Hi VAR,
watch out for the nifty details.
Section 3.17 is what I have been talking about, namely SMPTE and DIN. And that paragraph 3.17 in the paper you show is actually silent about how exactly the calculation shall be made for correct SMPTE and DIN readings.
Section 3.18 in your paper talks about generic “Dual Tone Intermodulation Distortion” which is different from SMPTE and DIN methods. The difference is twofold:
In the SMPTE and DIN methods the voltages of the same order of intermodulation must be linearly summed first before taking the square of the sum for each order. That is how each voltage for the same IM-order is obtained including the f1+nf1 AND f1+nf2 IM-components for the same order (same n). Then, In the second step, the obtained sum voltages for each order n must be geometrically (rms) summed, which means calculating the square root of the sum of the squares of each order. That is different in the nominator of your formula in paragraph 3.18, because that paragraph refers to the so called “power method” that is applied to generic Dual Tone IM measurements, but NOT to measurements according to SMPTE and DIN.
In generic Dual TONE IMD measurement one uses two frequencies 1 kHz apart, like 13 kHz and 14 kHz, or 18 kHz and 19 kHz and monitors the IM-products relative to the geometrical (rms) sum of Vf1 and Vf2. This is the so called “power method”, wherein the ratio of the power of the IM-products is related to the total power.
For SMPTE and DIN measurement however, the power method is not used, therefore the denominator is only Vf2, not the rms sum of Vf1 and Vf2.
It is unfortunate that IM Distortions are measured by different ways with different formulas and concepts behind. That is causing a lot of confusion and makes many measurements in different studies difficult to compare, especially if it isn’t said which method was used and how exactly.
For example in the so called “power method” of Intermodulation distortion measurement, employing f1 = 60 Hz and f2 = 7 kHz all IM-components (also those of the same order) are geometrically (rms) summed and related to f1 instead of f2 ((actually related to the rms sum of f1 and f2 and the sum of the power of all IM products , however since Vf1 and Vf2 are in a 4:1 ratio, the power of f2 can be neglected relatively to the power of f1 as well as the power of IM products relatively to the power of f1, that simplification isthe “simplified power method”). Clearly, that is not the SMPTE method, although it uses the same measurement set-up - but different calculation. It results in much lower distortion numbers (making it look better) than the calculation result according to the “real” SMPTE and DIN method. Linear summing the two components of the same IM-order of similar amplitude makes the sum about 3 dB larger than rms summing. Referring to f1 rather than to f2 as reference makes 12 dB difference! Overall, using the power method with two signals in a 4:1 ratio, results in an IMD value which is typically by about 9 dB “better” (lower) than if measured according to the SMPTE or DIN methods. For example, that is the case for IM-distortion values reported by RMAA (Right Mark Audio Analyzer).
Why is the sum of geometrical (rms) summing of two amplitudes by 3 dB less than with linear summing?
Linear summing of the amplitudes at the frequencies f2+nf1 and f2-nf1 for the same n, where both amplitudes are assumed to be equal, and of the size Vn:
Vn + Vn = 2x Vn
in dB: 20 x log(Vn) + 6 dB
(In SMPTE and DIN amplitudes belonging to the same IM-order are linearly summed)
Geometrical (rms) summing of the amplitudes at the frequencies f2+nf1 and f2-nf1 for the same n, where both amplitudes are assumed to be equal, and of the size Vn:
sqrt [(Vn)^2 + (Vn)^2] = sqrt [ 2 x (Vn)^2] = sqrt(2) x Vn = 1.414 x Vn
in dB: 20 x log(Vn) + 3 dB
(in SMPTE and DIN 4:1 IM methods amplitudes belonging to different IM-order are rms-summed)
However, in the power method all amplitudes of IM-products are rms-summed, regardless of IM-order)
If - like in the power method - all IM components (also those of the same order) are geometrically (rms) summed but the sum is related to f2, which one can find sometimes, makes the final IMD value by 6 dB better (lower) than with the correct SMPTE and DIN methods.
It is therefore mandatory that a method designated as Intermodulation Distortion measurement according to SMPTE and DIN uses the correct formula behind and not "some other, which is known from another, but different measurement method. Just this case, that we are talking here, shows, how important it is to stick to the standards in the official documents and not "something which sometimes may come close or which we believe may be applicable without having that confirmed.
Virtins Technology (Multi Instrument) had it wrong (have been using the simplified power method for SMPTE and DIN) for years until they corrected it finally in 2024 (I quoted the paper). I think, we should apply the right math, so tht the results with the QA40x is comparable with the results of an Audio Precision tool or a Multi-Sim tool or the softwares REW or ARTA, which all do it the right way.
Unfortunately the initial white paper related to IM-Measurement with the QA40x
[QA40x and IMD Measurements – QuantAsylum] from August 08, 2013
had it initially wrong as well as early software versions. But from QA402 / 403 software V. 1.198 onwards it was corrected, since then for the SMPTE and DIN method the right math was used.
Regards
Reinhard
