Quote:
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

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.

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

Great Stuff!

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.