Non linear distortion and harmonics: A Subjective Approach

In the past years, while I documented myself on sacred texts, I was struck in reading of Cap. XIV in the Radiotron Designer’s Handbook, since in the designing of an Electroacustic System, both technical and subjective questions were mixed in order to produce the final result. In fact studies led by Olson, Shorter and others, although different in the conclusions always put in relief the correlations between instrumental measures and psychophysical feeling on listeners. Something must be happened somewhere in the ’50 and/or ’60 since instrumental measures have supplanted almost completely the subjective aspect of the matter. During the ’70 this trend has conducted to the immision on the market of cheap audio equipments with notable instrumental performances but unsatisfactory under the sonic profile. Exceptions don’t have softened this trend. The eighties paved the way for the current soft "revolution" both characterized by the Vacuum Tubes return on the audio arena and the fall of a conception based on all-technical approach. Unfortunately this years "see" even the emerging of an opposite trend (as much as harmful) that refuse totally the technical approach to advantage of a "subjective designing"; you can often ear about amplifiers and bias point "tuned by ears" or observe an excessive affection for the passive components as resistors and/or capacitors. Clearly audio equiments are neither measurement instruments nor by-product of subjectivity therefore an one-way approach is certainly unsatisfactory and the hope is that as soon as possible an equilibrium between these two opposite tendencies is recovered in order to take again the journey interrupted on the fifties.

The correlation between instrumental measures and psychophysical experience connected with listening is extremely complex: on the one hand we have the limitations of the electroacustical system unable to perfectly recreate the real event, on the other hand we must admit a limitated knowledge of the processes involved in our auditory system, Fig. 1.

Fig. 1

The source event is at first capted by the ears. The subsequently transduction process is non linear. Further it seems transduction is based on a "mechanism" involving a time-integration on intervals of 0.25s for very complex signals (i.e. when complex signals are involved the signal energy on intervals of 0.25sec. is calculated). Subsequently, the elaborated signals pass through an "Entropic Channel" . The "entropy" term is here used from a Communication-Theory point of view not "thermodynamichally", further the "channel" cannot have solely a physical evidence. However the signal passing this channel is subjected to a degrade quantifiable with difficulty and the Modern Communication Theory tries to fill the gap with a Statistical characterization. Therefore the elaboration processes involved in our brain are based on extrapolations often subjective and not perfetcly quantifiable.

The "statistical approach", at the moment, it’s the only way easily practicable and you can consider even good the approach followed by the fathers of electroacoustic.

In the course of this investigation I have organized "samples" of Audiophile groups not prone to mutual influences. The results have confirmed the important role, although not fundamental, played by the THD on the listening experience. Results shown in Table 1 seem to confirm classical results [1] with some exceptions.

Fig. 2

I have limited this analysis to triode circuits, further inevitable "boundary conditions" exists correlated with reference components (as source and/or loudspeakers) selected from time to time. Clearly the fact that small values of THD are perceived cannot compromise the enjoyment of the listening experience.

This eventuality is surely present when the well IMD mechanisms are involved; nevertheless small values of THD are necessary in order to limit IMD. The hearing experience could be compromised in a more sly manner when phenomena of timbric alteration are involved. In this case the listener still perceives a good sound altough not very close to the real event. In this case the signal harmonic content plays a very important role. For example, signals with 5% of 2^nd harmonic only are certainly less perceptibles than signals with wider spectra having the same THD value; nevertheless timbric alteration in the first case can be more evident (I have experienced this phenomenon during the listening of chamber music).

The problem is therefore twofold. On the one hand you must contain the THD levels in order to avoid that non linearities due to IMD reveal themselves, on the other hand you must control the spectral content for a satisfactory timbric response. However the problem is very complex because it’s very difficult to foresee in the real listening conditions the true harmonic content of the signal; further THD is a quantity referred to a steady-state signal while the nature of real signals is impulsive. Nevertheless a correlation between THD, harmonic content and subjective response exists.

The schematic in Fig. 2 was utilized in order to analyse, in a not rigorous manner, this correlation. The power amplifier A is a low power low distortion low sensibilty solid state amplifier with J-fet input. The SRPP represents a kind of booster for this power amplifier and thanks to R variabilty permits to control the produced THD both quantitatively and qualitatitvely. Audiophile groups have formulated their opinions when a quantifiable electric power was furnished to high efficiency loudspeakers. I have found almost unanimous opinions. The increase in R and therefore the approach to the minimun in THD condition, involved always a subjective amelioration of the musical reproduction with an increase on detail, transient response and image to detriment of a loss in body and warmth. Groups A,B, and C have recognized this effect until the minimum condition was reached. Subsequently this condition they picked-up an excessive sound depersonalization. D and E groups instead recognized a costant and progressive amelioration with the increase of R.

I find this results very intersting since the change in the subjective sphere is given by an alteration of the higher order content present in the signal produced by the booster as well as by a THD reduction. Similar experiments on the power amplifiers side have shown the same pattern as an proof that the spectral content alteration acts on parameters often connected with listening experience.

[1] F. Langford-Smith Radiotron Desogner's Handbook RCA 4th Ed. 1953