Distortion in amplifiers. Nonlinear distortion Nonlinear distortion level
Thanks to retail chains and online stores, the variety of audio equipment offered for sale goes beyond all reasonable limits. How to choose a device that meets your quality needs without significantly overpaying?
If you are not an audiophile and selecting equipment is not the meaning of life for you, then the easiest way is to confidently navigate technical specifications sound amplification equipment and learn how to extract useful information between the lines of passports and instructions, critical of generous promises. If you feel no difference between dB and dBm, rated power If you don’t differ from PMPO and want to finally find out what THD is, you can also find something interesting under the cut.
Summary of the article
Gain. Why do we need logarithms and what are decibels?
Sound volume. What is the difference between dB and dBm?
Divide and conquer - we decompose the signal into a spectrum.
Linear distortion and bandwidth.
Nonlinear distortions. KNI, KGI, TDH.
Amplitude characteristic. Very briefly about noise and interference.
Weekend standards ULF power and acoustics.
Practice - best criterion truth. Disassembly with the audio center.
A kettle of tar in a jar of honey.
I hope that the materials in this article will be useful for understanding the next one, which has a much more complex topic - “Cross distortion and feedback, as one of their sources.”
Gain. Why do we need logarithms and what are decibels?
One of the main parameters of an amplifier is the gain - the ratio of the output parameter of the amplifier to the input parameter. Depending on the functional purpose of the amplifier, amplification factors are distinguished by voltage, current or power:
Voltage Gain
Current gain
Power gain
The ULF gain can be very large; the gain of operational amplifiers and radio paths of various equipment is expressed in even larger values. Numbers with a large number of zeros are not very convenient to operate; it is even more difficult to display on a graph various types of dependencies that have values that differ from each other by a thousand or more times. A convenient way out is to present values on a logarithmic scale. In acoustics, this is doubly convenient, since the ear has a sensitivity close to logarithmic.
Therefore, the gain is often expressed in logarithmic units - decibels (Russian designation: dB; international: dB)
dB was originally used to estimate the power ratio, so the value expressed in dB assumes the logarithm of the ratio of the two powers, and the power gain is calculated using the formula:
The situation is slightly different with “non-energy” quantities. For example, let's take current and express power through it, using Ohm's law:
then the value expressed in decibels through the current will be equal to the following expression:
The same goes for voltage. As a result, we obtain the following formulas for calculating the gain factors:
Current gain in dB:
Voltage gain in dB:
Sound volume. What is the difference between dB and dBm?
In acoustics, "intensity level" or simply the volume of sound L are also measured in decibels, and this parameter is not absolute, but relative! This is because the comparison is made with the minimum threshold of audibility for the human ear. harmonic vibration- sound pressure amplitude 20 μPa. Since the sound intensity is proportional to the square of the sound pressure, we can write:
where is not the current, but the intensity of the sound pressure of sound with a frequency of 1 kHz, which approximately corresponds to the threshold of human audibility.
Thus, when we say that the volume of a sound is 20 dB, it means that the intensity of the sound wave is 100 times higher than the threshold of human hearing.
In addition, the absolute value of power measurement is extremely common in radio engineering dBm(Russian dBm), which is measured relative to a power of 1 mW. Power is determined at the rated load (for professional equipment - usually 10 kOhm for frequencies less than 10 MHz, for radio frequency equipment - 50 Ohm or 75 Ohm). For example, " output power amplifier stage is 13 dBm” (that is, the power released at the nominal load for this amplifier stage is approximately 20 mW).
Divide and conquer - we decompose the signal into a spectrum.
It's time to move on to a more complex topic - assessing signal distortion. First, we have to make a short introduction and talk about spectra. The fact is that in audio engineering and beyond, it is customary to operate with sinusoidal signals. They are often found in the surrounding world, since a huge number of sounds are created by vibrations of certain objects. In addition, the structure of the human auditory system is perfectly adapted to perceive sinusoidal oscillations.
Any sinusoidal oscillation can be described by the formula:
where the length of the vector, the amplitude of the oscillations, is the initial angle (phase) of the vector at zero time, is the angular velocity, which is equal to:
It is important that using the sum of sinusoidal signals with different amplitudes, frequencies and phases, it is possible to describe periodically repeating signals of any shape. Signals whose frequencies differ from the fundamental one by an integer number of times are called harmonics of the original frequency. For a signal with a base frequency f, signals with frequencies
will be even harmonics, and the signals
odd harmonics
Let's draw a graph of a sawtooth signal for clarity.
To accurately represent it through harmonics would require an infinite number of terms.
In practice, a limited number of harmonics with the largest amplitude are used to analyze signals. You can clearly see the process of constructing a sawtooth signal from harmonics in the figure below.
And here’s how a meander is formed, accurate to the fiftieth harmonic...
You can read more about harmonics in the wonderful article habrahabr.ru/post/219337 by user dlinyj, but it’s time for us to finally move on to distortions.
Most simple method assessing signal distortion involves applying one or the sum of several harmonic signals to the amplifier input and analyzing the observed harmonic signals at the output.
If the output of the amplifier contains signals of the same harmonics as the input, the distortion is considered linear, because it boils down to a change in the amplitude and phase of the input signal.
Nonlinear distortion adds new harmonics to the signal, which leads to distortion of the input signal shape.
Linear distortion and bandwidth.
Gain TO of an ideal amplifier does not depend on frequency, but in real life This is far from true. The dependence of amplitude on frequency is called amplitude- frequency response- Frequency response and is often depicted in the form of a graph, where the voltage gain is plotted vertically and the frequency horizontally. Let us plot the frequency response of a typical amplifier.
The frequency response is measured by sequentially applying signals of different frequencies of a certain level to the input of the amplifier and measuring the signal level at the output.
Frequency range ΔF, within which the amplifier power decreases by no more than two times from the maximum value is called amplifier bandwidth.
However, the graph usually plots the gain by voltage rather than by power. If we denote the maximum voltage gain as , then within the bandwidth the coefficient should not fall lower than:
The values of the frequency and level of the signals with which the ULF operates can change very significantly, therefore the frequency response is usually plotted in logarithmic coordinates, sometimes called LFC.
The gain of the amplifier is expressed in decibels, and frequencies are plotted on the abscissa axis through decade(frequency interval differing ten times). Isn’t it true that this way the graph looks not only prettier, but also more informative?
The amplifier not only unevenly amplifies signals of different frequencies, but also shifts the phase of the signal by different meanings, depending on its frequency. This dependence is reflected by the phase-frequency characteristic of the amplifier.
When amplifying oscillations of only one frequency, this does not seem to be scary, but for more complex signals it leads to significant distortion of the shape, although it does not generate new harmonics. The picture below shows how a dual-frequency signal is distorted.
Nonlinear distortions. KNI, KGI, TDH.
Nonlinear distortion adds previously non-existent harmonics to the signal and, as a result, changes the original waveform. Perhaps the most obvious example of such distortions is the amplitude limitation of a sinusoidal signal, shown below.
The left graph shows distortions caused by the presence of an additional even harmonic of the signal - limiting the amplitude of one of the half-waves of the signal. The original sinusoidal signal has number 1, the second harmonic oscillation is 2, and the resulting distorted signal is 3. The right figure shows the result of the third harmonic - the signal is “cut off” on both sides.
In Soviet times, it was customary to express the nonlinear distortion of an amplifier using the THD harmonic distortion factor. It was determined as follows: a signal was supplied to the input of the amplifier certain frequency, usually 1000 Hz. Then the level of all harmonics of the output signal was calculated. The THD was taken to be the ratio of the rms voltage of the sum of the higher harmonics of the signal, except the first, to the voltage of the first harmonic - the one whose frequency is equal to the frequency of the input sinusoidal signal.
A similar foreign parameter is called total harmonic distortion for fundamental frequency.
Harmonic Distortion Factor (THD or )
This technique will only work if the input signal is ideal and contains only the fundamental harmonic. This condition cannot always be met, therefore, in modern international practice, another parameter for assessing the degree of nonlinear distortion - SOI - has become much more widespread.
The foreign analogue is total harmonic distortion for root mean square.
Total harmonic distortion (THD or )
SOI is a value equal to the ratio of the root-mean-square sum of the spectral components of the output signal that are absent in the spectrum of the input signal to the root-mean-square sum of all spectral components of the input signal.
Both THD and THI are relative values that are measured as a percentage.
The values of these parameters are related by the relation:
For simple waveforms, the amount of distortion can be calculated analytically. Below are the THD values for the most common signals in audio technology (THD values are indicated in parentheses).
0% (0%) - the waveform is an ideal sine wave.
3% (3%) - the signal shape is different from sinusoidal, but the distortion is invisible to the eye.
5% (5%) - deviation of the signal shape from sinusoidal, noticeable to the eye on the oscillogram.
10 % (10 %) - standard level distortion, at which the real power (RMS) of the UMZCH is considered, is noticeable by ear.
12% (12%) is a perfectly symmetrical triangular signal.
21% (22%) is a “typical” trapezoidal or stepped signal. 43% (48%) - a perfectly symmetrical rectangular signal (meander).
63% (80%) is an ideal sawtooth signal.
Even twenty years ago, complex, expensive instruments were used to measure harmonic distortion of the low-frequency path. One of them SK6-13 is shown in the figure below. 
Today, this task is handled much better by an external computer audio card with a set of specialized software, the total cost of which does not exceed 500USD.
Input signal spectrum sound card when testing a low frequency amplifier.
Amplitude characteristic. Very briefly about noise and interference.
The dependence of the amplifier's output voltage on its input, at a fixed signal frequency (usually 1000 Hz), is called the amplitude characteristic.
Amplitude characteristic of an ideal amplifier is a straight line passing through the origin of coordinates, since its gain is a constant value at any input voltage.
There are at least three different sections in the amplitude response of a real amplifier. In the lower part it does not reach zero, since the amplifier has its own noise, which at low volume levels becomes commensurate with the amplitude of the useful signal.
In the middle part (AB) the amplitude characteristic is close to linear. This is the working area, within its limits the distortion of the signal shape will be minimal.
In the upper part of the graph, the amplitude characteristic also has a bend, which is due to the limitation on the output power of the amplifier.
If the amplitude of the input signal is such that the amplifier operates on curved sections, then nonlinear distortions appear in the output signal. The greater the nonlinearity, the more the sinusoidal voltage of the signal is distorted, i.e. New oscillations (higher harmonics) appear at the output of the amplifier.
Noise in amplifiers comes in different types and is caused by different reasons.
White noise.
White noise is a signal with uniform spectral density at all frequencies. Within the operating frequency range of low-frequency amplifiers, an example of such noise can be considered thermal noise, caused by the chaotic movement of electrons. The spectrum of this noise is uniform over a very wide frequency range.
Pink noise.
Pink noise is also known as flicker noise. The power spectral density of pink noise is proportional to the ratio 1/f (density is inversely proportional to frequency), that is, it is uniformly decreasing on a logarithmic frequency scale. Pink noise is generated by both passive and active electronic components, scientists are still arguing about the nature of its origin.
Background from external sources.
One of the main causes of noise is background induced from extraneous sources, for example from the network alternating current 50 Hz. It has a fundamental harmonic of 50 Hz and its multiples.
Self-excitation.
Self-excitation of individual amplifier stages can generate noise, usually of a certain frequency.
ULF and acoustics output power standards
Rated power
Western analogue RMS(Root Mean Squared - root mean square value) In the USSR, it was defined by GOST 23262-88 as the average value of the supplied electrical power of a sinusoidal signal with a frequency of 1000 Hz, which causes nonlinear distortion of the signal not exceeding set value THD. Indicated for both speakers and amplifiers. Typically, the indicated power was adjusted to the GOST requirements for the complexity class of the design, with the best combination of measured characteristics. For different classes of devices, the SOI can vary very significantly, from 1 to 10 percent. It may turn out that the system is stated at 20 watts per channel, but the measurements were carried out at 10% SOI. As a result, it is impossible to listen to acoustics at this power. Speaker systems are capable of reproducing a signal at RMS power for a long time.
Noise power rating
Sometimes also called sinusoidal. Closest Western analogue DIN- electrical power limited exclusively by thermal and mechanical damage(for example: slipping of the voice coil turns due to overheating, burnout of conductors in places of bending or soldering, breakage of flexible wires, etc.) when pink noise is supplied through the correction circuit for 100 hours. Usually DIN is 2-3 times higher than RMS.
Maximum short-term power
Western analogue PMPO(Peak Music Power Output - peak music output power). - electrical power that the speakers can withstand without damage (checked by the absence of rattling) for a short period of time. Pink noise is used as a test signal. The signal is sent to the speaker for 2 seconds. Tests are carried out 60 times at intervals of 1 minute. This type power makes it possible to judge the short-term overloads that a loudspeaker can withstand in situations that arise during operation. Usually 10-20 times higher than DIN. What is the benefit of a person knowing that his system can possibly endure a short, less than a second, low-frequency sine wave with high power? However, manufacturers are very fond of displaying this particular parameter on the packaging and stickers of their products... Huge numbers this parameter are often based solely on the wild imagination of the manufacturers’ marketing department, and here the Chinese are undoubtedly ahead of the rest.
Maximum long-term power
This is the electrical power that the speakers can withstand without damage for 1 minute. The tests are repeated 10 times with an interval of 2 minutes. The test signal is the same.
The maximum long-term power is determined by a violation of the thermal strength of the speakers (sliding of the turns of the voice coil, etc.).
Practice is the best criterion of truth. Disassembly with the audio center
Let's try to apply our knowledge in practice. Let's take a look at a very famous online store and look for a product from an even more famous company from the Land of the Rising Sun.
Yeah - a music center with futuristic design is on sale for only 10,000 rubles. for the next promotion:
From the description we learn that the device is equipped not only powerful speakers, but also a subwoofer.
“It delivers superior sound clarity at any volume level. In addition, this configuration helps make the sound rich and spacious.”
Fascinating, perhaps it’s worth looking at the parameters. “The center contains two front speakers, each with a power of 235 Watts, and an active subwoofer with a power of 230 Watts.” Moreover, the dimensions of the first ones are only 31*23*21 cm
Yes, this is some kind of Nightingale the Robber, both in the strength of his voice and in size. Back in 1996, I would have stopped my research at this point, and later, looking at my S90 and listening to a homemade Ageev amplifier, I would have vigorously discussed with friends how far behind the Japanese our Soviet industry was - by 50 years or still forever. But today, with the availability of Japanese technology, the situation is much better and many myths associated with it have collapsed, so before purchasing we will try to find more objective data on sound quality. There is not a word about this on the website. Who would doubt that! But there is an instruction manual in pdf format. Download and continue searching. Among the extremely valuable information that “the license for the audio encoding technology was obtained from Thompson” and which end to insert the batteries with difficulty, but it is possible to find something resembling technical parameters. Very scant information is hidden in the depths of the document, towards the end.
I quote it verbatim, in the form of a screenshot, because, starting from that moment, I began to have serious questions, both about the given figures, despite the fact that they were confirmed by a certificate of conformity, and about their interpretation.
The fact is that just below it was written that the power consumed from the AC network of the first system is 90 watts, and the second is generally 75. Hmm.
Has a perpetual motion machine of the third kind been invented? Or maybe in the building music center Are the batteries hidden? It doesn’t look like it - the stated weight of the device without acoustics is only three kilos. Then, how can consuming 90 watts from the network, you can get an output of 700 mysterious watts (for reference) or at least a pitiful, but quite tangible 120 nominal. After all, the amplifier must have an efficiency of about 150 percent, even with the subwoofer turned off! But in practice, this parameter rarely exceeds the bar of 75.
Let's try to apply the information obtained from the article in practice.
The stated power for reference is 235+235+230=700 - this is clearly PMPO. There is much less clarity at face value. By definition this is rated power, but it cannot be 60+60 only for two main channels, excluding the subwoofer, with a rated power consumption of 90 watts. This increasingly resembles not a marketing ploy, but an outright lie. Judging by the dimensions and the unspoken rule, the ratio of RMS and PMPO, the real rated power of this center should be 12-15 watts per channel, and the total should not exceed 45. This arises logical question- how can you trust the passport data of Taiwanese and Chinese manufacturers, when even a well-known Japanese company allows itself to do this?
Whether to buy such a device or not is up to you. If it’s to annoy your neighbors in the country in the morning, yes. Otherwise, without first listening to several pieces of music in different genres, I would not recommend it.
A kettle of tar in a jar of honey.
It would seem that we have an almost exhaustive list of parameters necessary to assess the power and sound quality. But, upon closer attention, this turns out to be far from the case, for a number of reasons:
- Many parameters are more suitable not so much for an objective reflection of the signal quality, but for the convenience of measurement. Most are carried out at a frequency of 1000 Hz, which is very convenient for obtaining the best numerical results. It is located far from the background frequency electrical network at 50 Hz and in the most linear part of the amplifier's frequency range.
- Manufacturers often commit the sin of overtly adjusting the characteristics of the amplifier to the tests. For example, even during the times of the Soviet Union, ULFs were often designed in such a way as to provide the best THD indicator, with the maximum output nameplate power. At the same time, at half power level in push-pull amplifiers step type distortion often appeared, which is why the harmonic distortion coefficient at the middle position of the volume knob could go off scale beyond 10%!
- Datasheets and operating instructions often contain non-standard fake, absolutely useless characteristics of the PMPO type. At the same time, it is not always possible to find even such basic parameters such as frequency range or rated power. There’s nothing to say about the frequency response and phase response!
- Parameters are often measured using deliberately distorted methods.
It is not surprising that many buyers fall into subjectivity under such conditions and focus their purchases, at best, solely on the results of a short listening session, and at worst, on the price.
It's time to wrap up, the article is already too long!
We will continue our conversation about quality assessment and the causes of distortion of low-frequency amplifiers in the next article. Armed with a minimum amount of knowledge, you can move on to such interesting topics as intermodulation distortion and its relationship with feedback depth!
In conclusion, I would like to express my sincere gratitude to Roman Parpalak parpalak for his project of an online editor with support for latex and markdown. Without this tool, the already difficult work of introducing mathematical formulas into the text would become truly hellish.
The change in the shape of a harmonic signal resulting from its passage through a device containing nonlinear elements is called nonlinear distortion. A distorted non-harmonic signal contains in its spectrum a constant component, the first harmonic (fundamental frequency and higher harmonics with frequencies). Nonlinear distortion of a harmonic signal is estimated by the harmonic coefficient equal to the ratio of the rms voltage of the signal harmonics (except the first) to the rms value of the first harmonic voltage:
Harmonic distortion is often expressed as a percentage.
Nonlinear distortions of a signal of any shape are assessed by the nonlinearity coefficient, which is calculated by the formula
(the ratio of the root mean square value of the higher harmonics to the root mean square value of the voltage of all harmonics, i.e., to the signal voltage).
Formulas and are related by the relation
from which it follows that both expressions give almost identical results.
There are other methods for assessing nonlinearity - combinational, statistical, which characterize the nonlinear properties of radio devices more than signal distortion.
Rice. 6-9. Block diagram of harmonic voltage measurement
Nonlinear signal distortions are measured using the harmonic method, which is implemented in two ways - analytical and integral. Analytical method is based on the formula and is carried out according to the scheme in Fig. 6-9. The harmonic signal of the generator is fed to the input of the measured object, at the output of which a spectrum analyzer or harmonic analyzer is turned on. Using a spectrum analyzer, a spectrogram of the output signal is obtained, absolute or relative values the amplitudes of the higher harmonics and the first harmonic and the harmonic coefficient is calculated using the formula. If a harmonic analyzer is used, it is manually adjusted to each subsequent harmonic, their values are recorded and calculated using the same formula. The analytical method is labor-intensive and is used to clarify the role of each harmonic separately.
The integral method is based on a formula and allows you to evaluate the influence of all higher harmonics on the signal shape without determining their values separately. To do this, first measure the root mean square value of the signal, and then the value of the higher
harmonic, which will remain after suppression of the first harmonic voltage. The integral method is often called the first harmonic (fundamental frequency) voltage suppression method.
The measurement of the coefficient of nonlinear distortion is carried out using a device - a nonlinear distortion meter (Fig. 6-10). Matching device The control system is designed to provide symmetrical or asymmetrical input and match the output impedance of the object with the input impedance of the meter.
Rice. 6-10. Nonlinear distortion meter: a - block diagram; b - notch filter circuit
Using the PRR operating mode switch, a calibration mode is carried out when the voltage of the entire signal is measured, a measurement mode when the voltage of higher harmonics is measured, and a voltmeter mode for the usual measurement of the root mean square value of any voltage.
The attenuator is designed to set the voltage level to ensure normal operation of subsequent components of the device. The input amplifier must have a bandwidth from the minimum frequency of the signal under study to a multiple of its upper frequency. The frequency, phase and amplitude characteristics of the amplifier in this band are linear. The notch amplifier is designed to suppress the first harmonic voltage using an RC blocking filter (Wien bridge) included in the feedback circuit. Filter fig. 6-10, b) tuned to the frequency of the first harmonic
In steps divisible by 10, by switching resistors and smoothly using a dual block of variable capacitors C. Sharpening the characteristics of the notch filter, necessary for precise balancing of the bridge, completely suppressing the first harmonic voltage and reducing the measurement error, is achieved by performing the equality The resistor control knobs are marked: “ Balancing: rough, fine.” The voltmeter consists of a UV amplifier attenuator and an optocoupler-type rms converter with a magnetoelectric indicator. The indicator scale is calibrated in voltage units, percent and decibels of the nonlinearity coefficient.
For visual observation of the signal shape at the input and output of the measured device and higher harmonics after filtering the first harmonic, clamps are provided for turning on the oscilloscope. There is a calibration generator for checking the voltmeter.
Nonlinear distortion meters are available to operate in the frequency range of the signal under study from 20 Hz to with a bandwidth of up to. They are widely used for quality control of any amplification devices and modulation paths. The nonlinearity coefficient is measured within the range of input voltages from 0.1 to 100 V. The voltage measurement limits when operating in voltmeter mode are in the frequency range 20 Hz - 1 MHz. The measurement error depends on the accuracy of the notch filter adjustment, which is carried out by successively approaching the voltmeter reading to the minimum, i.e., to the voltage of some higher harmonics. The error is
When measuring nonlinear signal distortions, the nonlinearity of the device through which the signal passed is simultaneously assessed. However, this assessment is inaccurate, since it is made under the influence of a single signal and at one point in the frequency range. In real operating conditions, the input of a radio amplifier in most cases receives random signals with a wide spectrum or many deterministic signals of various frequencies. Therefore, nonlinearity products arise throughout the entire passband of the measured object.
The statistical method allows the most complete
characterize the nonlinear properties of an object under conditions that well simulate operating conditions. A low-frequency noise generator (Fig. 6-11, a) with a uniform spectrum in the operating frequency range of the measured object is used as a signal source. The noise voltage is applied to a notch filter, with the help of which a narrow band of signal components located around the middle frequency of the band is cut out from the input signal spectrum transmission of the notch filter (Fig. 6-11, b). At the output of the measured object, components of the output signal are formed in this band, which are products of nonlinearity.
Rice. 6-11. Measurement of nonlinear distortions using a statistical method: a - block diagram; b - spectral density of the signal at the input of the measured object; in - the same at the output
The voltage of these components is measured with a selective voltmeter tuned to the frequency. The voltage of the total signal at the output of the object is measured with a conventional broadband voltmeter V rms value (Fig. 6-11, c). The value of nonlinearity measured by the statistical method is
Using a set of notch filters with different average frequencies, it is possible to measure and plot the dependence of nonlinearity on frequency over the entire operating range of the object.
From CHP and TPP courses we know that electrical circuits are divided into linear, nonlinear and parametric. The last two types of circuits differ from linear ones in that they can create new harmonic components in the response spectrum compared to the spectrum of the input signal.
Nonlinear signal transformation can be desirable and useful (for example, in detection), or it can be harmful and concomitant (for example, in amplifiers). In this case, when this phenomenon is not used in a device containing this circuit, it is highly undesirable, since it often creates harmful side effects. Therefore, the waveform at the output of these devices will be different from the waveform at their input. The change in waveform is called nonlinear distortion.
The reason for nonlinear distortion is that when a harmonic signal with frequency f is applied to the input, a signal appears at the output containing a constant component, a fundamental frequency and higher harmonics with frequencies 2f, 3f, 4f, etc. The amplitudes of higher harmonics quickly decrease as their numbers increase. The second and third harmonics are usually decisive.
The source of nonlinear distortions are circuit elements in which the current is not proportional to the applied voltage, i.e. having a nonlinear current-voltage characteristic. These are, as a rule, vacuum tubes, transistors, diodes, coils with ferromagnetic cores.
The need to measure nonlinear distortions is associated with studying the parameters of amplifiers and sinusoidal generators.
Nonlinear distortions are a complex phenomenon that depends on many parameters: composition electrical circuit, its amplitude-frequency characteristic, signal shape, its amplitude, etc. With increasing amplitude, nonlinear distortions increase. Typically, as the frequency increases, the nonlinear distortion in the amplifier also increases.
Nonlinear distortions are assessed by the harmonic coefficient K G , as well as nonlinear distortion coefficient K N.
Harmonic coefficient K G is defined as the ratio of the root-mean-square (rms) voltage value of the sum of all signal harmonics, except the first, to the root-mean-square (rms) voltage value of the first harmonic according to formula (34):
where U 1, U 2, U 3 , … Un – root mean square voltage values of individual harmonics of the output signal.
Coefficient KG characterizes the difference between the shape of a given periodic signal and the harmonic one.
It is easy to see that in the absence of higher harmonics in the output signal, K G = 0, i.e. a sinusoidal signal from input to output is transmitted without distortion.
The nonlinear distortion factor Kn is defined as the ratio of the root-mean-square (rms) value of the voltage of higher harmonics to the root-mean-square (rms) value of the entire signal according to formula (35):
The most common single-frequency measurement methods are:
1. Fundamental harmonic suppression method.
2. Stress analysis method.
Nonlinear distortion measurement using fundamental harmonic suppression method
In accordance with the formula for determining the nonlinear distortion factor, it is necessary to measure the effective value of the signal under study and the effective value of the higher harmonic components.
There are special instruments that measure nonlinear distortion, called nonlinear distortion meters.
A simplified block diagram of an analog nonlinear distortion meter is shown in Figure 1.
Figure 1 – Simplified block diagram of an analog harmonic distortion meter
Soda device diagramHolds an input device, a tunable notch filter and a square-law voltmeter with an attenuator.
The operating principle of the device is based on separate measurement of the root-mean-square voltage value of the signal under study and the root-mean-square voltage value of the higher harmonics of the same signal.
The input device provides the required value of input resistance and serves to match measuring instrument with the source of the signal being studied.
A notch filter should ideally have infinitely large attenuation at the frequency of the first (fundamental) harmonic and zero attenuation at higher harmonic frequencies. Typically, a notch filter is implemented using a Wien bridge circuit consisting of resistors and capacitors (see Figure 2).
Measuring harmonic distortion using stress analysis
Measurement of nonlinear distortions by voltage analysis (by individual harmonics) is carried out using a selective level meter (SLM).
The circuit for measuring the harmonic distortion using an IMU is shown in Figure 3, and consists of a generator, a low-pass filter, a quadripole under study, and an IMU.
Figure 3 – Harmonic distortion measurement using voltage analysis method
The IMU is connected to the output of the object under study. With a single-frequency sinusoidal signal to control the voltage of any frequency that appears in it as a result of nonlinear distortions. In this case, the IMU is sequentially adjusted to the first, second, third harmonics (and, if necessary, to higher ones), the voltage (level) of which must be controlled. Thus, the levels of all harmonics of interest in the signal under study are measured separately, and the attenuation of nonlinearity is found for each of them, taking the difference between the level of the first harmonic and each of the monitored frequencies:
A Кn = L 1 – L n
IN The entire history of sound reproduction has consisted of attempts to bring the illusion closer to the original. And although a huge distance has been traveled, we are still very, very far from fully approaching live sound. Differences in numerous parameters can be measured, but quite a few of them still remain outside the field of view of equipment developers. One of the main characteristics that a consumer with any background always pays attention to is nonlinear distortion factor (THD) .
And what value of this coefficient fairly objectively indicates the quality of the device? Those who are impatient may immediately find an attempt to answer this question at the end. For the rest we will continue.
This coefficient, which is also called the total harmonic distortion coefficient, is the ratio, expressed as a percentage, of the effective amplitude of the harmonic components at the output of a device (amplifier, tape recorder, etc.) to the effective amplitude of the fundamental frequency signal when a sinusoidal signal of this frequency is applied to the input of the device. Thus, it makes it possible to quantify the nonlinearity of the transfer characteristic, which manifests itself in the appearance in the output signal of spectral components (harmonics) that are absent in the input signal. In other words, there is a qualitative change in the spectrum of the musical signal.
In addition to the objective harmonic distortions present in the audible sound signal, there is the problem of distortions that are not present in the real sound, but are felt due to the subjective harmonics that arise in the cochlea of the middle ear at high sound pressure values. The human hearing aid is a nonlinear system. The nonlinearity of hearing is manifested in the fact that when the eardrum is exposed to a sinusoidal sound with a frequency f in hearing aid harmonics of this sound are generated with frequencies 2f, 3f, etc. Since these harmonics are not present in the primary influencing tone, they are called subjective harmonics.
Naturally, this further complicates the idea of the maximum permissible level of harmonics in the audio path. As the intensity of the primary tone increases, the magnitude of the subjective harmonics increases sharply and may even exceed the intensity of the primary tone. This circumstance gives grounds for the assumption that sounds with a frequency of less than 100 Hz are not felt by themselves, but because of the subjective harmonics they create, falling in the frequency range above 100 Hz, i.e. due to the nonlinearity of hearing. The physical reasons for the resulting hardware distortions in different devices are of a different nature, and the contribution of each to the overall distortions of the entire path is not the same.
The distortion of modern CD players is very low and almost unnoticeable compared to the distortion of other units. For loudspeaker systems, low-frequency distortion caused by the bass head is the most significant, and the standard specifies requirements only for the second and third harmonics in the frequency range up to 250 Hz. And for a very good sounding speaker system they can be within 1% or even slightly more. In analog tape recorders, the main problem associated with the physical basis of recording on magnetic tape is the third harmonic, the values of which are usually given in the mixing instructions. But maximum value, at which, for example, noise level measurements are always made, this is 3% for a frequency of 333 Hz. The distortion of the electronic part of tape recorders is much lower.
Both in the case of acoustics and analog tape recorders, due to the fact that the distortions are mainly low-frequency, their subjective noticeability is greatly reduced due to the masking effect (which consists in the fact that of two simultaneously sounding signals, the higher-frequency one is better heard).
So the main source of distortion in your circuit will be the power amplifier, in which, in turn, the main source is the nonlinearity of the transfer characteristics of the active elements: transistors and vacuum tubes, and in transformer amplifiers nonlinear distortions of the transformer are also added, associated with the nonlinearity of the magnetization curve. It is obvious that, on the one hand, distortion depends on the shape of the nonlinearity of the transfer characteristic, but also on the nature of the input signal.
For example, the transfer characteristic of an amplifier with smooth clipping at large amplitudes will not cause any distortion for sinusoidal signals below the clipping level, but as the signal increases above this level, distortion appears and will increase. This type of limitation is inherent mainly in tube amplifiers, which to some extent may serve as one of the reasons for the preference of such amplifiers by listeners. And this feature was used by NAD in a series of its acclaimed amplifiers with “soft limiting”, produced since the early 80s: the ability to turn on a mode with imitation of tube clipping created a large army of fans of transistor amplifiers of this company.
In contrast, the amplifier's center-cutting (step-step distortion) characteristic, which is typical of transistor models, causes distortion in musical and small sine signals, and the distortion will decrease as the signal level increases. Thus, distortion depends not only on the shape of the transfer characteristic, but also on the statistical distribution of input signal levels, which for music programs is close to the noise signal. Therefore, in addition to measuring SOI using a sinusoidal signal, it is possible to measure nonlinear distortions of amplifying devices using the sum of three sinusoidal or noise signals, which, in light of the above, gives a more objective picture of the distortions.
The term “total harmonic distortion” THD (voltage curve sinusoidal distortion coefficient (see GOST 13109-97)) is widely used when determining the level of harmonic content in alternating signals.
THD Definition
For signal y, the THD coefficient is defined as:
This is consistent with the definition given in IEC 61000-2-2.
Note that this value can exceed 1.
According to this standard, the parameter h can be limited to 50. The THD coefficient allows you to express in one number the degree of distortion affecting the current or voltage anywhere in the electrical installation.
THD is usually expressed as a percentage.
Total distortion factor for current or voltage
For current harmonics this formula looks like:
Below is an equivalent formula, which is more visual and easier to use if the full effective value is known:
For voltage harmonics, the formula is:
Relationship between power factor and THD
(rice. M13)
The THD coefficient, which reflects in one value the degree of distortion of the current or voltage waveform, is an important indicator. The spectrum displays individual harmonics that affect the distorted signal (sinusoidal distortion factor of the voltage curve (see GOST 13109-97).
Hence: 