Calculation of a filter for an acoustic system online program. Calculation of buildings. Professional subwoofer calculation program

Case without back wall

The main resonance frequency of such a case is

where I is the depth of the box, m; S is the area of ​​the hole, m2. An increase in acoustic power at the main resonance frequency by 3-6 dB for relatively flat cases and 6-10 dB for deep cases gives the sound being studied an unnatural timbre. If fI = fG, then the increase in acoustic power at lower frequencies is most significant. It is advisable to use a loudspeaker with a resonance frequency lower than the resonance frequency of the box; the most common ratio is fG / fY = 0.5 - 0.7.

A case without a back cover is currently not used as an acoustic design in high-quality playback systems. If there is no alternative, then the case should be as flat as possible. The case without a back cover with a loudspeaker should be placed no closer than 20 cm from the wall, which is recommended to be dampened with a heavy carpet. If the loudspeaker must be placed along one of the walls, then preferably along a short one, closer to its middle.

Calculation of a closed case

Installing a loudspeaker in a closed case of sufficiently large volume allows for satisfactory reproduction of low frequencies, since the front side of the diffuser is completely protected from radiation from the rear side. This results in a slower decrease in acoustic power at lower frequencies than when installing a loudspeaker in an acoustic baffle of finite dimensions.

The resonance frequency of a loudspeaker installed in a closed case of medium size fP, provided that the loudspeaker occupies less than a third of the area of ​​the wall on which it is mounted, is determined in the following order:

1) determine the flexibility of the suspensions of the mobile loudspeaker system SR;

2) calculate the flexibility of the air volume in the case using the formula

where V is the volume of air in the case, m 3, equal to its internal volume minus the volume of the loudspeaker, which to a first approximation is equal to 0.4 d4; d - diffuser diameter, m;

3) in relation to SG / SV using the nomogram in Fig. 4-20 determine the ratio fP / fG provided by a case of a given volume V. The mechanical resonance frequency of a loudspeaker in an acoustic screen can be taken from table. 4-11.

If you need to get an acoustic system with an existing loudspeaker in the form of a closed case with a resonant frequency fP, then the required volume of the case is determined in the following order:

1) take the value of the resonant frequency of the loudspeaker fG in the acoustic screen from the table. 4-11;

2) determine the flexibility of the suspensions of the moving system of the SG loudspeaker;

3) having set the desired ratio fР / fГ, determine according to the graph in Fig. 4-20 the corresponding ratio SG/SV and find the required flexibility of air volume CD in a closed case;

4) calculate the required volume of air inside the case in cubic meters using the formula

The total internal volume of the case is obtained by adding the loudspeaker volume to the calculated V value.

If the value of fG is unknown or it is difficult to determine it in an acoustic screen of a sufficiently large size, then you can measure the mechanical resonance frequency of the loudspeaker fB, without a screen, and when calculating, use the fP / fB curve in Fig. 4-20.

The above calculation is valid only for frequencies f <; 40/L (L is the depth of the case in meters). In this regard, the rear side of the loudspeaker cone in a closed case must be protected from sound waves corresponding to higher frequencies reflected by the internal walls by covering these walls with sound-absorbing material.

The dimensions of a closed case can be reduced by filling it with glass wool or other similar material. This filling is equivalent to increasing the volume of the case by 40%.

If the frequency fP obtained by calculation is sufficiently low, then the loudspeaker should have a Q of about 1. If the frequency fP is unacceptably high, then good results are obtained by reducing the quality factor to a Q value of about 0.1; in this case, of course, it is necessary to raise the lower frequencies in the amplifier by about 6 dB/octave starting from the frequency

Bass reflex calculation

The bass reflex is a case 1 (Fig. 4-21) with an additional hole 3, located next to the loudspeaker 2 mounted on the same wall and having an area, as a rule, equal to the area of ​​the diffuser. Having specified the depth of the phase inversion hole, the ratio of its sides, calculating the effective area of ​​the diffuser (determining the area of ​​the hole) and taking the resonant frequency of the phase inverter fФ = fГ, according to the nomogram in Fig. 4-22 you can determine the required volume of the case.

The distance from the end of the tunnel to the back wall of the box should not be less than dG /2.

At frequency fФ, the bass reflex can be considered as an acoustic transformer that improves the matching of the loudspeaker with the air load. Although the acoustic power delivered by the front of the cone decreases at this frequency, the overall acoustic power can increase significantly. At the same time, nonlinear distortions are significantly reduced and the rated power of the loudspeaker increases due to a decrease in the amplitude of the cone displacement.

The depth of the phase-inverted hole can vary from the thickness of the case wall (Fig. 4-21, a) to a value approximately equal to 30 / fF when using tunnel 5 (Fig. 4-21, b). The considerable length of the tunnel allows the use of a small box.

At frequencies below fФ, the flexibility response of the air volume increases and forms a rigid connection between the mass of air in the hole and the mass of the moving loudspeaker system. The mass of air is thus added to the mass of the moving system and, together with the flexibility of the suspensions, forms a mechanical circuit with a resonant frequency f1< fФ. Когда диффузор на этой частоте смещается вперед, воздух в отверстии движется назад (и наоборот) и эффективность излучения ничтожна.

At frequencies above fФ, the resistance of the air mass in the hole becomes high and the bass reflex can be considered as a completely closed case. The rigidity of the air volume is added to the rigidity of the suspensions and, together with the mass of the moving system, forms a circuit with a resonant frequency f2 > fФ. The emission from the phase-inverted hole at frequency f2 is very small.

The total electrical impedance of the loudspeaker RG in a bass reflex usually has two maxima (solid curve in Fig. 4-23) at frequencies f1 and f2, located on either side of the resonance frequency of the loudspeaker in a flat acoustic screen fG (dashed line in Fig. 4-23, where R is the resistance of the loudspeaker coil to direct current).

The impedance peaks of the loudspeaker in the bass reflex are significantly lower than the peak of the loudspeaker in the acoustic screen, but the corresponding values ​​of Q1 and Q2 are higher than the Qr of the loudspeaker in the acoustic screen. This disadvantage is especially pronounced at frequency f1, since an increase in the speed of movement of the diffuser leads to an increase in nonlinear distortions, the noticeability of which is facilitated by the absence of useful radiation at this frequency. This phenomenon can be combated by limiting the output power of the amplifier at frequencies close to f1.

If it is desirable that the frequency response of the loudspeaker in the bass reflex is horizontal in the lower part of the operating frequency range, starting from /g, then the condition QG = 0.6 must be met.

As QG increases, the Qg value increases, and the QФ value decreases, and this causes uneven frequency characteristics. If it is not possible to reduce Qr, then it is necessary to at least suppress the peak in the frequency response at frequency f2, which occurs at QG > 0.6. This is achieved by introducing sound-absorbing material 4 into the box (see Fig. 4-21). Sometimes the entire volume is filled with glass wool. In this case, the area of ​​the phase-inverted hole, obtained by calculation using the nomogram in Fig. 4-22, should be increased by 2.5 times.

The introduction of a large amount of sound-absorbing material into the bass reflex leads to a weakening of the low-frequency radiation, and if you want to extend the characteristic towards these frequencies, at least up to fG, you should ensure a significant increase in the low frequencies in the amplifier.

The bass reflex is adjusted by changing the area of ​​the hole (for example, with a plate fixed so that its rotation changes the area of ​​the hole) or the depth of the tunnel. It is necessary to strive to ensure that the frequency interval separating the resonant peaks of the impedance does not differ significantly from the octave; the peak amplitudes were equal; any additional peaks caused by standing waves in the box were eliminated by adding damping material.

The advantage of a bass reflex in comparison with a closed box of the same volume is an increase in acoustic power by approximately 5 dB in the range from one to two octaves and a reduction in nonlinear distortions in the frequency range fФ - 2/ф at the same acoustic power.

The disadvantage of a bass reflex is a faster decrease in acoustic power at frequencies below fФ than in a closed box, and the need for tuning.

Case design

In the case where the loudspeaker is mounted, resonance is possible at one or more frequencies of the audio range, leading to an unpleasant change in the timbre of sound reproduction. This phenomenon is most pronounced in partially or completely closed cases.

The use of high-density materials helps reduce wall vibrations. The plywood used for these purposes must have a thickness of at least 20 mm. A good result is obtained by dry river sand, poured between two thin plywood sheets. The walls, especially the back and partly the front, must be reinforced with wooden blocks. It is possible to use chipboard.

Damping the walls of the case

The internal surfaces of the case 1 (Fig. 4-24) are covered with a layer of sound-absorbing material 6 with a thickness of at least 10 mm (or one of the pairs of parallel surfaces with a layer of double thickness). However, standing waves at lower frequencies are not eliminated.

The best result is obtained by dividing the volume of the case with one or more sound-absorbing partitions 2, for example, made of felt 5-10 mm thick. Sections of the box that are separated from the loudspeaker by one or more partitions in this case require very little acoustic treatment. The high-frequency loudspeaker 4 must be protected from radiation from the rear side of the low-frequency loudspeaker diffuser by several layers of sound-absorbing material, or a metal cap 5. The low-frequency loudspeaker 3 is located at the bottom of the case.

Speaker placement

The hole in which the speaker is placed behaves like a pipe, the length of which is equal to the thickness of the wall or board. Resonances and anti-resonances of this pipe, as well as reflections from the edges of the hole, cause unevenness in the frequency response. Obvious recommendations are to chamfer the edges of the hole or install the speaker in a thinner screen, which is then placed in a wall or screen of normal thickness.

Drawer shape

At lower frequencies, the loudspeaker emits spherical waves, and the ribs of the box, especially those that make up the front wall, form obstacles in the path of the sound waves. This causes bending of the wave front (diffraction) and secondary radiation from the fins, which leads to interference phenomena, causing peaks and valleys of up to ± 5 dB in the frequency response. From the point of view of combating secondary radiation, the ideal shape is a sphere, the worst is a cube with a loudspeaker in the center of one of the sides. A rectangular parallelepiped with a loudspeaker placed closer to one of the short sides is preferable to a cube. However, the best approximation to the ideal is provided by a rectangular truncated pyramid placed on a rectangular parallelepiped (Fig. 4-25). For any shape, it is desirable that the box have different linear dimensions; none of the linear dimensions was much larger or much smaller than the others; The largest box size should not exceed 1/4 of the wavelength of the lower frequency of the operating range.

Decorative fabric should not cause significant losses of acoustic power. The most suitable fabric is made from hard, strong (cotton or plastic) loosely woven threads. The use of fabrics made from soft and fluffy threads is undesirable.

Grouping and phasing of loudspeakers

A group connection is formed by several identical loudspeakers placed close to one another in one acoustic screen. A group of loudspeakers has a large radiation area at lower frequencies (which would require a significant increase in the size and weight of the moving system when using one loudspeaker); At the same time, the advantages of a separate loudspeaker with a relatively light moving system are retained - from the point of view of transient mode and reproduction of high frequencies.

The air resistance to radiation from each loudspeaker in a group increases at lower frequencies n times (ha is the number of loudspeakers in the group). This would make it possible to obtain a significant gain in acoustic power if the mass of the oscillating air did not simultaneously increase by the square root of n times. As a result, when n == 2 -:- 4, the acoustic power increases significantly, but still not by a factor of i (at the same electrical power), and a further increase in n gives almost no gain.

An increase in the mass of oscillating air lowers the resonance frequencies of each loudspeaker in the group and, therefore, expands the operating frequency range, especially significantly at high i.

The most satisfactory connection of loudspeakers in a group is parallel; then Q of the system will not differ from QG. If it is necessary that the resistance of the group is equal to the resistance of one loudspeaker, then from the point of view of the best Q of the group it is better to use a series-parallel connection of loudspeakers (the number of which should be equal to n2, where n = 1, 2, 3 ...). Whenever loudspeakers are connected in a group, they must be correctly phased: when a DC source (such as a low-voltage battery) is connected to the input terminals, the cones of all loudspeakers must be biased in the same direction. Changing the direction of displacement of the speaker cone is done by changing the order in which its input ends are turned on.

If placing a group of loudspeakers in a closed box is difficult - the required volume of the case is calculated to be unacceptably large, then the loudspeakers can be placed in a small acoustic screen or a smaller box filled with absorbing material, compensating for the attenuation of radiation at lower frequencies by appropriate correction in the amplifier.

The disadvantages of a group connection include significant irregularity in the frequency response and directivity characteristics at high frequencies.

Two- and three-way speaker systems

Speaker selection. Sound reproduction with Class I quality can usually be achieved by using a wideband loudspeaker, such as 4GD4, 4GD7 or 4GD28, or by dividing the full frequency range corresponding to this class into two bands. To ensure sound reproduction with quality in the “highest” class, it is necessary to divide the full range into three bands.

The nominal frequency range of a loudspeaker intended to reproduce a particular band must be wider than this band by two octaves when using filters with a slope of 6 dB/octave and by one octave when using filters with a slope of 12 dB/octave. The crossover frequency of a two-way system is usually selected from 400 to 1,200 Hz. In a three-band system, the low-frequency section can operate up to 300-600 Hz, the mid-frequency section can operate up to 2,000-5,000 Hz.

Near the crossover frequency there is often significant distortion caused by the speakers working together. If the distances from each loudspeaker to the listener are unequal, then the frequency response of the system may have significant unevenness, determined by the phase relationships of the incoming signals.

Separation filters. The simplest connection for a tweeter is through a capacitor, which protects the tweeter from overload at lower frequencies. This switching is used when the main speaker does not have a wide enough frequency range. The capacitance of the capacitor is calculated by the formula

where fP is the crossover frequency, Hz; RP - loudspeaker impedance at frequency fР, Ohm.

With a properly constructed filter, each loudspeaker should operate only in the frequency range for which it is designed. The filter losses in the passband should be minimal.

The inductance and capacitance of the filter at different cutoff slopes, which is defined as the change in attenuation as the frequency changes by an octave, are calculated using the following formulas.

In formulas (4-11) and (4-12), inductances have the dimension of millihenry and capacitances - microfarads.

Based on the calculation, capacitors with the nearest larger rated standard capacitances are selected. To select a capacitance, it is possible to connect several capacitors in parallel. Obviously, if the capacitance of the capacitor deviates from the value obtained by calculation, the cutoff frequency will differ from the specified one.

If the filter requires capacitances of the order of tens of microfarads and higher, then in order to reduce its dimensions it is advisable to use electrolytic capacitors. Since the latter are polar and will operate in an alternating current circuit, in each filter link it will be necessary to use two back-to-back capacitors, each of which should have a capacitance as close as possible to that obtained by calculation. In the isolation filter sections of a transformerless transistor amplifier, one electrolytic capacitor can be used, observing the correct polarity of their connection.

The filter for a three-way acoustic unit (Fig. 4-28) is a combination of the two filters discussed above. The first separates the low-frequency region from the mid-frequency region; the latter is then divided by a second filter. Both filters do not have to have the same cutoff slope; they should only be calculated for one resistance.

The method for calculating crossover filters is based on the assumption of equality and the active nature of the loudspeakers in the separated bands. Since the impedance of the loudspeaker at the crossover frequency can have a significant inductive component, in order to avoid frequency distortions in the overlap region, the inductance of the mid- and low-frequency loudspeakers should be taken into account when calculating as part of the filter, i.e., make a filter coil connected in series with the loudspeaker with inductance less than the calculated inductance of the loudspeaker.

If the impedances of the loudspeakers in the links of a multi-band system are not equal, then you should try to select equal impedances of the links by means of a group connection (a series connection of high-frequency loudspeakers is acceptable).

Parallel connection of two or three high-frequency loudspeakers makes it possible to use them in combination with almost any low-frequency loudspeaker. A possible discrepancy in the impedance values ​​of the speaker system sections can be eliminated by increasing the input impedance of the high-frequency link using a voltage divider made of resistors.

If several high-frequency loudspeakers are used in a two- or three-link system (for example, 1GD-3), then they should be placed in a case so that the angle between their axes in the horizontal plane is about 20-30°.

If, in a multi-way sound reproduction system, only one high-frequency loudspeaker is used, which has an impedance greater than that of the low-frequency loudspeaker, then in order to equalize the load resistance of the crossover filter in the high-frequency region, the high-frequency loudspeaker should be bypassed with a resistor of the appropriate resistance.

Stereo speaker systems

The loudspeakers of a two-channel stereo system must be strictly identical. They should be placed in accordance with Fig. 4-29, where the zone of optimal stereophonic effect is shaded.

The orientation of loudspeakers depends on their directional characteristics and must be determined experimentally. The loudspeaker axes should not intersect in the listening area.

Publication: N. Bolshakov, rf.atnn.ru

Read and write useful

The proposed method for calculating a bass reflex is based on the simplest measurements carried out with a very specific instance of a loudspeaker installed in an acoustic bass reflex and on a nomographic determination of the dimensions of the latter.

First of all, guided by Fig. 1 and the table, it is necessary to make a “standard volume” - a sealed plywood box, all joints of which are carefully adjusted, glued and coated with plasticine to avoid air leaks.

Compact speakers for high-quality sound reproduction

Closed box calculation (Version 2)

Acoustic design in the form of a closed box can be considered as an extreme case of a bass reflex box with an infinitesimal opening. An equivalent acoustic circuit of a low-frequency head in a closed box can be obtained if in the circuit of Fig. 3 discard the elements related to the inverter. The corresponding frequency response of the loudspeaker coincides with equation (17) with y3 = y4 = 0.

Among the many types of frequency responses that can be obtained for a closed box loudspeaker. Of greatest interest are the smooth second-order Butterworth frequency responses. These characteristics are formed under the condition that the relationships between the head and box parameters, expressed by equation (27) at f b / f s = 0, are satisfied. A feature of loudspeakers with second-order Butterworth frequency characteristics is the fact that the cutoff frequency f 3 (29) coincides with the resonant frequency of the head in box f c .

Bass reflex calculation

Due to frequent letters asking for help in calculating this or that acoustic design, I am writing this article. I will not calculate the design for anyone, I don’t always have time. I created this site specifically for those who are interested in acoustics and want to understand it. I’d rather lay out ready-made options and examples of calculations for the lazy, and then figure it out yourself, use your brain. So.

In the low frequency range, the performance of the loudspeaker does not depend on the shape of the box or the type of bass reflex, but is determined only by two parameters of acoustic design - the volume of the bass reflex box V and frequency of its adjustment Fb. The calculation of acoustic design basically comes down to finding these quantities.

FAQ on speakers and subwoofers

In connection with multiple questions about how to calculate housings for speakers, I am posting several articles related to the calculation of acoustic design for speakers. Don't forget that acoustic design is important for LF heads. And so we begin....

Lately we have been hearing a lot of questions about speakers and subwoofers. The vast majority of answers can be found in the first three pages of any book written by professionals. The material is addressed primarily to beginners, lazy ;) and rural home-made workers, prepared on the basis of books by I.A. Aldoshchina, V.K. Ioffe, partly Ephrussi, magazine publications in Wireless World, AM and (a little) personal experience. Information from the Internet and FIDonet was NOT used. The material in no way pretends to cover the problem completely, but is an attempt to explain the basics of acoustics at a glance.

Most often the question sounds something like this: “I found a speaker, what should I do with it?”, or “Comrade, they say there are such subwoofers...”. Here we will consider only one option for solving this problem: Using the existing speaker, make a box with optimal parameters for the low frequencies, as far as possible. This option is very different from the task of the factory designer - to tighten the lower frequency of the system to the value required according to the specifications

Sound at the end of the tunnel

“Volodya, when you’re in the warehouse, grab the ports for the phasics...”
(overheard in one of the Moscow installation studios)

When AutoZvuk was still small and sat under the wing Salon AB, the first two parts of a trilogy about subwoofers have been published - about what to expect from different types of acoustic design and how to choose a speaker for a closed box.

A significant portion of those who, contemplating life, decided to treat the bass armament of their car with understanding, could, in principle, get by with this. But not all. Because there is at least one more, extremely popular type of acoustic design, which is not inferior in popularity to a closed box.

Bass reflex in Russian literature, bass reflex, ported box, vented box in English - all this is, in fact, a sound engineering implementation of the Helmholtz resonator idea. The idea is simple - a closed volume is connected to the surrounding space using an opening containing a certain mass of air. It is precisely the existence of this mass - that same column of air that, according to Ostap Bender, puts pressure on any worker, and produces miracles when a Helmholtz resonator is hired to work as part of a subwoofer. Here, a sophisticated thing named after a German physicist takes on the prosaic name of a tunnel (in bourgeois port or vent).

Charging....

Then he began to calculate the volume of the violin box, and this work was long and exciting. …. The volume cannot be reduced - the violin will wheeze and begin to drone dully. If you increase it, it will squeal piercingly, the bass will become dull and weak.…
(A.A. Weiner, G.A. Weiner Visit to the Minotaur)

The article found out what is good and what is bad about different types of acoustic design. It would seem that now “the goals are clear, let’s get to work, comrades..” But that was not the case. Firstly, the acoustic design, in which the speaker itself is not installed - just a box assembled with varying degrees of care. And often it is impossible to assemble it until it is determined which speaker will be installed in it. Secondly, and this is the main fun in designing and manufacturing car subwoofers - the characteristics of a subwoofer are worth little outside the context of the characteristics, at least the most basic ones, of the car where it will work. There is also a third thing. A mobile speaker system that is equally suited to any music is an ideal rarely achieved. A competent installer can usually be recognized by the fact that, when “taking readings” from a client ordering an audio installation, he asks to bring samples of what the client will listen to on the system he ordered after its completion.

As you can see, there are a lot of factors influencing the decision and there is no way to reduce everything to simple and unambiguous recipes, which turns the creation of mobile audio installations into an activity very much akin to art. But it is still possible to outline some general guidelines.

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Crossover calculation for acoustics75

Calculating the crossover for acoustics, as you know, is a very important operation. There are no ideal acoustic systems in the world that can reproduce the entire frequency range.
And then certain parts of the speaker spectrum come to the rescue. For example, if you need to reproduce low frequencies, use a subwoofer, and to reproduce high frequencies, install midbass.
When all these speakers together start playing, confusion can occur before reaching one or another emitter. For this reason, an active or passive crossover for acoustics is necessary.
In this article we will learn why filter calculations are needed, consider passive crossovers, and learn how they are built using inductors and capacitors.

Crossover calculation

To connect a 2-way (see) or other acoustics with a large number of bands to 1 channel of an amplifier or PG, you need some kind of separate device that separates the signal. At the same time, it must allocate its own frequencies for each band. These devices are called filters or crossovers.

Note. As a rule, component speakers already come with a passive crossover. It was prepared by the manufacturer and was designed from the very beginning.

But what to do if you need to divide the frequencies according to a different scheme (for example, if a set of acoustics is assembled from separate components)?
In this case, we are talking about calculating the crossover. Let us note right away that calculating the crossover is not at all difficult and you can even make it yourself.

Below are instructions on how to calculate the crossover:

• Download a special program. This could be Crossover Elements Calculator on your computer;

• We enter the resistance of the low-frequency and high-frequency speakers. Impedance is the nominal value of the acoustic impedance, expressed in Ohms. Typically, the average value is 4 ohms;
• Enter the crossover frequency. Here it will be useful to know that the frequency must be entered in Hz, but in no case in kHz.

Note. If the crossover is of the second order, then you must also enter the type of crossover.

• You can get the expected result by clicking on the calculation button.

In addition, you need to know the following:

• The capacitance of capacitors, or rather their value, is entered in Farads;
• Inductance is calculated in Henry (mH).

The filter calculation scheme looks something like this:

Filters of different order

To clearly understand the crossover calculation scheme (see), you need to understand the difference between filters of different orders. This will be discussed below.

Note. There are several orders of crossover. In this case, order means the crossover parameter, which characterizes its ability to attenuate unnecessary frequency signals.

First order

The circuit of a 2-way crossover of this order looks like this:

The diagram shows that the low-pass filter or low-pass filter is built on an inductor, and the high-pass filter is built on a capacitor.

Note. This choice of components is not accidental, since the resistance of the inductor increases in direct proportion to the increase in frequency. But as for the capacitor, it is inversely proportional. It turns out that such a coil perfectly transmits low frequencies, and the capacitor is responsible for transmitting high frequencies. Everything is simple and original.

You should also know that first-order crossovers, or rather their rating, depend on the selected crossover frequency and the value of the speaker impedance. When designing a low-pass filter, you must first of all pay attention to the cutoff frequency of the bass and midrange speakers (see).
But when designing a high-pass filter, you need to do the same with the high-pass filter.

Passive crossover

Passive filtration is considered the most accessible today, since it is relatively simple to implement. On the other hand, not everything is so simple.
We are talking about the following disadvantages:

• Coordinating the parameters and values ​​of filters with the characteristics of speaker drivers is a very difficult thing;
• During operation, instability of parameters may be observed. For example, if the resistance of the voice coil increases when heated. In this regard, the coordination achieved during the development process will significantly deteriorate;
• The filter, having internal resistance, takes away some of the amplifier's output power. At the same time, damping deteriorates, and this affects the sound quality and clarity of the lower register.

As you know, today the most common acoustic systems are 2-component options.
In them, the filter divides the sound signal into two ranges:

• The first range is intended exclusively for low and mid frequencies. In this case, a low-pass crossover or low-pass filter is used;
• The second range is for HF. Another high-pass filter is already used here.

Note. There may be several options for implementing a filter, but it must all meet certain rules.

Below is a list of requirements that a crossover must meet:

• The filter should not affect the frequency spectrum and waveform of the output audio signal;
• Must create an active load for the amplifier, independent of frequency;
• Must be able to provide directional pattern formation together with acoustic systems. This must be implemented in such a way that maximum radiation reaches the listener.

From the article we learned how to calculate the crossover of speaker systems with your own hands. During the work process, it will also be useful to study the diagrams, watch the video review and photo materials.
If you learn how to calculate the filter yourself, you won’t have to pay specialists for services. Thus, the cost of the operation is reduced to a minimum, because you just need to apply a little patience and spend some time studying.

UniBox program for calculating acoustic systems with various types of acoustic design:

• Closed Box
• bass reflex (Vented Box)
• system with a passive radiator (Passive Radiator Box)
• Bandpass Single Tuned Box

A very simple and logical program, it works in the Microsoft Windows Excel 2000 shell. According to reviews, it also functions normally under Excel 97, if it is updated accordingly. Allows you to simulate sound pressure level, speaker impedance curve, frequency response and much more.

On the manufacturer's website you can find a database of many well-known speakers:
Audax, Focal, Monacor, Scan Speak, Vifa, Seas, Peerless, Altec, Audio Concepts, Bag End, BBC, Blaupunkt, Boston Acoustics, Celestion, Dayton, Dynaudio, Electro-Voice, Eminence, Fane, Focal, Gauss, JBL, JL Audio, Klipsch, McCauley, MCM, MG Electronics, Morel, Parts Express, Peavey, Performance Plus, Phoenix Gold, Pioneer, Pyle, Pyramid, Reflex, Rockford-Fosgate, SoundStream, Stillwater Designs, Tekton, Thruster, Ultimate, Vieta.
In addition, you can manually add speaker characteristics and create new databases.

Speaker Workshop

Speaker Workshop calculation program for acoustics and subwoofers. Allows you to calculate housings and filters; various measurements: speaker impedance, frequency response, harmonic distortion, passive components (capacitors, inductors, resistors); and much more. There is a description of how to work with the program in Russian. We recommend.

JBL SpeakerShop

JBL SpeakerShop acoustics and subwoofer calculation program. JBL SpeakerShop consists of two independent and complementary parts: Enclosure Module - for calculating acoustic design and Crossover Module - for calculating the parameters of crossover filters. In addition, there is a database of speakers from various manufacturers. We recommend.

BassBox 6 Pro

One of the best programs of its kind for calculating acoustic systems of all types: closed box, bass reflex, bandpass, as well as for measuring the parameters of dynamic heads. A huge database of speaker parameters from almost all well-known manufacturers. We recommend.

A very useful program for graphically displaying (drawing) circuits and printed circuit boards. At your disposal: a user-friendly interface and more than 1,300 standard elements - you don’t have to “draw” each microcircuit or resistor. Nice program :-). We recommend.

PSU Designer

A very useful program. With its help, any power sources can be easily calculated - bridge, single- and full-wave, kenotrons and diodes, with L and C filters. The database already contains the necessary data for the most popular rectifiers; all you have to do is set the voltage on the secondary winding of the network transformer and the load current (resistance). The program simulates the voltage and current waveform at any point in the circuit and warns if any limit value for the rectifier is exceeded. The new version of PSU Designer allows you to save files and edit them (information from the AV Salon website)

Attenuation Curve Calculator

The Danish company Danish Audio Connect, which produces precision discrete regulators and selectors, offers software for independent calculation of attenuators. The program is written in Excel and, despite its simplicity, takes into account a lot of parameters - total resistance, characteristics, number of steps and even the depth of adjustment. This love for DIYers can be explained simply - DACT offers not only ready-made products, but also kits, allowing the designer to independently choose the type of resistors to his liking - carbon, metal film or tantalum.
(information from the “AV Salon” website)

Optimizing speaker placement in a rectangular room

To achieve high quality sound reproduction, the acoustic characteristics of the listening room must be brought closer to certain optimal values. This is achieved by forming an “acoustically correct” room geometry, as well as using special acoustic finishing of the internal surfaces of the walls and ceiling.

But very often you have to deal with a room whose shape can no longer be changed. At the same time, the room’s own resonances can have an extremely negative impact on the sound quality of the equipment. An important tool for reducing the influence of room resonances is to optimize the relative position of acoustic systems relative to each other, enclosing structures and the listening area.

The offered calculators are designed for calculations in rectangular symmetrical rooms with low sound absorption capacity.

Application of the results of these calculations in practice will reduce the influence of room modes, improve the tonal balance and equalize the frequency response of the "AC-room" system at low frequencies.
It should be noted that the calculation results do not necessarily lead to the creation of an “ideal” sound stage; they relate only to the correction of acoustic defects caused, first of all, by the influence of unwanted room resonances.
But the calculation results can be a good starting point for further search for the optimal location of the speakers from the point of view of the individual preferences of the listener.

Determining the sites of the first reflections

A listener in a room listening to music perceives not only the direct sound emitted by acoustic systems, but also reflections from the walls, floor and ceiling. Intense reflections from some areas of the internal surfaces of the room (areas of the first reflections) interact with the direct sound of the speakers, which leads to a change in the frequency response of the sound perceived by the listener. At the same time, at some frequencies the sound is amplified, and at others it is significantly weakened. This acoustic defect, called "comb filtering", results in unwanted "coloration" of the sound.

Controlling the intensity of early reflections allows you to improve the quality of the sound stage, making the speakers sound clearer and more detailed. The most important early reflections are from areas located on the side walls and ceiling between the listening area and the speakers. In addition, reflections from the rear wall can have a big impact on the sound quality if the listening area is located too close to it.

In areas where early reflection sites are located, it is recommended to place sound-absorbing materials or sound-diffusing structures (acoustic diffusers). The acoustic finishing of early reflection sites must be adequate to the frequency range in which acoustic distortion is most observed (comb filtering effect).

The linear dimensions of the acoustic coatings used should be 500-600 mm larger than the dimensions of the first reflection areas. It is recommended to coordinate the parameters of the required acoustic finishing in each specific case with an acoustic engineer.

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Calculation
Helmholtz resonator

The Helmholtz resonator is an oscillatory system with one degree of freedom, so it has the ability to respond to one specific frequency corresponding to its natural frequency.

A characteristic feature of the Helmholtz resonator is its ability to perform low-frequency natural oscillations, the wavelength of which is significantly greater than the dimensions of the resonator itself.

This property of the Helmholtz resonator is used in architectural acoustics to create so-called slot resonant sound absorbers (Slot Resonator). Depending on their design, Helmholtz resonators absorb sound well at medium and low frequencies.

In general, the absorber structure is a wooden frame mounted on the surface of a wall or ceiling. A set of wooden planks is fixed to the frame, with gaps left between them. The internal space of the frame is filled with sound-absorbing material. The resonant frequency of absorption depends on the cross-section of the wooden planks, the depth of the frame and the sound absorption efficiency of the insulating material.

fo = (c/(2*PI))*sqrt(r/((d*1.2*D)*(r+w))), Where

w- width of the wooden plank,

r- gap width,

d- thickness of the wooden plank,

D- frame depth,

With- speed of sound in air.

If in one design you use strips of different widths and fix them with unequal gaps, and also make a frame with variable depth, you can build an absorber that operates effectively over a wide frequency band.

The design of a Helmholtz resonator is quite simple and can be assembled from inexpensive and accessible materials directly in a music room or in a studio room during construction work.

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Calculation of a panel LF absorber conversion type (NCHKP)

The conversion-type panel absorber is a fairly popular means of acoustic treatment for music rooms due to its simple design and fairly high absorption efficiency in the low frequency region. A panel absorber is a rigid frame-resonator with a closed volume of air, hermetically sealed with a flexible and massive panel (membrane). The membrane material used is usually plywood or MDF sheets. Effective sound-absorbing material is placed in the internal space of the frame.

Sound vibrations set the membrane (panel) and the attached air volume in motion. In this case, the kinetic energy of the membrane is converted into thermal energy due to internal losses in the membrane material, and the kinetic energy of air molecules is converted into thermal energy due to viscous friction in the sound absorber layer. Therefore, we call this type of absorber conversion.

The absorber is a mass-spring system, so it has a resonant frequency at which it operates most effectively. The absorber can be tuned to the desired frequency range by changing its shape, volume and membrane parameters. Accurate calculation of the resonant frequency of a panel absorber is a complex mathematical problem, and the result depends on a large number of initial parameters: the method of fastening the membrane, its geometric dimensions, housing design, characteristics of the sound absorber, etc.

However, the use of some assumptions and simplifications allows us to achieve an acceptable practical result.

In this case, the resonant frequency fo can be described by the following evaluation formula:

fo=600/sqrt(m*d), Where

m- surface density of the membrane, kg/sq.m

d- frame depth, cm

This formula is valid for the case when the internal space of the absorber is filled with air. If a porous sound-absorbing material is placed inside, then at frequencies below 500 Hz the processes in the system cease to be adiabatic and the formula is transformed into another ratio, which is used in the online calculator "Calculation of a panel absorber":

fo=500/sqrt(m*d)

Filling the internal volume of the structure with porous sound-absorbing material reduces the quality factor (Q) of the absorber, which leads to an expansion of its operating range and an increase in the absorption efficiency at low frequencies. The sound absorber layer should not touch the inner surface of the membrane; it is also advisable to leave an air gap between the sound absorber and the rear wall of the device.
The theoretical operating frequency range of a panel absorber is within +/- one octave relative to the calculated resonant frequency.

It should be noted that in most cases the simplified approach described is quite sufficient. But sometimes the solution to a critical acoustic problem requires a more accurate determination of the resonant characteristics of a panel absorber, taking into account the complex mechanism of bending deformations of the membrane. This requires more accurate and rather cumbersome acoustic calculations.

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Calculation of studio space dimensions in accordance with EBU/ITU recommendations, 1998

It is based on a technique developed in 1993 by Robert Walker after a series of studies conducted by the Research Department Engineering Division of the Air Force. As a result, a formula was proposed that regulates the ratio of the linear dimensions of a room within a fairly wide range.

In 1998, this formula was adopted as a standard by the European Broadcasting Union, Technical Recommendation R22-1998 and the International Telecommunication Union Recommendation ITU-R BS.1116-1, 1998 and recommended for use in construction of studio premises and music listening rooms.
The ratio looks like this:

1.1w/h<= l/h <= 4.5w/h - 4,

l/h< 3, w/h < 3

where l is the length, w is the width, and h is the height of the room.

In addition, integer ratios of the length and width of the room to its height should be excluded within +/- 5%.

All dimensions must correspond to the distances between the main enclosing structures of the room.

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Schröder diffuser calculation

Carrying out calculations in the proposed calculator involves entering data online and then displaying the results on the screen in the form of a diagram. The reverberation time is calculated according to the method outlined in SNiP 23-03-2003 “Protection from Noise” in octave frequency bands according to the Eyring formula (Carl F. Eyring):

T (sec) = 0.163*V / (−ln(1−α)*S + 4*µ*V)

V - hall volume, m3
S - total area of ​​all enclosing surfaces of the hall, m2
α - average sound absorption coefficient in the room
µ - coefficient taking into account sound absorption in air

The resulting estimated reverberation time is graphically compared with the recommended (optimal) value. The optimal reverberation time is the one at which the sound of the musical material in a given room will be the best or at which speech intelligibility will be the highest.

Optimal reverberation time values ​​are standardized by relevant international standards:

DIN 18041 Acoustical quality in small to medium-sized rooms, 2004
EBU Tech. 3276 - Listening conditions for sound programme, 2004
IEC 60268-13 (2nd edition) Sound system equipment - Part 13, 1998