Request: Study of Damping Factor and Planar Magnetic Headphones

Discussion in 'Measurement Techniques Discussion' started by Klasse, Feb 16, 2016.

  1. feilb

    feilb Coco the monkey - Friend

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    True*

    This really only matters when the line is long relative to the wavelength of the signal, which is material/geometry and frequency dependent.

    Imagine a hypothetical transmitter and receiver connected by a length of wire. If the length of wire is 1/4 wavelength long (taking into account frequency and propagation speed), i can fit half of a low to high transition on the line (i.e the transmitter will reach 1/2 peak value before the receiver sees a voltage rise). If there is an impedance mismatch at the receiver end, some energy will be reflected back and cause artifacts on the remaining half of the rise.

    If the line is very short relative to the wavelength, you may only be able to fit, say, a 20th of a transition at a time. If there is only 1/20th of the magnitude difference between one end of the line and the other, the damage that can be done to the signal due to reflection is at most 1/20th of an amplitude.
     
  2. ultrabike

    ultrabike Measurbator - Admin

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    We are kind of deviating here but yes, the context of that was:

    For audio range signals and with reasonable wire lengths we are better off considering the amp -> driver wire as part of an electronic network, instead of going down the transmission line theory path.

    Maximum power transfer still applies.

    I likely misread @T.Rainman post.
     
  3. T.Rainman

    T.Rainman Acquaintance

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    Maximum power transfer is always at the lowest output resistance of the source.
    For audio signals that is ...
    The simple reason is there is a limit to output voltage and available current.
    This is what Purrin already mentioned.
    It's those 2 factors that determine the maximum output power in different loads.

    The higher the voltage on the load can be the higher the power dissipation in that load.
    ANY added output resistance will reduce the voltage across the load (voltage division) and thus reduce maximum power.

    And yes, impedance matching has to do with lowering reflections and always has maximum power transfer with the widest possible frequency range as well BUT is not the primary goal unless you are talking about wireless transmissions of course.
     
  4. ultrabike

    ultrabike Measurbator - Admin

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    I think amp current and voltage limitations (due to power supply and internal device limitations) are to some extent indepenent of source output impedance. I mean, they may not be completely independent (in terms of amp topology and whatever), but the effects in my mind are sort of independent. Both seem to contribute to maximum power transfer though.

    This affects wireline transmissions. Wireless is another beast.
     
  5. Armaegis

    Armaegis Friend

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    Most amplifiers go for Impedance bridging, which is maximizing the voltage signal (and thus current draw) across the load.

    If I can throw some math at people...
    ZL = load impedance
    ZS = source impedance (assume given constant)
    VL = voltage across load
    VS = voltage from source (assume constant)

    VL = VS * [ ZL / (ZS + ZL) ]

    if we differentiate with respect to ZL, we get
    (I know this is ugly; too lazy to export some images for this)

    VL' = VS * ZS / (ZS + ZL)
    we can see that there is no zero slope solution, but the slope is always positive and asymptotically decreasing towards zero as ZL increases

    Basically, as ZL increases the ratio in the [ ] approaches unity and VL will equal VS


    If we look at this from a power perspective
    PL = power across the load

    PL = VL^2 / ZL = VS^2 * ZL / (ZS + ZL)^2

    differentiating with respect to ZL again we get

    PL' = VS^2 * (ZS - ZL) / (ZS - ZL)^3

    this is a first year calculus min/max problem, solve for PL' = 0 and everything literally drops away leaving us with:

    ZS - ZL = 0

    thus ZS = ZL for maximum power transfer (for posterity, we recognize that slope is positive to the left of ZS, and negative to the right; if it was flipped then this would be a solution for local minimum)
     
  6. Klasse

    Klasse Friend

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    Almost everywhere, the output impedance (source impedance) is taken as constant across the spectrum.

    Are there objective evidences (read measurements) or at least a confident explanation about this topic?

    In other words, do we have a good reason to assume source impedance is constant?

    Without intetions of derailing this thread I think this (side-topic) is something we should be able answer while we wait for the main measurements of this thread.
     
  7. purr1n

    purr1n Desire for betterer is endless.

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    The caveat to the above Zout = Zin is that it pertains to fixed source impedance.

    The other way around with a given load impedance, going towards zero source impedance will maximize power transfer.

    For example. Take an amp with 100V output into a fixed 20 ohm load of say an LCD-X.

    If Zout is 20 ohms, power into the load will be 125W. If Zout is lowered to 5 ohms, power into load will be 320W.

    In other words, running the LCD-X on the low Z setting (3 ohm Zout) on the ZDS yields significantly more power than the 20ohm high Z setting, assuming all other things equal (enough current).
     
    Last edited: Feb 18, 2016
  8. ultrabike

    ultrabike Measurbator - Admin

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    Yes. The math looks correct. And the fact that infinite ZL maximizes voltage drop accross the load passes the "stink factor". In other words, it makes sense and it's sort of obvious.

    However, maximizing voltage drop, assuming constant ZS, does not necessarily maximize current draw. To maximize both I think we go to power transfer maximization.

    The maximization of power is not that obvious. And indeed I feel your equations look reasonable.

    For planar magnetics, yes. There are objective evidences (measurements) that show that the load is resisitive through the audio band. For dynamics, the load is more often than not complex.

    Yup.
     
  9. Klasse

    Klasse Friend

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    I'm referring to Source impedance

     
  10. ultrabike

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    I think source impedance is mostly resistive, or at least in most cases I know.

    You can always do an impedance vs frequency measurement by doing an DAC to ADC loopback. I've done that before, and in the cases I tested, a few SS amps I think, it comes out resistive... from what I remember.
     
  11. purr1n

    purr1n Desire for betterer is endless.

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    Caps on the output will result in an impedance rise in the bass.
     
  12. ultrabike

    ultrabike Measurbator - Admin

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    Yes, which in some cases, if too far up, results in an amp with no ballz.

    But past the low pass corner frequency I think it's mostly resistive... until it hits the high frequencies, depending.

    I think one basically has a bandpass filter in the audio band, mostly flat in that range.
     
  13. Armaegis

    Armaegis Friend

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    The second differential equation I posted is solving for power as a function of load impedance (assuming no weird wiggly bits and simple resistor divider topology). which gives the ZL = ZS solution for max power. It's all kinda academic though, as the desire for max power transfer isn't really relevant to our discussion at hand (I think).

    Maximizing current is really just dropping impedance as low as possible. High current is not fun to work with though. In audio it's way easier to work with high voltages and low currents rather than the other way around (which is pretty much what 70V/100V installation amplifiers are)

    Anyhow, how about that damping factor stuff eh? We seem to have veered off course.
     
  14. T.Rainman

    T.Rainman Acquaintance

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  15. ultrabike

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    To me, damping factor means that the amplifier and the driver are decoupled due to the low output impedance of the amplifier. And that's that.

    In some ways it seems to me that it is a term that someone somehow pulled out of his ass, since I don't see the resemblance to the more standard damping ratio concept of second order systems (mechanical or electrical).

    As far as whether it maters or not if the source impedance is resistive, I think it does not matter as long as the source impedance remains low relative to the load impedance throughout the whole audio band.

    Otherwise, it probably does matter. Fortunately, I think most amps are somewhat resistive through out most of the audio band. Some more than others. And fortunately, planar drivers seem to present somewhat resistive loads.

    Note no discussion or claims are made about non-linear behavior. That IMO is a bit more tricky and perhaps more difficult to generalize.
     
  16. Cspirou

    Cspirou They call me Sparky

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    From my understanding damping factor has to do with the back EMF generated by a driver. In other words when a voltage is applied to a driver coil a magnetic field is generated which moves in response to the magnet present, however moving the coil itself through the magnetic field will also generate a counter voltage (Faraday's Law) which the amp has to deal with. The low output impedance of an amp would mean this back EMF is effectively neutralized and doesn't further contribute to the (unwanted) motion of the driver.

    Planar magnetic drivers however are not coils. This does not mean that you can't generate a voltage from moving the membrane (otherwise how do Audeze microphones work?), but it does mean that the generated EMF is very weak compared to a coiled driver.

    Probably can't say that damping factor doesn't matter to planar magnetics but it seems like it matters less.
     
  17. Klasse

    Klasse Friend

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    It's all in your hands, mate!
    It would be really interesting to see how that Alpha Dog compares when driven with 0.47 vs 47 ohm output impedances.
     
  18. philipmorgan

    philipmorgan Member of the month

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    Should have the measurement rig up and running by Sunday. :)
     
  19. T.Rainman

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    Back EMF is not neutralized by a low output R.
    low output R acts as 'short' in series with the generator (R from the driver), a higher output R just lowers the maximum current the driver can generate and thus lowers the damping current.
    You will need to go below DF10 to make a difference.

    Planars will also generate reverse currents.
    It doesn't matter if a wire, moving through a magnetic field, is wound in a coil or any other geometry as long as the magnetic field strength and total length of the wire is the same and equal amount of current is generated.
    When 2 drivers have a similar efficiency (dB/mW) it is reasonable to assume the magnetic field strength/wire length is also approximately the same.
     
  20. ultrabike

    ultrabike Measurbator - Admin

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    This is the issue I have: A dynamic speaker driver model is a bit more involved than an inductor (driver coil) from what I've found in the webz:

    http://www.roomeqwizard.com/help/help_en-GB/html/thielesmall.html

    The driver does store energy (depending, planars don't seem to store much), and it will release it at some point in time. These effects are part of the driver electrical model. However, if you were to form up a complete electrical network model with the driver and the source impedance, you'll likely end up with a high order system (higher than second order lets say). For those cases, talking about damping is a bit controversial, because damping is well defined for second order systems, but for higher order systems it's somewhat debatible.

    What you can do is find the poles and zeros of the system. Where there is a pole there will be a resonance. Where there is a zero, there will be a null.

    With all that said, end of the day it seems to me that most folks are concerned about "damping factor" when talking about the effects the source impedance has on sonics. Which seems to boil down to the eletric decoupling of the amplifier and the driver, by having a sufficiently low source impedance.

    This matters if the driver has reactance, but perhaps not that much if the driver and the source are resitive in the bands of interest.

    As far as back EMF, well, pretty much any eletcrical network element capable of storing energy would generate "back" (and out of phase) currents.
     
    Last edited: Feb 19, 2016

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