I think a look at history will help rationalize this IM discussion. https://www.rfcafe.com/references/e...istortion-electronics-world-february-1960.htm
Look at how audio IM was measured before digital systems were possible. Modern digital systems are trying to emulate the analog solutions originally for compatibility. The analog systems used filters and demodulators. RMS sensing was not practical so RMS indicating average reading instruments were used.
The digital emulations become difficult when there isn't clarity on how to measure amplitude in a narrow band the way the analog system did.
Look at how audio IM was measured before digital systems were possible. Modern digital systems are trying to emulate the analog solutions originally for compatibility. The analog systems used filters and demodulators. RMS sensing was not practical so RMS indicating average reading instruments were used.
The digital emulations become difficult when there isn't clarity on how to measure amplitude in a narrow band the way the analog system did.
The flaw in IMD SMPTE measurement (12 dB too good), that I described has been removed a couple of hours ago with QA's software update v. 1.197, available on their web page
https://github.com/QuantAsylum/QA40x/releases
https://github.com/QuantAsylum/QA40x/releases
In the meantime clarification on the method (for deriving SMPTE IMD from FFT) was obtained.
While there seems to be no agreement here in this forum on the question, if the IM-signals are generally uncorrelated or maybe correlated within each linear combination pair of the same order, the answer is clearly given by the methods prescribed by SMPTE and DIN and TGL (and others).
In a nutshell:
Within a (symmetrical) pair of the same order both IM-signals are correlated due to their origin from amplitude modulation. Hence, f1+ nf2 and f1 - nf2 are both correlated for the same order n, but are not correlated for different orders n.
This explanation is eplicitely given in a remark contained in the TGL Intermodulation measurement standard 17175-04 (TGL was the GDR equivalent to DIN).
That reason lead to the SMPTE and DIN formula for calculation from FFT, which is applied i.e. in ARTA (well known audio measurement software usable with soundcards) and described in DIN 45403:
and is consistent with the same method applied by Audio Precision in its measurement equipment, as described by Richard C. Cabot of that company:
"The modulation components of the upper signal appear as sidebands spaced at multiples of the lower frequency tone. The amplitudes of the sidebands are added in pairs, root square summed, and expressed as a percentage of the upper frequency level."
"added in pairs" = linear addition first, then the sums of the linear addition for each order are rms-summed.
As a matter of fact, the theoretical background for the formula is "nice to know" but actually not essential. It is sufficient to follow the method prescribed by SMPTE or DIN (the same in this case) according to the formula contained therein and shown here.
So far, QA403 v. 1.197and former QA40x software versions do not follow the SMPTE procedure but apply throughout rms-summing for all IM-signals up to the chosen order, regardless if the belong to (symmetrical, linear combination) pairs of same order or not. This results in IMD-distortion values that are too good (too low) by typically 3 dB.
I assume, that QA may want to address this also in one of the future software versions to make Quant Asylum tools readings compatible with the ordinary SMPTE standard. Up to then, with software versions prior to v. 1.197 one has to add hefty +15 dB (explained before, +12 dB due to wrong carrier reference and +3 dB because of non-SMPTE/DIN summing formula) and from v. 1.197 until this final issue is corrected, one has to add +3 dB (typically, if only one order dominates the IM) to the SMPTE IMD readings from the QA40x equipment.
Best Regards,
Reinhard
While there seems to be no agreement here in this forum on the question, if the IM-signals are generally uncorrelated or maybe correlated within each linear combination pair of the same order, the answer is clearly given by the methods prescribed by SMPTE and DIN and TGL (and others).
In a nutshell:
Within a (symmetrical) pair of the same order both IM-signals are correlated due to their origin from amplitude modulation. Hence, f1+ nf2 and f1 - nf2 are both correlated for the same order n, but are not correlated for different orders n.
This explanation is eplicitely given in a remark contained in the TGL Intermodulation measurement standard 17175-04 (TGL was the GDR equivalent to DIN).
That reason lead to the SMPTE and DIN formula for calculation from FFT, which is applied i.e. in ARTA (well known audio measurement software usable with soundcards) and described in DIN 45403:
and is consistent with the same method applied by Audio Precision in its measurement equipment, as described by Richard C. Cabot of that company:
"The modulation components of the upper signal appear as sidebands spaced at multiples of the lower frequency tone. The amplitudes of the sidebands are added in pairs, root square summed, and expressed as a percentage of the upper frequency level."
"added in pairs" = linear addition first, then the sums of the linear addition for each order are rms-summed.
As a matter of fact, the theoretical background for the formula is "nice to know" but actually not essential. It is sufficient to follow the method prescribed by SMPTE or DIN (the same in this case) according to the formula contained therein and shown here.
So far, QA403 v. 1.197and former QA40x software versions do not follow the SMPTE procedure but apply throughout rms-summing for all IM-signals up to the chosen order, regardless if the belong to (symmetrical, linear combination) pairs of same order or not. This results in IMD-distortion values that are too good (too low) by typically 3 dB.
I assume, that QA may want to address this also in one of the future software versions to make Quant Asylum tools readings compatible with the ordinary SMPTE standard. Up to then, with software versions prior to v. 1.197 one has to add hefty +15 dB (explained before, +12 dB due to wrong carrier reference and +3 dB because of non-SMPTE/DIN summing formula) and from v. 1.197 until this final issue is corrected, one has to add +3 dB (typically, if only one order dominates the IM) to the SMPTE IMD readings from the QA40x equipment.
Best Regards,
Reinhard
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A couple of days ago QA have issued software v. 1.198 which is addressing the remaining 3 dB mismatch of v. 1.197 when compared to SMPTE IMD measurement with other FFT-based gear.
Finally, from v. 1.198 the QA40x (QA403) yields SMPTE (MOD) IMD measurement results which are in line with those from other common instruments, like i.e. soundcard / audio interface based REW (Room EQ Wizard), ARTA and the latest (Feb. 2024) version of Multi Instrument (Virtins Technology), hence complies with the standards
A comparative measurement for a particular test amplifier gave identical SMPTE IMD results (2nd + 3rd order IM) within the boundaries of repeatability (approx. +/- 0.5 dB):
1. QA403 with software v. 1.198 IMD (up to 3rd order) = - 46.9 dB
2. REW IMD SMPTE = - 46.8 dB
3. ARTA SMPTE IMD 60:7000 Hz, 4:1 = - 46.6 dB
RMAA:
It shall be noted, that RMAA (Right Mark Audio Analyzer) IMD measurements apply the so called power method with the 60:7000 Hz 4:1 signal pair. Different from the SMPTE (MOD) method, the power method relates the rms power sum of the IM-products to the total power (= essentially the power of the 60 Hz signal). That results in an IMD (power) value, that is always 9 dB (= factor 2.82) smaller than the corresponding SMPTE IMD value. That's why RMAA IMD looks so much "better" than SMPTE IMD.
Finally, from v. 1.198 the QA40x (QA403) yields SMPTE (MOD) IMD measurement results which are in line with those from other common instruments, like i.e. soundcard / audio interface based REW (Room EQ Wizard), ARTA and the latest (Feb. 2024) version of Multi Instrument (Virtins Technology), hence complies with the standards
DIN IEC 60268-3:2019-02
IEC 60268-3:2018
SMPTE RP 120 (2005)
A comparative measurement for a particular test amplifier gave identical SMPTE IMD results (2nd + 3rd order IM) within the boundaries of repeatability (approx. +/- 0.5 dB):
1. QA403 with software v. 1.198 IMD (up to 3rd order) = - 46.9 dB
2. REW IMD SMPTE = - 46.8 dB
3. ARTA SMPTE IMD 60:7000 Hz, 4:1 = - 46.6 dB
RMAA:
It shall be noted, that RMAA (Right Mark Audio Analyzer) IMD measurements apply the so called power method with the 60:7000 Hz 4:1 signal pair. Different from the SMPTE (MOD) method, the power method relates the rms power sum of the IM-products to the total power (= essentially the power of the 60 Hz signal). That results in an IMD (power) value, that is always 9 dB (= factor 2.82) smaller than the corresponding SMPTE IMD value. That's why RMAA IMD looks so much "better" than SMPTE IMD.
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