Consider a simple two-way speaker having a first order crossover consisting of a capacitor in series with the tweeter, and an inductor in series with the woofer. For each driver that will result in well behaved 6 db/octave rolloff characteristics, which will result in time and phase coherence if other aspects of the design are also supportive, **IF** the impedances of the woofer and tweeter are purely resistive.

However I believe Bruce has been alluding to the fact that the impedances of the drivers are not purely resistive. And it would be more accurate (if still somewhat oversimplified) to electrically model them as consisting of a resistor and an inductor in series.

So the question then becomes: Doesn't the presence of that inductive component of the driver impedance (especially in the case of the tweeter) cause a deviation from first order 6 db/octave behavior? And if so, to a degree that may audibly compromise phase and time coherence? And if so, is that or can that be compensated for in other aspects of the speaker's design?

thanx to the above question posed by Bifwynne & well enunciated by Almarg, I did some research to try to understand what the issue might be.

As I stated in my prev post, my understanding is that if the driver is used within its flat frequency response range of frequencies then that particular driver can be considered linear or purely resistive. And, some research seemed to indicated exactly that! Allow me to share:

When Bifwynne asked the above question, I discovered that it took the me towards understanding the Thiel/Small (or T/S) parameters of loudspeaker drivers. There's much to learn here but that's a subject for another day. Some info that I thought is pertinent to this subject:

There is a T/S parameter called Re (R-little-e) & a cut/paste from Wikipedia

"

Re

Measured in ohms (Ω), this is the DC resistance (DCR) of the voice coil, best measured with the cone blocked, or prevented from moving or vibrating because otherwise the pickup of ambient sounds can cause the measurement to be unreliable. Re should not be confused with the rated driver impedance, Re can be tightly controlled by the manufacturer, while rated impedance values are often approximate at best.. American EIA standard RS-299A specifies that Re (or DCR) should be at least 80% of the rated driver impedance, so an 8-ohm rated driver should have a DC resistance of at least 6.4 ohms, and a 4-ohm unit should measure 3.2 ohms minimum. This standard is voluntary, and many 8 ohm drivers have resistances of ~5.5 ohms, and proportionally lower for lower rated impedances. "

there's also a T/S parameter called Le (L-little-e)

"

Le

Measured in millihenries (mH), this is the inductance of the voice coil. The coil is a lossy inductor, in part due to losses in the pole piece, so the apparent inductance changes with frequency. Large Le values limit the high frequency output of the driver and cause response changes near cutoff. Simple modeling software often neglects Le, and so does not include its consequences. Inductance varies with excursion because the voice coil moves relative to the polepiece, which acts as a sliding inductor core, increasing inductance on the inward stroke and decreasing it on the outward stroke in typical overhung coil arrangements. This inductance modulation is an important source of nonlinearity (distortion) in loudspeakers. Including a copper cap on the pole piece, or a copper shorting ring on it, can reduce the increase in impedance seen at higher frequencies in typical drivers, and also reduce the nonlinearity due to inductance modulation. "

So, it looks like a significant source of distortion is due to voice-coil inductance modulation (variation) & not so much the fact that the voice-coil has actually a DC resistance associated with it (as Bifwynne & Almarg were thinking).

So, how to tell when viewing/reading a driver's specifications that this inductance modulation is an issue? I don't really know but I took up Roy's advice to look at driver specs on Madisound. On the Madisound I randomly selected "Seas Prestige" - Seas makes good drivers, "Prestige" seems like its upper-end line. Here's the link to one of their 8" woofer drivers:

http://www.madisoundspeakerstore.com/approx-8-woofers/seas-prestige-8-woofer-cd22rn4x-h1192

Lots of good info on this page but reading the specs might be Greek to most of us - I wanted to call your attention to the graph which shows SPL (left vertical axis) vs freq & impedance (right vertical axis) vs freq.

From a Wikipedia page on Speaker Electrical Characterisitics I learnt

".....the effective electrical impedance of the speaker to be at its maximum at Fs, shown as Zmax in the graph. For frequencies just below resonance, the impedance rises rapidly as the frequency approaches Fs and is inductive in nature.

At resonance, the impedance is purely resistive and beyond itas the impedance dropsit behaves capacitively. The impedance reaches a minimum value (Zmin) at some frequency where the behaviour is fairly (but not perfectly) resistive over some range. A speaker's rated or nominal impedance (Znom) is derived from this Zmin value (see below)."

This Seas driver seems to have a 6.1 Ohms impedance at, say, 150Hz. Using the info from the Wikipedia site, the driver must be mostly resistive at 150Hz to give its minimum impedance at that frequency. Look at this driver's frequency response from 90Hz - 400Hz: practically ruler flat & look at the impedance variation over this same range - goes from 6.1 Ohms to 10 Ohms on both sides of 6.1Ohms, which is a small change in driver impedance compared to the change over the entire 20Hz-20KHz. The driver appears to be mostly resistive in this frequency range.

I *think* the answer to Bifwynne's question is that if you use this driver in the 90Hz-400Hz range, you will get a mostly resistive driver whose impedance varies very little (between 6-10 Ohms), it's frequency response will be flat/linear & the phase distortion will be minimal meaning that the voice-coil inductance modulation/variation (which is a significant source of distortion) will be negligible.

Roy, please correct me if I'm wrong. Thanks.