Input signal, to the root mean square sum of the spectral components of the input signal, a non-standardized synonym is sometimes used - clearfactor(borrowed from German). SOI is a dimensionless quantity, usually expressed as a percentage. In addition to SOI, the level of nonlinear distortion can be expressed using harmonic distortion factor.
Harmonic Distortion Factor- a value expressing the degree of nonlinear distortion of a device (amplifier, etc.), equal to the ratio of the root-mean-square voltage of the sum of the higher harmonics of the signal, except the first, to the voltage of the first harmonic when a sinusoidal signal is applied to the input of the device.
The harmonic coefficient, like the SOI, is expressed as a percentage. Harmonic distortion ( K G) is related to CNI ( K N) ratio:
Measurements
- In the low-frequency (LF) range (up to 100-200 kHz), nonlinear distortion meters (harmonic distortion meters) are used to measure SOI.
- At higher frequencies (MF, HF), indirect measurements are used using spectrum analyzers or selective voltmeters.
Typical SOI values
- 0% - the waveform is an ideal sine wave.
- 3% - the signal shape is different from sinusoidal, but the distortion is not noticeable to the eye.
- 5% - deviation of the signal shape from sinusoidal is noticeable to the eye on the oscillogram.
- 10 % - standard level distortion at which the real power (RMS) of the UMZCH is considered.
- 21% - for example, a trapezoidal or stepped signal.
- 43% - for example, a square wave signal.
see also
Literature
- Handbook of radio-electronic devices: In 2 volumes; Ed. D. P. Linde - M.: Energy,
- Gorokhov P.K. Dictionary in radio electronics. Basic terms- M: Rus. language,
Links
- MAIN ELECTRICAL CHARACTERISTICS OF THE SOUND TRANSMISSION CHANNEL
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harmonic distortion factor- SOI A parameter that allows you to take into account the influence of harmonics and combinational components on the signal quality. Numerically defined as the ratio of the power of nonlinear distortions to the power of the undistorted signal, usually expressed as a percentage. [L.M. Nevdyaev...
harmonic distortion factor- 3.9 coefficient of nonlinear distortion (total distortion): The ratio, as a percentage, of the root mean square value of the spectral components of the output signal of the acoustic calibrator, which are absent in the input signal, to the root mean square value... ...
harmonic distortion factor- netiesinių iškreipių faktorius statusas T sritis fizika atitikmenys: engl. non linear distortion factor vok. Klirrfaktor, m rus. nonlinear distortion factor, m pranc. taux de distorsion harmonique, m … Fizikos terminų žodynas
THD of UPS input current Characterizes deviations of the UPS input current shape from sinusoidal. The higher the value of this parameter, the worse it is for equipment connected to the same power supply network and the network itself, in this case it worsens... ... Technical Translator's Guide
THD of UPS output voltage Characterizes the deviation of the output voltage shape from sinusoidal, usually given for linear (motors, some types lighting fixtures) and nonlinear load. The higher this value, the worse the quality... ... Technical Translator's Guide
amplifier THD- - [L.G. Sumenko. English-Russian dictionary on information technology. M.: State Enterprise TsNIIS, 2003.] Topics information Technology in general EN amplifier distortion factor... Technical Translator's Guide
Loudspeaker THD- 89. Coefficient of nonlinear distortion of the loudspeaker Coefficient of nonlinear distortion Ndp. Harmonic coefficient Expressed as a percentage, the square root of the ratio of the sum of squares of the effective values of the spectral components emitted... ... Dictionary-reference book of terms of normative and technical documentation
Laryngophone nonlinear distortion coefficient- 94. Coefficient of nonlinear distortion of the laryngophone Expressed as a percentage, the value of the square root of the ratio of the sum of squares of the effective values of the harmonics of the electromotive force developed by the laryngophone during harmonic air movement, to... ... Dictionary-reference book of terms of normative and technical documentation
permissible nonlinear distortion factor- - [L.G. Sumenko. English-Russian dictionary on information technology. M.: State Enterprise TsNIIS, 2003.] Topics information technology in general EN harmonic tolerance ... Technical Translator's Guide
- (harmonic distortion meter) a device for measuring the coefficient of nonlinear distortion (harmonic distortion) of signals in radio devices. Contents... Wikipedia
When electrical signals are amplified, nonlinear, frequency, and phase distortions may occur.
Nonlinear distortion represent a change in the shape of the curve of amplified oscillations caused by the nonlinear properties of the circuit through which these oscillations pass.
The main reason for the appearance of nonlinear distortions in an amplifier is the nonlinearity of the characteristics of the amplifying elements, as well as the magnetization characteristics of transformers or chokes with cores.
The appearance of signal waveform distortions caused by the nonlinearity of the input characteristics of the transistor is illustrated in the graph in Fig. 1. Let us assume that a sinusoidal test signal is applied to the input of the amplifier. Getting into the nonlinear section of the input characteristic of the transistor, this signal causes changes in the input current, the shape of which differs from sinusoidal. In this regard, the output current, and therefore the output voltage, will change its shape compared to the input signal.
The greater the nonlinearity of the amplifier, the more it distorts the sinusoidal voltage supplied to the input. It is known (Fourier's theorem) that any non-sinusoidal periodic curve can be represented by the sum of harmonic oscillations and higher harmonics. Thus, as a result of nonlinear distortions, higher harmonics appear at the output of the amplifier, i.e. completely new vibrations that were not present at the input.
The degree of nonlinear distortion of an amplifier is usually estimated by the value nonlinear distortion factor(harmonic distortion)
Where 
- the sum of electrical powers released at the load by harmonics resulting from nonlinear amplification; 
- electric power first harmonic.
In cases where the load resistance has the same value for all harmonic components of the amplified signal, the harmonic coefficient is determined by the formula
,
Where - 
etc. – effective or amplitude values of the first, second, third, etc. output current harmonics; 
etc. effective or amplitude values of output voltage harmonics.
The harmonic coefficient is usually expressed as a percentage, so the value found by the formulas 
should be multiplied by 100. The total amount of nonlinear distortion that occurs at the output of the amplifier and created by the individual stages of this amplifier is determined by the approximate formula:
Where - 
nonlinear distortions introduced by each amplifier stage.
The permissible value of harmonic distortion depends entirely on the purpose of the amplifier. In instrumentation amplifiers, the permissible value of harmonic distortion is 
is tenths of a percent.
Frequency are called distortion , caused by changes in the gain at different frequencies. The cause of frequency distortion is the presence of reactive elements in the circuit - capacitors, inductors, interelectrode capacitances of amplifying elements, mounting capacitance, etc.
For example in Fig. Figure 2 shows the amplitude-frequency response of the ULF.
Rice. 2. Amplitude-frequency Fig. 3. Phase frequency response
ULF characteristics. amplifier
When constructing amplitude-frequency characteristics, it is more convenient to plot the frequency along the abscissa axis not on a linear, but on a logarithmic scale. For each frequency, the value is actually plotted along the axis lgf , and the frequency value is signed.
The degree of distortion at individual frequencies is expressed frequency distortion factor
M, equal to the ratio of the gain at a given frequency 
Typically, the greatest frequency distortion occurs at the edges of the frequency range f n and f V. The frequency distortion coefficients in this case are equal to
,
Where TO n And TO c – respectively, the gain factors at the lower and upper frequencies of the range.
For low-frequency amplifiers, the ideal frequency response is a horizontal straight line (line AB in Fig. 2).
Where TOn And TOV- respectively, the gain factors at the lower and upper frequencies of the range. From the definition of the frequency distortion coefficient it follows that if M> 1, then the frequency response in the region of this frequency has a block, and if M < 1, - то подъем. Для усилителя низкой частоты идеальной частотной характеристикой является горизонтальная прямая (линия АВ на рис. 12.5).
The frequency distortion coefficient of a multistage amplifier is equal to the product of the frequency distortion coefficients of individual stages
M = M1 M 2 M 3 . ..Mn.
Consequently, frequency distortion occurring in one amplifier stage can be compensated in another so that the overall frequency distortion factor does not go beyond the specified limit. It is convenient to express the frequency distortion factor, as well as the gain factor, in decibels:
M DB = 20lg M.
In the case of a multistage amplifier
M DB = M 1 dB + M 2 dB + M3 DB +…+ Mn DB
The permissible amount of frequency distortion depends on the purpose of the amplifier. For instrumentation amplifiers, for example, permissible distortion is determined by the required measurement accuracy and can be tenths or even hundredths of a decibel.
It should be borne in mind that frequency distortion in an amplifier is always accompanied by the appearance of a phase shift between the input and output signals, i.e., phase distortion. In this case, phase distortions usually mean only shifts created by the reactive elements of the amplifier, and the phase rotation by the amplifying element itself is not taken into account.
Phase distortion, contributed by the amplifier are assessed by its phase-frequency characteristic, which is a graph of the dependence of the phase shift angle φ between the input and output voltages of the amplifier on the frequency (Fig. 3. There is no phase distortion in the amplifier when the phase shift depends linearly on frequency. The ideal phase-frequency characteristic is a straight line starting at the origin of coordinates - the dotted line in Fig. 3. The phase-frequency characteristic of a real amplifier has the form shown in Fig. 3. solid line.
Total Harmonic Distortion (THD)
Irina Aldoshina
All electroacoustic transducers (loudspeakers, microphones, telephones, etc.), as well as transmission channels, introduce their distortions into the transmitted sound signal, that is, the perceived sound signal is always not identical to the original. The ideology of creating sound equipment, which in the 60s was called High-Fidelity, “high fidelity” to live sound, largely did not achieve its goal. In those years, distortion levels sound signal in the equipment were still very high, and it seemed that it was enough to lower them - and the sound reproduced through the equipment would be practically indistinguishable from the original one.
However, despite advances in the design and development of technology, which have led to a significant reduction in the levels of all types of distortion in audio equipment, it is still not particularly difficult to distinguish natural sound from reproduced sound. That is why currently in various countries in research institutes, universities and manufacturing companies in large volume work is being carried out to study auditory perception and subjective assessment various types distortions. Based on the results of these studies, many scientific articles and reports are published. Almost all AES congresses present papers on this topic. Some modern results obtained over the past two to three years on the problems of subjective perception and assessment of nonlinear distortions of the audio signal in audio equipment will be presented in this article.
When recording, transmitting and playing music and speech signals through audio equipment, distortions in the temporal structure of the signal occur, which can be divided into linear and nonlinear.
Linear distortion change the amplitude and phase relationships between the existing spectral components of the input signal and due to this distort its temporal structure. This kind of distortion is subjectively perceived as distortion of the signal timbre, and therefore the problems of their reduction and subjective assessments of their level have been given a lot of attention by specialists throughout the entire period of development of audio engineering.
The requirement for the absence of linear signal distortion in audio equipment can be written in the form:
Y(t) = K x(t - T), where x(t) is the input signal, y(t) is the output signal.
This condition allows only a change in the signal on a scale with a coefficient K and its time shift by an amount T. It defines a linear relationship between the input and output signals and leads to the requirement that the transfer function H(ω), which is understood as a frequency-dependent ratio of complex signal amplitudes at the output and input of the system under harmonic influences were constant in magnitude and had a linear dependence of the argument (that is, phase) on frequency | H(ω) | = K, φ(ω) = -T·ω. Since the function 20·lg | H(ω) | is called the amplitude-frequency response of the system (AFC), and φ(ω) is the phase-frequency response (PFC), then ensuring a constant level of AFC in the reproduced frequency range (reducing its unevenness) in microphones, acoustic systems, etc. is the main requirement for improving their quality. Their measurement methods are included in all international standards, for example, IEC268-5. An example of the frequency response of a modern control unit from Marantz with an unevenness of 2 dB is shown in Figure 1.
Frequency response of the Marantz control monitorIt should be noted that such a reduction in the magnitude of the frequency response unevenness is a huge achievement in the design of audio equipment (for example, control monitors presented at the exhibition in Brussels in 1956 had an unevenness of 15 dB), which became possible as a result of the use of new technologies, materials and design methods.
The influence of uneven frequency response (and phase response) on the subjectively perceived distortion of sound timbre has been studied in sufficient detail. We will try to review the main results obtained in the future.
Nonlinear distortion are characterized by the appearance in the signal spectrum of new components that are absent in the original signal, the number and amplitudes of which depend on changes in the input level. The appearance of additional components in the spectrum is due to the nonlinear dependence of the output signal on the input, that is, the nonlinearity of the transfer function. Examples of such dependence are shown in Figure 2.
Various types of nonlinear transfer functions in hardwareThe cause of nonlinearity may be the design and technological features of electroacoustic transducers.
For example, in electrodynamic loudspeakers (Figure 3), the main reasons include:
Electrodynamic loudspeaker designNonlinear elastic characteristics of the suspension and centering washer (an example of the dependence of the flexibility of suspensions in a loudspeaker on the magnitude of the voice coil displacement is shown in Figure 4);
Dependence of suspension flexibility on voice coil displacement valueNonlinear dependence of the voice coil displacement on the applied voltage due to the interaction of the coil with the magnetic field and due to thermal processes in the loudspeakers;
- nonlinear oscillations of the diaphragm with a large magnitude of the acting force;
- vibrations of the housing walls;
- Doppler effect during the interaction of various emitters in an acoustic system.
Nonlinear distortions occur in almost all elements of the audio path: microphones, amplifiers, crossovers, effects processors, etc.
The relationship between input and output signals shown in Figure 2 (for example, between applied voltage and sound pressure for a loudspeaker) can be approximated as a polynomial:
y(t) = h1 x(t) + h2 x2(t) + h3 x3(t) + h4 x4(t) + … (1).
If a harmonic signal is applied to such a nonlinear system, i.e. x(t) = A sin ωt, then the output signal will contain components with frequencies ω, 2ω, 3ω, ..., nω, etc. For example, if we limit ourselves only a quadratic term, then second harmonics will appear, because
y(t) = h1 A sin ωt + h2 (A sin ωt)² = h1 A sin ωt + 0.5 h2 A sin 2ωt + const.
In real converters, when a harmonic signal is supplied, harmonics of the second, third and higher orders, as well as subharmonics (1/n) ω, may appear (Figure 5).
To measure this type of distortion, the most widely used methods are measuring the level of additional harmonics in the output signal (usually only the second and third).
In accordance with international and domestic standards, the frequency response of the second and third harmonics is recorded in anechoic chambers and the n-order harmonic distortion coefficient is measured:
KГn = pfn / pav·100%
where pfn is the root mean square sound pressure value corresponding to the n-harmonic component. It is used to calculate the total harmonic distortion coefficient:
Kg = (KG2² + KG3² + KG4² + KG5² + ...)1/2
For example, in accordance with the requirements of IEC 581-7, for Hi-Fi loudspeaker systems, the total harmonic distortion factor should not exceed 2% in the frequency range 250 ... 1000 Hz and 1% in the range above 2000 Hz. Example of THD for a 300 mm (12") subwoofer versus frequency for different meanings input voltage varying from 10 to 32 V is shown in Figure 6.
Dependence of THD on frequency for different input voltage valuesIt should be noted that the auditory system is extremely sensitive to the presence of nonlinear distortions in acoustic transducers. The “visibility” of harmonic components depends on their order; in particular, hearing is most sensitive to odd components. With repeated listening, the perception of nonlinear distortions becomes more acute, especially when listening to individual musical instruments. The frequency region of maximum hearing sensitivity to these types of distortions is within the range of 1...2 kHz, where the sensitivity threshold is 1...2%.
However, this method of assessing nonlinearity does not allow taking into account all types of nonlinear products that arise during the conversion of a real audio signal. As a result, there may be a situation where a speaker system with a 10% THD may be subjectively rated higher in sound quality than a system with a 1% THD due to the influence of higher harmonics.
Therefore, the search for other ways to assess nonlinear distortions and their correlation with subjective assessments continues all the time. This is especially relevant at the present time, when the levels of nonlinear distortions have decreased significantly and to further reduce them it is necessary to know the real thresholds of audibility, since reducing nonlinear distortions in equipment requires significant economic costs.
Along with measurements of harmonic components, methods for measuring intermodulation distortion are used in the practice of designing and evaluating electroacoustic equipment. The measurement technique is presented in GOST 16122-88 and IEC 268-5 and is based on supplying two sinusoidal signals with frequencies f1 and f2 to the emitter, where f1< 1/8·f2 (при соотношении амплитуд 4:1) и измерении амплитуд звукового давления комбинационных тонов: f2 ± (n - 1)·f1, где n = 2, 3.
The total intermodulation distortion coefficient is determined in this case as:
Kim = (ΣnKimn²)1/2
where kim = /pcp.
The cause of intermodulation distortion is the nonlinear relationship between the output and input signals, i.e., the nonlinear transfer characteristic. If two harmonic signals are applied to the input of such a system, then the output signal will contain harmonics of higher orders and sum-difference tones of various orders.
The type of output signal taking into account nonlinearities of higher orders is shown in Figure 5.
Products of nonlinear distortion in loudspeakersThe characteristics of the dependence of the intermodulation distortion coefficient on frequency for a low-frequency loudspeaker with voice coils of different lengths are shown in Figure 7 (a - for a longer coil, b - for a shorter one).
Dependence of intermodulation distortion (IMD) on frequency for a loudspeaker with a long (a) and short (b) coilAs stated above, in accordance with international standards, only second- and third-order intermodulation distortion coefficients are measured in the equipment. Intermodulation distortion measurements can be more informative than harmonic distortion measurements because they are a more sensitive measure of nonlinearity. However, as shown by experiments carried out in the works of R. Geddes (report at the 115th AES Congress in New York), a clear correlation between subjective assessments of the quality of acoustic transducers and the level of intermodulation distortion could not be established - the scatter in the results obtained was too large (as can be seen from Figure 8).
Relationship between subjective assessments and intermodulation distortion (IMD) valuesAs a new criterion for assessing nonlinear distortions in electroacoustic equipment, a multi-tone method was proposed, the history and methods of application of which were studied in detail in the works of A. G. Voishvillo et al. (there are articles in JAES and reports at AES congresses). In this case, a set of harmonics from the 2nd to the 20th with an arbitrary amplitude distribution and a logarithmic frequency distribution in the range from 1 to 10 kHz is used as an input signal. The harmonic phase distribution is optimized to minimize the crest factor of the multi-tone signal. The general appearance of the input signal and its temporal structure are shown in Figures 9a and 9b.
Spectral (a) and temporal (b) view of a multi-tone signalThe output signal contains harmonic and intermodulation distortions of all orders. An example of such distortion for a loudspeaker is shown in Figure 10.
Common harmonic distortion products when applying a multi-tone signalA multi-tone signal in its structure is much closer to real music and speech signals; it allows one to identify significantly more different products of nonlinear distortions (primarily intermodulation) and better correlates with subjective assessments of the sound quality of acoustic systems. With an increase in the number of harmonic components this method allows you to get more and more detailed information, but this increases computational costs. The application of this method requires further research, in particular the development of criteria and acceptable standards on the selected products of nonlinear distortions from the standpoint of their subjective assessments.
Other methods, such as Voltaire series, are also used to evaluate nonlinear distortions in acoustic transducers.
However, all of them do not provide a clear connection between the assessment of the sound quality of transducers (microphones, loudspeakers, acoustic systems, etc.) and the level of nonlinear distortions in them, measured by any of the known objective methods. Therefore, the new psychoacoustic criterion proposed in the report of R. Geddes at the last AES congress is of considerable interest. He proceeded from the considerations that any parameter can be assessed in objective units, or according to subjective criteria, for example, temperature can be measured in degrees, or in sensations: cold, warm, hot. The loudness of a sound can be assessed by the sound pressure level in dB, or it can be assessed in subjective units: background, sleep. The search for similar criteria for nonlinear distortions was the goal of his work.
As is known from psychoacoustics, hearing aid is a fundamentally nonlinear system, and its nonlinearity manifests itself at both large and small signal levels. The causes of nonlinearity are hydrodynamic processes in the cochlea, as well as nonlinear signal compression due to a special mechanism for elongation of outer hair cells. This leads to the appearance of subjective harmonics and combination tones when listening to harmonic or total harmonic signals, the level of which can reach 15...20% of the input signal level. Therefore, the analysis of the perception of nonlinear distortion products created in electroacoustic transducers and transmission channels in such a complex nonlinear system as a hearing aid is a serious problem.
Another fundamentally important property of the auditory system is the masking effect, which consists in changing hearing thresholds to one signal in the presence of another (masker). This property of the auditory system is widely used in modern systems compression audio information when transmitted over various channels (MPEG standards). Advances in reducing the volume of transmitted information through compression using auditory masking properties suggest that these effects are also of great importance for the perception and assessment of nonlinear distortions.
The established laws of auditory masking allow us to state that:
- masking of high-frequency components (located above the frequency of the masker signal) occurs much stronger than in the direction of low frequencies;
- masking is more pronounced for nearby frequencies (local effect, Figure 11);
- with an increase in the level of the masker signal, the zone of its influence expands, it becomes more and more asymmetrical, and it shifts towards high frequencies.From this we can assume that when analyzing nonlinear distortions in the auditory system, the following rules are observed:
- nonlinear distortion products above the fundamental frequency are less important for perception (they are better masked) than low-frequency components;
- the closer to the fundamental tone the products of nonlinear distortions are located, the greater the likelihood that they will become invisible and will not have a subjective meaning;
- additional nonlinear components arising from nonlinearity may be much more important for perception at low signal levels than at high levels. This is shown in Figure 11.
Masking EffectsIndeed, as the level of the main signal increases, its masking zone expands, and more and more distortion products (harmonics, total and difference distortions, etc.) fall into it. At low levels this area is limited, so higher order distortion products will be more audible.
When measuring nonlinear products on a pure tone, mainly harmonics with a frequency higher than the main signal n f appear in the converters. However, low harmonics with frequencies (1/n) f can also occur in loudspeakers. When measuring intermodulation distortions (both using two signals and using multi-tone signals), total-difference distortion products arise - both above and below the main signals m f1 ± n f2.
Taking into account the listed properties of auditory masking, the following conclusions can be drawn: products of nonlinear distortions of higher orders can be more audible than products of lower orders. For example, the practice of loudspeaker design shows that harmonics with numbers higher than the fifth are perceived much more unpleasantly than the second and third, even if their levels are much lower than those of the first two harmonics. Usually their appearance is perceived as rattling and leads to the rejection of loudspeakers in production. The appearance of subharmonics with half and lower frequencies is also immediately noticed by the auditory system as an overtone, even at very low levels.
If the order of nonlinearity is low, then with an increase in the input signal level, additional harmonics can be masked in the auditory system and not be perceived as distortion, which is confirmed by the practice of designing electroacoustic transducers. Speaker systems with a nonlinear distortion level of 2% can be rated quite highly by listeners. In the same time good amplifiers should have a distortion level of 0.01% or lower, which is apparently due to the fact that Acustic systems create distortion products of low orders, and amplifiers create much higher ones.
Nonlinear distortion products that occur at low signal levels can be much more audible than at high levels. This seemingly paradoxical statement may also have practical implications, since nonlinear distortions in electroacoustic transducers and paths can also occur at low signal levels.
Based on the above considerations, R. Geddes proposed a new psychoacoustic criterion for assessing nonlinear distortions, which was supposed to satisfy the following requirements: to be more sensitive to higher-order distortions and to be of greater importance for low levels signal.
The problem was to show that this criterion was more consistent with the subjective perception of harmonic distortion than the currently accepted rating methods: total harmonic distortion factor and intermodulation distortion factor on two-tone or multi-tone signals.
To this end, a series of subjective assessments was conducted, organized as follows: Thirty-four experts with tested hearing thresholds (average age 21 years) participated in a large series of experiments assessing the sound quality of musical passages (for example, male vocals with symphonic music), in which various types of nonlinear distortions have been introduced. This was done by “convolution” of the test signal with nonlinear transfer functions characteristic of converters various types(loudspeakers, microphones, stereo phones, etc.).
First, sinusoidal signals were used as stimuli, they were “convolved” with various transfer functions, and the harmonic distortion coefficient was determined. Then two sinusoidal signals were used and the intermodulation distortion coefficients were calculated. Finally, the newly proposed coefficient Gm was determined directly from the given transfer functions. The discrepancies turned out to be very significant: for example, for the same transfer function, the SOI is 1%, Kim - 2.1%, Gm - 10.4%. This difference is physically explainable, since Kim and Gm take into account many more high-order nonlinear distortion products.
Auditory experiments were performed on stereo phones with a range of 20 Hz...16 kHz, sensitivity 108 dB, max. SPL 122 dB. The subjective rating was given on a seven-point scale for each musical fragment, from “much better” than the reference fragment (i.e., the musical fragment “collapsed” with a linear transfer function) to “much worse.” Statistical processing of the results of the auditory assessment made it possible to establish a fairly high correlation coefficient between the average values of subjective assessments and the value of the Gm coefficient, which turned out to be equal to 0.68. At the same time, for SOI it was 0.42, and for Kim - 0.34 (for this series of experiments).
Thus, the connection between the proposed criterion and subjective assessments of sound quality turned out to be significantly higher than that of other coefficients (Figure 12).
Relationship between the Gm coefficient and subjective assessmentsThe experimental results also showed that an electroacoustic transducer with Gm less than 1% can be considered quite satisfactory in terms of sound quality in the sense that nonlinear distortions in it are practically inaudible.
Of course, these results are not yet sufficient to replace the proposed criterion with the parameters available in the standards, such as harmonic distortion coefficient and intermodulation distortion coefficient, but if the results are confirmed by further experiments, then perhaps this is exactly what will happen.
The search for other new criteria is also actively continuing, since the discrepancy between existing parameters (especially harmonic distortion coefficient, which evaluates only the first two harmonics) and subjectively perceived sound quality becomes more and more obvious as the overall quality of audio equipment improves.
Apparently, further ways to solve this problem will go towards creating computer models auditory system, taking into account nonlinear processes and masking effects in it. The Institute of Communication Acoustics in Germany is working in this area under the leadership of D. Blauert, which was already written about in an article dedicated to the 114th AES Congress. Using these models, it will be possible to evaluate the audibility of various types of nonlinear distortions in real music and speech signals. However, while they have not yet been created, assessments of nonlinear distortions in equipment will be made using simplified methods that are as close as possible to real auditory processes.
Nonlinear distortions are signal distortions caused by the nonlinearity of the relationship between the secondary and primary signals in stationary mode. As a result of nonlinear inertia-free distortions of the input signal of a sinusoidal shape, an output signal of a complex shape is obtained y = y0 + v1x + v2x2 + v3x3 + ... where: x is the input quantity; y0 - constant component; v1 - linear gain; v2, v3 ... - nonlinear distortion coefficients.
In a system with a nonlinear transfer characteristic, spectral components appear that were not present at the input - products of nonlinearity. When a signal with a single frequency f1 is applied to the input of such a system, components with frequencies f1, 2f1, 3f1, etc. will appear at the output. If a signal consisting of several frequencies f1, f2, f3, ... is supplied to the input, then at the output of the system, in addition to harmonic components, so-called “combination components” with frequencies n1f1 ± n2f2 ± n3f3 ± ... will additionally appear, where n=1, 2, 3, ... When feeding sounds with a continuous spectrum, a continuous spectrum is also obtained, but with a changed shape of the spectrum envelope.
Nonlinear distortion is usually assessed by the nonlinear distortion factor, which is the ratio of the effective values of harmonics to the effective value of the total output signal and is measured as a percentage. Here An are the amplitudes of components with frequencies nf. The simplified formula given next is valid for cases where the distortions are small (K<=10%). Различают два типа нелинейности: степенную и нелинейность из-за ограничения амплитуды. Последняя делится на ограничение сверху и ограничение снизу (центральное). При первом виде ограничения искажаются только громкие сигналы, при втором - все сигналы, но более слабые искажаются сильнее, чем громкие. Нелинейность искажения гармонического вида и комбинационных частот ощущается как дребезжание, переходящее в хрипы при значительном искажении на высоких частотах. Нелинейные искажения в виде разностных комбинационных частот вызывают ощущение модуляции передачи. При сужении полосы частот нелинейные искажения становятся менее заметными. Линейные искажения изменяют амплитудные и фазовые соотношения между имеющимися спектральными компонентами сигнала и за счет этого искажают его временную структуру. Такие изменения воспринимаются как искажения тембра или «окрашивание» звука.
During sound transmission, the primary relationships between the frequency components of sound must be preserved. In this regard, the quality of any section of the audio channel is assessed by its amplitude-frequency (abbreviated frequency) characteristic, which is often denoted by the abbreviation frequency response. Frequency response is understood as a graph of the dependence of the transmission coefficient on the frequency of the signals supplied to the input of a given section of the channel or a separate audio device. The transmission coefficient is the ratio of the magnitudes of the signals at the input of the amplifier and its output.
The frequency response of the transmission path (frequency dependence of the transmission coefficient) changes the relationships between the amplitudes of the frequency components. This leads to a subjective sensation of timbre change. An indicator of the degree of frequency distortion that occurs in any device is the unevenness of its amplitude-frequency characteristic; a quantitative indicator at any specific frequency of the signal spectrum is the frequency distortion coefficient.
Nonlinear distortions are caused by the nonlinearity of the signal processing and transmission system. These distortions cause the appearance in the frequency spectrum of the output signal of components that are absent in the input signal. Nonlinear distortions are changes in the shape of vibrations passing through an electrical circuit (for example, through an amplifier or transformer), caused by violations of proportionality between the instantaneous voltage values at the input of this circuit and at its output. This occurs when the output voltage characteristic varies nonlinearly with the input voltage. Nonlinear distortion is quantified by the total harmonic distortion factor or harmonic distortion factor. Typical SOI values: 0% - sinusoid; 3% - shape close to sinusoidal; 5% - a shape close to sinusoidal (shape deviations are already visible to the eye); up to 21% - trapezoidal or stepped signal; 43% is a square wave signal.
If a sinusoidal voltage is applied to the input of the amplifier, then the amplified voltage at the output will not be sinusoidal, but more complex. It consists of a series of simple sinusoidal oscillations - the fundamental and higher harmonics. Thus, the amplifier adds extra harmonics that were not present at the amplifier input.
Fig.2 - Nonlinear distortion
Figure 2 shows the sinusoidal voltage at the input of the amplifier Uвx and the distorted non-sinusoidal voltage at the output Uout. In this case, the amplifier introduces the second harmonic. On the voltage graph Uout, the dash shows the useful first harmonic (fundamental oscillation), which has the same frequency as the input voltage, and the harmful second harmonic with double the frequency. The output voltage is the sum of these two harmonics.
Distortion of the shape of amplified oscillations, i.e. The addition of extra harmonics to the fundamental oscillation is called nonlinear distortion. They manifest themselves in the fact that the sound becomes hoarse and rattling. To evaluate nonlinear distortions, use the nonlinear distortion coefficient kH, which shows what percentage are all the extra harmonics created by the amplifier itself in relation to the fundamental oscillation 1
If kn is less than 5%, that is, if the harmonics added by the amplifier add up to no more than 5% of the first harmonic, then the ear does not notice the distortion. When the nonlinear distortion coefficient is more than 10%, sound hoarseness and rattling already spoil the impression of artistic programs. At kH of more than 20%, distortion is unacceptable and even speech becomes unintelligible.
Nonlinear distortions also arise when vibrations of complex shapes are amplified during the transmission of speech and music. In this case, the shape of the amplified oscillations is also distorted and unnecessary harmonics are added. Complex vibrations themselves consist of harmonics, which must be correctly reproduced by the amplifier. They should not be confused with additional harmonics created by the amplifier itself. Harmonics of the input voltage are useful because they determine the timbre of the sound, while harmonics introduced by the amplifier are harmful. They create nonlinear distortions.
The causes of nonlinear distortions in amplifiers are: non-linearity of the characteristics of lamps and transistors, the presence of control grid current in the lamps and magnetic saturation of the cores of transformers or low-frequency chokes. Significant nonlinear distortions are also created in loudspeakers, telephones, microphones, and sound pickups.
3. Other types of distortion. The presence of reactance in the amplifier device leads to the appearance of phase distortions. The phase shifts between different oscillations at the output of the amplifier are not the same as at the input. When reproducing sounds, these distortions do not play a role, since the human hearing organs do not sense them, but in some cases, for example in television, they have a harmful effect.
Every amplifier produces dynamic range distortion. It is compressed, i.e. the ratio of the strongest vibration to the weakest at the output of the amplifier is less than at the input. This disrupts the natural sound. In order to reduce such distortions, a special device is sometimes introduced to expand the dynamic range, called an expander. Compression of the dynamic range also occurs in electroacoustic devices.
Basic parameters of amplifiers
Any amplifier designed for processing medical and biological signals can be represented as an active quadripole (Fig. 1.1). A signal source with EMF Evx and internal resistance Ri is connected to the input of the amplifier. An input current Iin flows in the input circuit, the value of which depends on the input resistance of the amplifier Rin and the internal resistance of the signal source. Due to the voltage drop across the internal resistance of the signal source, the input voltage, which is actually amplified by the amplifier, differs from the EMF of the signal source:
Figure 1.1 - Equivalent amplifier circuit
The output current of the amplifier is the load current Rн. The magnitude of this current depends on the output voltage, which differs from the open-circuit voltage kUin due to the output resistance of the amplifier
To evaluate the properties of the amplifier, a number of parameters are introduced.
- Voltage and current gains
These coefficients show how many times the output voltage and current values change compared to the input values. The power gain can be found as
Any amplifier has K P >>1, while the current and voltage gains can be less than unity. However, if at the same time K I<1 и K U <1, устройство не может считаться усилителем.
It should be noted that most amplifier circuits contain reactive elements (capacitance and inductance), therefore, in the general case, the amplifier gain will be complex
Where the angle determines the amount of phase shift of the signal as it passes from input to output.
The amplitude-frequency response (AFC) of the amplifier determines the dependence of the gain on the frequency of the amplified signal. An approximate view of the amplifier's frequency response is shown in Fig. 1.2. The gain coefficient K 0 is taken to be the maximum value of the coefficient at the so-called “middle” frequency. Two characteristic points on the frequency response define the concept of “passband” of the amplifier. The frequencies at which the gain decreases by a factor (or by 3 dB) are called cutoff frequencies. In Fig. 1.2 f 1 is the lower limit frequency f N, and f 2 is the upper limit frequency of the gain (f B). Difference:
F = f B – f H
is called the amplifier's bandwidth, which determines the operating frequency range of the amplifier.
In general, the frequency response shows how the amplitude of the output signal changes with a constant amplitude of the input signal in the frequency range, while it is assumed that the signal shape does not change. To assess the change in gain with a change in frequency, the concept of frequency distortion is introduced
M N = M B = . Frequency distortions are classified as linear, i.e. the appearance of which does not lead to distortion of the shape of the original signal.
Based on the type of frequency response, amplifiers can be divided into several classes.
DC amplifiers: f H = 0 Hz, f B = (103 3 - 108 8) Hz;
Audio frequency amplifiers: f H = 20 Hz, f B = (15 - 20) 10 Hz;
High frequency amplifiers: f H = 20*103 Hz, f B = (200 - 300) · 103 3 Hz.
Narrowband (selective) amplifiers. A distinctive feature of the latter is that they practically amplify one harmonic from the entire frequency spectrum of the signal and their ratio of the upper and lower limit frequencies is:
Figure 1. 2- Amplifier frequency response
The amplitude characteristic of the amplifier reflects the characteristics of the change in the magnitude of the output signal when the input signal changes. As can be seen from Fig. 1.3 the output voltage is not zero (UOUTmin) in the absence of input voltage. This is due to the internal noise of the amplifier, which limits the minimum value of the input voltage that can be applied to the amplifier input and determines its sensitivity:
A significant increase in the input voltage (point 3) leads to the fact that the amplitude characteristic becomes nonlinear and further increase in the output voltage stops (point 5). This is due to the saturation of the amplifier stages. An acceptable value of the input voltage is considered to be one at which the output voltage does not exceed UOUTmax, which, as can be seen from Fig. 1.3, is located on the boundary of the linear section of the amplitude characteristic. The amplitude characteristic determines the dynamic range of the amplifier:
Sometimes, for convenience, dynamic range is calculated in decibels, as follows:
Figure 1. 3 - Amplitude characteristic of the amplifier
The amplifier's total harmonic distortion (THD) determines the degree to which the sinusoidal waveform is distorted during amplification. Signal distortion means that in its spectrum, along with the main (first) harmonic, harmonics of higher orders appear. Based on this, the nonlinear distortion factor can be found as:
where U i is the voltage of the harmonic with number i>1. It is easy to see that in the absence of higher harmonics in the output signal, K Г = 0, i.e. a sinusoidal signal from input to output is transmitted without distortion. Input and output impedance have a fairly noticeable effect on the operation of the amplifier. When amplifying changing or variable signals, resistances can be found as:
At direct current, these parameters can be determined using simplified formulas
When determining the input and output resistances, it must be remembered that in some cases they can be complex due to the reactive elements of the circuit. In this case, significant frequency distortion of the signal may occur, especially in the high frequency range. Cellular boost: cellular signal booster gsm.
Let's look at the main characteristics of amplifiers.
The amplitude characteristic is the dependence of the amplitude of the output voltage (current) on the amplitude of the input voltage (current) (Fig. 9.2). Point 1 corresponds to the noise voltage measured at Uin=0, point 2 corresponds to the minimum input voltage at which the signal can be distinguished from the background noise at the amplifier output. Section 2–3 is the working section in which the proportionality between the input and output voltage of the amplifier is maintained. After point 3, nonlinear distortions of the input signal are observed. The degree of nonlinear distortion is estimated by the nonlinear coefficient
distortion (or harmonic distortion):
,
where U1m, U2m, U3m, Unm are the amplitudes of the 1st (fundamental), 2nd, 3rd and nth harmonics of the output voltage, respectively.
Magnitude 
characterizes the dynamic range of the amplifier.
Rice. 9.2. Amplifier amplitude response
The amplitude-frequency response (AFC) of an amplifier is the dependence of the gain modulus on frequency (Fig. 9.3). The frequencies fн and fв are called the lower and upper limit frequencies, and their difference
(fн–fв) – amplifier bandwidth.
Rice. 9.3. Amplifier frequency response
When a harmonic signal of sufficiently small amplitude is amplified, distortion of the shape of the amplified signal does not occur. When a complex input signal containing a number of harmonics is amplified, the harmonics are amplified unequally by the amplifier because the circuit reactances vary with frequency, resulting in a distorted waveform of the amplified signal.
Such distortions are called frequency distortions and are characterized by the frequency distortion coefficient:
Where Kf is the magnitude of the gain at a given frequency.
Frequency distortion coefficients
And they are called the distortion coefficients at the lower and upper limit frequencies, respectively.
The frequency response can also be plotted on a logarithmic scale. In this case, it is called LFC (Fig. 9.4), the gain of the amplifier is expressed in decibels, and frequencies are plotted along the abscissa axis through a decade (frequency interval between 10f and f).
Rice. 9.4. Logarithmic amplitude-frequency response
amplifier (LAFC)
Typically, frequencies corresponding to f=10n are chosen as reference points. The LFC curves have a certain slope in each frequency region. It is measured in decibels per decade.
The phase-frequency response (PFC) of an amplifier is the dependence of the phase angle between the input and output voltages on frequency. A typical phase response is shown in Fig. 9.5. It can also be plotted on a logarithmic scale.
In the mid-frequency region, additional phase distortion is minimal. The phase response makes it possible to evaluate phase distortions that arise in amplifiers for the same reasons as frequency distortions.
Rice. 9.5. Phase-frequency response (PFC) of the amplifier
An example of the occurrence of phase distortions is shown in Fig. 9.6, which shows the amplification of an input signal consisting of two harmonics (dotted line), which undergo phase shifts when amplified.
Rice. 9.6. Phase distortion in the amplifier
The transient response of an amplifier is the dependence of the output signal (current, voltage) on time under an abrupt input action (Fig. 9.7). The frequency, phase and transient characteristics of the amplifier are uniquely related to each other.
Rice. 9.7. Amplifier transient response
The high-frequency region corresponds to the transient response in the region of small times, and the low-frequency region corresponds to the transient response in the region of large times.
Based on the nature of the amplified signals, they are distinguished:
o Continuous signal amplifiers. Establishment processes are neglected here. The main characteristic is frequency transfer.
o Pulse signal amplifiers. The input signal changes so quickly that transients in the amplifier are decisive in determining the output waveform. The main characteristic is the pulse transfer characteristic of the amplifier.
According to the purpose of the amplifier they are divided into:
o voltage amplifiers,
o current amplifiers,
o power amplifiers.
All of them amplify the power of the input signal. However, the power amplifiers themselves must and are capable of delivering the given power to the load at a high efficiency.
1. Compose program fragments in mnemonic codes and machine codes for the following operations:
