The damping factor (in Russian literature - damping coefficient) is a characteristic of the amplifier that determines its interaction with the load (speaker system). In the description of many amplifiers, this parameter takes on an almost mystical meaning. What damping coefficient is needed and is it worth chasing record numbers?
Audio frequency power amplifiers (APPA) in relation to the load are divided into two classes - voltage sources and current sources. The latter find very limited use, and almost all serial models are amplifiers - voltage sources.
An ideal amplifier produces the same output voltage at any load resistance. In other words, the output impedance of an ideal voltage source is zero. However, ideal things do not exist in nature, so a real amplifier has a certain internal resistance. This means that the voltage across the load will depend on its resistance (Fig. 1).
However, the loss of output voltage is not the most important consequence of the fact that the amplifier has output impedance. With any movement of the voice coil in the gap of the magnetic system, an electromotive force (EMF) is induced in it. This EMF, closing through the output resistance of the amplifier, creates a current that counteracts the movement of the coil. The magnitude of this current and the braking force are inversely proportional to the output impedance of the amplifier. This phenomenon is called electrical damping of the loudspeaker and largely determines the nature of the reproduction of pulsed signals.
A dynamic head is a complex oscillating system that has several resonance frequencies (mechanical resonance of the moving system, internal resonances of the suspension and diffuser, etc.). When a pulse signal is reproduced, oscillations occur at the resonant frequencies of the system. The trouble is that with weak damping, these damped oscillations can continue even after the impulse that caused them has ended (Fig. 2). As a result, playback will be accompanied by side sounds that color the sound.
Fig.2.
The task of the audio system designer is to dampen the loudspeaker so that its own vibrations decay as quickly as possible. However, there are not so many funds for this. There are three possible ways to dampen the head:
- mechanical damping, determined by losses due to internal friction in the suspension
- acoustic damping, determined by the characteristics of the acoustic design
- electrical damping determined by the amplifier's output impedance
Mechanical damping is determined by the design features of the dynamic head and is laid down at the design stage. It is rarely possible to change its value in a finished speaker. As an independent solution, acoustic damping is used in the form of filling the body of the acoustic system with sound-absorbing material. In addition, acoustic damping is included in the design of closed midrange and high-frequency heads. The radiation resistance of the dynamic head also has some influence on the acoustic damping. However, the contribution of all these components to the overall degree of damping of the head is small. Thus, electrical damping becomes the main tool for influencing the transient characteristics of the amplifier-speaker system.
The relationship between the character of the sound and the output impedance of the amplifier was noticed back in the days of tube amplifiers, in the 50s. The difference in the sound of amplifiers with an output stage based on triodes and pentodes was especially noticeable. Pentode amplifiers had a significant output impedance, as a result of which the dynamic heads were underdamped and the sound acquired a booming overtone. The introduction of negative feedback made it possible to reduce the output impedance of the amplifier, but did not completely solve the problem. It's surprising that the debate about which amplifier is better continues half a century later. But it’s not only about the amplifier, but also about the speaker system.
To evaluate the damping properties of an amplifier, a new parameter was proposed - the damping factor, which is the ratio of the load resistance to the output impedance of the amplifier.
Experiments carried out at the same time made it possible to establish the minimum value of this parameter - 5...8. Further reduction in the amplifier's output impedance had virtually no effect on the system's pulse characteristics. By the way, the ideology of Hi-Fi (short for High Fidelity) and the term itself took shape by the end of the 50s. At this point, the minimum requirements for the audio system were determined - the reproduced frequency band, the harmonic coefficient (then called clear factor - degree of purity) and output power. Subsequently, with the advent of transistor amplifiers and specialized low-frequency drivers with lightweight suspension, the lower limit of the dumping factor was raised. This made it possible to unambiguously determine the degree of damping of the head by the parameters of the amplifier, regardless of the characteristics of the acoustic design. At the same time, within certain limits, the sound of a particular speaker with different amplifiers was ensured to be identical.
The famous DIN45500 standard defined the damping coefficient for Hi-Fi amplifiers unambiguously - no less than 20. This means that the output impedance of the amplifier when operating at a load of 4 Ohms should be no more than 0.2 Ohms. However, the output impedance of modern amplifiers is much lower - hundredths and thousandths of an ohm, and the damping factor, respectively, is hundreds and thousands.
What is the meaning of such a significant improvement in this indicator? The damping coefficient in this case, oddly enough, has nothing to do with it. Only one component is important - the output impedance of the amplifier. In this case, the magic of numbers takes place, since everyone is accustomed to the hundreds of watts of output power of modern amplifiers and it is necessary to attract the buyer with something new. Agree that a damping factor of 4000 looks much nicer than an output impedance of 0.001 Ohm. And in any case, this means only one thing - the amplifier has a very low output impedance and is capable of delivering significant current to the load (even if only for a short time). And the connection between output power and the dumping factor, although direct, is not unambiguous. So a term that was previously of interest only to specialists has found a new application.
However, in the story of the dumping factor there is another character - the speaker cable. And it can greatly spoil not only the numbers, but also the sound quality. After all, the cable resistance is summed up with the output impedance of the amplifier and becomes a component of the dumping factor.
For a cable 2 m long, a resistance of 0.05 Ohm is quite a decent indicator. But for an amplifier with an output impedance of 0.01 Ohm, the damping factor at a 4 Ohm load with such a cable will decrease from 400 to 66. There is no reason to worry yet. But if you use a thin cord from a set of speakers and dubious twists with a total resistance of 0.3...0.4 Ohms (the situation, unfortunately, is still not uncommon), then the damping factor will drop to 10, regardless of the amplifier's performance. Therefore, there is no need to skimp on wires.
A passive crossover creates similar problems. Therefore, coils with a ferromagnetic core are used in crossovers more often than air coils - this allows not only to save expensive (for them) copper wire, but also to significantly reduce the resistance of the coil. Of course, when the core is remagnetized, additional nonlinear signal distortions occur, but in most cases this is a lesser evil than underdamped speakers. By the way, the difference in the sound of systems with crossovers of different designs is often determined not so much by the nature of the distortion introduced, but by the different damping of the speaker. In cases where conscience does not allow installing coils with a core, the lack of damping can be compensated for by acoustic methods. But acoustic damping does not have all the capabilities of electrical damping and can end up being more expensive.
You can calculate the output resistance of an amplifier in amateur conditions if, with the same input signal, you measure its output voltage at idle (Eo) and at load (U) of a certain resistance (R). However, the accuracy of this simple method decreases when the amplifier output impedance is less than 0.05 ohms.
- a high damping factor (more than 50) is required for dynamic drivers with light suspension and a large mass of the moving system, operating close to the main mechanical resonance (subwoofer or midbass with an active crossover, wideband drivers without a crossover);
- for dynamic heads whose resonant frequency is outside the operating frequency band (MF, HF), the damping factor with multi-band amplification does not matter, since electrical damping is most effective for suppressing the main mechanical resonance of the moving system;
- when working with a passive crossover, the system's dumping factor is determined mainly by the crossover's output impedance in its passband, so the requirements for the amplifier's dumping factor can be reduced (20...30). Further increases in the amplifier's output impedance may cause a change in crossover cutoff frequencies;
- Damping of structural resonances in the material of the diffuser and suspension is not part of the function of the amplifier and can only be carried out mechanically. This is a dynamic head problem;
- For amplifiers with high output impedance (current sources), the concept of a dumping factor is meaningless. In this case, only acoustic damping can be used to suppress the main mechanical resonance of the moving system.
QUESTION
I'm going to buy an amplifier and during the selection process I asked myself: what is the load damping factor? It is not indicated in the documentation for all amplifiers - is it not important?
I read on one forum that the damping factor does not affect the sound, so there is no point in looking at it at all. And they say it is indicated only on old amplifier models that have been produced for decades with minor changes. Is it really?
Pavel Zazygin
ANSWER
The damping factor (sometimes also called the damping factor) refers to the ratio of the load impedance (that is, the acoustics) to the output impedance of the amplifier. For an ideal amplifier, the output voltage should not depend on changes in the load, but for this it must have its own zero impedance. In practice, this is, of course, impossible, although at one time many circuits with negative output resistance were developed. We are, naturally, talking about transistor amplifiers, since tube models have a high impedance due to the resistance of the secondary winding of the output transformer or the internal resistance of the output lamp if the circuit is transformerless.
So, the lower the output impedance of the amplifier and, accordingly, the greater the damping factor, the less, in theory, the voltage at the output terminals of the amplifier depends on the impedance of the speakers. This is especially important since the latter parameter in most cases depends on frequency.
Naturally, this explanation is extremely simplified, since a loudspeaker is a very complex electromechanical resonant system. Nevertheless, even from this primitive interpretation it should be clear that a high damping coefficient is a good thing. The only question is how designers achieve its increase. Mainly by increasing the depth of feedback. At the same time, the level of distortion is reduced, the frequency response is leveled, and in general, all the main parameters of the amplifier are improved. However, in the 1970s, engineers noticed that deep negative feedback increases the amplifier's response time to fast pulses in the music signal, which has a detrimental effect on fidelity. The understanding has come that increasing the damping coefficient due to feedback does more harm than good. Moreover, the coefficient calculated using formulas or measured in the laboratory in practice turns out to be much smaller due to cables and passive crossovers that have their own resistance - it adds up to the output impedance of the amplifier, making the actual damping coefficient very small. That is why manufacturers have stopped boasting about the high damping factor and indicating it in the technical characteristics of amplifiers.
Definition
Dumping factor (damping coefficient) is a characteristic of an amplifier that determines its interaction with the load (speaker system).
A little theory
The damping factor (DF) is one way (and not a very good one) of expressing the output impedance of an amplifier. An ideal amplifier would have zero output resistance - regardless of the current it supplies, the output voltage would not change or drop.
In reality, amplifiers have some output impedance. In a good design it is very small, on the order of hundredths of an ohm. The DF expresses this as a ratio to the load impedance, so an amplifier with an output impedance of 80 milliohms loaded into an 8 ohm speaker will have a DF of 8/0.08=100. An amplifier with an output impedance of 8 milliohms will have a diffraction factor of 8/0.008=1000. Damping factors vary greatly, but the difference in amplifier performance is only a small fraction of an ohm.
It is not always understood that the DF changes depending on frequency, remaining constant at low frequencies (say up to 1 kHz) and falling in the high-frequency part of the range. The data sheet always gives the value at low frequencies.
The problem with the term "Damping Factor" is that the name makes it sound like it greatly affects the damping of the speaker, but it doesn't. Of course, the resonance of a woofer driver is affected by the series resistance of its electrical circuit, but almost all of it consists of the resistance of the speaker coil, which is usually in the range of 5-7 ohms. The crossover (filter) adds about 1 ohm, and the connecting cable also adds about 1/4 ohm. It is clear that the output impedance of a good amplifier is a very small fraction of this impedance, and thus the difference between a DF 100 and a DF 1000 in terms of loudspeaker damping is negligible. (In addition, the low-frequency resonance of a loudspeaker is carefully selected by its designer and arbitrarily changing it is unlikely to improve the sound.)
This doesn't mean that the amplifier's output impedance doesn't matter. The load that a loudspeaker presents to an amplifier is highly dependent on frequency, so if the output impedance is high, the output level will vary with frequency, introducing undesirable changes to the frequency response of the system. The lower the output impedance, the better.
What in practice?
Subwoofer speakers have a large area, and accordingly they have a large cone mass, since they have to push a large mass of air during operation. This fact leads to the fact that at the moment when there is no signal (transition of the sinusoid through “0”) the speaker makes oscillations not controlled by the amplifier, which are perceived by ear as humming, smearing, or lagging sound. In order to avoid this effect, it is necessary either to make the diffuser weightless, or to ensure that all vibrations that are not in the original sound signal are compensated. Such compensation (holding the speaker cone) is nothing more than a damping factor. Good class AB amplifiers have a damping factor of about 200-300. When a class AB amplifier is bridged, its damping factor drops by almost 2 times. A different picture is observed for class D amplifiers. Despite the fact that the load is included in the bridge, due to the characteristics of the amplifier, a double damping effect (DDX) occurs. In this case, the dumping factor, on the contrary, increases. True, at the same time, the utilization factor of the supply voltage drops and the efficiency drops by several percent.
Example
Connecting a 2-coil subwoofer (4+4 Ohms) to an amplifier (monoblock). Those. + and - with possible inclusion options of 8 or 2 Ohms:
1. When the amplifier is loaded at 8 Ohms, the damping factor will increase, i.e. Control over the speaker will increase and playback accuracy will improve. But at the same time the power will drop.
2. With a load of 2 ohms, everything is exactly the opposite - control is lost (the sound is blurred, dirtier), but the gain is in power.
In custody
A high damping factor is required for dynamic drivers with light suspension and a large mass of the moving system, operating close to the main mechanical resonance (subwoofer or midbass with an active crossover, wideband drivers without a crossover);
For dynamic heads whose resonant frequency is outside the operating frequency band (MF, HF), the damping factor with multi-band amplification does not matter, since electrical damping is most effective for suppressing the main mechanical resonance of the moving system;
When assessing the value of the DF, one must take into account the value of the frequency at which it was measured (usually measured at 1 kHz), but the principle “the more the better” is valid for DF.
The constructive estimated value of the DF and the ability of the amplifier to adequately control the woofers (subwoofers) depends on the quality of the voltage converter. "Food is everything to us!"
Total:
Minimum damping coefficient value can be considered 20, good - 200-400. Modern high-end amplifiers have a value of this parameter of 200 or higher.
When connecting speakers to an amplifier, you should pay attention to the quality of the cable and connectors. With a high damping factor (and, accordingly, a low output impedance of the amplifier), the resistance of the cable and connectors begins to play a significant role.
The main parameter characterizing the elastic properties of foundation foundations is the coefficient of elastic uniform compression With z. It should be determined experimentally. In the absence of experimental data, the value With z, kN/m 3, can be determined for foundations with a base area A no more than 200 m2 according to the formula
Where b 0 - coefficient, m -1, taken equal to: for sands 1, for sandy loams and loams 1.2, for clays and coarse soils 1.5; E— soil deformation modulus, kPa, determined in accordance with the requirements of the SNiP chapter “Foundations of buildings and structures. Design standards"; A- area of the foundation base, m2; A 0 = 10 m2.
The soil deformation modulus, as a rule, should be determined from the results of field stamp tests. In the absence of such tests, it is permissible to use tabular data.
For foundations with a base area A exceeding 200 m 2, the value of the coefficient C z accepted as for foundations with a base area A= 200 m 2.
Coefficient With z characterizes the rigidity of the base during translational vertical movement of the foundation.
Besides With z the calculations use the coefficient of elastic uneven compression With φ, kN/m 3 (when the foundation is rotated relative to the horizontal axis passing through its base), elastic uniform shear C x, kN/m 3 (with horizontal translational movement of the foundation), and elastic uneven shear With ψ, kN/m 3 (when rotating about a vertical axis). Their values are accepted:
Stiffness coefficients for natural foundations are determined by the formulas:
During vertical translational vibrations of the foundation,
k z = C z A;
During horizontal translational vibrations of the foundation
k x = C x A;
During rotational vibrations relative to the horizontal axis passing through the base of the foundation,
k φ = C φ I φ;
During rotational vibrations about a vertical axis passing through the center of gravity of the base of the foundation,
k ψ = C ψ I ψ,
Where Iφ And I ψ— moments of inertia of the base of the foundation relative to the horizontal and vertical axes.
The main reason that determines the damping of foundation vibrations is the loss of energy to excite elastic waves in the soil, which transfer energy from the foundation to parts of the soil mass distant from it, where this energy is gradually absorbed due to the inelastic resistance of the soil. However, when describing vibrations of the foundation itself, it is more convenient to take into account energy losses due to the radiation of elastic waves within the framework of the theory of viscous resistance, which depends on the same parameters as the rigidity of the natural foundation, i.e. on the type of soil, its elastic properties and the area of the sole. Consequently, damping coefficients and stiffness coefficients for natural foundations are related. Damping properties are determined by relative damping coefficients ξ (fraction of critical vibration damping), determined, as a rule, based on test results.
ξ z related to the damping coefficient of the elastic-viscous base B z in equation (9.4) as follows:
,
Where λz— angular frequency of free vertical vibrations of the installation.
In the absence of experimental data, the relative damping coefficient during vertical vibrations of the foundation can be determined using the formulas:
For steady (harmonic) oscillations
For transient (impulse) oscillations
,
Where R- average static pressure, kPa, on the base under the base of the foundation from the calculated static loads with an overload factor equal to 1.
Values ξ z, calculated using formula (9.13), are approximately 1.5 times less than those obtained using formula (9.14). Values ξ z are calculated using formula (9.13) when determining the amplitudes of forced steady vibrations and when determining the rate of decrease in the amplitudes of free vibrations of the foundation at the end of the vibration process (approximately after two or three cycles of free vibrations excited by some reason - impact, impulse, initial deflection, etc. ). Formula (9.14) is applicable to estimate the largest displacements of the foundation during free vibrations under the influence of an impulse. Smaller values ξ z, calculated using formula (9.13), take into account the partial return of energy to the oscillating foundation by elastic waves reflected from denser deeper layers of soil.
Values of relative damping coefficients for horizontal vibrations ξ x and rotational vibrations relative to the horizontal ξ φ and vertical ξ ψ axes accepted:
ξ x = 0,6ξ z ; ξ φ = 0,5ξ z ; ξ ψ = 0,3ξ z.
If the damping moduli are known from experiments F, s, vibrations of foundations, then the relative damping coefficients can be calculated using the formula
ξ z,x,φ,ψ = Ф z,x,φ,ψ λ z,x,φ,ψ/2,
Where λ z, λ x, λ φ, λ ψ - respectively, the angular purity of free vibrations of the foundation - vertical, horizontal and rotational relative to the horizontal and vertical axes.
9.2.2. Stiffness and damping coefficients for pile foundations. Determination of reduced mass
When determining the compliance of piles in the vertical direction, a design scheme was adopted in the form of a compressible rod in an elastic Winkler medium, which prevents vertical movements of each section of the rod (along its axis); the end of the rod rests on the spring.
Below are the formulas for determining the reduced mass m red pile foundation and reduced stiffness coefficients k φ,red , k x,red , k ψ,red , which are used in calculations of vertical, horizontal rotational and torsional vibrations of foundations in all formulas instead of mass m(foundation and machine) and stiffness coefficients k z , k φ , k x , k ψ .
For vertical vibrations of foundations:
;
;
; α = C * z /E bt,
Where m r— total mass of the grillage with the machine installed on it, t; mpi- weight i th piles, t; N— number of piles; β * = k 2 ; th—hyperbolic tangent; C*z- coefficient of elastic uniform compression of the soil at the level of the lower ends of the piles, kN/m 3, determined by formula (9.6), in which A is taken to be equal to the cross-sectional area of the pile, and the value b 0 for driven piles is doubled; Ebt— initial modulus of elasticity of concrete, kPa, taken in accordance with the chapter of SNiP “Concrete and reinforced concrete structures. Design standards"; l— length of piles, m; d— length of the cross-sectional side of the pile, m; k 1 coefficient taking into account the elastic resistance of the soil along the side surface of the pile; is taken equal to 3 · 10 2 kPa 1/2 · m -1/2; k 2 - coefficient taking into account the influence of the properties of the soil cut by the pile on the reduced mass of the pile foundation, is taken equal to 2.
For horizontal rotational vibrations of foundations:
m red = m r;
;
θ 0,red = θ red + h 2 0 m r;
.
Where θr— moment of inertia of the grillage and machine mass relative to the horizontal axis passing through their common center perpendicular to the plane of oscillation, t m 2 ; h 0 - distance from the center of mass m r to the bottom of the grillage, m; r i— distance from the axis i th pile to the axis of rotation of the foundation base, m; k z,red— reduced stiffness coefficient of the pile foundation, kN/m, determined by formula (9.18).
For horizontal vibrations of foundations, the reduced mass of the foundation m red is determined by formula (9.17), as for vertical vibrations, with k 2 = 2/3. The stiffness coefficient for elastic uniform shear, kN/m, is determined by the formula
k x,red = Nα´ 3 E bt I/q,
Where E bt I— bending rigidity of the cross-section of the pile, kPa m 4 ; α´ – coefficient of elastic deformation of the “pile-soil” system: α´ = 1.6 α d(here α d— pile deformation coefficient, determined as when calculating piles for static horizontal loads).
Damping Factor is the ratio of the nominal impedance of the loudspeaker to the output impedance of the power amplifier. It is believed that the minimum damping factor should be at least 20. From a practical point of view, a damping factor greater than 50 does not make sense.
In real transistor power amplifiers, its value reaches 1000; naturally, there are no problems if there is no general feedback (GFE), which can both increase and decrease the damping coefficient of the amplifier. In addition, without OOS (Damping Factor) it is stable and does not depend on the nature of the complex load - capacitive, inductive, resistive.
The output transformer in tube power amplifiers produces an output impedance (at different frequencies) of tens of ohms, so the damping factor can be less than 20. This is the main disadvantage of a tube amplifier. We must not forget that the secondary winding of the output transformer has practically zero resistance at direct current and infra-low frequencies, which partially negates such a characteristic as the damping coefficient.
Moreover, to equalize the sensitivity of dynamic heads, many speakers (in filters) have resistors, which somehow reduces the criticality of such speakers to the output impedance of the power amplifier.
From the course of elementary physics it is known that all conductors (audio cables) have electrical resistance, which naturally affects the pass-through signal, and therefore the damping of the audio amplifier as a whole.
Since (Damping Factor) is indicated by bare numbers (in our opinion, instead of it), it is necessary to indicate only the output impedance of the power amplifier in the classical units of “Ohm”, and not the result of mathematical calculations that are obscure (for the consumer).
