[higbvuyb]

  And the original thread is?

 
If you click the icon to the right of 'Originally Posted by ab initio ', it will take you straight to the quoted post.

 

[Currawong]

Moving the posts changes the thread owner by the way, but about 2 pages of the HD-800s being picky about amps thread have been put here.

 

[castleofargh]

thank you

 

[ab initio]

Ok, here's the thread. So what makes you think I have my fundamentals mixed up a bit?

se

 
One example is the comment that "damping" is meaningless outside of resonance. ironically, you said that immediately after your link to wikipedia on damping.
 

I think its important to flesh out the details and get the whole story of "damping factor" organized into a coherent storyline.

 
Any speaker design is an electromechanical system. Let's first start by looking at the mechanical system before introducing the electro- bit....
 
I've argued that the zeroth order model for a speaker is a mass-spring-damper system. Fortunately, this system is extremely well studied and understood.
 
The classic 1 degree of freedom dynamical system is the mass-spring-damper system. If the position of the oscillator is x and letting ' denote the derivative with respect to time, then the system can be written as
 
M*x'' + C*x' + K*x = F. [1]
 
M is the mass, C is the the viscous damping, and K is the spring stiffness. The system may be subjected to an external forcing F.
 
The point here is that the dynamics of the system are influenced by the damping, C, whether the system is subject to a sinusoidal excitation, an impulse, a step response, etc. The damping in the system affects the response whether resonance is of interest or not.
 
Of interest in the above single DOF system are the quantity sqrt( K / M ), which is called the natural frequency and is usually denoted by omega, and the quantity C / (2 * sqrt( M * K ) ), which is called the damping ratio and is usually denoted by zeta. These will look familiar to anybody who's peaked at the wiki article on damping to which SE linked.
 
The natural frequency is important because it gives the frequency that the system would oscillate at in the absence of damping.
 
The damping ratio is important because it tells us strong the damping in the system is. When the damping ratio is < 1, then the system will be oscillate about equilibrium with decaying amplitude in time. When the damping ratio is > 1, then the damping is strong such that the system will slowly decay toward equilibrium without ever over-shooting. Finally, there is the critical case where the damping ratio is exactly 1. In this case, the perturbed system decays toward equilibrium as fast as possible without ever overshooting.
 
Now, let's add in the forcing, which is where the "electro" in "electromechanical" comes into play... Here, the field equations required to analyze a the electromotive forces on a speaker are a bit more complicated that the single degree of freedom oscillator; however, a good starting point for electromagnetic induction can be found on wikipedia. basically, the forcing term, F, will be proportional to the current in the headphone coil/etched traces (in a dynamic/orthodynamic headphone) times the strength of the magnetic field. Namely, one integrates i  x B over the contour of the circuit to find F, where i is the current and B is the magnetic field.
 
When you plug a speaker into an amplifier, the speaker is (to some approximation) a mass-spring-damper system and the amplifier's voltage drives current through the speaker coils/etched traces that generates a force that excites the system. This would be the force F. The force on the transducer is due to the magnetic field through with the speaker coils/etched traces run through. Likewise, as the coils/etched traces move through this magnetic field, current is induced in the coils/traces which forms an magnetic field that tends to resist further motion of the coils/traces (given that the coils/traces experience little resistance). That force is proportional to the rate which the speaker travels through the magnetic field and opposes the motion (Lenz's law)---it is essentially a viscous damping force! This electrical damping force could be moved from F and included on the left hand side of the dynamics equation [1], augmenting the physical damping. Hence, the electrical damping is an effect which effects the mechanics of the transducer.
 
A neat visual for the mechanical forces generated by the relative motion of magnetic field lines and closed circuits can be seen in any of the demos where magnets are dropped through electrically conducting, yet nonmagnetic tubes. The eddy currents generated by the moving magnetic field lines relative to the conductor generate their own magnetic field which opposes the motion. Because the tubes are very low resistance conductors forming closed circuits, large induced currents are allowed to flow, generating significant mechanical resistance to motion. In the absolute absence of resistive losses (i.e., superconduction), the magnets may even be completely suspended (levitated).
 
Moving the opposite direction of superconduction.... if you increase the resistance in the circuit through which the induced current flows, then the increased resistive losses reduces eddy current and consequently reduces the counterelectromotive force. One nice visualization of this is to compare the speed of the magnets falling through a solid copper tube vs the magnet falling through a copper tube with slots cut into the side (thus decreasing the conductivity of the eddy current circuit.) This is what is happening with the "damping factor" in amplifier outputs. The "eddy current circuit" in headphones consists of the circuit from the amplifier, through the cable, through the headphone coil/traces, and back through the cable and into the amp. The amplifier output impedance is the resistance contributed by the amp to this circuit. The larger the output impedance, the less induced current can flow, and the lower the counterelectromotive force which damps the speaker.
 
This is what the damping factor is here to tell us---how the output impedance of the amp compares to the rest of the headphone circuit. The higher the damping factor, the less the resistance in the amplifier output reduces the effectiveness of electrical damping in the speaker. It doesn't matter whether the speaker design is classic or orthodynamic. If the speaker design is such that it is driven by current flowing through wires/traces in a magnetic field, then the motion of that speaker through the magnetic field will induce a back emf which can drive a (damping) current if the circuit impedance allows it.
 
 
 
So, that's my overview of speakers and damping from first principals. I can try to elaborate on specific points. I'm not arguing whether electrical damping is or isn't critical in the performance of headphones/speakers/orthos/etc. I just want to bring transparency to the physical processes at play and hopefully learn more about when, where, and why they make an impact on sound (when they do) and when, where, and why they don't matter (when they don't).
 
Cheers

 

[Steve Eddy]

*sigh*

se

 

[ab initio]

Help me out here. Here are the first principles, what are typical M, C, K, and F? How big is the electrical damping compared with the mechanical damping, C? Obviously i think in a bottom-up sort of way, help me connect to the top-down approach.

Cheers

 

[jcx]

planar orthodynamics have abysmal electrical to mechanical coupling so electrical damping is not very effective/not a big part of their response - the membrane motion is mostly damped by the mechanical/acoustic elements
 
the coupling coefficient being low can be seen in the low sensitivity number and the fact that diaphragm mass-spring resonance is barely visible in the electrical terminal impedance vs frequency
 
 
 
if you really want to hear the effect of electrical damping with orthodynamics there is a trick that could be used - you can make a amp with negative output Z over some frequency range - if you cancel most of the electrical series resistance then you can get significant electrical damping
 
but this only works when the amp negative resistance and the load series resistance match well - any excess negative resistance causes instability, and load+cable Z change with frequency too so the amp negative resistance would have to be frequency shaped too, has to return to safe positive Z above audio 

 

[ab initio]

planar orthodynamics have abysmal electrical to mechanical cothing so electrical damping is not very effective/not a big part of their response - the membrane motion is mostly damped by the mechanical/acoustic elements

This was my understanding why t50rp mods are so popular. One cracks open the headphone and makes adjustments to the damping in the headphone. (That and cup acoustics)

Cheers

 

[castleofargh]

 

planar orthodynamics have abysmal electrical to mechanical cothing so electrical damping is not very effective/not a big part of their response - the membrane motion is mostly damped by the mechanical/acoustic elements

This was my understanding why t50rp mods are so popular. One cracks open the headphone and makes adjustments to the damping in the headphone. (That and cup acoustics)

Cheers

I'll go with that too. the tension on the membrane is strong even when motionless, part of why it's harder to get strong low freqs on those compared to dynamic drivers and why the transient responses are so fast.  being kept inside the magnetic field at all times must also help compared to the dynamic coil getting away from the magnet.

 

[davidsh]

How can impedance in an amp be negative?

 

[Speedskater]

How can impedance in an amp be negative?

It's easily possible. It's done by modifying the feedback loop. Audio Amateur magazine had a section on doing it many decades ago.

 

[SilverEars]

Capacitance.  The graph shows magnitude.

 

[davidsh]

I kinda see, it just sounds counter intuitive.

 

[jcx]

http://sound.westhost.com/project56.htm is simplistic, no working examples but maybe useful generalities
 
plenty more in the usual search https://www.google.com/#q=negative+output+impedance+amplifier

 

[ab initio]

This article seems relevant to this discussion.
 
http://www.silcom.com/~aludwig/Sysdes/Thiel_small_analysis.htm#Top
 
I still can't find any published Thiele/Small parameters for orthodynamic headphone drivers. If anyone can point me in the right direction, it would be much appreciated.
 
Cheers