Filters for a three-way high-quality speaker system. Active three-band filter based on NM2116. Methodology for calculating active low-pass filters and high-pass filters

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 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 comply with certain canons.

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

• The filter should not affect the frequency spectrum and wavelength 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.

Before a detailed consideration of the problem, we will outline the range of tasks; knowing the final goal, it will be easier to choose the right direction. Making speaker systems with your own hands is a rare occurrence. Practiced by professionals and novice musicians when store-bought options are not satisfactory. The problem arises of integrating into furniture or high-quality listening to existing media. These are typical examples that can be solved using a set of generally accepted methods. We'll take a look at it. We do not recommend scrolling diagonally through the speaker system, delve into it!

Acoustic system design

There is no chance of making an acoustic system yourself without understanding the theory. Music lovers should know that the biological species Homo Sapiens hears sound vibrations with frequencies of 16-20,000 Hz through the inner ear. When it comes to classical masterpieces, the variation is high. The lower edge is 40 Hz, the upper edge is 20,000 Hz (20 kHz). The physical meaning of this fact is that not all speakers are capable of reproducing the full spectrum at once. Relatively slow frequencies are better handled by massive subwoofers, and squeaking at the lower edge is reproduced by smaller speakers. Obviously, this means nothing to most people. And even if part of the signal disappears or is not reproduced, no one will notice it.

We believe that those who set the goal of making their own acoustic system should critically evaluate the sound. It will be useful to know that a suitable speaker has two or more speakers in order to be able to reflect the sound of a wide swath of the audible spectrum. But even in complex systems there is only one subwoofer. This is due to the fact that low frequencies cause the environment to vibrate, even penetrating through walls. It becomes unclear where exactly the bass is coming from. Consequently, there is only one low-frequency speaker – a subwoofer. But as for other things, a person will confidently say from which direction this or that special effect came (the ultrasound beam is blocked by the palm).

In connection with the above, we will divide the acoustic systems:

1. Sound in Mono format is unpopular, so we avoid touching on historical excursions.
2. Stereo sound is provided by two channels. Both contain low and high frequencies. Equal speakers equipped with a pair of speakers (bass and squeak) are better suited.
3. Surround Sound is distinguished by the presence of a larger number of channels, creating a surround sound effect. We avoid getting carried away with subtleties; traditionally, 5 speakers plus a subwoofer convey the range to music lovers. The design is varied. Research is still underway to improve the quality of acoustic transmission. The traditional arrangement is as follows: in the four corners of the room (roughly speaking) there is a speaker, the subwoofer is on the floor to the left or in the center, the front speaker is placed under the TV. The latter is in any case equipped with two or more speakers.

It is important to create the correct enclosure for each speaker. Low frequencies will require a wooden resonator, but for the upper end of the range it doesn’t matter. In the first case, the sides of the box serve as additional emitters. You will find a video demonstrating the overall dimensions corresponding to the wavelengths of low frequencies according to science, practically all that remains is to copy ready-made designs; the topic is devoid of relevant literature.

The range of tasks is outlined, readers understand that a homemade acoustic system is built with the following elements:

• a set of frequency speakers according to the number of channels;
• plywood, veneer, body boards;
• decorative elements, paint, varnish, stain.

Acoustics design

Initially, select the number of columns, type, location. Obviously, producing more channels than a home theater has is an unwise tactical move. A cassette recorder will only need two speakers. At least six buildings will be released for the home theater (there will be more speakers). According to the needs, accessories are built into the furniture, the quality of low frequency reproduction is poor. Now the question of choosing speakers: in the publication by Naidenko and Karpov the nomenclature is given:

1. Low frequencies - CA21RE (H397) head with an 8-inch fit.
2. Mid range - MP14RCY/P (H522) 5" head.
3. High frequencies – head 27TDC (H1149) by 27 mm.

They presented the basic principles of designing acoustic systems, proposed an electrical circuit of a filter that cuts the flow into two parts (a list of three subranges is given above), and gave the name of purchased speakers that solve the problem of creating two stereo speakers. We avoid repetition; readers can take the trouble to look through the section and find specific titles.

The next question will be the filter. We believe that National Semiconductor will not be offended if we screenshot the drawing of the Ridico translation amplifier. The figure shows an active filter with a power supply of +15, -15 volts, 5 identical microcircuits (operational amplifiers), the cutoff frequency of the subbands is calculated by the formula shown in the image (duplicated in text):

P – number Pi, known to schoolchildren (3.14); R, C – resistor and capacitance values. In the figure, R = 24 kOhm, C is silent.

Active filter powered by electric current

Taking into account the capabilities of the selected speakers, the reader will be able to select a parameter. The characteristics of the speaker's playback band are taken, the overlap junction between them is found, and the cutoff frequency is placed there. Thanks to the formula, we calculate the value of the capacitance. Avoid touching the resistance value, reason: it can (disputed fact) set the operating point of the amplifier, the transmission coefficient. On the frequency response given in the translation, which we omit, the limit is 1 kHz. Let's calculate the capacity of the specified case:

C = 1/2P Rf = 1/2 x 3.14 x 24000 x 1000 = 6.6 pF.

It’s not that big of a capacitance; it’s selected based on the maximum permissible voltage. In a circuit with sources of +15 and -15 V, it is unlikely that the nominal value exceeds the total level (30 volts), take a breakdown voltage (the reference book will help) of at least 50 volts. Do not try to install DC electrolytic capacitors; the circuit has a chance of blowing up. There is no point in looking for the original circuit diagram of the LM833 chip due to Sisyphean labor. Some readers will find a replacement chip that is different... we hope for your understanding.

Regarding the relatively small capacitance of the capacitors (retail and total), the description of the filter says: due to the low impedance of the heads without active components, the ratings would have to be increased. Naturally causing the appearance of distortions due to the presence of electrolytic capacitors and coils with a ferromagnetic core. Feel free to move the range division boundary, the total throughput remains the same.

Passive filters will be assembled with your own hands by anyone trained in soldering in a school physics course. As a last resort, enlist the help of Gonorovsky; there is no better description of the intricacies of the passage of signals through radio-electronic lines that have nonlinear properties. The presented material interested the authors in low and high frequency filters. Those wishing to divide the signal into three parts should read works that reveal the basis of bandpass filters. The maximum permissible (or breakdown) voltage will be scanty, the nominal value will become significant. Matching the mentioned electrolytic capacitors are capacitances with a nominal value of tens of microfarads (three orders of magnitude higher than those used by an active filter).

Beginners are concerned about the issue of obtaining a voltage of +15, -15 V to power speaker systems. Wind a transformer (an example was given, PC program Trans50Hz), equip it with a full-wave rectifier (diode bridge), filter, enjoy. Finally, buy an active or passive filter. This thing is called a crossover, carefully select the speakers, correlate the ranges more accurately with the filter parameters.

For passive speaker crossovers, you will find many calculators on the Internet (http://ccs.exl.info/calc_cr.html). The calculation program takes the input impedances of the speakers and the division frequency as the initial numbers. Enter the data, the robot program will quickly provide the values ​​of capacitances and inductances. On the page below, specify the filter type (Bessel, Butterworth, Linkwitz-Riley). In our opinion, this is a task for the pros. The above active stage is formed by 2nd order Butterworth filters (rate of frequency response reduction 12 dB per octave). It concerns the frequency response (frequency response) of the system, understandable only to professionals. When in doubt, choose the middle ground. Literally check the third circle (Bessel).

Acoustics of computer speakers

I happened to watch a video on YouTube: a young man announced that he would make an acoustic system with his own hands. The boy is talented: he ripped out the speakers of his personal computer - well, none at all - brought out an amplifier with a regulator, placed it in a matchbox (speaker system housing). Computer speakers are notorious for poor bass response. The devices themselves are small, light, and secondly, the bourgeoisie saves on materials. Where does bass come from in a speaker system? The young man took... read on!

The most expensive component of a music center. Hi-end acoustics cost less than a cheap apartment. Repairing and assembling speakers is a good business.

The low-frequency amplifier of the speaker system will be assembled by an advanced radio amateur; no Kulibins are needed. The volume control knob sticks out of the matchbox, the input is on one side, the output is on the other. The speakers of the old sound system are small. The young man got hold of an old loudspeaker, not of fabulous size, but solid. From a Soviet-era speaker system.

To prevent the sound from disturbing the air with squeaking, the clever youth nailed together one-inch boards into a box. The speaker of the old acoustic system was placed in the size of a mailbox, moved, as is done by the manufacturers of modern home theater subwoofers. I was too lazy to decorate the inside of the speaker with soundproofing. Anyone can use batting or other similar material for the acoustic system. Small speakers are placed inside oblong boxes that just contain a loudspeaker at the end. The proud youth connected one channel of the speaker system to two small speakers, the second to one large one. Works.

The young man is a fabulous fellow, he doesn’t drink in the gateway, like his peers, he doesn’t spoil future brides in his free time, he’s busy with business. As one acquaintance said: “The younger generation is forgiven for a lack of knowledge and experience, not an excess of arrogance, strengthened by indifference.”

Improvements

We decided to improve the method; we sincerely hope that the addition will help make the acoustic system itself somewhat better. Problem? The concept was invented by radio engineers and creators of acoustic systems - frequency. The vibration of the Universe has a frequency. They say that it is even inherent in a person’s aura. It’s not for nothing that every good speaker can accommodate several speakers. Large ones are intended for low frequencies, bass; others - for medium and high. Not only the size, but also their structure is different. We have already discussed this issue and refer those interested to the written reviews, which provide a classification of acoustic systems and reveal the operating principles of the most popular ones.

Computer scientists know the system buzzer, which operates via a BIOS interrupt, which seems to be capable of producing one sound, but talented programmers wrote elaborate melodies on it, even with an attempt at digital synthesis and voice reproduction. However, such a tweeter cannot produce bass if desired.

Why this conversation... A large speaker should not just be adapted to one of the channels, but should be given a specialization for bass. As you know, most modern compositions (We don’t take Sound Around) are designed for two channels (stereo playback). It turns out that two identical speakers (small) play the same notes, this makes little sense. At the same time, from the same channel, the bass is lost, and the high frequencies die on a large speaker. What should I do? We propose to introduce passive bandpass filters into the circuit, which will help split the flow into two parts. We take the diagram from a foreign publication for the simple reason that it was the first one that caught our eye. Here is a link to the original site chegdomyn.narod.ru. The radio amateur copied it from the book, we apologize to the author for not indicating the original source. This happens for the simple reason that he is unknown to us.

So, here's the picture. The words Woofer and Tweeter immediately catch your eye. As you might guess, this is, respectively, a subwoofer for low frequencies and a speaker for high frequencies. The range of musical works is covered from 50-20000 Hz, with the subwoofer accounting for the low frequency band. Radio amateurs themselves can calculate the passbands using well-known formulas; for comparison, A of the first octave, as is known, is 440 Hz. We believe that such a division is suitable for our case. I would just like to find two large speakers, one for each channel. Let's look at the diagram...

Not exactly a musical scheme. In the position occupied by the system, the voice is filtered. Range 300-3000 Hz. The switch is signed Narrow, translated as a stripe. To get Wide playback, lower the terminals. Music fans may want to throw out the Narrow bandpass filter; those who like to surf Skype should avoid a hasty decision. The circuit will completely eliminate the microphone loop effect, which is known everywhere: a high-pitched buzz due to over-amplification (positive feedback). A valuable effect, even a military man knows the difficulties of using a speakerphone. The owner of the laptop is aware...

To eliminate the feedback effect, study the issue, find at what frequency the system resonates, cut off the excess with a filter. Very comfortably. Regarding popular music, we turn off the microphone, move it away from the speakers (in the case of karaoke), and start singing. We will leave the high and low pass filters unchanged, the products were calculated by unknown Western friends. For those who have difficulty reading foreign drawings, we explain that the diagram depicts (the Narrow bandpass filter is discarded):

1. Capacitance 4 µF.
2. Non-inductive resistances R1, R2 with a nominal value of 2.4 Ohm, 20 Ohm.
3. Inductance (coil) 0.27 mH.
4. Resistance R3 8 Ohms.
5. Capacitor C4 17 uF.

The speakers must match. Advice from this site. The subwoofer will be MSM 1853, the tweeter (the word has not been written off) will be PE 270-175. You can calculate the bandwidth yourself. The capital letter Ω means kOhm - no big deal, change the value. We remind you that the capacitances of parallel-connected capacitors add up, like series-connected resistors. In case it is difficult to get suitable denominations. It is unlikely that you will be able to make speakers with your own hands; it is realistic to obtain small resistance values. Do not use coils; we cut out plates of nichrome or similar alloys. After manufacturing, the resistor is varnished; high current is not planned; the element should not be protected.

It is easier to wind inductors yourself. It is logical to use an online calculator, by setting the capacitance, we will get the parameters: number of turns, diameter, core material, core thickness. Let's give an example, avoiding being unfounded. We visit Yandex, type something like “online inductance calculator”. We receive a number of output responses. We choose the site we like, and begin to think about how to wind the inductance of an acoustic system with a nominal value of 0.27 mH. We liked the site coil32.narod.ru, let's get started.

Initial information: inductance 0.27 mH, frame diameter 15 mm, PEL wire 0.2, winding length 40 millimeters.

The question immediately arises, seeing the calculator, where to get the nominal diameter of the insulated wire... We worked hard, found a table on the website servomotors.ru, taken from the reference book, which we present in the review, consider it for your health. The diameter of the copper is 0.2 mm, the insulated core is 0.225 mm. Feel free to feed the values ​​to the calculator, calculating the required values.

The result was a two-layer coil with 226 turns. The length of the wire was 10.88 meters with a resistance of about 6 ohms. The main parameters have been found, we begin to wind. The homemade speaker system is made in a hand-made housing; there is room to attach a filter. We connect a tweeter to one output, and a subwoofer to the other. A few words about amplification. It may happen that the amplifier stage will not support four speakers. Each circuit is characterized by a certain load capacity; you cannot jump higher. The speaker system is designed with a fixed headroom in mind; to match the load, an emitter follower is often used. The cascade that makes the circuit work, full impact on any speaker.

Parting words for beginning designers

We believe that we have helped readers understand how to properly design an acoustic system. Passive elements (capacitors, resistors, inductors) can be obtained and manufactured by anyone. All that remains is to assemble the speaker system body with your own hands. And we believe that this will not be the case. It is important to understand that music is formed by a range of frequencies that are cut off by improper manufacturing of the device. When you are planning to make a speaker system, think about it and look for the components. It is important to convey the magnificence of the melody, there will be a strong confidence: the work was not in vain. The speaker system will last a long time and will give you joy.

We believe that readers will enjoy making speaker systems with their own hands. The coming time is unique. Believe me, at the beginning of the 20th century it was impossible to obtain tons of information every day. Training resulted in hard, painstaking work. I had to rummage through the dusty shelves of libraries. Enjoy the Internet. Stradivarius impregnated the wood of his violins with a unique composition. Modern violinists continue to choose Italian examples. Think about it, 30 years have passed, the cart has been left behind.

The current generation knows the brands of adhesives and the names of materials. Necessities are sold in stores. The USSR took away the abundance of people, providing them with relative stability. Today, advantage is described by the ability to invent unique ways to earn money. A self-taught professional will cut down cabbages everywhere.

Irina Aldoshina

Date of first publication:

Feb 2009

Crossover filters in acoustic systems.

Almost all modern high-quality speaker systems are multi-band, that is, consisting of several loudspeakers, each of which operates in its own frequency range. This is due to the fact that it is practically impossible to create a dynamic loudspeaker that would provide radiation in a wide range of frequencies with a low level of distortion (primarily intermodulation, as well as transient, nonlinear, etc.) and a wide directivity characteristic. Therefore, in acoustic systems (both professional and household) several loudspeakers are used (low-frequency, mid-frequency, high-frequency, sometimes super-high-frequency), and electrical isolation filters are included to distribute the energy of the sound signal between them.

The influence of crossover filters on the formation of the characteristics of acoustic systems was underestimated in previous years: they were assigned only the role of attenuating the signal outside the operating frequency band of the loudspeakers. However, the development of technology for Hi-Fi loudspeaker systems has forced us to reconsider the role of crossover filters in loudspeaker systems and the methodology for their design. Numerous theoretical and experimental works devoted to the influence of crossover filters on the correction of the characteristics of emitters and the formation of objective and subjective characteristics of acoustic systems have led us to consider crossover filters as one of the most important components of acoustic systems, with the help of which it is possible to synthesize many of the necessary electroacoustic characteristics and achieve significant progress in ensuring naturalness sound.

Before moving on to the analysis of various types of filters used in acoustic systems and methods for their calculation, let us dwell on determining the basic parameters of filters.

Filter options
Filter is a device that transmits certain spectral components in a signal and does not transmit (attenuates) the rest. The filter can be implemented as an analog circuit (passive and active filters), or implemented in software or as a digital device (digital filters).

Modern speaker systems use both passive and active filters (crossovers). The first ones are turned on after the common amplifier in each channel, the second ones are turned on before the amplifier. The general connection diagram is shown in Fig. 1. Active filters have a number of advantages over passive filters, since they are much easier to tune, can be implemented in various ways, there are no power losses, etc. However, active filters are inferior to passive filters in such parameters as dynamic range, nonlinear distortion, noise level, etc. Methods for designing active filters are widely covered in specialized literature, so here we will focus only on methods for designing passive filters, which are widely used in modern acoustic systems.

The main parameters that determine the properties of filters are:
- bandwidth- frequency range in which filters pass the signal;
- detention lane- frequency range where filters significantly suppress the signal;
- cutoff frequency f cf is the frequency at which the signal is attenuated by 3 dB relative to the average level in the passband.

Based on the nature of the arrangement of the passband and stopband, filters are divided into four main types.

Low Pass Filters(LPF) pass low-frequency components in the signal spectrum (from zero to cutoff frequency) and suppress high-frequency ones. Used for low-frequency loudspeakers. The shape of the frequency response is shown in Fig. 2.

High Pass Filters(HPF) pass high-frequency components (from the cutoff frequency and above) and suppress low-frequency ones. Used for high-frequency loudspeakers. The shape of the frequency response is shown in Fig. 2.

Bandpass filters(PF) pass certain frequency bands (from f Wed1 to fср2) and suppress low and high frequencies. Used for mid-frequency loudspeakers, fig. 2.

There are also notch filters, which are a combination of low-pass and high-pass filters. They suppress the spectral components of the signal in a certain frequency band and transmit in other bands. They are sometimes used in acoustic systems to cut out individual peaks and dips in the frequency response.

In addition, each of the listed filters is characterized by the following parameters: the slope of the frequency response during the transition from the passband to the stopband, unevenness in the passband and stopband, resonant frequency and quality factor (Q). Depending on the structure of the filter and the number of elements in it, different slopes of the frequency response decline can be provided. Typically, acoustic systems use filters with slopes of 12 dB/oct, 18 dB/oct and 24 dB/oct (Fig. 3), which are called second-, third-, and fourth-order filters, respectively.

The simplest structure of a second-order LC low-pass filter is shown in Fig. 4. It includes the following elements: inductance L, whose reactance is directly proportional to frequency (XL = 2πfL), and capacitance C, whose reactance is inversely proportional to frequency (XC = 1/2πfC). Therefore, shown in Fig. 4a the circuit passes low frequencies (since the inductive resistance L is small at low frequencies) and provides attenuation of high frequencies. The high-pass filter has an inverse structure (Fig. 4b) and, accordingly, passes high frequencies and delays low ones.

The type of frequency response of second-order high-pass filters for different values ​​of quality factor is shown in Fig. 5. The resonant frequency of such a filter is defined as f=1/(LC)1/2, and the quality factor as Q = [(R2 C)/L]1/2.

From Fig. 5 it can be seen that changes in the value of the quality factor changes the nature of the decline in the frequency response from smooth (at Q = 0.707) to a decline with an increase at the resonance frequency (Q = 1).

Based on the names of the scientists who mathematically described the transfer functions of filters (that is, their shapes of frequency characteristics), they received different names: filters with a quality factor Q = 1 are called Chebyshev filters, Q = 0.707 - Butterworth, Q = 0.58 - Bessel, Q = 0.49 - Linkwitz-Riehle. Each of these types of filters has its own advantages and disadvantages.

Transmission function

The transfer function of a filter is understood as the ratio of the complex voltage amplitude at the filter output to the complex voltage amplitude at the input. Typically, transfer functions of physically realizable and stable linear circuits are described in the form of mathematical formulas, the denominators of which are expressions of the following form (polynomials): Gn(s) = an sn +a n-1 sn-1 +…….+a1 s+1. The order of the filter is determined by the power n of the complex frequency s, which is related to the ordinary circular frequency as s = jω. (the quantity j is called the imaginary unit). The choice of the type of coefficients an determines whether the filters belong to the Butterworth, Chebyshev, etc. type. For example, Butterworth polynomials of different orders have the form B1 (s) = (1+s); B2 (s) = (1+1.414s+s2) etc.

In acoustic systems, the problem of choosing filters is complicated by the fact that it is necessary to select three or two (depending on the number of bands) types of filters of the same or different orders, which, together with the loudspeakers, would provide the overall characteristics of the acoustic system (such as amplitude-frequency response, phase-frequency response characteristic - phase response, group delay time - group delay, etc.) with the required parameters within an effectively reproducible frequency range.

History of filter creation
The history of creating crossover filters begins simultaneously with the advent of multi-band speaker systems. One of the first theories was developed in the 30s by engineers G. A. Campbell and O. J. Zobel from Bell Labs (USA). The first publications date back to the same period, their authors K. Hilliard and H. Kimball worked in the sound department of Metro Goldwin Meyer. In 1936, their article, “Loudspeaker Isolation Filters,” was published in the March 1936 issue of the Academy Research Council Technical Bulletin. In January 1941, K. Hilliard also published "Loudspeaker Isolation Filters" in Electronics Magazine, which contained all the necessary formulas for creating first- and third-order Butterworth circuits (for both parallel and series circuits). By the 1950s, Butterworth filters were recognized as the filters of choice for speaker separation purposes. At the same time, in the 60s, J. R. Ashley and R. Small first described the properties of “all-passing” filter circuits, as well as linear-phase circuits.

The article “Filter Circuits and Modulation Distortion” (by R. Small), published in JAES in 1971, was devoted to elucidating the quantitative relationship between the attenuation introduced by out-of-band filters and the amount of intermodulation distortion due to overlapping speaker bands. It showed that the minimum attenuation value should be 12 dB/oct to prevent distortion in the overlap band. At the same time, Ashley and L. M. Henne investigated the “all-passing” and “phase coherent” properties of third-order Butterworth filters. In 1976, S. Linkwitz studied the polar radiation pattern for two-way systems with spaced drivers and was convinced that speaker systems with Linkwitz-Riehle crossover filters ensure its symmetry.

A little later, P. Garde gave a complete description of all-pass filters and their varieties. Using his ideas, D. Fink, in collaboration with E. Long, developed a method for correcting horizontal (that is, depth) displacement of loudspeaker heads in acoustic systems by introducing delay lines into the filter. Significant contributions to the theory of filtration were made by W. Marshall-Leach and R. Bullock, who first introduced the concept of optimizing filters by type and order, taking into account the displacement of heads along two axes. In continuation of these works, R. Bullock described the properties of three-band symmetrical filters and proved that a three-band filter system cannot be obtained as a simple combination of two-band ones, contrary to popular belief. S. Lipshitz and J. Vanderkooy, in a series of articles, examined various options for constructing filters with minimal phase characteristics.

A new stage in the research and design of multiband acoustic systems with crossover filters began with the beginning of active computerization of calculations based on the programs HORT, CACD, CALSOB, Filter Designer, LEAP 4.0, etc.

Until recently, the design of crossover filters in acoustic systems was carried out practically by trial and error. This is explained by the fact that all theoretical works of past years devoted to the calculation of crossover filters in acoustic systems were based on the condition that the loudspeakers themselves were ideal. When analyzing the properties of crossover filters of one type or another and considering their influence on the characteristics of speaker systems, the directional properties of loudspeakers and the conditions of their physical placement in the speaker system housing were neglected. It was believed that loudspeakers have a flat frequency response, do not introduce phase shifts into the reproduced signal, and have an active input impedance. As a result of the above, developers often encountered the fact that crossover filters that provide the required characteristics under idealized conditions turned out to be unacceptable when working with real loudspeakers that have their own amplitude-frequency and phase-frequency distortions, complex input impedance and directional properties. This was the reason for the intensification in recent years of work on the creation of optimization methods for calculating separation filters-correctors.

Selecting Crossover Frequencies
As already noted, separation filters have a significant impact on such characteristics of multi-band acoustic systems as frequency response, phase response, group delay, directivity characteristics, distribution of input signal power between emitters, input impedance of the acoustic system, and the level of nonlinear distortion.

The initial stage in the design of crossover filters in multi-band acoustic systems is a well-founded selection of crossover frequencies (cutoff frequencies) low-frequency, mid-frequency and high-frequency channels. When choosing crossover frequencies, the following assumptions are usually used.

1. Ensuring the most uniform directional characteristics possible, that is, the absence of “jumps” in the width of the radiation pattern when moving from low-frequency to mid-frequency and from mid- to high-frequency loudspeakers, since in the frequency region where they work together, in the absence of a filter, the radiation pattern is sharp narrows due to the expansion of the radiation area.

2. Maintaining a smooth change in the width of the directivity characteristic (for the same reason). We try to place the loudspeakers as close to each other as possible and place them on top of each other in the vertical plane (this avoids distortion of the directivity characteristics in the horizontal plane, as this negatively affects the reproduction of stereo panorama). If the choice of crossover frequency and distance between loudspeakers affects the width of the directivity characteristic, then the ratio of the phases and amplitudes of the signals of the separated frequency channels affects the orientation of the directivity characteristic in space. Different types of filters, as will be shown below, influence the slope of the directivity characteristic in space in the region of crossover frequencies to varying degrees.

3. Weakening of peaks and dips in the frequency response of loudspeakers that arise due to the loss of the piston nature of the movement of the diffuser. They try to select the cutoff frequency and slope of the frequency response of filters for low-frequency and mid-frequency loudspeakers in such a way that the first resonant peaks and dips are attenuated by no less than 20 dB.

4. Limiting the displacement amplitude of moving systems of mid- and high-frequency loudspeakers in the low-frequency part of the spectrum they emit (and, accordingly, the supplied power) to values ​​​​determined by their mechanical and thermal strength, which increases the reliability of their operation and reduces the level of nonlinear distortions. These tasks are regulated by both the choice of cutoff frequency and the choice of cutoff slope, which must be at least 12 dB/oct.

5. Providing the required sound pressure level, since with an increase in the cutoff frequency in the high-frequency region, the level of applied voltage can be increased, for example, to a high-frequency loudspeaker (since the amplitudes of the cone displacement decrease with increasing frequency). This allows you to increase, accordingly, the sound pressure level in the high-frequency part of the frequency response.

6. Reducing the level of nonlinear distortions, in particular, due to the Doppler effect (arising when high-frequency components are modulated by low-frequency components of the signal).

As a rule, cutoff frequencies in modern three-way speaker systems are in the range: for a low-frequency loudspeaker - 500...1000 Hz, for a mid-frequency loudspeaker - from 500...1000 Hz to 5000...7000 Hz, for a high-frequency loudspeaker - 2000... 5000 Hz.

Impact on overall characteristics
It is convenient to analyze the influence of isolation filters on the formation of the total frequency response, phase response and other characteristics of acoustic systems using some idealized model, in which it is assumed that the loudspeakers have active impedance and ideal characteristics (flat frequency response, linear phase response, constant phase shift between the emitters, etc.) . When calculating filters, you must first select the cutoff frequency (as shown earlier), the order and type of filter (Butterfort, Chebyshev, Linkwitz-Riehle, etc.).

Based on the resulting overall characteristics, filters usually used in acoustic systems can be divided into three groups: linear-phase filters (in-phase), all-pass filters and all others.

Linear-phase filters (in-phase) provide a frequency-independent total frequency response, a linear phase response (more precisely, equal to zero at all frequencies), as well as a group delay equal to zero. An example is first-order Butterworth filters. The overall characteristics for a two-way system with such filters are shown in Fig. 6. The experience of using them in acoustic systems has shown that they have a number of disadvantages: poor selectivity, large unevenness of signal power characteristics, poor directional characteristics in the interface band, etc. Therefore, they are currently not used in Hi-Fi loudspeaker systems.

All-pass filters provide a flat total frequency response, frequency-dependent phase response and group delay. The requirements for linearity of the phase response response are excessive for acoustic systems - it is enough that their group delays are below the audibility thresholds (as measurement results show, filters of this type introduce group delay distortions in the interface band that satisfy these requirements). This type of filter includes Butterworth filters of fuzzy orders and Linkwitz-Riehle filters of even orders. In this case, the properties of the filters are realized with different polarities of switching on the channels: for 2, 6, 10 orders the switching on of channels in antiphase is required, for 4, 8, 12 - not. For odd orders: 1, 5, 9 should be switched on in phase, 3.7... - out of phase. The total and channel-by-channel characteristics of the second-order Linkwitz-Riehle and third-order Butterworth filters for a two-channel idealized acoustic system are shown in Fig. 7 and fig. 8. It should be noted (will be shown later) that fuzzy order filters create a rotation of the main lobe of the directivity characteristic in the crossover frequency region.

There is a fairly large class of filters that are used in acoustic systems, but they are not of the “all-passing” type. This includes filters of the second and fourth order of Butterworth, second and fourth order of Bessel, a group of asymmetric filters of the fourth order of Legendre, Gauss, etc. They do not give a total flat response, but this drawback can be partially corrected if the cutoff frequencies between the loudspeakers are made unequal. For example, in Fig. Figure 9a shows the characteristics of a fourth-order Butterworth filter with a frequency response peak of 3 dB at a crossover frequency of 1000 Hz. If you separate the frequencies somewhat, that is, make the crossover frequency for low frequencies 885 Hz, and for high frequencies 1138 Hz, then the peak in the frequency response disappears (Fig. 9b).

As already mentioned, the choice of filter types for low-, mid- and high-frequency loudspeakers, in addition to ensuring a flat frequency response in the crossover bands, is determined by the requirement to ensure symmetry of directivity characteristics speaker system.

Within the passband of each filter, the directivity characteristic of the speaker system is determined by the directivity characteristic of each loudspeaker, but within the cutoff band (filter overlap band), they work together, that is, there are two emitters (for example, mid- and high-frequency), which are spaced apart and operate on the same the same crossover frequency. An example of such a system is shown in Fig. 10. For simplicity, let these be two identical emitters operating in piston mode with the same directivity characteristics. On the OA axis, the signals arrive in the same phase and are added. If we estimate the sound pressure on the axis OA", where the phase shift due to the difference in path from one and the other loudspeaker will be φ = π (that is, 180 degrees), then the signals will add up in antiphase and a dip will appear in the directivity characteristic. With a further shift from the axis at points where the phase difference is 2π (that is, 360 degrees), a peak will appear again.In general, the directivity characteristic will have a three-lobe character (Fig. 10).

The width of the main lobe of the directivity characteristic at the crossover frequency depends on the ratio of the distance between the loudspeakers to the wavelength, and the slope of the lobe depends on the ratio of the amplitudes and phases of the separated channels, which is also determined by the type of filters chosen.

To reduce this phenomenon, one should try to reduce the distance between loudspeakers (for example, through the use of coaxial loudspeakers), reduce the crossover bandwidth (by choosing higher-order filters) and, finally, select the appropriate filter type, since each filter contributes its own frequency-dependent phase shifts.

For example, when using third-order Butterworth-type filters, the main lobe of the directivity characteristic rotates downward (when the speakers are turned on in the same phase), Fig. 11. When the speakers are turned on in antiphase (that is, their polarity is changed), the lobe of the directivity characteristic shifts to the other side relative to the axis.

Analysis of filters of various types and orders showed that filters of even orders (all-passing type) do not change the symmetry of the direction of the lobes, filters of odd orders turn the lobe down or up. Symmetrical directivity characteristics provide the greatest uniformity of emitted acoustic power.

In addition to influencing the directivity characteristic along the frequency response, filters can affect the phase-frequency characteristics and group delays in the interface band. That is, the nature of transient processes, despite the symmetry of the frequency response, may differ at the same displacement angles in the upper and lower half-planes, and group delays, being below the audibility thresholds on the axis, can exceed the audibility thresholds at other points in space, thereby deteriorating the sound quality.

It should be recalled once again that all conclusions drawn relate only to the case of ideal loudspeaker characteristics. Real characteristics are taken into account using modern computer programs.

Calculation of passive acoustic filters
When starting to calculate passive acoustic filters, it is necessary to clearly define the system configuration (number of playback bands, types of loudspeaker heads and their parameters, type of design - housing), and also choose the order and type of filters depending on the main tasks that must be solved during the design acoustic system: flat frequency response, linear phase response, symmetrical directivity characteristic, etc.

Since nowadays acoustic systems most often use “all-pass” filters with a flat frequency response, we will give an approximate calculation of this type of filter (more accurate calculations are performed using computer methods).

First, the isolation filters are calculated from the condition that they are loaded with purely active resistance and are powered by a voltage generator with low output resistance. Care is then taken to take into account the effects of complex frequency-dependent loudspeaker loading.

The calculation begins with determining the order of the filters and calculating the elements of the prototype filter. A prototype filter is a ladder-type filter, the elements of which are normalized relative to a unit cutoff frequency and a unit load. The low-pass filter is then calculated for the actual cutoff frequency and the actual load, and from this the high-pass and bandpass filter elements are found by frequency conversion.

The normalized values ​​of the prototype filter elements from the first to the sixth order are shown in Table 1.

The values ​​of these elements are given only for all-pass filters; for other types of filters, the values ​​of the elements in the table will be different. The prototype sixth-order filter circuit is shown in Fig. 12. Filters of lower orders are obtained by discarding the corresponding α elements (starting with the largest ones).

Values ​​of real filter parameters for a given order, load resistance R n (Ohm) and cutoff frequencies f i (Hz) are determined as follows.

1. For low pass filter:
- each prototype inductance α1, α3, α5 (Fig. 12) is replaced with a real inductance according to the formula L=αi Rн/2πf1, (1) where i=1,3,5, f1 is the cutoff frequency of the low-pass filter;
- each prototype capacity α2, α4, α6 is replaced with a real capacity according to the formula C=αi /2πf1 Rн,(2) where i=2,4,6.

2. For high pass filter(calculation happens the other way around):
- each prototype inductance α1, α3, α5 is replaced by a real capacitance C=1/2πf2 Rнαi, (3) where i=1,3,5, f2 is the cutoff frequency of the high-pass filter;
- each prototype capacitance is replaced with a real inductance L=Rн/2πf2 αi, (4) where i=2,4,6.

3. For bandpass filter:
- each prototype inductance α1, α3, α5 is replaced by a series circuit of real L- and C-elements, calculated by the formulas:
L=αi Rн/2π(f2 -f1),(5) С=1/4π2 f0 2 L,(6)
where is the average frequency of the bandpass filter;
- each capacitance element α2, α4, α6 is replaced by a parallel circuit of real L- and C-elements, calculated by the formulas:
С=αi /2π(f2 -f1 )Rн,(7) L=1/4π2 f0 2 C.(8)

An example of calculating crossover filters for a three-way speaker

For the calculation, we select the following parameters: all-pass filters of the second order, that is, the prototype filter circuit will include only elements α1, α2, Rн (Fig. 12). The crossover frequencies between the low-frequency and mid-frequency channels are 500 Hz, and between the mid- and high-frequency channels are 5000 Hz. Speaker impedance (DC): low-frequency and mid-frequency Re=8 Ohms, high-frequency Re=16 Ohms. The value of the normalized parameters of the elements will be determined from the table. 1: α1 =2.0, α2 =0.5.

Real Element Values low pass filter we find from expressions (1) and (2):
L1LF = α1 Rн/2πf1 = 2.0∙8.0/(2∙3.14∙500) = 5.1 mH,
C1LF = α1 /2πf1 Rн = 0.5/(2∙3.14∙500∙8.0) = 20 µF.

Element values bandpass filter(for a mid-frequency loudspeaker) is determined in accordance with expressions (5)... (8):
L1SCh = α1 Rн/2π(f2 -f1 ) = 2.0∙8.0/2∙3.14 (5000 - 500) = 0.566 mH,
C1СЧ =1/4π2 f0 2 L = 1/4∙3.142 ∙5000∙500∙5.66∙10-4 = 18 µF,
С2СЧ = α2 /2π(f2 -f1) Rн = 0.5/2∙3.14 (5000-500) ∙8.0 = 2.2 µF,
L2SCh =1/4π2 f0 2 C2SCh = 1/4∙3.142 ∙5000∙500∙2.2∙I0-6 = 4.6 mH.

Element values high pass filter determined in accordance with expressions (3.4):
S1HF = 1/2πf2 Rн α1 = 1/(2∙3.14∙5000∙2.0∙16) = 1.00 µF,
L2BЧ = Rн/2πf2 α2 = 16/(2∙3.14∙5000∙2.0) = 0.25 mH.

Calculations made using these formulas are correct only if the filters are loaded with active (ohmic) resistance. To match the parameters of the filters with the real complex impedance of the loudspeakers, it is necessary to additionally connect a matching circuit in parallel with each loudspeaker. The parameters of such a circuit are found from the condition that the complex resistance of this circuit Zag and the complex resistance of the loudspeaker Zgg compensate each other when connected in parallel and provide a total active resistance, that is, 1/ Zag+1/ Zgg = 1/Re.

To calculate the elements of such a circuit, an equivalent electrical circuit of the loudspeaker is constructed (see the previous article in the December 2008 issue of the Moscow Region), and a dual compensating circuit is created in relation to it. The diagram of the equivalent loudspeaker circuit and the corresponding compensating circuit are shown in Fig. 13. To compensate for the input impedance of a low-frequency loudspeaker, you can use a simplified circuit (since the loudspeaker resonance is significantly lower than the cutoff frequency of the filter and does not affect its parameters), consisting of two elements Rk1 = Re and Ck1 = Lvc/Re2, where Re and Lvc - resistance and inductance of the loudspeaker voice coil.

For a mid- and high-frequency loudspeaker, the full compensating circuit is turned on only if the cutoff frequency and resonances of the loudspeakers are close to each other - otherwise, it is enough to use a simplified circuit (calculation of the parameters of the full circuit is given in the book by Aldoshin I.A., Voishvillo A.G. "High-quality acoustic systems"). In addition, additional notch filters are sometimes included in the circuit to remove individual peaks in the amplitude-frequency response.

An example of a filter circuit for a three-way acoustic system, taking into account the matching circuits of the notch section for a mid-frequency loudspeaker and an additional L-shaped attenuator, consisting of two resistors for leveling the sound pressure levels between the low-frequency, mid-frequency and high-frequency loudspeakers, is shown in Fig. 14.

Currently, computer methods for optimal synthesis of linear electronic circuits are used to calculate filtering and correction circuits. To do this, the filter structure and initial values ​​of the elements are set, then the total output values ​​of the frequency response, phase response and group delay are calculated, taking into account the actual measured parameters of the loudspeakers located in the housing, and by purposefully changing the circuit elements, the difference between the real and specified parameters is minimized. The use of optimal design methods allows us to ensure the best broadband matching of filter and loudspeaker parameters and obtain the optimal achievable value of the parameters of the acoustic system.

Currently, active research is being carried out on the use of digital filter processors in acoustic systems, which makes it possible to rearrange system parameters in real time depending on the type of sound signal, as well as to ensure optimal matching of the characteristics of the acoustic system with the parameters of the room, but this technique is still at the beginning of its development and has not yet found wide application in industrial development.

9. TWO AND THREE WAY LOUDSPEAKER SYSTEMS

Two- and three-way loudspeaker systems (units) provide the ability to reproduce a wider frequency range with significantly less frequency distortion and non-linear distortion than full-range loudspeakers could. To this we must add that two- and three-way systems improve the acoustic performance of the sound-reproducing section in a cheaper way, because a wide-band head will always cost much more than a narrow-band head. The division of the full frequency range into two and three frequency bands is shown in Fig. 55. The lower one is visible (f n) and upper ( f V ) boundaries of the reproduced frequency band and crossover frequency (f R , f P 1 and f P2).

Rice. 55. Conditional division of the reproduced frequency band with two-way and three-way acoustic systems

( fnAndfV- respectively the lowest and highest cutoff frequencies; f p, f pl Andfp2- crossover frequencies).

The characteristics given represent the voltage levels at the output of the corresponding isolation filters. The more expensive three-way system is capable of reproducing a wider frequency range (especially downstream) and with better frequency response flatness. Dual-band systems have become more widespread. The number of bands should be selected based on the acoustic data of the available heads and the requirements for the uneven frequency response of the system. The crossover frequencies are selected based on the conditions for obtaining the best frequency response of the system (unit), i.e. less frequency distortion. This is determined by the frequency characteristics of the heads. It is also known that the frequency distortion of a loudspeaker is minimal until the critical frequency of the cone, after which it stops oscillating like a piston. The choice of crossover frequency may be somewhat influenced by the power reserves of the existing heads. The curves of the required head power ratio shown in Fig. 32 show that as the crossover frequency increases, the high-frequency head is unloaded and the load of the low-frequency head increases. In some cases, it is not recommended to choose a crossover frequency between 1-4 kHz, since this may slightly worsen the auditory sensations due to the possible noticeability of two sound sources operating simultaneously at the crossover frequency, which in this case would be in the area of ​​greatest sensitivity of our hearing. Reducing the crossover frequency also reduces intermodulation distortion. Thus, the most suitable crossover frequencies may be frequencies lying in the region 400-800 Hz and 4-5 kHz. The simplest way to create a two-way unit is to connect one or two high-frequency heads via a coupling capacitor to an existing loudspeaker.

Most cone speakers range from 6 to 10 watt work well in the low and mid frequency range, i.e. reproduce a fairly wide frequency band. Most of our most powerful loudspeakers (5GD-3RR3, 6GD-1, 8GD-RR3, 10GD-28, etc.) have a main resonance frequency of 45-50 at best Hz(very rarely 42-40 Hz), and the decrease in output at higher frequencies starts from 5-6 kHz. Thus, the operating band in which these loudspeakers can operate more efficiently extends from 40-45 Hz up to 5 kHz. To reproduce the frequency range above 5 kHz additional small loudspeakers should be used, designed to reproduce a band of up to 16-20 kHz(for example, 1GD-1RR3, 1GD-2, 1GD-3). The crossover frequency with the above powerful heads should be about 5 kHz.

Rice. 56. Connection diagrams for loudspeakers reproducing the upper frequency band (conventionally shown as one head in each band).

a - with approximately equal speaker impedance; b - at

different resistance; c - the same, but with separate transformers in every lane.

In Fig. 56 shows possible connection diagrams for additional high-frequency heads. The power of these heads at this crossover frequency can be less than 0.1 of the power of the main speaker. Connecting additional heads will not disrupt the matching of the load with the output stage and will even improve it, since at higher frequencies the impedance of the main speaker increases and the amplifier load drops.

Scheme in Fig. 56. A designed to connect a high-frequency driver whose impedance is approximately equal to the impedance of the main loudspeaker. Schemes (Fig. 56, b, c) allow the use of loudspeakers with significantly different impedances. Load matching is achieved either by tapping into the output transformer or by a separate transformer (autotransformer). It is technically easier to make two good output transformers, each operating in a narrow frequency band, than one high-quality broadband one. This is especially important with a more powerful amplifier.

These diagrams conventionally show one head in each strip, whereas in reality two or more heads may be connected. Of course, all heads must be correctly phased and their total resistance must be taken into account. The capacity of the coupling capacitor is determined by the crossover frequency and the impedance module of the high-frequency head. At the crossover frequency, the capacitive reactance of the capacitor must be equal to the modulus of the head impedance, i.e.

Where fR- section frequency; | Z GR | - module of the head impedance at the crossover frequency.

Rice. 57. Basic circuits of separation filters.

Rice. 58. Graph for calculating the size of the separation capacitance C in the diagrams in Fig. 56 and capacitance C 1, in the diagrams in Fig. 57, a, b.

A coupling capacitor, the capacitance of which is calculated using this formula, gives an attenuation before the crossover frequency of 6 db per octave (0.5f R ).

The simplest filter, with the help of which only low-frequency voltage is supplied to the low-frequency head, and only high-frequency voltage is supplied to the high-frequency head, are the circuits shown in Fig. 57, a, b. They are designed for heads with the same impedance and have the same input impedance, equal to the impedance of one head, despite the fact that in the first circuit the heads are connected in series, and in the second - in parallel. The capacitance of the capacitor and the inductance of the inductor are determined from the condition that their capacitive or inductive reactance is equal to the total resistance of the head at the crossover frequency, so half the output power of the amplifier will be applied to each head; Thus,

From here the calculation formulas are easily obtained

The formula for calculating the capacitance of the capacitor turned out to be the same as the formula for calculating the capacitance of the separating capacitor of the high-frequency head, which is completely natural, since they meet the same conditions.

For convenience of calculating the filter in Fig. Figure 58 shows curves that allow you to determine the values ​​of capacitance and inductance depending on the modulus of the head impedance for two crossover frequencies.

The described filter gives attenuation near the section frequency 6 db per octave (0.5f p and 2 f p). However, filters with a steeper cutoff of the attenuation frequency response near the crossover frequency are preferable, i.e., greater attenuation per octave. This is desirable to reduce the frequency range in which both low-frequency and high-frequency heads operate (emit) simultaneously. Such filters have the circuits shown in Fig. 57, c, d: they give attenuation of about 12 db per octave and are also designed for heads with the same impedance. The input impedance of the filters is equal to the impedance of one head; The calculation condition for these filters is the same as for the previous ones: at the crossover frequency, the supplied power is divided equally between the heads. In this case, in a sequential circuit (Fig. 57, V) capacitance and inductance are determined by the formulas

and in a parallel circuit (Fig. 57, G)

So far we have talked about filters designed for heads with the same impedance (in their frequency bands). Heads with different input impedances are often used.

If the impedances of the loudspeaker voice coils are different, they should be equalized using a matching transformer. It is better to use such a transformer (or autotransformer) for the high-frequency group and, depending on the ratio of the resistance of the voice coils, use it either for increase (if the resistance of the low-frequency group is less) or for decrease. Its transformation coefficient is calculated using the formula

where | Z H | and | ZIN| - impedance modules for low-frequency and high-frequency heads.

Rice. 59. Connection diagram loudspeakers with different resistances through filters low and high frequencies.

Rice. 60. Scheme for calculating transformation ratios.

When such an equation of the head impedances is for some reason impossible, you can connect the speakers to different taps of the output transformer as shown in Fig. 59 (for the case when | Z N | less than | Z V |). In this case, the values ​​of the crossover filter elements are calculated as for ordinary simple low- and high-pass filters;

Here it may be appropriate to provide a formula for calculating the transformation ratio of each individual winding or individual transformer (Fig. 60, A), taking into account both the impedances of different heads and their rated powers:

where and - number of turns of primary and secondary windings;PU- amplifier power;Z H- amplifier load resistance;PGR - loudspeaker power;ZGR - loudspeaker impedance (average value).

The correctness of the calculated transformation ratios can be checked by calculating the total load resistance using the formula

(R must be equal to | Z H |).

Factory output transformers that have taps for connecting different load (loudspeaker) impedances are usually labeled as shown in Fig. 60, b. But these same taps allow you to connect a load of other resistance to individual parts of the winding. The resistance of these loads for the upper section and in the same way for the rest can be determined using the formula

Let's move on to the calculation of three-way systems. Despite the fact that the above calculation formulas apply to two-band systems, a valuable feature of the filters, the circuits of which are shown in Fig. 57 , c, d, is that their input impedance is equal to the total impedance of the head and allows such filters to be successfully used in a three-band circuit. The only condition is that all three heads have the same resistance in their frequency bands. The filter circuit for a three-band system is shown in Fig. 61, A. It contains two pairs of parallel-connected filters corresponding to the circuit in Fig. 57, G. The first pair of filters ( L 2 And C 2) calculated using the above formulas for a lower crossover frequency (fP1) and a low-frequency head is connected to one of them (low-frequency). The second pair of filters is connected to the first-stage high-pass filter, which passes signals with frequencies above the crossover frequency. This pair of filters (L"2 and C" 2) are calculated using the same formulas as the first pair, but for a higher crossover frequency (fP2). Thus, the second pair of filters divides the frequency region located above the first cutoff frequency (fP1), into two bands with crossover frequencyfP2between them. It is not difficult to create the same system from two pairs of series-connected filters, which are calculated in a similar way, but according to the formulas related to the circuit in Fig. 57, V; such a diagram is shown in Fig. 61, b. It may be of interest only because it requires different values ​​of capacitor capacitances and inductances of inductors, which can be more easily purchased or made than those required for parallel circuits.

Rice. 61. Diagram for connecting filters in a three-way loudspeaker system.

Rice. 62. Simplified filter circuits for a three-way loudspeaker system,

a - with a separating capacitor; b - with a serial circuit L 3 C 3 .

There is a simpler version of the circuit for connecting loudspeakers in a three-way system. It is shown in Fig. 62, A. Here, a two-band filter with a lower crossover frequency is used, and the high-frequency head is connected to the second band filter using a coupling capacitorC 3 . This circuit contains only two bandpass filters and a capacitor instead of the two pairs of bandpass filters described above. However, strictly speaking, the diagram in Fig. 62 is a two-way unit, to which a high-frequency head is added. As a result, both the tweeter and the midrange speaker may radiate at higher frequencies, which can increase frequency response flatness in that frequency range. Therefore, a scheme with filters dividing the entire range into three bands should be considered more effective. There is another variation of the three-way system where an additional speaker is connected in series with a simple series circuit to the two-way system. Such a diagram is shown in Fig. 62, b. This circuit can compensate for dips in the frequency response of the loudspeaker of the main two-way system. Sometimes there is a slight increase in output and mid-frequency range (no more than 8-10 db), created by an additional loudspeaker, significantly improves the quality of sound reproduction: individual instruments of the orchestra are better recognized. This is especially noticeable when comparing the sound with an acoustic unit, which has reduced output at mid frequencies, even if such a reduction is within the tolerances.

A capacitor and inductor for a bandpass filter, which are connected in series with the head that reproduces mid frequencies or compensate for any dip in the characteristic (Fig. 62, b), are calculated quite simply. From the course of radio engineering it is known that for a series circuit (L.C.) the following relationships exist:

AND ,

Where - angular resonant frequency, Hz; ZTO - characteristic resistance of the circuit, which is separately equal to the capacitive and inductive resistance of the capacitor and inductor at the resonant frequency, i.e.

Assuming the valueZ K equal to the impedance that an additional loudspeaker has at the correction frequency ( Z K = Z DOP ), switched on through a series circuit, you can calculate the required capacitance values ​​of the capacitorC 3 and inductance of the chokeL 3

It should be borne in mind that the width of the frequency region in which the additional head emits can be expanded by reducing the inductance valueL 3 , as follows from formulas

where

Here - width of the resonance curve at a height of 0.7 from the maximum, Hz; L 3 - inductance, gn; RGR - active resistance of the head, ohm

In this regard, if you want to expand the frequency band reproduced by an additional head, you should reduce the inductanceL 3 against the calculated value and increase the capacity by the same amountC 3 .

This method of correcting the frequency response of the sound pressure of a loudspeaker can also be successfully used to improve the reproduction of lower frequencies; in this case, an additional correcting loudspeaker is used mainly in the region of its main resonant frequency, for which the series circuit is designed, i.e.

If the additional loudspeaker is similar to the main one and differs in the main resonance frequency by no more than ±10 Hz, then when installing it near the main one (nearby), the level will increase by 3 db and the matching of the load with the amplifier will improve, since at the main resonance frequency the input impedance of the loudspeaker increases by 3-5 times. The inductance of the inductor and the capacitance of the capacitor are calculated using the above formulas for a series circuitL 3 C 3 . However, due to the fact that the resonant frequency of the circuit corresponds to the mechanical resonance frequency of the loudspeaker, the inductance according to the calculation will be significant. It is recommended to reduce it by 2-4 times, increasing the capacitance of the capacitor by the same amount.

It should be explained why all crossover filters are required to divide the power equally at the crossover frequency between heads operating in adjacent bands, i.e., reduce the voltage level at each head by 3 db. This value was chosen because, as will be shown later, adding two equal levels created by two sound sources increases the overall level by 3 db. Consequently, the reduction of the voltage on the heads (as well as the sound pressure) by the filters at the crossover frequency leads, as a result of addition, to the subsequent equalization of the overall sound pressure, of course, if they are turned on in phase and the output of both heads at the crossover frequency is the same. However, unfortunately, there is often a difference in the average standard sound pressure produced by different heads.

In connection with this situation, it is recommended to connect the mid- and high-frequency heads to the coupling filters through a low-resistance step attenuator with 3-5 adjustment steps, as shown in Fig. 63. An important feature of the attenuator is the constancy of its input resistance. It can be made equal to the head impedance for which the isolation filter is designed. Each adjustment step should provide a level reduction (attenuation) of the order of 2 db, which corresponds to a decrease in voltage (and sound pressure) by approximately 20%, i.e. up to 0.8 from the original value. Series resistance (r 1 ) to parallel (r 2 ) resistors are found using the formulas

Where ZGR- total resistance of the head;k - attenuator gain; we chose for the first stagek=0.8. When determining the resistor resistances for the second and further stages of adjustment, follow Fig. 1 define valuek, which for the second stage creating a total attenuation of 4 db, willk=0.63, for the third (6 db) k=0.5, etc. We must also keep in mind that the resistances of series and parallel resistors can be created either by separate resistors independently of each other, as shown in Fig. 63, b, or using resistors of the previous stage (Fig. 63, V). In the second option, it is necessary, having calculated the resistor resistances for a given attenuation, to subtract from the calculated value the sum of the resistances of the resistors connected between the zero contact and the previous one for which the calculation is being carried out (in this case, the calculation of the resistancer 2 lead starting from maximum attenuation). In other words, subtraction determines the resistance that must be added to those already calculated in order to obtain the resistance corresponding to a given attenuation. For convenience of determining the resistance of resistorsr 1 And r 2 depending on the impedance of the loudspeaker for different attenuations and provided that the input impedance of the attenuator is equal to the impedance of the head ( r ATT = Z GR ) in Fig. 64 shows the calculation graphs.

Rice. 63. Attenuator connection circuits.

a - fundamental; b, c - practical options.

It is advisable to have paper capacitors in all of the above frequency separation circuits and crossover filters. Their rated operating voltage can be selected as a minimum. Electrolytic capacitors can be used, but due to the lack of a constant component in the circuit, it is necessary to take two such capacitors, each with twice the capacity, and connect them in series with the same polarity. This connection of capacitors is called bipolar, and it is sometimes used (for example, in the Symphony radiogram) along with special types of bipolar electrolytic capacitors. You can specifically create a circuit with an auxiliary constant voltage source to polarize electrolytic capacitors. However, a sufficient assortment of the necessary types and sizes of paper capacitors of relatively small sizes is produced for an operating voltage of 120-160 V, for example the MBGO type. Their dimensions are also not significant when placed in a loudspeaker box. It is better to use chokes for blocking filter circuits without a steel core, since there is always a danger of additional nonlinear distortions due to the nonlinearity of the magnetization curve of the core. It is better to use simple multilayer coils without cores as chokes.

To reduce losses of sound energy, the winding of chokes connected in series with loudspeakers should be made with a thick enough enameled wire so that the active resistance of the winding is 10-20 times less than the resistance of all loudspeakers operating in a given frequency band. The inductance of the multilayer coil shown in Fig. 65, can be calculated using the formula

Where w - number of turns; D - average coil diameter, cm; IN- winding width, cm; A- winding height, cm.

Rice. 64. Graphs for calculating attenuator resistances.

If we take the coil configuration such thatd= A, A = 1,2 B, A D=2 A=2,4 B, then the formula for inductance and calculation of the inductor is greatly simplified:

The inductor is calculated as follows: we set the winding resistanceretc.(retc.=0,05/0,1 RGR) and coil widthB. The cross-sectional area of ​​the winding of the adopted configuration will beS 0 = AB=1,2 B 2 , a winding volume V 0 = S 0 3,14 D=9 B 3 . We determine using the one given here table 2 number of turns and winding resistance for calculatedS 0 And V 0 and any selected wire diameter and compare the resistance with the required one, and using the appropriate number of turns of the winding we calculate the inductance.

table 2

Copper diameter	The number is tight wound vitkovna 1 cm 2 winding sections	Resistance of a cubic centimeter of continuous winding, ohm
		0,668
		0,28
		0,137
		0,076
		0,0444
		0,0284
		0,0189
		0,013
		0,00924
		0,00678

Rice. 65. Configuration of the choke coil of the separating filter.

If the calculated inductance and resistance of the coil are less than required, then do the same for a smaller wire diameter. If the winding resistance cannot be increased, then, while maintaining the same wire diameter, increase the size of the coil, i.e.B, and thus the possible number of turns. Typically, chokes are made frameless, that is, the winding is wound on a blank with removable cheeks, which are removed after winding is completed, and the winding is tied together with tape or thread in 4-5 places around the circumference for strength.

Let us calculate, as an example, a choke with an inductance of 30 instant, resistance 2.5-3.5 ohm and winding widthB=3 cm. The cross-sectional area of ​​the winding is equal toS 0 =1,2 B 2 = 10,8 cm 2; winding volume is equal to Vo =9 B 3 =243 cm 3. We find using the table that from a wire with a diameter of 1 mm the winding will have a resistance of 4.6 ohm and the number of turns is 840. Using the formula, we calculate the inductance.

It will be equal to:

Since the resistance turned out to be too high and the inductance close, let’s increase the size of the coil a little (let’s takeB= 3,4 cm) and wire diameter (let’s take 1.2 mm). The new cross-sectional area of ​​the winding and its volume are equalS 0 =13,9 cm 2; V o=352 cm 3. We find from the table that the winding will have 765 turns and resistance 3.25 ohm; its inductance will beL=32 instant A choke with such inductance and resistance satisfies the task.

Page 4 of 4

About the performance of the loudspeaker in the mid and high frequencies

Smoothing the frequency response of a loudspeaker in terms of sound pressure in the low frequency region is not the only task that a radio amateur has to solve when trying to improve the parameters of his speaker. The fact is that none of the dynamic heads created to date is able to cover the entire audio range, and therefore all Hi-Fi class speakers are made using two or three-way circuits, which require the presence of separation filters in them. As a rule, these are passive filters of the first (less often second) order, the influence of which on the characteristics of loudspeakers is as great as that of the dynamic heads themselves. However, judging by the publications of the Radio magazine, this circumstance is not taken into account by the majority of readers and authors.

Let us illustrate this with an example taken from the work. In Fig. Figure 13 shows the frequency response of the 25GD-26, 15GD-11 and 3GD-31 heads installed in the 25AS-309 loudspeaker, connected through a factory isolation filter. The solid line shows the frequency response of the low-frequency and high-frequency heads (with the mid-frequency head turned off), the dashed line shows the frequency response of one mid-range head. In the last characteristic, attention is drawn to the rise in frequency response near the frequency of 100 Hz, reaching 10 dB. This rise noticeably increases the “mumbling” of the speaker, which prompted the authors to redesign the loudspeaker.

What are the reasons for this unwanted increase in frequency response? Obviously, the overall quality factor of the midrange head is quite high and most likely greater than 1.

However, instead of smoothing out the characteristic, if not with a negative, then at least with a zero output impedance of the UMZCH, the speakers developers connected a 5.1 Ohm resistor in series with the head, which led to an increase in the frequency response by at least 6 dB. It is impossible to refuse to use this resistor, since the output of the midrange head 15GD-11A (with the same input power) is approximately twice as high as that of the 25GD-26. The first-order crossover filter installed in the speakers, although tuned to a relatively high frequency (1600 Hz), is not able to sufficiently attenuate the midrange head signal at low frequencies. In addition, the crossover frequency is in the region of maximum hearing sensitivity to distortion, which could not but affect the sound quality.

Analysis of the characteristics of the HF head (solid curve in Fig. 13 in the region from 5...20 kHz) shows that, in comparison with the LF head, its output is also too high. In this regard, a 5.1 Ohm resistor also had to be connected in series with it. However, this was not enough and the increase in the frequency response of the HF head at frequencies of 10...15 kHz remained unreasonably large.

The indicated disadvantages are inherent in both many (if not most) of the speakers mass-produced in the country [b], and the majority of three-way speakers manufactured by radio amateurs (however, the latter can only be discussed tentatively, since practically none of the radio amateurs have the ability, like the authors, to remove the frequency response your speaker in the sound chamber). The methods proposed by the authors to combat these shortcomings, although they give positive results for a specific speaker, can hardly be recommended for all occasions, since the ratings of the filter elements strongly depend on the types of loudspeakers used and their acoustic design. This example demonstrates how neglecting at least one of the links of the sound-reproducing complex makes the sound quality noticeably worse than potentially achievable.

Of all the variety of literature devoted to loudspeakers, perhaps only the work has given due attention to crossover filters. Therefore, before discussing further ways to improve the parameters of loudspeakers, you need to at least briefly become familiar with modern views on the role of crossover filters in speakers, the types of filters used, their advantages and disadvantages.

Features of the operation of filters in speakers

Studies of the 40-50s showed that when designing multi-band speakers, it is not enough to take into account only the frequency response of filters and do not take into account their phase-frequency characteristics (PFC). Let's assume that the two-way speaker system at our disposal uses filters that are perfectly matched in terms of frequency response. In other words, in the region of the crossover frequency, the sum of the amplitudes of the signals at the outputs of the filters (with a constant amplitude at the inputs) is constant and equal to the amplitude of the signal at the output of any of them within its passband. If we neglect the unevenness of the frequency response of such a speaker, caused by the interference of sound waves in a closed volume, then, it would seem, it should be horizontal in the crossover frequency region, without rises and dips.

However, it is not possible to obtain such a frequency response. The reason is the difference in the phase response of low-pass and high-pass filters. If at one of the frequencies in the crossover frequency region the amplitudes of the signals at the outputs of the low-pass and high-pass filters are approximately equal, but one of them delays the signal by 90°, and at the output of the other it is present with a phase advance by the same amount, then the signals reproduced by the high-frequency and low-frequency heads at the same time will not be summed up, but subtracted, as a result of which a deep dip will appear in the frequency response at the mentioned frequency. For this reason, not all filters can be used in high-quality speakers.

Currently, the developers of most Western companies, as well as the developers of the best domestic speakers, use only a few types of filters, called “constant input impedance”, “all-passing type” and “constant voltage” filters.

“Constant input impedance” filters are essentially Butterworth filters of the appropriate order. If the load resistances of the LF and HF channels are equal and active, their input resistance is constant. Filters of even orders at the crossover frequency create a rise in the total frequency response of speakers in terms of sound pressure, reaching 3 dB, and therefore they are not used by developers of high-quality speakers. The total frequency response of speakers using odd-order filters does not depend on frequency, but these filters have a frequency-dependent phase shift in both the HF and LF channels. The phase responses of the LF and HF channels of odd-order Butterworth filters are identical, but are characterized by a phase shift of the HF signal relative to the LF,

equal to n * π/2, where n = 1, 3, 5,... The radiation pattern of speakers using odd-order Butterworth filters is asymmetrical in the crossover frequency region due to the mentioned phase shift.

Let us note a fact unknown to most radio amateurs and speakers developers: in Butterworth filters of the 3rd, 7th, etc. orders, antiphase inclusion of the heads of the separated channels is preferable from the point of view of reducing phase distortions and asymmetry of the radiation pattern; in Butterworth filters of the 1st, For the 5th, etc. orders, in-phase switching is preferable.

A distinctive feature of “all-passing type” filters is the independence of their total frequency response from frequency for filters of odd and even orders. For filters of even orders, the difference between the phase response of the high-frequency and low-frequency channels is n * (π/2), where n = 1, 2, 3,..., for odd orders - n * (π/2), where n = 1, 3, 5,... Butterworth filters of odd orders described above have the mentioned properties. Thus, Butterworth filters of odd orders simultaneously belong to both the class of “constant input resistance” filters and the class of “all-passing type” filters.

But filters of the “all-passing type” of even orders are no longer Butterworth filters, although they are described by a transfer function, which is the squared transfer function of a Butterworth filter of twice the lower order [3]. Even-order “all-passing type” filters have a symmetrical radiation pattern in the crossover frequency region (relative to the axis passing through the centers of the dynamic heads of the separated bands). They also have their own rules for phasing dynamic heads: for even-order filters with a degree equal to 4 m, where m==l, 2, 3,... the heads must be switched in phase in the separated bands. If the order is 2(2m+1), where m==0, 1, 2,..., then only antiphase switching of the heads is permissible.

The third class of filters - “constant voltage” - is used less frequently than the first two and is difficult to calculate and implement even for trained radio amateurs. Those who want to get to know these filters better, as well as those who want to get more complete information about the filters described above, can recommend the work of [Z]. We will return to the question of how, with the help of circuit modifications of the UMZCH, you can improve the sound quality of the speakers.

About choosing filters for speakers

The difficulties experienced by speaker developers when choosing a pair of high-pass-low-pass filters that have a flat total frequency response and a satisfactory phase response are largely due to the fact that they must satisfy another requirement - to be connected between the UMZCH and the dynamic heads, i.e., to be passive. The last condition limits the capabilities of developers, since it excludes from consideration the so-called additional function filters (AFF), in which one of the channels, for example, the low-frequency one, is supplied with a signal from the output of the high-pass filter, and the other (high-frequency) receives the difference between the input signal and the low-frequency signal. channel. In such a filter, the requirements for the device that extracts the difference signal are quite high, and therefore it is performed, as a rule, on an op-amp. However, in this case, to amplify the difference signal, an additional UMZCH will be required, since the signal from the output of a widely used op-amp cannot be supplied directly to a dynamic head with a resistance of several ohms. As a result, the amplifier turns into a multi-band amplifier, i.e. the number of independent UMZCHs in a stereophonic complex increases from 2 to 4-6.

This option, as a rule, is unacceptable for development companies and manufacturers of sound-reproducing equipment, since the cost of additional costs per unit of production does not decrease with increasing output. In other words, as long as there is hope of finding a pair of high-pass-low-pass filters with well-matched characteristics, manufacturers (for economic reasons) will adhere to the traditional scheme for constructing such equipment: broadband high-quality UMZCH - passive isolation filters - dynamic heads.

For radio amateurs, this path is far from optimal. The fact is that due to the lack of appropriate measuring equipment, the vast majority of radio amateurs are not able to reliably judge the reasons for the low sound quality of their speakers and purposefully choose ways to eliminate them, since the only way to evaluate the results of speaker modifications is for them to evaluate the improvement in sound quality, "aurally".

In this case, a guaranteed achievement of a positive result is possible either by repeating designs proposed by highly qualified specialists who have the ability to objectively evaluate their work with instruments, or by choosing such technical solutions that give results close to the calculated ones.

According to the author of the article, such solutions, first of all, include replacing a single-band UMZCH with a multi-band one, in which active filters and FDFs are used to separate the bands. Much has been said about the advantages of such a UMZCH in,. Let's just add the following to this.

When winding filter coils for high-quality speakers, whether they are “all-pass type”, “constant voltage” or “constant input impedance” filters, the radio amateur should strive to ensure that not only the inductance, but also the active resistance of the coil is equal to the calculated one. Otherwise, the quality factor of the coil changes, and therefore the type of filter. When using active filters, this problem is easily solved, since the quality factor of the filter is set, as a rule, by one trimming resistor.

Installation of passive filters involves the use of elements with a spread of values ​​of 2...3%. When these tolerances are exceeded, the tuning frequencies of each of the filters of the HF-LF pair and the type of filters change. The frequency response and phase response of the speakers deviate from the calculated ones, which again reduces the quality of the speakers. The use of FDF eliminates this problem, since the frequency response and phase response of pairs of such filters are automatically matched, and for any type of filter.

The use of passive filters and dynamic heads with different active resistances and developed sound pressure levels requires the use of ballast resistors to match these heads in speakers. As shown above, this can lead to the appearance of a rise in the frequency response of the speakers, caused by the resonance of the midrange head, which cannot be suppressed even by the negative output impedance of the UMZCH. All these problems are automatically solved by using a multi-band UMZCH with gain adjustment in each band and direct connection of the dynamic head to the UMZCH output of the corresponding band.

As already noted, the greatest distortions in the speaker radiation pattern are observed near the crossover frequency, when the signal is emitted simultaneously by two dynamic heads spaced apart in space. The use of active filters of the 3rd and 4th orders in a multiband UMZCH makes it possible to narrow these areas several times in comparison with speakers using passive separation filters of the first (less often second) order.

In addition, the dynamic heads themselves introduce their own phase shifts into the signals they emit. Compensating for these shifts when using passive filters in amateur conditions is practically impossible, as it requires a large number of complex measurements and machine calculations. The use of multi-band UMZCH facilitates the solution of this problem, since in this case it is necessary to adjust the system amplifier - reactive element at the output, which is much easier to do. If we add to the listed advantages the ease of calculating correctly designed high-order active filters and better correspondence to the calculation of real high-order active filters (due to the small influence of one link on another), it becomes obvious that for a radio amateur who decides to create a truly high-quality speaker system, but does not have in his At the disposal of equipment for a quantitative analysis of all the reasons for the decrease in its sound quality, it is optimal to use a multi-band UMZF with high-order active filters and FDF.

Multiband UMZCH with distribution filters

In Fig. Figure 14 shows a diagram of a filtering device and the formation of a negative output impedance for a three-way UMZCH, developed in accordance with the recommendations given in this article. The device is connected to the output of the pre-amplifier, after the volume and tone controls. If the output resistance of the previous stage is sufficiently high, more than 1 kOhm, then an emitter follower or (which is better from the point of view of minimizing nonlinear distortions) an amplification stage using the K574UD1 op amp must be connected to the input of the device.

(larger)

The device consists of three 3rd order Butterworth filters on transistors VT1 - VT3, two FDFs on op-amps DA1, DA2, a unit for forming a negative output resistance on op-amp DA4 and a low-frequency band mixer on op-amp DA3. The RF channel signal is generated by an additional function filter on the differential amplifier DA1. The inverting input of the amplifier receives the entire input signal, and the non-inverting input receives the signal from the output of the low-pass filter on transistor VT1, tuned to a frequency of 6.5 kHz. The selected order of band allocation is optimal from the point of view of reducing intermodulation distortion - higher-order harmonics arising in the mid-range and low-frequency channels of the UMZCH cannot reach the UMZCH HF channel. For the same purpose, it is advisable to use broadband op-amps (for example, K574UD1 or K544UD2) with correction circuits for unity gain as an op-amp.

The mid and low frequency components of the input signal, separated by a filter on VT1, are supplied to the inverting input of the differential amplifier at op-amp DA2. Its non-inverting input receives a signal from the output of the low-pass filter on transistor VT2. This low-pass filter is set to a frequency of 650 Hz, so the midrange channel reproduces signals in the range of 650 Hz...6.5 kHz. The low-frequency components of the input signal, separated by a filter on transistor VT2, are supplied to a high-pass filter on transistor VT3, tuned to a frequency of 30 Hz. The purpose of the high-pass filter is to cut off the infra-low components of the input signal that overload the low-frequency head. From the output of the high-pass filter the signal is fed to the inverting input of the differential amplifier at the DAS op-amp. Its non-inverting input receives a signal from the POST and OOSN signal generation unit, made on the DA4 op-amp. The phasing of the cascade on the DAS op-amp is given for the case of a non-inverting UMZCH LF channel. When using an inverting UMZCH, the signal from the output of the cascade on transistor VT3 must be applied to the non-inverting input of the op-amp DA3, and the signal from the output of the op-amp DA4 to the inverting one.

As channel UMZCH (A1 - A3), you can use the amplifiers described in,, or similar ones. When choosing them, you only need to remember that the rated power of the UMZCH LF channel must be no less than the rated powers of the UMZCH HF and MF channels. The power of the HF UMZCH channel can be 1.5...2 times lower than the power of the MF UMZCH channel. It is also desirable that the sum of the maximum powers of the UMZCH LF and MF channels be in 3 3 = 9 times higher than the power at which the complex is supposed to be operated. The latter is determined by the fact that the crest factor of real music and speech signals is 3, i.e. the maximum value of the output voltage in almost any phonogram is three times higher than the average value and for its undistorted reproduction you need a three-fold margin in the amplitude of the output signal, which is equivalent to a nine-fold margin in power.

As op-amps DA2 - DA4, it is permissible to use any op-amps of wide application (with appropriate correction circuits, if necessary). Transistors VT1 - VT3 can be any silicon with a maximum permissible voltage between the collector and base of at least 20 V and a current gain of at least 200. It is advisable to use filter elements and resistors of differential amplifiers (with the exception of trimmers) with a deviation of their resistances and capacitances from the nominal values ​​no more than 5%. When tuning a filter to a different frequency, it is necessary to reduce the capacitance of the corresponding filter by as many times as the tuning frequency needs to be increased (and vice versa).

A device assembled without errors from serviceable parts does not require adjustment. When power is applied, the voltage at the emitters of its transistors should be within 0.6...0.7 V, and the voltage at the outputs of the op-amp DA1 - DA3 (SA1 in the lower position in the diagram) -1... + 1V. A similar voltage should be established at the output of op-amp DA4 when resistors R34 and R36 are short-circuited. Filters do not require any special settings. The POST and OOCH channels are adjusted similarly to those described earlier. The engines of trimming resistors R29 and R30 are set to a position at which the level of sound pressure developed by the speakers at frequencies of 100, 300, 500 Hz (LF channel), 1, 2, 4 kHz (MF channel, resistor R30) and 10, 15, . 18 kHz (HF channel, resistor R29) was approximately the same. The sound pressure level is measured using a microphone with an amplifier and an alternating voltage voltmeter at the output with a power supplied to the UMZCH of no more than 2...3 W at a distance of 1...2 m from the speaker. Measurements must be made at a minimum of three (preferably five to seven) frequencies within each band due to the unevenness of the frequency response in sound pressure due to the interference of sound waves in a closed volume of the speaker, the shape of which is different from spherical.

It should also be noted that the use of resistors R29 and R30 as tone controls, as previously assumed by a number of authors, is unacceptable. This is due to the high slope of the separation filter characteristics. The imbalance of sound pressure levels in different channels with such steep filters distorts the sound to a much greater extent than the acoustic deficiencies of the room.

A radio amateur seeking to create a high-quality speaker must take into account two more points. Firstly, you can significantly smooth out the frequency response of speakers in terms of sound pressure in the midrange and high frequencies by covering the midrange and high frequency heads with protective caps, the shape of which should be as close to spherical as possible. Secondly, in order to reduce phase distortions, the installation planes of the HF, MF and LF heads in the speakers should generally be different. The most complete information on this issue from a practical point of view can be found in.

Measuring low-frequency drivers and their acoustic design

The most convenient method for radio amateurs is the method of determining the parameters of dynamic heads from the frequency response of the head's total electrical resistance module. In Fig. Figure 15 shows a typical dependence of the impedance modulus | Z \ on frequency in free air. A similar form of dependence is observed when installing a dynamic head in a closed box. Having determined these dependencies, it is possible to obtain Qa, Qe, V AS /V and f S, necessary for calculating the loudspeaker.

The measurement diagram is shown in Fig. 16. The resistance of the current-setting resistor R should be approximately 150...200 times greater than the DC resistance of the dynamic head VA. In this case, the UMZCH turns into a current generator through the dynamic head and the voltage drop across it, measured using a voltmeter B, is directly proportional to the resistance of the head. The frequency value is measured on the scale of the generator G or more accurately on the scale of the frequency meter H.

First, it is necessary to measure the parameters of the head in free air. The head must be placed, if possible, far from reflective surfaces, for example, mounted on a rigid rod. The rigidity of the rod must be such that its natural resonant frequency is significantly higher than fs. Having constructed a curve similar to that shown in Fig. 15, determine fs", f 1, f 2, Re, Res, Rs, K 1,2 = 0.71Rs. Q"a and Q"e, characterizing the head in open air, are determined from the relations:

(apostrophes in the designation f, Qa "Qe" indicate that these values ​​do not take into account measurements in the attached air mass that occur when the head operates in an acoustic design).

In this case, resonance will be observed at frequency f"" 3. From parameters (1) and (2), the values ​​of Qa" and Qe" can be found. The exact values ​​of the parameters fs, Qa, Qe and V AS /V can be found from the relations:

f S = f S " SQR.((f S "Qe") / (f S "Qe)), (3)

Qa = (Qa" f S)"/fs, (4)

Qe = (Qe" f S)"/fs, (5)

V AS /V = (f S ""/f S)2 - 1, (6)

It should be noted that at a low natural resonant frequency of the head, losses in the box can distort the |Z| from the frequency and another maximum will appear on it, which can easily be mistaken for the main one. Therefore, when taking a curve, you need to be sure that the maximum found is the main one.

To do this, it is necessary to measure the dependencies | Z | from f in the range from 20 to 100 Hz, and if several resonant “humps” are detected, select the one with the maximum amplitude.

It should be noted that the slope of the dependence | Z | from f at maximum is very small, so it is very difficult to accurately measure the frequency fs. To increase the accuracy of measurements, it can be recommended to make at least 5-7 fs measurements and take the arithmetic mean of the given measurements as the base result. After this, it is necessary to compare the obtained fs value with fs* = SQR(f 1 f 2), and if they differ by no more than 1... 1.5 Hz, then the fs measurements can be considered complete. If fs and fs* differ by more than 1...1.5 Hz, then measurements must be taken again.

Readers can find a more detailed description of the measurement technique with numerical examples in.

LITERATURE

1. Maksimov S. Once again about improving the sound of 25AC-109. - Radio, 1991, No. 1, p. 46.
2. Aldoshina I, Voishvillo A. High-quality acoustic systems and emitters. - M.: Radio and Communications, 1985.
3. Saltykov O., Syritso A. Sound-reproducing complex. - Radio, 1979, No. 7, p. 28-31; No. 8, p. 34-38.
4. Vinogradova E. Design of loudspeakers with smoothed frequency characteristics M* Energy - 1978
5. Adamenko B., Demidov O. Usacheva E. Loudspeakers for household radio equipment. - Radio. 1979, No. 1. p. 35.
6. Shorov V. Improving the sound of loudspeaker 25AC-309.-Radio, 1985. No. 4, p. thirty.
7. A. Syritso. Power amplifier based on integrated op-amps. - Radio, 1984, No. 8, p. 35.
8. Lexins V. and V. Single-band or multi-band? - Radio, 1981, No. 4, p. 35.
9. Chanturia A. Three-band amplifier. - Radio, 1981, No. 5-6, p. 39.
10. Solntsev Yu. High-quality pre-amplifier.-Radio, 1985, No. 4, p. 32.
11. Gumelya E. Simple high-quality UMZCH. - Radio, 1989, No. 1, p. 44.
12. Dolnik A. Features of the operation of the loudspeaker head in acoustic design. - VRL, 1977, issue. 56, p. 34.
13. Zhbanov V. On the phase characteristics of loudspeakers.-Radio, 1989. No. 10, p. 58.