This article aims to address the topic covered in the research Properties of Nonlinear Distortions and Related Measures in Audio Amplifiers – see here – in the most simple and informative way possible. The research, found here, is downloadable for a fee, and has been published in the Journal of the Audio Engineering Society - JAES, better known internationally by its acronym AES, see website here. AES should need no introduction, find a description of it here. However, know that it is the only professional company in the world dedicated exclusively to audio technology. AES develops, reviews and publishes engineering standards for the audio and related media industry.
Title page of Mr. Parolo's research
Giuseppe Parolo is therefore and precisely a computer engineer. I leave it to his own words, written at the beginning of the above research, to introduce himself: "I am a SW engineer with the hobby of audio reproduction. I do not have extensive experience in electronics, but among my friends there are a couple who repair and build amplifiers (both solid-state and tube) for the local market (I live in Italy). Having measuring instruments, computer skills, and an acoustically treated room for listening to music, I help them fine-tune their creations. I was also lucky enough to measure and listen to dozens of preamplifiers from many brands, so after a few years of experience, I have embarked on the difficult task of correlating measurements to listening tests. This is based on the great work done by people like GedLee, Nelson Pass and Bob Katz and others".
In his course of study at the University of Rome La Sapienza, Parolo took exams on many subjects related to the field of electronics such as Signal Theory, Systems Theory, Automatic Controls, as well as Applied Acoustics. His main occupation is in the field of Telecommunications. His research that resulted in the aforementioned article has a relevance for us audiophiles, as, in extreme and approximate synthesis, he seeks a correlation between measurements and listening that is in a certain sense the heart of our audiophile interest and, certainly, of our magazine.
Methodological note - The article is structured as an interview to address the various issues related to the main topic in an orderly manner, as Parolo deals with it in a “systemic” way. This means that he will not discuss the different types of circuit – tubes or solid-state, with or without feedback, etc. – but will consider the amplifier as a black box, studying the alterations it causes to signals passing through it. This approach has the advantage that it is applicable to a very broad range of situations, as no special assumptions are made about the internal structure of the amplifier.
Question: Giuseppe, in your introductory lines to the research, again with phrases "carved in stone", you state that "The classical characterization of nonlinear distortions of electronic devices such as audio amplifiers involves the calculation of some indicators, such as total harmonic distortion, total harmonic distortion + noise and intermodulation distortion, obtained by measuring the additional spectral components generated by the device with respect to the input signals conventional." So let's start in a didactic and preparatory way from the beginning: what is technically a "linear distortion"?
Giuseppe Parolo: Let's start by considering a preamplifier or an audio power amp that we usually use. If we feed an input signal into the device and compare it with the output signal, on a macroscopic analysis they will appear identical. In reality, looking in more detail, the analysis will always reveal differences between the two signals. Some will be independent of the input signal. Others, on the other hand, will depend on this. In technical jargon, the former are called "noise", while the latter "distortions". In turn, the latter can be classified into two types: "linear" and "nonlinear". This nomenclature derives from how the "systems" that have one or the other characteristic are mathematically represented and therefore from their properties. To grasp the differences, it is necessary to analyze the effects on the signal in the frequency domain, that is, to observe the decomposition of the signal into “tones”, see here, each identified by a “frequency”, a “magnitude” - also referred to by the terms intensity or level - and a “phase”. The transition between these two domains is given by a mathematical operation called Fourier transform, see fig. 1 below. This representation approximates the behavior of our very sensitive auditory system and therefore also lends itself well to describing the effects of any type of alteration.
Fig. 1 - The time signal (graph above, in red) is given by the sum of two tones H1 and H2 of frequency of 100 Hz and 300 Hz (in blue and light blue). This decomposition is highlighted by the frequency analysis, which shows for each of the two tones respectively the intensity, of 1 and 0.5 (graph at the bottom left), and the phase, at -90° and 60° (graph at the bottom right).
Linear distortion refers to a signal alteration in which the intensity or phase of the tonal components contained in the input signal is changed, without the addition of new ones. In amplifiers, this type of distortion is caused by the capacitive or inductive effects of the electronic components in which the signal transits, which retain a memory of the signal's trend over time. An effective representation of these effects is by measuring the Frequency Response, which is the function that expresses the alteration in intensity -expressed in % or decibels, dB - and phase rotation - expressed in degrees - that each tonal component undergoes. Fig. 2 shows an example of the classic graphical representation of this function for a preamplifier.
Fig. 2 - Example of measure of the Frequency Response. At the top is the curve of the magnitude, with the range of values on the left; at the bottom that of the phase, with the range of values on the right.
The desirable trend is the neutral one, where the intensity curve is horizontal in the audio band, 20 Hz – 20 KHz, to slowly decrease outside this band. The phase curve is linked to the intensity trend and a horizontal trend is also desirable for this, i.e. at 0°, throughout the audio band. The typical pattern is very similar to that of a bandpass filter, and is determined by design choices: therefore, by the type of circuit and the characteristics of the components. A property of systems that have only linear distortions is that the attenuations or phase shifts by one system can be recovered, in theory perfectly, by the next one in cascade with an opposite action.
The effect on perception due to deviations from neutrality is perceived primarily as a change in the timbre of the sound, called coloration. For example, with regard to intensity:
- an exaltation in the high frequencies determines sensations of "brilliance" and an increase in "sibilance";
- conversely, an attenuation determines a "muffled", "boring" sound;an exaltation in the low frequencies causes "rumble" effects, while an attenuation determines a "thin" sound, devoid of body;
- an exaltation in the midrange frequencies will result in a "nasal" or "hard" sound.
For phase rotations, if they are not properly controlled in the mid/high frequencies, there will be delays between the tonal components of the sound which can translate in the most serious cases into a loss of "coherence" when listening.
Therefore, obtaining a frequency response with the described trend is one of the primary requirements that a designer should observe in order not to alter the balance of the musical message. In fact, this requirement can now be met quite easily in preamplifiers; For power amps it is a bit more problematic, given the complex load of the speakers to which they are connected. In general, under normal home listening conditions, this type of distortion is the highest.
Question: What is a nonlinear distortion?
Parolo: Nonlinear distortions are more challenging to characterize, both physically and perceptually. They come in the form of new tonal components, i.e. new sounds, added to the source signal. In amplifiers, these effects are due to the fact that electronic components do not behave in a perfectly linear way: the output quantity, the voltage or the current, does not have a fixed proportion with the input level for each value in the working range.
For an audio amplifier this behavior can be represented through the Characteristic Function, which expresses the output level of the device as a function of the input level. The graph on the left in fig. 3 shows an example of a characteristic function with unity gain, i.e. 0 dB, which presents an "asymmetrical soft clipping" where the signal is compressed in proportion to its level. On the right in the same figure is shown the effect of this function on a signal containing a pure tone, a sine wave. The resulting curve is shown in blue and the overall distortion component in red resulting from the difference between the distorted tone and the undistorted tone.
Fig. 3 – Left: example of a characteristic function, in blue, with unit gain. The curve, relative to a distortion of -70 dB and -60 dB on the second and third harmonics respectively, is amplified by 40 dB compared to the linearity, in orange, to better show the details. Right: Corresponding output signal for a sine input in the time domain.
In practice, measuring this function for an audio device is not very easy, given the effects of linear distortion acting simultaneously on the signal. Furthermore, correlating a given trend of the curve with the effects on listening is not so immediate. The strategy followed is therefore to measure the effects caused by distortion on simple and stationary, i.e. periodic, test signals by detecting the tonal components added by the device.
The simplest case is to introduce into the device a monotonic signal at 1 KHz, of the form shown in Fig. 3, called the “fundamental”. At the output we will observe the creation of new tones at multiple frequencies of the fundamental: at 2 KHz i.e. second harmonic, at 3 KHz i.e. third harmonic and so on, up to the maximum "distortion order" of the device. Fig. 4 shows an example of frequency analysis of the output signal of a preamplifier. The distortion tones at 2 KHz and 3 KHz are evident at levels of HD2 = -78.3 dB and HD3 = -84.8 dB respectively; other tones below -130 dB are due to noise.
Fig. 4 - Example of measuring harmonic distortions for a tone at 1 KHz.
This type of nonlinear distortion is called "harmonic" since the tones created occur at multiple frequencies from the fundamental. Most musical instruments generate harmonic multitonal signals, but not all harmonics are "consonants", i.e. pleasant to listen to as a musician would say. For example, if the sound’s energy is mainly concentrated in the harmonics up to the sixth harmonic, the sound is “soft”; if there are major energy components beyond the sixth harmonic, especially of odd order, the sound is “harsher”.
In the case of complex signals, another phenomenon can be observed. If we consider the case of a signal with two tones, the nonlinearities will generate, in addition to the harmonic components related to each of the two frequencies, other components due to interaction effects between the two fundamental tones. These tones are called "intermodulation products" and occur at frequencies given by the sums and differences of integer multiples of the frequencies of the source tones. The new tones are generally non-harmonic, that is, not multiples of the fundamentals and therefore "dissonant". Fig. 5 shows the case of two fundamental tones at 19 KHz and 20 KHz - CCIF test.
Fig. 5 - Example of measurement of intermodulation products for a two-tone signal - CCIF test.
Here we can see the intermodulation products created at frequencies of 1 KHz, from the difference of frequencies at 20 KHz and 19 KHz, around the fundamentals (differences 2*20 – 19, 2*19 – 20, ...), around the second harmonics at 38 KHz and 40 KHz (differences 3*20 – 19, 3*19 – 20, ...); others of higher order ultrasonic do not appear in the figure.
The number of products generated increases rapidly as the maximum distortion order of the device increases. Moreover, if the number of fundamentals is increased to trace back to more realistic signals, even more interactions and thus more intermodulation products will be created, forming a kind of “carpet of distortion”, that is, a multitude of tones that can potentially mask the finer aspects of the signal. Fig. 6 shows the output for a complex signal consisting of 31 tones of the same level, equally spaced 1/3 octave from 20 Hz to 20 KHz, again for the same preamplifier. Note the product created between the fundamentals, around -95 dB.
Fig. 6 - Example of measurement of intermodulation products for a multitonal signal: 31 tones at 1/3 octave.
Unlike linear distortions, those nonlinear are further multiplied when connecting cascaded systems, with results that are not easily predictable and difficult, if not impossible, to compensate for. Although they can be used in production to give musical instruments a particular character, they are less desirable in reproduction, as they can produce sound characteristics that are extraneous to the original artistic intentions. If too intense, they can cause various effects in the perception of sound that are not always pleasant, such as "harshness" or "roughness".
In general, reducing these distortions to inaudible levels is difficult. There are at least two schools of thought on the desirable structure of their frequency patterns. The first approach involves reducing high orders of distortion as much as possible while allowing greater tolerance of second- and third-order distortions, which are theoretically less audible due to certain characteristics of our auditory system. The second approach allows high orders of distortion as long as the trend is monotonically decreasing with increasing order. In this case, even if the overall distortion is higher, the alterations to the sound are still considered perceptually preferable to other types of trends.
End part 1 of 4 - To the second part
For further info:
write to Eng. Parolo
to JAES website
to AES website
