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"Close-3rd Order" Intermodulation Distortion Measurement

When "distortion" is discussed, many think only of "harmonic" distortion. The concept of harmonic distortion is easy to understand -- you apply a clean sine wave, with very low content at its harmonic frequencies, and then analyze the output from the device you are testing for increased relative levels at those harmonic frequencies. It is also easy to imagine a measurement setup for determining harmonic distortion, and such a scheme is done with relative ease in many measurement systems, including LAUD.

There are some limitations associated with the harmonic distortion concept, particularly as concerns loudspeakers and other acoustic or frequency selective audio devices.

First is the limitation of frequency range. If the sensing system is limited to the traditional 20kHz audio bandwidth, then no harmonic distortion will be measurable for applied frequencies above 10kHz (all harmonics will be out-of-band). No third harmonic content will be measurable with applied tones above about 6.6kHz, no fourth harmonic with tones above 5kHz, and so forth. One may be naively lulled into believing that linearity and distortion do not matter at these high frequencies, because the harmonics occur above our hearing range. For speaker drivers, it may seem that there is no need to be concerned with distortion at frequencies near where the driver rolls off in the higher frequencies, because the harmonic distortion products won't be radiated (and if measured, they may in fact appear to be negligible). It may seem that we only need a mechanic filter (like a cloth grille or a low-pass resonator box arrangement) after the driver to make the speaker system nearly distortion free, no matter what signal corruption may occur in the drivers themselves. These beliefs might perhaps be true if only single tones were ever applied to the loudspeakers. But if multiple tone or continuous spectra are applied (such as from music or speech), then more complex distortions will result, and these will occur both above and below the frequencies that the speaker is attempting to reproduce. They can occur very close in frequency to the signals that are applied. The Intermodulation products, if audible, will usually tend to be more objectionable than would simple overtones on a single sine wave; yet a simple harmonic distortion test covering the audio range only might imply that there is no problem .

A second, more severe limitation may be encountered when loudspeaker distortion is being measured. A loudspeaker is often measured in a room or laboratory under less than ideal anechoic conditions. The consequence of echo contamination in a measurement is that some frequencies are accentuated by the arrival of reflections and some are attenuated, sometimes quite severely. In a typical room, the peaks and notches that result will be very closely spaced in frequency. When harmonic distortion is measured in such a room, the result is often unsatisfactory -- the echoes can affect the fundamental tone and the harmonic tones quite differently. As the harmonic distortion is calculated as a ratio involving both, the accuracy or even the intelligibility of the resulting curve will be badly degraded. The technique "Temme's Normalization" (which weights the fundamental and the harmonics before the calculation with the measured response at both frequencies, taken under the same conditions) , available in LAUD, can help with this problem to a limited extent. But harmonic distortion measurements of speakers, other than in anechoic chambers, must usually be done in the near field to try to avoid contamination by reflections.

Close Thirds: The "close third order" type of intermodulation distortion measurement can show a better immunity to echo contamination. For instance, if a distortion product frequency is very close to the stimulus frequencies, the effect of echoes is more likely to be similar at both frequencies. This avoids the double-corruption (both fundamental and harmonics being affectged by the room) that can occur when measuring harmonic distortion.

When the close-third IMD distortion result is used in "normalized" form, that is, when the distortion product level is given as being "so-many dB below" a stimulus level, the common effect of the echo contamination on the tones cancels out. A "close third order" distortion occurs at twice the frequency of one stimulus minus one times the frequency of the other stimulus: at (2*f1-f2) or (2*f2-f1). Therefore, if the two stimulus frequencies are "x" Hz away from each other, the close third order products will appear at "x" Hz to the outsides of the pair of stimulus frequencies.

Closer spacing provides a tightly packed set of stimuli and products and thus better echo immunity for the measurement, but is more demanding on the frequency resolution of the measurement. It is advisable to keep the stimulus spacing to about ten times the resolution (but closer is often ok, depending on the severity expected of the distortion). For instance, at a 48kHz sample rate with a SIZE of 16384, the frequency resolution is about 48e3/16384 or 3Hz; so a spacing between the stimulus frequencies of 50Hz would be a good choice.

Measurement of "close" third-order intermodulation is not subject to the same frequency range constraints of harmonic distortion. The distortion products occur close in frequency to the tones that are applied, so all can remain in the audio band. In a loudspeaker, the product frequencies remain in the freqeuncy range of the transducer being tested, which is the range where the transducer is presumed to be better configured for sound radiation and in which distortion might be expected to be more of a concern.

Close-3rd Order distortion plot of a two-way dynamic loudspeaker. The surround of the woofer in this speaker has a resonance at about 1.2kHz, which may cause the distortion peaks seen

In a loudspeaker, the output energy occurs as a result of numerous movements, resonances, bending, deformations and complex vibrations, and the distortion generation will vary considerably over relatively small frequency ranges. Like the harmonic distortion method, close-third intermodulation can concentrate the applied energy within a narrow frequeny band (allowing the effects to be isolated), but can also take its measured result from the same narrow frequency band rather than from octaves higher in frequency. With LAUDv3, close-3rd intermodulation (as well as other type third order, second order, fourth order, etc., IMD) can be tracked and plotted as a function of the applied stimulus frequencies or of reproduced level, allowing investigation of problem areas.