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Originally Posted by gerG
Hi Rick!
I think the biggest effect of series resistance on dynamics is to change the effective output impedance of the amp. Zero ohm load is the highest dissipation of the back emf current, resulting in maximum damping of the driver motion. Higher impedance results in less damping, so greater driver excursion, I have no idea what is required for "critical" damping of the driver, but it is probably measurable. Damping below critical will allow overshoot, and eventually ringing. The results in the frequency response plots is pretty obvious. I posted a comparison for the DT931 some time ago. I will try to find it.
Now I am curious. For any specific headphone, I would love to know what impedance results in critical damping. Any ideas on how to measure system Q of a headphone?
gerG
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!gerG yad'G
Being electromechanical devices, headphones (like their overgrown brethren -- loudspeakers) rely on a combination of electrical and mechanical effects to control the motion of their diaphragms. On the mechanical side, the diaphragm has mass, its suspension has elasticity, and damping is provided by friction (mainly within the suspension but also to a lesser extent between the diaphragm and the air it moves). This is a classic resonant system, which can also be described in terms of its resonant frequency and "Q" (a measure of the "peakiness" or narrowness of the resonance). The force that excites the system is provided by the interaction between current flowing in the voice coil and a (usually fixed) magnetic field.
All the mechanical properties have direct electrical counterparts:
mass <--> inductance
elasticity <--> capacitance
damping <--> resistance
The voice coil of the headphone provides an electrical "gateway" to the mechanical system; this allows the mechanical properties to be deduced by measuring the complex electrical impedance seen at the voice coil terminals and separating out the constituent quantities. (Description of how to do this is beyond the scope of this thread but can be found in many articles directed at the DIY loudspeaker designer/builder.) These can then be used to model the mechanical system, allowing the use of familiar filtering theory to describe its behavior. This "transformation" works well at low frequencies, where the diaphragm behaves as a single "piston", but becomes less accurate and reliable above a few hundred Hertz, due to localized effects in parts of the diaphragm that are not tightly coupled to (and, therefore, controlled by) the voice coil.
In addition, the electrical characteristics of the external environment can actually alter the effective mechanical properties of the headphone, at least at low frequencies. Typically, this will comprise the output impedance of the amplifier driving the headphone. Usually, the external inductance and capacitance are so small and large respectively that they have a negligible effect on the "native" mass and elasticity of the mechanical system. Since the resonant frequency depends only on these quantities, it is not affected. The external resistance, on the other hand, can have a profound effect on the overall damping of the system.
In order for the listener to perceive a flat acoustic response across the frequency range, it is desirable to control any system resonances. At high frequencies, this is achieved by careful selection and treatment of the diaphragm material; at low frequencies, it is achieved by suitable damping of the fundamental "piston" resonance. The latter end can be met mechanically (by deliberately introducing friction into the diaphragm suspension), electrically (by adding controlled amounts of resistance into the external circuit), or a combination of the two. The HeadRoom web site publishes impedance curves for many of the headphones it sells (or used to sell). These are interesting for the insight they provide into undamped mechanical resonances, which show up as peaks in the electrical impedance. Some headphones, such as the Grados, have a substantially constant impedance, indicating that the diaphragms are damped mechanically. Others, such as the high-end Sennheisers, have pronounced impedance peaks, indicating little mechanical damping.
Feeding a headphone from an amplifier with significant resistance in series with its output will affect the acoustic response in two ways. Firstly, it limits the amplifier's ability to contribute to the damping of the mechanical resonance. This is the origin of the term "damping factor". mathematically defined as the impedance of the load (headphone or loudspeaker) divided by the output impedance of the amplifier (including any additional series resistance). Secondly, it forms a frequency-selective voltage divider that passes a greater proportion of the amplifier's output voltage to the load where the latter's impedance is highest. Note that the term "amplifer" in this context may be just the output stage of a PCDP, MP3 player or computer sound card: these typically have output impedances of a few ohms (more at low frequencies, due to constraints on the size of output coupling capacitors), which is much higher than those of dedicated headphone amplifiers. Even worse are the headphone jacks on stereo amplifiers designed to drive loudspeakers: these typically have output impedances in the hundreds of ohms to avoid damage to the headphones and to protect the amplifier from accidental shorting of its output.
Most headphone manufacturers assume that the amplifier will have an output impedance close to zero in order to achieve the specified response. For Grado headphones, which are mostly mechanically damped, this is not a big issue; for high-end Sennheisers, it is vitally important. If you plug your HD-580/600/650 into the headphone jack of a stereo amplifier, the resultant lack of damping will impart a serious upper-bass boominess around the piston resonance frequency. Other manufacturers, such as beyerdynamic (in the case of the DT-831/931) and Etymotic (in the case of the ER6i), assume a higher amplifier output impedance and deliberately exploit the resonance to lift an otherwise sagging bass response.
In the end, however, gerG is wise in his assertion that personal preference should be one's guide. By all means be aware of what the manufacturer intended but don't be afraid to experiment and remember that what sounds right to you, is right for you.
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