Impedance - The most ignored and useful measurement tool

I haven’t read this entire thread, but so far, I’m finding it to be a very smart conversation, just the kind of thing that I wish was posted more often on platforms like Audiogon.

The only thing I want to add is that anybody seriously interested in this topic should try to search out a copy of Joe D’Appolito’s long-out-of-print book "Testing Loudspeakers," published in a 1988 small-print run by Audio Amateur Press (which at the time was publishing Audio Amateur and Speaker Builder magazines).  Yes, this book was writtten by THAT D'Appolito.

It’s an outstanding reference, a bit technical for some, but written from an audiophile / speaker-designer’s perspective.

It took me several years to find a copy in the early 90s, and it cost me over $150 from a rare-book seller.  But it was worth the cost & effort to me b/c at the time, I was testing speakers for mainstream magazines. Today, though, even Amazon has copies of a 2018 reprint in the $40-50 range and I believe it's also on Google Books.

Highly recommended.

I wonder if Joe is still alive.  Last I heard, he was at Snell, but that was 15 or 20 years ago...

Honestly, if anyone is interested, head over to DIYaudio were a lot over talented and helpful builders hang out.

I didn't mean to start a whole conversation on impedance, just on how having basic diagnostic tools like this one can be really helpful..

@erik_squires +1 "You’d be surprised how many speakers have a woofer or tweeter that has stopped working but the listeners don’t even realize it. “ I will be not!

speakers impedance is good start, but it will not tell us whole story!

whole amp+cable+speakers system need to be characterized on frequency and time domain, incl. distortions etc., using precise measurement microphone in listening room, using fuzzmeasure software or audio analyzer. I wouldn’t be surprised to see large number of setups will show >5% distortions, +/-10dB amplitude deviation in freq. response, and bad resonances! Tests should be done at different power level, starting 50mW. 

speakers impedance is good start, but it will not tell us whole story!

Nor do I ever claim it is.

whole amp+cable+speakers system need to be characterized on frequency and time domain, incl. distortions etc.,

Why? I was only posting this to show how an important tool can help audiophiles diagnose their problems faster, fix broken systems and mod safely.

I never claimed it was a replacement for full speaker analysis, which in the use cases I spoke about is not needed.  When you say need I think you are thinking far beyond the limited situations I was discussing.

So I emailed Mr. John Atkinson regarding what exactly the fomula they have used in Stereophile for reporting the EPDR. He kindly repsond promptly as follows:

I use a formula created by editor Jim Austin. after importing the Impedance magnitude and phase data into an Excel spreadsheet.

Data = R (magnitude) ohms & R (phase) degrees

Calculate Vdiss = 1+4.2 x ABS(R Phase)/90

Then EPDR = R(Magnitude)/Vdiss

For example:

If R = 4.0 ohms and Phase = +45 degrees

VDiss= 3.1 and EPDR = 1.2903 ohms

Here Vdiss represents voltage dissipation. As a further analysis, this linear equation for Vdiss provides two exact boundary values: one at 0 degrees (which is obvious) and the other at 90 (-90) degrees, as derived by Mr. Jack Oclee-Brown, shown below. However, the linear equation overestimates Vdiss values in between, which in turn results in even lower reported effective impedance.

One possible remedy is to fit the data range with an exponential term, as illustrated in the attached figure. Instead of using 1 + 4.2 * abs(phase angle)/90, nonlinear fitting yields 1 + 4.196 * (abs(phase angle)/90)¹.¹⁷⁸, which provides a much closer approximation to Jack’s formulation.