Here is an AES paper describing an equivalent electrical circuit model for electrodynamic transducers. Of particular interest to this discussion is the introduction which outlines the equivalent electrical circuit for an electrodynamic driver including the origin of impedance variation with frequency in dynamic drivers and how the back emf generated by transducer motion fits into the picture.
All these papers deal with loudspeakers and seem to confirm that electrical damping is one of the smallest forces involved in loudspeaker function
Scaled down to headphone values the electrical damping factor becomes so small it is of little consequence
Other factors like mass loading , mechanical damping and baffle design are much more relevant in headphone sq
All these papers deal with loudspeakers and seem to confirm that electrical damping is one of the smallest forces involved in loudspeaker function
Scaled down to headphone values the electrical damping factor becomes so small it is of little consequence
Other factors like mass loading , mechanical damping and baffle design are much more relevant in headphone sq
Engineering papers dealing with loudspeaker design apply to headphone drivers only at a very basic level
Try inputting headphone driver parameters into some of those formula
While the principals are the same , scale , power levels and enclosure dynamics are very different
A simple examination of headphone workings
Strongest force : the motive power from the amp must be stronger than any damping or air resistance or the diaphragm will not move
Weaker force : mechanical damping , primarily to return the diaphragm to a neutral position and hold the voice coil in place . In addition the diaphragm must be mounted in a manner rigid enough to resist distortion under load and movement due to inertia (head movement) and gravity (head tilt) .
For closed or semi-closed headphones the air chamber is additional and part of the mechanical damping as is the air around an open driver
Weakest force : electrical damping , energy created by the action of the voice coil being pulled back through the magnetic field by mechanical damping
If the electrical damping force was greater than the mechanical force that generates it you would have perpetual motion
Headphone drivers are designed by very capable engineers who balance all these forces to yield a driver which in combination with its enclosure give the frequency response they consider most desirable
Reading through the many modders threads here on HeadFi shows that the greatest changes are brought by altering the dynamics of the enclosure . Where impedance is used to modify driver performance it is by altering the load presented to the amplifier not to increase or decrease electrical damping
Engineering papers dealing with loudspeaker design apply to headphone drivers only at a very basic level
That is what we are doing in this thread, trying to establish how electrodynamic speakers function at the very basic level so that we can understand how certain commonly quoted parameters (e.g., damping factor) actually affect the physical operation of the driver.
There is no difference between the physical description of the loudspeaker in the paper and dynamic drivers in headphones. Only the actual numbers quoted as "typical for woofers" do not apply. The physical mechanisms remain the same.
Try inputting headphone driver parameters into some of those formula
I'd really like to know some typical headphone driver parameters. I've been asking for them in this thread. Please show me a source of information with complete descriptions of various headphone driver designs.
While the principals are the same , scale , power levels and enclosure dynamics are very different
Yes, I don't think anybody is confused about this
A simple examination of headphone workings
We have a complete model for electrodynamic headphone mechanics. We don't need this simple description because we already have a mathematical one which offers physical insight into the driver's mechanics.
Strongest force : the motive power from the amp must be stronger than any damping or air resistance or the diaphragm will not move
Weaker force : mechanical damping , primarily to return the diaphragm to a neutral position and hold the voice coil in place . In addition the diaphragm must be mounted in a manner rigid enough to resist distortion under load and movement due to inertia (head movement) and gravity (head tilt) .
For closed or semi-closed headphones the air chamber is additional and part of the mechanical damping as is the air around an open driver
Weakest force : electrical damping , energy created by the action of the voice coil being pulled back through the magnetic field by mechanical damping
Perhaps you simply weren't careful with your wording, but these descriptions are incorrect. Electrical damping is not the energy created by a voice coil being pulled by mechanical damping because mechanical damping never pulls anything anywhere. Mechanical damping is a force proportional to the velocity of the system and when the damping is positive, the force resists the motion. Electrical damping results from the magnetic field generated by the currents induced from the motion of thecoil through magnetic field of the stator... this induced magnetic field always opposes the motion and is proportional to the velocity; hence it is called the "electrical damping".
No amount of any damping force ever can prevent a speaker diaphragm from moving because no damping force ever exists unless there is already motion. The magnitude of the damping force varies proportionally to the amplitude of the diaphragm excursion.Furthermore, mechanical damping is a completely different aspect of the dynamic system of a driver than the compliance of the diaphragm support. Mechanical damping does not restore a diaphragm to its equilibrium position because the damping force doesn't exist unless there is a motion. The support of the driver, often called the "spider", provides a restoring force that is proportional to the displacement of the diaphragm from equilibrium. It is quantified as a spring constant K or a compliance C where C = 1/K.
If the electrical damping force was greater than the mechanical force that generates it you would have perpetual motion
Damping always opposes the motion; this statement is absolutely incorrect.
Headphone drivers are designed by very capable engineers who balance all these forces to yield a driver which in combination with its enclosure give the frequency response they consider most desirable
This is unrelated to what we are trying to understand in this thread. It is also the same argument used by fancy cable proponents to justify fancy cables *must* make a difference. Appeal to authority is a logical fallacy.
Reading through the many modders threads here on HeadFi shows that the greatest changes are brought by altering the dynamics of the enclosure . Where impedance is used to modify driver performance it is by altering the load presented to the amplifier not to increase or decrease electrical damping
I concur with regards to modders focusing most on the enclosure; however, I think the reason for this is a practical one. It is infinitely easier to modify the cups than it is to modify the much smaller, much more complex, much more delicate driver.I cannot think of anyone who has the means to modify a transducer directly. These things are made in factories using equipment and techniques beyond the means of the DIYer. Once you take this into cosideration, there are only three things a modder can do 1) attempt to modify the acoustics of the headphone cups (including earpad mods, mass-loading mods, absorption mods, cavity geometry mods, etc.) 2) modify the electrical circuit of the headphone drivers (zobel networks, cross over networks, adding resistive volume sliders, etc.) and 3) modify the aesthetics of the headphone (this has no impact on the sound)
While this might be true, but electrostats operate via a fundamentally different principle than the *dynamic type of drivers. The driving force on an electrostatic driver comes from the electric force due to charges in an E-field. here, the force is F = q * E(where bold denotes a vector quantity). F is the force vector, q is the charge, and Eis the electric field.
In electrodynamic drivers, the driving force comes from the magnetic force due to current in a B-field. Here, the force is f = J xB (where "x" denotes the cross product). fis the force density, J is the current density, and B is the magnetic field. This would need to be integrated over the voice coil (or etched traces in a orthodynamic diaphragm).
I understand what you're getting at, but I think in this case there is some confusion because of the way some folks try and oversimplify things.
Let me try and lay this thing out as completely as a I can so I can be transparent about my argument and if there are any issues then folks can point me in the right direction.
INTRO
The original question that started this whole thing rolling was something like "does damping factor have no effect on orthodynamic because orthodynamic headphones' impedance appears constant with frequency?"
The correct answer to that is "no". The confusion stems from the fact that folks tend to use "damping factor" as a replacement for the amplifier's output impedance. The output impedance of an amplifier acts in conjunction with the headphone impedance to form a sort of voltage divider. This impacts the power delivered to the headphone vs the power dissipated in the amplifier's output impedance. When the headphone impedance varies with frequency (as is very common in traditional voice coil dynamic drivers) then there is a frequency-dependence to the power delivered to the headphone. Two amplifiers with different output impedance will deliver different amounts of power across the frequency spectrum thus leading to a potentially audible differences in the spectrum.
As for the damping factor being a "damping factor," this is only the case when talking about the impact that the output impedance of the amplifier affects the electrical damping of the diaphragm.
DERIVATION
Using the notation of Kinsler, Frey, Coppens, and Sanders (4th ed):
The electrical impedance of a general moving coil transducer (i.e., a dynamic or orthodynamic driver, not an electrostat) is
Zeb = R0 + j w L0. (bold denotes complex number)
Here, the diaphram is blocked (decoupling mechanical effects) where R0 and L0 are the resistance and inductance of the speaker (w is the angular frequency and j is the jmagjnary number = sqrt(-1)).
The force pushing on the diaphragm is given by
F = B*l*i [ * ]
where B is the magnetic field strength acting over a length of wire l and carrying a currenti.
When the diaphram is no longer blocked and allowed to oscillate, by Lenz's law the motion of the voice coil on the diaphragm through a magnetic field induces a back emf equal to
Back EMF = B*l*u
where the velocity is denoted by u.
Applying Kicrchoff's voltage law to the entire closed circuit consisting of the amplifier + cable + driver gives
V = (Zeb + Zext)*i + B*l*u [ ** ]
Zextis the sum of the impedances of the amp and cable and anything else outside of the headphone (typically resistive), i is the current, and V is the voltage signal from the amplifier.
For convenience, lets define the damping factor as the ratio of the driver's impedance abs(Zeb) to the external impedences abs(Zext) as
d = abs(Zeb) / abs(Zext)
In the absence of a driving signal, equation [ ** ] can be rearranged to show the current flowing through the circuit due to the induced emf:
(note that I've substituted Zeb*(1+ 1/d) for (Zeb + Zext) )
The last step here is to look at how the electrical damping force on the diaphragm depends on the damping factor. We do this by plugging [ *** ] into equation [ * ]
F = B*l*i [ * ]
substitute [ *** ] in for i -> F = - ( (d / (1 + d) )/abs(Zeb) )* (B*l)^2 *u [ **** ]
DISCUSSION
First, note the negative sign---that means that the force due to electrical damping opposes the motion.
Secondly, note how the damping factor affects the magnitude of the damping force. In the limit as the damping factor increases to infinity (i.e., amp+cable impedance goes to zero) the factor in front approaches 1with the error going as 1/d; namely, once the damping factor is reasonably large, (say 50 or so) further increases in the damping factor impact the electrical damping by increasingly vanishingly small amounts. As the damping factor becomes very large, the electrical damping force on the transducer is limited by the transducer's own impedance.
In my previous post, i wrote the dynamics of a single degree of freedom oscillator as
and then I said that the electrical damping can be used to augment the mechanical damping (here given by C). If I'm a headphone transducer designer, I will design my speaker's mechanical response around the fact that the electrical damping will augment the dynamics as
M*x'' + ( C + (B*l)^2 /Zeb ) *x' + K*x = 0
Where I make the reasonable assumption that folks will hook my speaker up to a low output impedance amplifier.
In the limit that the damping factor goes to zero (high amplifier output impedance relative to the speaker impedance) then the electrical damping also goes to zero. In this case, the forcing of the diaphragm has been completely decoupled from the motion of the diaphragm.
The difference this has on the speaker depends on the factor (B*l)^2 /Zeb , or, perhaps even more on the the difference between the effective mechanical damping ratio zeta in each of the situations:
zeta_mechanical = C / (2 * sqrt( M * K ) )
vs
zeta_mech+elec = (C + (B*l)^2 /Zeb)/ (2 * sqrt( M * K ) )
For a well designed, efficient transducer, zeta should be close to 1. As I mentioned previously, when zeta = 1, the system is critically damped and below mechanical resonance, it will follow the position of the forcing input (to some scale factor) as quickly as possible without overshoot (ringing). If a speaker is designed with the expectation of high damping factor, but instead a low damping factor amplifier is used, then the mechanical damping ratio zeta < 1 and there is a tendency for the diaphragm to overshoot and ring at frequencies below mechanical resonance. This is the reason why underdamped speakers can sound like they have flabby bass---namely, the amplifier cannot exert enough control over the motion of the speaker.
CONCLUSIONS
Here, I have tried to demonstrate that there is nothing fundamental about the electrical characteristics of any type of moving coil transducer (e.g., dynamic headphones, orthodynamic headphones, woofers, etc.) that renders the concept of electrical damping (which depends on the damping factor) not applicable. The above analysis is completely valid even if the headphone exhibits a purely resistive load that doesn't vary with frequency (i.e., orthodynamic headphones).
So with that, with respect to the origins of this discussion, I think I have clearly and fully elaborated on the position I took at the beginning of this discussion while trying to address some of the confusion regarding "damping factor" and whether or not planardynamic headphones are theoretically immune to it.
I understand it's not efficient and with HD800's case the uneven impedance characteristic would change the signature. But, what would this do to a flat impedance, resistive planar?
Damping factor means nothing for planars, though it matters with dynamics. It has to do with the induced current when the driver moves, as I understand it. Not sure about the details. Anyway, planar drivers induce no or a negligible small current when the diaphragm moves.
Probably a very simplified explanation.
The traces on a planar diaphragm move through a magnetic field, which induces back emf. If there was no magnetic field present, then running current through the transducer wouldn't induce the the force that creates physical motion of the transducer.
Damping factor is just as relevant to planar magnetics as it is to traditional dynamic drives when it comes to electrical damping!
So basically, don't use bottle head crack with LCD-X.
If you don't get the humor, the LCD-X is 20ohms and crack has over 100ohms output impedance. The tube should be nice and toasty. Would be nice to have during the winter to keep you warm and cozy.
Anyway, ok, the electrical damping in the case of resistive load is just power delivery issue. That's good to know.
If you can ask questions about the parts you don't get, then we can move the conversation forward. However, continually asserting that planarmagnetic headphones aren't affected by the amplifier's damping factor because they don't exhibit a strongly frequency dependent impedance is both wrong and not helping anybody address the question in a meaningful way. I am happy to try and elaborate on the points that need elaboration, just point me where the pieces are missing. I link the wiki article because it introduces what the damping factor is and how it relates to speakers. It's a good foundation to start the discussion where all parties involved can use common terminology.
There is a "coil" on planardynamic drivers as well. It's the copper/aluminum/whatever trace etched into the driver. You can clearly see it in the picture you've included above. The fundamental operating principle of operation is exactly the same in both dynamic and planardynamic drivers. You might notice that the two names differ by only the addition of "planar" in the name "planardynamic". The difference comes from the way the magnetic field lines are distributed in the planarmagnetic drivers compared to the classic drivers. Rather than having one large magnet with a coil on the driver as in classic dynamic drivers, planarmagnetic drivers have an array of magnets with the etched coil winding through the magnetic field. Innerfidelity has a nice little description about it here. you can also read a wiki excerpt here.
Please point to anything that corroborates this claim. Thanks. The fact that my headphones be effin' ringin' suggests that the dynamics of headphone speakers could benefit from electrical damping.
The driver in a speaker, whether of dynamic or planardynamic desgin, will have inertia. Remember, it's the motion of the speaker cone that generates the sound waves. Whether or not that speaker motion requires electrical damping depends on the mechanics of the speaker. The zeroth order model for the driver is a mass-spring-damper system with external (the electronics) forcing. Unfortunately, I don't know what "typical" parameters are for a headphone speaker. As for the 500-Ohm resistor, you can always try it and see.
All I'm trying to do is to address what appears to be a lack of fundamental understanding on the mechanics of "dynamic" type headphones. Whether that lack of understanding is mine or other peoples' might still yet not be clear, but I do think I have a good grasp on the mechanics involved. I'm always welcome to counterpoints from anyone willing to explain it to me
about the dynamic vs planar, there are simply too many reasons for differences to just try and deduce a behavior from the dynamic drivers IMO.
the magnetic field is different and if the principles obviously remain the same, as I said, the fact that the magnetic field can be the same in all positions with a planar has to impact the capacity for control. but it needs more power to work the same, so that means more opposing force... it's hard to get a clear view of the entire system(at least for me).
the weight and flexibility of the moving part is different too, so the mechanical damping might not be the same as dynamic drivers(I say might but I'm pretty sure it's not).
also the air flow has to be massively impacted by the magnets on each side that are obstructing the path. I'm not sure you can assume the electrical damping to always be of same importance be it to get the membrane at a precise position, or to make the driver stop.
I'm sorry I can't follow you on the formulas, my last years at school where about optic and photography ^_^.
maybe someone can kidnap Tyll, I remember a video where he had broken opened a planar. and he often mentioned talking a great deal with the audeze boys.
This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.
By continuing to use this site, you are consenting to our use of cookies.
