correlation between the impedance and sensitivity. For example the Beyerdynamic models have the same sensitivity for different impedances. I feel its determined by the speaker design. Maybe someone can input on this.
    Thanks for raising the damping issue. I've added it in the main section.
     
     
     
  4. firev1
     
    Quote:
     
    Indeed, there is no correlation between impedance and sensitivity. But in portable audio, if a phone can have both high impedance and sensitivity, it will not suffer from damping factor based distortions while being very easy to drive from say a regular mobile which some models have relatively high output impedances. 
     
  5. stv014
    Regarding sensitivity, some manufacturers (Sennheiser in particular) reference the SPL to 1 Vrms instead of 1 mW, which makes the number look better. Sometimes no reference level is mentioned at all, making the spec useless. The sensitivity may also be significantly worse (or less commonly better) than advertised.
     
  6. proton007
    Thanks for the practical info![​IMG]
    Added to the thread.
     
  7. BrownBear
    Hey! I like this thread, very informative. Thanks very much.
     
  8. proton007
     
    Quote:
     
    No Problem. Glad to know you like it.[​IMG]

     
  9. doublea71
    This is a bit hard for me to follow, not having any background in recording or any science for that matter...merely trying to match a phone with the Cowon J3...I want to get a custom IEM for the J3, but I want to make sure the J3 can handle it.
     
  10. proton007
    Quote:
     
    Its ok.
    Use the Cowon's own earphone impedance as a guide. Just don't go for too high an impedance, try to keep it < 64 Ohms if not using any amp.
     
  11. doublea71
    Quote:
    So the player's output impedance should be less than the earphone's impedance...is there an ideal ratio between the two?
     
  12. RexAeterna

    1/8 rule they usually go by. so say nominal impedance of a headphone is 600ohms nominal, so the ideal output impedance should be 75ohms or less. like for example, speaker amps always went by atleast the 1/8 rule. that's why well built amps had no resistance at the speaker outs(0hm output impedance) which makes them perfect voltage sources for reactive loads like speakers.
     
  13. proton007
    Quote:
     
    +1.
    But you'll seldom find media player companies telling you their output impedance, thats why I said take the stock earphones as reference, a good design means that the output impedance should be < 1/8th the earphone impedance. Hence anything around the earphone impedance should be fine. I just take the upper limit to be ~64 because it gets harder to get loud with too high impedance.
     
  14. doublea71
    Quote:

    Maybe this is a better question for my pea-brain to ask:  What is the highest impedance IEM you could use with a J3 and still expect good results? I'm using GR07s at 50 ohms with an ipod 5.5 and it does a good job. I know the J3 is more powerful, but I'm not sure how this affects synergy with the GR07s or custom IEMs which tend to be low impedance.
     
  15. proton007
    If the Cowon is more powerful, it should play well with low impedance.
    Higher side I'd say max 64.
     
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