In the two previous parts of this interview that began here, Mr. Giuseppe Parolo, author of the research Properties of Nonlinear Distortions and Related Measures in Audio Amplifiers, published in the Journal of the Audio Engineering Society, showed us how nonlinear distortions can help make listening to music more audiophile. The definition "audiophile" in this case is to be understood as a mix of the terms fidelity, truthfulness, naturalness and so on, all descriptive linguistic metaphors that we reviewers – and first and foremost audiophiles – use to connote a home reproduction that seems closer to the real or recorded event. The "why" this happens has been explained to us, in the simplest way possible, precisely in the first two parts of this article. The time has now come to address "how" this happens, how in short, nonlinear distortions can be introduced, even intentionally, in the amplifications, obtaining a greater subjective/objective listening satisfaction.
Question: Electroacoustics says that tube amplifiers typically exhibit second harmonic distortions. This would seem to make them "pleasant" and many audiophiles confirm. How much do this data and these observations have to do, if any, with your research?
Giuseppe Parolo: Second harmonic distortions are typically observed in tube circuits, but can also be found in circuits based on solid-state components. The listening effects produced by an amplifier with predominant second harmonic distortion are those of increased “smoothness” and “warmth”. If in excess, there can be a feeling of “swelling” of low frequencies and less definition of sound. These effects are due to the intermodulation products created by the frequency differences between all combinations of tones in the original signal. In my study, I tried to visualize the effect on a complex “music-like” test signal. Fig. 8 shows an input signal x(t) consisting of 64 tones spaced 1/6 octave apart starting at 30 Hz, with a level decreasing in frequency linearly by 2 dB/decade starting at -24 dB and with random phases. I specify that even non-small changes in these values do not result in substantial changes in what is described below.
Fig. 8 - Frequency trend of a "music-like" synthesized signal, in blue, and its envelope, in orange.
The diagrams in Fig. 9 show the simulation of the frequency trend of distortions created by a system with only the second harmonic distortion at -60 dBs. Fig. 9(a) shows the distortion component added to the signal (v(t) of Fig. 7, while Fig. 9(b) shows the same response without the components at frequencies coincident with those of the fundamentals.
Fig. 9 - Simulation of the transit of the "music-like" signal in a nonlinear system with only second-order distortion at -60 dB, referred to the envelope of the source signal. The upper graph shows all intermodulation products, while in the lower one are shown only those that do not coincide with the fundamentals.
The distortion carpet created by the intermodulation products - about 3400 components - which resembles white noise but is actually related to the signal is evident. In the figure, no substantial differences between the two signals can be seen, a sign that the frequencies of the fundamentals undergo alterations of the same magnitude. Fig. 10(a) shows the density of intermodulation products per octave.
Fig. 10 - Density of the number of intermodulation products per octave: on the left for a system with only second-order distortion; on the right for one with only third order distortion.
It can be seen that high values in low frequencies gradually decrease as frequency increases. This tendency, combined with our ear's masking effect, which is milder in frequencies below the masking frequency, justifies the perception of greater tonal components in the low frequencies, the more pronounced the higher the distortion. It appears from the models that the presence of second-harmonic distortion - or, rather, even orders of distortion - actually also hides a DC component, which is usually elided by coupling capacitors, an effect visible in the first part of the curve in Fig. 2.
In my study, I also tried to characterize the structure of the distortion of the second harmonic by analysing the effects over time on the signal due not only to the level of the distortion but also to its phase, which is normally neglected. Simulations show that in the case where the second harmonic has a phase of -90° or +90° relative to the fundamental, the impact of the distortion on the signal has the following characteristics:
- in the case of distortion with phase at -90° the transients - positive - are enhanced and advance in time, while the opposite occurs when the phase is at +90°;
- the intensity of the distortion increases in value by increasing the signal level, but is independent of frequency, while the phase, on the other hand, always remains unchanged.
If the phases deviate significantly from the values of +90° or -90°, a situation that indicates the influence of memory effects in distortions as well, these two properties become progressively less true. The result is that the physical effect of distortion on the signal is as smooth as possible when the phases are exactly close to the values of +90° or -90° throughout the audio band or nearly so.
It also appears from the models that all even harmonics are related to each other, and those of lower order are influenced by those of higher order. The latter - of order 4, 6, 8, etc. - if of non-negligible magnitude, can cause faster changes in the levels of the lower harmonics, depending on the level of the signal, and in some cases can change the sign to the phases.
Thus, at the same level, not all second harmonic distortions are equal. This result also extends to all even-order harmonics.
Question: On the contrary, solid-state amplifiers, transistor ones in general, being current regulators generally "control" the speakers better, offering on paper more theoretical correctness and a more correct sound from an electroacoustic point of view. However, they tend to exhibit third harmonic distortions, or in general of the odd order, and this often makes them unpleasant, not only to the ears of audiophiles but also to the common listener. How much does this entail, if any, with your research?
Parolo: In common experience, predominant third harmonic distortion is associated with a more “airy” and “bright” sound effect. If excessive, it can cause a feeling of “roughness”. In this case, the effect on the signal is to apply a kind of contrast effect to the signal.
Again, in my study I tried to physically visualize the effect on the “musical” signal of Fig. 8 by simulating its transit in a system with only third harmonic distortion. Fig. 11(a) shows the distortion component added to the signal (v(t) of fig. 7) where the presence of a distortion carpet of well over 43000 components is always noted.
Fig. 11 - Simulation of the transit of the "music-like" signal in a nonlinear system with only third-order distortion at -60 dB, referred to the envelope of the source signal. The upper graph shows all intermodulation products, while in the lower one are shown only those that do not coincide with the fundamentals.
Fig. 11(b) always shows the distortion without the components at frequencies coincident with the fundamentals. Here the differences are obvious: these are in fact components hidden by the third harmonic - more generally, of all odd orders of distortion - that cannot be detected by direct measurements. However, different models predict their presence and they are to be considered for all intents and purposes distortion, since they depend nonlinearly on the level of the original signal. Unlike the second harmonic, the density per octave of intermodulation products shown in Fig. 10(b) does not vary much with frequency.
Regarding phases, I found that these distortions can be classified according to the phase of the third harmonics:
- 180° / -180° phase is “expansive” for the signal;
- the 0° phase is “compressive” for the signal.
For the same intensity of third harmonic distortion, the effects on the signal can thus be diametrically opposed: in the first case the original tones gain energy; in the second case they lose energy. In the case of 180° or 0° phase values, these effects are independent of frequency; for significant deviations from these values there is also the influence of memory effects, with effects similar to those described for second harmonic distortions.
The models also show here that all odd harmonics are related to each other, with those of higher order affecting those of lower order, by level and phase.
Therefore, at the same level, even the distortions of the third harmonic are not all the same. The result extends to all harmonics of odd order.
Question: In addition to the theoretical models, have you been able to apply or verify your research on real devices? With what confirmations?
Parolo: This is the more practical and at the moment less objective, but more challenging, part of my research, in which I involved several experienced people, including musicians. As already anticipated, the results summarized below are still the subject of experimentation, thus not fully established; however, most of them turn out to be in line with those of Nelson Pass, with whom I have had the privilege of confronting several times.
Over several years I have been fortunate to have over thirty preamplifiers and about ten power amplifiers available for testing, of different technologies and brands such as Audio-gd, Audio Research, Gryphon, Jeff Rowland, Kondo, Krell, LTA, Luxman, Mark Levinson, Threshold and others. Also, on Tino's and Roberto's equipment – Ed. | See first part here – I performed tests by changing for the same preamplifier, thus on the same circuit, the working points or a component, tubes or capacitors. The listenings were performed by changing only the preamplifier on one or more reference chains with well-known characteristics. The tests were performed at controlled sound pressure levels with several people unaware of the details of the measures. The main listening room was acoustically treated with the help of a Sound Engineer/Acoustic Designer, Mr. Luigi Bisogno, see here.
In cases where it was possible to make a correct comparison, since it is necessary that the other measurements were also similar, the effects found on listening, correlated with the classical measurements, were sometimes in line with common experiences, others a little less. By also examining the phases of the distortions, I have often found a plausible explanation.
More specifically, when the predominant distortion is of second harmonic we have, relative to its phase:
- Phase +90° approximately, the soundstage is deeper, away from the listener
- Phase -90° approximately, the soundstage is closer to the listener
The tonal balance is not altered. The reason for this effect could be traced to the way the distortion acts on the signal transients that our brain uses to derive information about spatial location: in the case of distortion with phase at -90°, the transients - positive - are enhanced and brought forward in time; the opposite happens when the phase is +90°.
When the predominant distortion is of the third harmonic, in relation to the value of its phase the following effects occur:
- Phase +180° or so, more dynamic and “rougher” sound
- Phase 0° or so, “flatter” sound
The reason for this is that the fundamentals in the former case have contributions from the distortions that add up; in the latter they subtract. This energy contribution is predominantly on the higher levels of the signal, much more pronounced than those of the second harmonic. Which of these two effects is preferable to listening seems to depend both on the musical genre - and thus on the musical instruments - and on the room acoustics: in rooms with good acoustics, an expansive effect is preferable; in those rooms, a compressive effect, which helps to reduce the feeling of “edginess” created by room reflections not at textbook levels, may be more pleasant.
When second- and third-harmonic distortions are comparable, different effects are observed at varying volumes. Generally, second-harmonic distortions predominate at low-medium levels, while third-harmonic distortions predominate at high-medium levels. The situation becomes much more complex with higher orders of distortion since there are many more variables. The result depends on how the energy of the distortions is distributed among the different orders. Generally, the amplifier imparts a more distinctive sonic signature to the sound, which negatively affects sound fidelity but not necessarily pleasantness. If the phases deviate significantly from the indicated values, the magnitude and phase of distortions become dependent on both signal level and frequency, and the effects on listening become variable and less decipherable. On average, there is a greater feeling of artificiality of the sound.
End part 3 of 4 - To the fourth part
For further info:
write to Eng. Parolo
to JAES website
to AES website
