Hi,

I just read Keith Howard's article, "Heavy Load: How Loudspeakers Torture Amplifiers" and was wondering what the formula was that he used to generate the EPDR graphs? I tried deriving it myself, but got stuck halfway though.

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I just read Keith Howard's article, "Heavy Load: How Loudspeakers Torture Amplifiers" and was wondering what the formula was that he used to generate the EPDR graphs?

Keith generally makes his programs available on his website:

www.audiosignal.co.uk/freeware.html

However, the program to calculate a speaker's EPDR index is not yet available.

John Atkinson

Editor, Stereophile

Thanks John. I checked his site before which is the reason for my post here. I hope Mr. Howard can make it available, or at least the source code (in any language), so that others can analyze and learn from his take on "viewing the load as if I'm an amplifier" to then graph the extremity points. Source code for gnuplot would work best for me.

His take on this so intrigues me, I've opened my old college math textbooks to reteach myself differential convolutions..

But alas, I'm not as good with this stuff like I once was..

Thank you for your interest in 'Heavy Load', David. I didn't include any formulas in the article because I generally try to keep my writing free of them, particularly when they are moderately complex as these are. I didn't make the software available on my web site because my freeware is intended principally for the use of general readers and few of them will have access to the modulus and phase data files that are required. Audio professionals can make their own arrangements!

The easiest way to access the relevant equations is by purchasing a copy of the Eric Benjamin paper from the AES web site. It costs $5 if you are a member, $20 if not.

Hi Keith,

Looks like I'm on my own.. I have Eric's paper, in my hands. A true eye opener. Any hints how to put this stuff into Matlab? I'm lost in the math of "Peak transient current and power into a complex impedance" preprint 2337 as I write this post.

Keith, I adore your articles. Please keep experimenting and writing.

Great Stuff!

i agree. An eye opening concept with this.

Thanks, Elk, I will endeavour to.

Can't help you directly with the Matlab programming, David, as I don't use Matlab myself. I could never find anyone to pay for it! The key thing to remember when calculating the EPDR versus frequency is that at each frequency step you must first identify the signal phase at which peak dissipation occurs, from 60-phi/3 (degrees), where phi is the speaker phase angle. (See column 1, page 672 in the Benjamin paper.) BTW, Benjamin doesn't include a proof of this expression but I can send you one if you're interested. You then use this signal phase in eqn 4, together with the speaker modulus at this frequency (|Z|), to calculate the peak instantaneous dissipation. For a worst-case figure, set Vss=Vo. You can calculate the dissipation for a pure resistance by using a signal phase of 60 degrees and phi=0 in eqn 4. Hope this helps.

Interesting as the Preis article is, and the later Vanderkooy/Lipschitz paper on the same subject, like the Otala experiments these deal with the theoretical worst case which requires waveforms which appear not to occur with any significant frequency in music.

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Interesting as the Preis article is, and the later Vanderkooy/Lipschitz paper on the same subject, like the Otala experiments these deal with the theoretical worst case which requires waveforms which appear not to occur with any significant frequency in music.

Yes, thanks. I've abandoned those. I've spent the last 2 days of my evening time in SPICE wrapping my head around this EPDR idea. This is the emulation circuit of a basshorn speaker I have

Which gives an Impedance response of this which matches the measured data quite well

Experimenting running steps and plot overlays, I found the worst case transient @ 94Hz which goes to 2.6 times the average. And just looking at average for that freq, 7.5ohm@-40deg is equivalent to 5.9 ohms of resistance based on the same amp dissipation.

This concept is so cool.

Oh, about Matlab.. There's a free (freedom/beer) one called Octave which is a Matlab workalike.

Thanks for your help, I think I'm "on the path'.

Keith,

Here's the results of trying EPDR on a bass horn loudspeaker of mine. I'm quite pleased with this way of looking at a loudspeaker load in terms of the work an amplifier has to do.

Keith,

Wouldn't the next step be to rate amplifiers for a minimum EPDR? For example, say an amp had a minimum rating of 2 ohms with 45 degrees of phase shift. What's the EPDR for that?