What happened to "impedance" as a complex number measurement?

typical single driver dynamic headphones are mostly resistive at the default 1 KHz frequency used in audio measurements when another standard isn't mentioned

the "impedance" plot is the magnitude of the complex impedance |Z| - in simple (ie minimum phase) circuits the slope of the magnitude plot vs frequency indicates a complex component - where the magnitude impedance plot is flat there is little complex part and the impedance at that frequency is primarily resistive (in fact in minimum phase circuits you can recover the phase, and therefore the full complex impedance from a integral transform of the |Z| vs frequency)

there is a mass spring resonance that appears as an electrical impedance peak at the voice coil at low bass - but depending on magnet, voice coil, diaphragm mass, surround compliance, damping in the driver design the peak may be nearly invisible or up to 2-3x the nominal resistive impedance - the smaller higher frequency peak may be diaphragm modal resonance - in the region of rising magnitude impedance the load is inductive, falling |Z| vs frequency looks like a capacitive load (for single order slopes)

at the highest audio frequencies some impedance rise due to voice coil inductance is sometimes visible, seldom more than few 10% @ 20KHz

see HeadRoom's technical sections headphone graphs - you can select impedance graph http://www.headphone.com/

the "deal" between amp and loudspeaker designers is that amps should be as close to true Voltage sources as possible, - its also considered "polite" for the speaker impedance to not dip below 50% of the nominal rating (usually a crossover network problem)

headphone amps are mostly designed as Voltage sources - although a unused "standard" of 120 series impedance for measuring headphone response exists

Voltage source amps provide whatever current demanded by the load - there is no interaction with the load impedance variations

tube amps, esp OTL, can have large output impedance and the Voltage at the headphone terminals does change with the headphone's impedance/frequency curve - a high output Z amp would allow the bass impedance peak to cause greater SPL output at those frequencies compared to the headphone's response graph when driven with a near zero output Z "Voltage Source" amp

headphones with relatively flat impedance curves with no visible peaking should give the same frequency response with any (constant with frequency) impedance source

some solid state amps include switchable output resistors to tailor the response with headphones that have large impedance variations

You cannot hear the phase shift. 

Quote:

Originally Posted by xnor 

You cannot hear the phase shift. 

Very confident about that, aren't you?

I didn't see that he mentioned loudspeakers, but in the context of headphones I'm pretty confident, yes.

How did Sony get such a nice flat impedance line with the Sa5000's ????

Quote:

Originally Posted by Budgie 

How did Sony get such a nice flat impedance line with the Sa5000's ????

Because the driver is completely uncontrolled it seems.

Flat frequency response, little overshoot or ringing? No chance!