It's best to keep in mind that if the ammeter you use is not a "true RMS" meter, it will have material errors in its RMS measurements. I could not tell the exact model number of the DMM you are using, so please make sure you look up its exact specs, and I recommend junking it if it's not a true RMS DMM - no need to include avoidable errors in your reviews.

## Measuring Loudspeakers, Part One Page 5

Fig.2 Typical two-way loudspeaker, measured electrical impedance magnitude (solid trace) and phase (dashed trace) plotted against frequency in Hz.

In private communications back in 1991, both Fred Davis and Don Keele pointed out that *Stereophile*'s loudspeaker impedance phase curves published between late 1990 and early 1991 were upside down, in that the positive and negative phase angles were reversed [22]. (Negative phase angle, the current leading the voltage, is due to the load being capacitive; positive phase angle, with the current lagging the voltage, is due to the load being inductive.) This appeared to be due to a software bug; *Stereophile*'s published curves since then have been corrected, with negative phase angles plotted below the frequency axis. However, looking at impedance plots published in books and other magazines reveals wide disagreement on this. Some writers still appear to confuse capacitive and inductive phase angle, while others conventionally plot negative phase angle *above* the frequency axis.

What is a typical loudspeaker impedance? Fig.3 tabulates the mean impedance magnitudes of 330 of the loudspeakers measured from January 1991 through June 1997 (six speakers had integral amplifiers or were intended to be used with external line-level crossovers; the impedance of the others were not measured for various reasons). Only a small number of models feature mean impedances below 4 ohms or above 15 ohms, with the overall mean equal to 8.6 ohms. The median value is 9.25 ohms. According to Martin Colloms [18], the German DIN standard requires that a loudspeaker's impedance magnitude not vary more than ±20% from its nominal value. However, I have found loudspeaker impedances tend to range higher than this, the average standard deviation on the mean 8.6 ohms being 3.7 ohms or 43%. As long as the driving amplifier has a low source impedance, this variation in impedance magnitude will not introduce any sonic effects. But when a tube amplifier is used, which can have a so! urce impedance of perhaps a few ohms, the result can be a significant variation of the loudspeaker's perceived frequency balance, as has been pointed out in *Stereophile* [23].

Fig.3 330 loudspeakers, mean impedance magnitudes.

Fig.4 tabulates the *minimum* impedance magnitudes of the same 330 loudspeakers. It can be seen that there is much less variation than with the mean values, with the majority of models having a lowest impedance between 2.76 and 4.26 ohms. The mean and median were 4.3 ohms. In fact, disregarding an exotic electrostatic design that resembled a short circuit above 30kHz, and early samples of two speakers that featured an exotic crossover and dropped below 0.5 ohms above 100kHz, only 6 models had a lowest measured magnitude below 2 ohms. For interest's sake, the loudspeaker with the highest minimum value—8.33 ohms at 171Hz, with a phase angle of -3.1 degrees—was a 1977-vintage BBC LS3/5A. One interesting national difference emerged: moving-coil speakers designed by British engineers tended to have their minimum impedance in the high treble, around 10kHz, while those from US engineers tended to have it in the low midrange.

Fig.4 330 loudspeakers, minimum impedance magnitudes.

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I could not tell the exact model number of the DMM you are using, so please make sure you look up its exact specs, and I recommend junking it if it's not a true RMS DMM - no need to include avoidable errors in your reviews.

Both the Audio Precision analyzers and the Fluke 87 multimeter I use to produce Stereophile measurement sidebars are true-RMS-reading instruments. See, for example, https://physics.ucsd.edu/neurophysics/Manuals/Fluke/87______umeng0800.

John Atkinson

Editor, Stereophile