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ENCYCLOPEDIA OF RADIO ELECTRONICS AND ELECTRICAL ENGINEERING On the distortion of the frequency characteristics of small-sized acoustic systems and "deep bass". Encyclopedia of radio electronics and electrical engineering
Encyclopedia of radio electronics and electrical engineering / Speakers Every radio amateur who has ever independently built acoustic systems (AS) knows that even the exact execution of the project, the recommendations of the authors of the design do not always lead to the desired result. For all the complexity or simply impossibility of assessing the quality of home-made speakers at home, other than "by ear", the authors of the designs often do not provide either methods for evaluating their projects or recommendations for their use (placement and connection of speakers). It happens that after the repetition of the next "masterpiece", when the joy of finishing work on it passes, a period of painful assessments and conclusions begins. Enthusiasm and momentary euphoria are often replaced by almost disappointment. Indeed, it is already difficult to look for the reasons for unsatisfactory work in the finished design, when "everything was done as it should" was done. Or maybe the design is good, but the amplifier is "not like that" or something else... Familiar? Look in amateur radio magazines of past years for articles on the design of speaker systems. Dear authors, they created their versions almost blindly, without taking into account the physics of electromechanical transformations and acoustics as such. Undoubtedly, a number of designs of home-made speakers, methods for improving industrial speakers and dynamic heads are successful and deserve attention. Many designs have become a good "school" for lovers of high-quality sound reproduction in the endless cyclical process of creating or remaking speakers according to the principle: "It's about to become very good ...". But, note that the authors compared their developments (maximum) with industrial designs of the AS factories of the former USSR. Would they try to compare their projects with the products of such companies as BOSE or JBL ... The objection to the purchase of lower and middle price imported speakers is as follows: "Who told you that such a speaker in your living room will sound, and not radiate sweet-voiced sounds?". Motives like: "Don't do it anyway" don't convince. Of course, there are samples of branded acoustics that are incomparable in their design and sound, but their cost (as well as all know-how) is very high. Even now, when there is a real possibility of using high-quality modern dynamic heads, descriptions of self-made speakers (already on a new element base) continue to be encountered, inheriting design errors from previous years. It seems that in the current variety of choice of source material, we can calculate and competently build only the speaker cabinet (box). In fact, not only the volume of AS is a defining indicator of quality. Sometimes even a case correctly calculated from the point of view of a uniform frequency response does not sound. By reducing the main drawback of existing dynamic heads - a significant frequency response unevenness in the mid-high frequency range, they will not be inferior to a good third of imported ones, and they can be used to build speakers that will satisfy the demanding listener. The beauty of DIY speaker building is the freedom to design and get what you want regardless (or nearly so) of cost, something you can't achieve with mass production. So, there was and still is a sense to try to replenish your knowledge and start over. Despite the fact that this material does not provide a specific design of the speaker system, some aspects of the operation of the low-frequency section of the speaker are presented from a practical point of view and are available for repetition or independent analysis with sufficient accuracy. First. The acoustics of the room, or more simply the living room, is far from perfect. If you cannot improve the acoustics of the room according to all the rules (proportions of the "golden section 0,618: 1: 1,618", the reasonable use of sound-absorbing materials, the choice of speaker placement, the choice of listening point, etc.), then you really should look at the mini complex and calm down. Otherwise, we move on. On the one hand, every room sounds different even after making all reasonable changes to the environment. On the other hand, each of us knows the features of his home, we are accustomed to the "home" coloring of sounds. Our brain subconsciously begins to transform what we hear to its original color. So what you really need to try to do in the room is to minimize standing waves, bring the reverb level to an acceptable level, remove or dampen resonant objects (surfaces) and organize the correct listening area. Second. The emergence of new sound sources based on digital technologies, such as Hi-Fi video (with FM sound recording), tape recorders, PC (MPEG), compact and mini-discs, imposes new requirements on speakers: increased uniformity of phase and amplitude-frequency characteristics , wide dynamic range, minimal intermodulation distortion. The nature of distortion in speakers is determined by the physics of the sound reproduction process and is so multifaceted that all types of distortion can hardly be eliminated in practice. However, some of them are well studied in the amateur radio world, and therefore can be controlled in the design process. The main rule should be this: each kind of distortion is reduced individually and carefully. Third. Cost of work. In any case, the cost of materials and components spent on the manufacture of a good "home" speaker will be disproportionately less than the cost of the speaker, which you would have purchased if it were possible. This means that it is very profitable to invest your knowledge in the design, which is called "for yourself". Last thing. When buying a branded speaker, no one except the manufacturer will give you recommendations on its placement and correct "tuning" for a specific situation. Neither the sellers nor the Internet have this information - only the subjective opinions of "experts" from the same stores. With the exception of some speaker models, which are accompanied by printouts of the measured frequency response and harmonics in the operating frequency band, we are forced to buy almost any branded acoustics on a "pig in a poke" basis. We start with the choice of dynamic heads. This will determine the type of speaker, namely, a two-way or three-way design. From experience I can say that it is very difficult to build a three-way speaker system at home. The cost of research and experimentation is doubled compared to a two-way speaker. Try to choose dynamic heads for two-way speakers based on their acoustic power (nominal power, taking into account sensitivity) LF-MF to MF-HF as 1,5 ... 3,0 to 1,0. The overlap of the frequency ranges of the heads must be at least 2 octaves (4 times), otherwise it will not be possible to ensure accurate matching and smooth transitions of the phase-frequency characteristics of the heads in the region of the filter section frequency. It is desirable to use crossover filters of the 2nd order for LF and the third for HF heads. These seemingly trivial requirements are actually difficult to fulfill, but easier than doing the same for a three-way speaker. The next parameter that affects the selection of a pair of heads is the diameter of their diffusers. It is known that the larger the effective diameter of the radiator (Deff.=Dg/sqrt(2), Dg is the cone diameter measured at the center of the corrugation), the narrower the head pattern at the upper operating frequency. There is a formula that relates the radiation directivity angle of the dynamic head with the emitted wavelength (l) and the effective diameter of the diffuser Deff. Radiation forward into the half-space (p) is provided under the condition pi*Deff.D=0,25 [1,6]. At high frequencies, the radiation pattern narrows even more. For example, for a low-frequency head of the 6GD-2 type (Deff.=13 cm) at a frequency of 7 kHz (the limit for heads of this type, measured along the radiation axis), the radiation pattern has an opening angle of the order of TC/24 at a level of -3 dB. This direction of radiation is not applicable for use in a residential area (except for you, sitting in the center of the listening area, no one will hear anything). This determines the choice of the frequency section of the LF-HF bands for this head in the region of 1500 ... 2000 Hz, while providing an opening angle of the radiation pattern of the order of TC / 6. When using a woofer with a smaller cone diameter, the allowable crossover frequency can be proportionally increased. Arguing in a similar way, the choice of an RF head should be made in favor of designs with a small diameter of the radiating surface (6GDV-1, 6GDV-6, 10GDV-2, etc.). It is also recommended to refine the selected dynamic heads in order to reduce the overtones and parasitic resonances of the diffusers according to the methods repeatedly cited in the literature [2]. The only thing that is not advisable, in my opinion, to do is to reduce the own quality factor of the woofer in all ways. The design parameters of the selected head are much more profitable to measure and take into account when calculating the acoustic design, the output parameters of the power amplifier (PA) and the electrical circuit of the filters. Otherwise, the efficiency of the head decreases at low frequencies, which will further complicate the task of matching with the high-frequency head to obtain a uniform acoustic frequency response of the speakers. The use of methods for reducing the intrinsic quality factor of a low-frequency head has another significant drawback. The distortion of the radiation phase of the speaker, in which a damped head is installed, at low frequencies is greater than when using an undamped head and special correction circuits. For example, speakers at 6GD-2, Qts = 0,37 (damped by an acoustic impedance panel) have a flat frequency response, but the phase shift at a frequency of 50 Hz is + pi / 2, while at Qts = 0,71 (without PAS) with frequency response correction in the PA - the phase shift at the same frequency is only + pi / 6, i.e. 3 times less. The next step is the choice of acoustic design. To make it easier to set up speaker crossovers and provide more freedom when placing systems in a room, it is recommended to choose a design with separate housings for each of the heads. This allows you to move the HF emitter relative to the LF in depth to adjust the radiation phase in the region of the filter section frequency, and in the case of installing the HF head in a spherical housing on a ring stand, direct the acoustic axis of the HF head directly at the listener at any orientation of the low-frequency link body. How many housing designs exist for the same woofers. It would seem that all of them are calculated using the same well-known methods, but they are so different both in volume and in types. Having measured the parameters of 7 6GD-2 heads of different years of manufacture, you are really amazed at the results. The resonant frequency values of the heads Fr are in the range of 31...55 Hz, the equivalent quality factor Qts - 0,62...1,38, the equivalent volume Vas - from 65 to 380 liters! It is possible for a head instance with an equivalent volume of 65 liters and a quality factor of 0,62 to calculate the design with dimensions acceptable for a living room, but for the case of 300 liters and Qts = 0,93, family and relatives are unlikely to understand you. For compression heads from 20GDN-1 to 75GDN-1, the spread of parameters turned out to be smaller, but their values differed greatly from the data given in the technical data sheets. Acceptable for the home design of the speakers (in terms of the thickness of the materials used for the walls of the case, the weight and dimensions of the finished speaker, the convenience of placing it in the room) is a case with a volume of 30-45 liters. Moreover, a case with a volume of 30-35 liters should be made in compliance with the internal dimensions in the proportion of the "golden section". Cases of large volumes should be made in the form of a floor structure with mandatory stitching of opposite side panels with spacers. The thickness of the body material is 16-25 mm with the obligatory gluing of the inner surface with linoleum and foam mats 15-30 mm thick or home-made mats (cotton wool + gauze) 20-30 mm thick. The woofer is placed at the top edge of the narrow side panel, which will be the front. There is no doubt that in most cases a closed speaker of this size with a low-frequency head installed at its disposal will have a resulting quality factor greater than unity, i.e. on the frequency response in the region of the resonant frequency, a "hump" of +2 ... +6 dB will be observed. Moreover, the lower limit of the reproducible frequencies of such a speaker will be 75-100 Hz, which is clearly not enough. Nevertheless, these types of distortions in the frequency response of the speakers are perfectly modeled mathematically [3] and can be predetermined by the choice of a dynamic head, easily measured and minimized by active filters included before the PA or otherwise. On the choice of body type. Yes, a closed speaker is easier to manufacture, but it allows you to use the potential of a dynamic head in the bass region by only 25-40%, regardless of the head's own resonant frequency! The reason for this lies in the impossibility of the dynamic head to develop the required level of acoustic power in the resonant frequency region due to the design limitations of the diffuser stroke and, as a result, the appearance of large nonlinear and intermodulation distortions. With a decrease in the frequency of the reproduced signal below 50-80 Hz, most low-frequency heads in closed speakers with a volume of 30-45 liters are physically unable to provide the level of acoustic pressure at the level created by the same head at a nominal input electrical power at frequencies of 300-2000 Hz. The decrease in the maximum acoustic power (not to be confused with the frequency response) as the frequency decreases below the resonant one (Fs is the resonant frequency of the head in the volume of the speaker cabinet) is almost linear with a slope of 24 dB per octave. I suggest you recalculate the maximum acoustic power level of a closed speaker at a frequency of 30 Hz with Fs equal to 60 Hz - we will get an analog of less than 1 W for a 100-watt head! Therefore, the only acceptable for creating a "home" small-capacity speakers is a design using a phase inverter (FI). At the frequencies of the reproducible signal near the FI tuning frequency Ff, the amplitude of the diffuser oscillations sharply decreases. As a result, non-linear and intermodulation distortions are reduced due to the design of the diffuser suspension, the boundary dimensions of the magnetic system and the voice coil. However, non-linear distortions caused by insufficient diffuser rigidity, on the contrary, increase. All this speaks in favor of the use of the so-called. compression heads. With the correct design of the AS, the oscillation amplitude of the moving system of the head at the FI tuning frequency can be 25-30 times less than at the same frequency in a closed case. This means that at low frequencies, a FI speaker has a much larger dynamic range than a closed-design speaker with comparable non-linear and intermodulation distortions. The most interesting thing is to choose the tuning frequency of the phase inverter Ff. The classical way of tuning Ff to the resonant frequency of the head in free space is justified in the vast majority of cases. In this case, a compromise is reached between the uniformity of the frequency response and the maximum possible acoustic power of the speakers at frequencies close to the resonant one (but not lower than Ff). The equivalent quality factor of the low-frequency head Qts for this case should be in the range of 0,35 ... 0,55. In the case of using low-frequency heads with a high quality factor of 0.15 = 0,65 ... 1,5 in a small-sized speaker system, it is generally difficult or impossible to obtain an even frequency response in a case of any volume. Therefore, it is advisable to tune Ff to a frequency 2 ... 3 times (more precisely - see below) below the resonant frequency of the head Fp. At the same time, the frequency response of the speaker above the frequency Ff will practically repeat the frequency response of a closed speaker of the same volume.
The lower Ff, the closer the similarity of frequency response. At a low frequency Ff, there are also smaller phase distortions and a smaller group delay time of the AS radiation at low frequencies (Fig. 1-4). Head 6GD-2, Qts(5=0,62, Fр=31 Hz, Vаs=241 l, SPL=92,3 dB/W*m. Estimated data for different acoustic design: 1. Speakers with phase inverter, optimal volume 550 liters, Ff = 20 Hz 2. Speakers with a phase inverter, volume 32 liters, Ff = 25 Hz 3. Speakers of a closed type, optimal volume 386 liters 4. Speakers of a closed type, volume 32 liters Level 108 dB is provided by a head in a wide frequency band of 300- 2000 Hz at rated input power b W. The calculated dimensions of the FI are as follows: For a speaker with a volume of 550 liters - a diameter of 15 cm, a length of 7 cm. For a speaker with a volume of 32 liters - a diameter of 5 cm, a length of 24 cm -10% to calculate the optimal (minimum possible) FI tuning frequency (Ffi min) for a specific low-frequency head. Otherwise, this is a criterion for determining the frequency, starting from which a specific dynamic head (in speakers with FI) is able to provide maximum acoustic pressure not less than at medium frequencies when the rated electric power is applied to it: Fphi min=15 / SQRT( Dg * sqrt(Ng)) * SPL/Xmax, where Ng is the number of heads of the same type installed in the speaker cabinet Dg is the diameter of the diffuser (at the center of the corrugation), cm SPL- is the sensitivity of the head dB/W*m Xmax is the maximum displacement of the diffuser (in one direction ), cm. The main thing is that the frequency Ffi min, below which the maximum acoustic pressure created by the head, begins to decrease sharply, practically does not depend on either the body volume or the natural resonant frequency of the head. Thus, it makes no sense to calculate a case with a FI tuned to a frequency below Fphi min - you will not be able to get an acceptable acoustic return from a low-frequency driver in a speaker cabinet of even a very large volume, although the frequency response of the speaker may be optimal. Examples: 10GD-34 (25GDN-1-4): Ffi min = 0,8 / sqrt10,5 * 84 / 0,6 = 35 Hz (98dB) 6GD-2: Ffi min = 0,8 / sqrt21 * 91,4, 0,5/32 = 104 Hz (10dB) 30GD-20 (1GDN-4-0,8): Ffi min = 16,7/sqrt86 * 0,8/21 = 98 Hz (30 dB) 2GD-75 (1GDN -4-0,8): Fphi min = 21 / sqrt86 * 0,8 / 19 = 105 Hz (XNUMX dB)
You ask: "Is this the secret to deep bass?" These are real FI tuning frequencies, up to which these heads can provide acoustic pressure comparable to the pressure at medium frequencies at rated input power. Further - everything is simple: 1. If the head has its own resonant frequency not lower than Ffi min and quality factor Qts=0,3...0,5, then feel free to calculate the body with FI according to the well-known method [3]. As a result, you will get an optimal loudspeaker with a flat frequency response without applying additional PA correction. 2. If the head has its own resonant frequency not lower than Ffi min and quality factor Qts=0,6...1,5, then there is a chance to create speakers of any acceptable volume with a FI tuned to the frequency Ffi min. In this case, a flat frequency response of the speaker can only be obtained using the appropriate correction of the frequency response of the PA (Linkwitz corrector - see below). 3. If the head has its own resonant frequency Fр < 0,85 * Ffi min, then you can think about installing two or more heads of the same type in the speakers, and then follow option 1 or 2 or completely abandon the use of this type of heads in the low-frequency section of your speaker . Other ways to "force" the low-frequency head to work at 100% are to build two-, three-volume speakers with the placement of the low-frequency head inside the case with radiation through the FI port (ports). Such an AC is really difficult to calculate at home. A little about the designs of phase inverters. The standard design of a tubular FI must satisfy the following conditions: rigidity and the absence of resonant overtones in the pipe material, the diameter of the hole (pipe) of the FI should be chosen not less than 1/4 of the diameter of the low-frequency head cone. Since the FI, like the dynamic head, is a source of sound vibrations, the FI pipe should not create any additional overtones. Tap the wall of the PHI pipe with a pencil. If it "rings", then glue the outer surface of the FI pipe in one layer with rubber, linoleum and / or wrap it with plaster, insulating tape (not adhesive tape) in 5-6 layers. The FI hole on the front panel of the speaker must be placed no closer than 10-15 cm from the edge of the low-frequency head. In principle, the FI output can be placed on any side or rear wall of the speaker cabinet. Only in the event that the speaker is installed in the space between the furniture sections or close to the wall or other objects that limit radiation from the side or rear, the FI hole must be placed on the front panel. When calculating the length of the FI pipe, it is assumed that the inner edge of the pipe must be at least at a distance of its diameter from the inner surface of the opposite wall of the AU case. If this condition is not met, then the FI with a smaller diameter is recalculated. Instead of one FI, you can use two with an inner diameter of 0,71 of the calculated one AI. It is also useful to round the ends of the pipes. Filling the speaker cabinet with a sound absorber - at will, excluding the FI area, but not more than 15 g / liter. Another type of distortion that affects the sound quality of any speaker is the loss of diffraction of sound waves. This type of distortion appears in the 100-800 Hz frequency region and is a gradual decrease in acoustic pressure generated by speakers below a certain frequency. Despite the fact that this type of distortion is well known, its description in our amateur radio literature was given incorrectly, apparently during the first translations of foreign articles into Russian. This type of distortion was explained to us as "Distortions in the frequency response of various forms of speaker cabinets" [6]. However, when placing speakers "in the wall" diffraction distortion can be small in any shape of the cabinet. In fact, when the inner surface of the speaker walls is pasted over with sound-absorbing material, the inner surface of the speaker can be made almost spherical. Will the behavior of the AX of such an AU change, in principle? No. The point is this. At low frequencies, the wavelength emitted by the speaker is much larger than the physical dimensions of the speaker itself, so sound waves go around the speaker housing, i.e. are radiated into space 2pi (around). At high frequencies, where the emitted wavelength is smaller than the size of the speaker front panel, radiation is possible only forward, i.e. into a half-space [4]. Thus, at a constant electric power supplied to the speaker, and with a horizontal AH of the dynamic head (and in the region of 200-500 Hz, rare instances of low-frequency heads have anomalies), starting from a certain frequency, the AH of the system along the radiation axis increases to +6 dB. The smoothest behavior of the AC is observed in the absence of sharp external edges in the design of the AC (Fig. 5). In the case of a standard housing, the AX of diffraction distortion has local minima and maxima, but with increasing frequency, the recoil of the AU along the radiation axis still increases by a factor of 2 (Fig.b). The average frequency (Hz) at which the loudspeaker output is (ideally) increased by 3 dB can be calculated in Hz using the following empirical formula: Fd=115/W, where W is the front panel width of the loudspeaker in meters. The amount of distortion due to diffraction loss of +6 dB takes place only when the speakers are placed in free space, which is not a living room. Low-frequency sound waves that envelope the speaker are reflected to some extent from the wall, near which the speaker is usually installed and come to the listener. Thus, the actually measured loss value is 3-4 dB. The existence of diffraction distortions can be verified by the acoustic characteristics of industrial speakers given by manufacturers (Fig. 7-9):
It is quite simple to compensate for these AX distortions by including the simplest corrective chain R4C4R5 in the sound reproducing path between the preamplifier and the power amplifier (Fig. 10). Having chosen the ratio of resistances R4=R5/2 (the correction value is about 3,5 dB) and their ratings in kOhm, we determine the capacitance C4 in microfarads using the formula: C4=130/(R5*Fd).
Calculation example: 1. Speaker front panel width: 25 cm 2. Determine the frequency Fd= 115/0,25=460 Hz 3. Select R5=4,7 kΩ, R4=4,7/2=2,4 kΩ 4. Determine С4=130/(4,7*460)=0,062 µF (62 nF) you can just not remember. After applying such a correction to some speakers, the latter may begin to "mumble". This is quite normal, because. the resulting quality factor of most small-volume speakers built on common low-frequency heads is obviously higher than 0,71. Every fan of high-quality sound reproduction could notice that when placing the speakers on stands 0,4 ... 0,7 meters high, especially if they are also moved away from the wall by 0,3 ... 0,6 meters, the speaker output level drops noticeably on woofer. In this case, intuitively increase the signal level at low frequencies with a tone control +3 ... + 5 dB and what do you observe? That's right - a more "true" sound and, maybe, "mumbling". The tone control of the low-frequency amplifier in this case reduces just the distortion of the diffraction of sound waves. By the way, such placement of speakers along the long wall of the room is the most optimal in terms of minimizing the effect of room acoustics on the frequency response of the speakers.
Now imagine the AX speakers shown in Figures 7-9, if the designers of these "household" speakers took care of compensating this type of distortion with passive filters. AS "Corvette" and "Vega" would "mumble", but "Estonia" would not. By the way, the first one is made in a closed case, "Estonia" and "Vega" - with AI tuned to 40-45 Hz. Analysis of the AH of these speakers shows that: 15AC-111 "Vega" - due to the high quality factor of the low-frequency head used in the AU, the AX has a rise at a frequency of 80-90 Hz by 2-3 dB (the quality factor of the speaker is 1,3). In any case, "mumbling" is observed and correction of the AH with active filters is required. The use of an AI tuned to 40 Hz is close to optimal (35 Hz), but should not be used to correct the AH, but for a completely different purpose - to provide the maximum acoustic power of the woofer. • 35AC-021 "Estonia" - almost the most even AH, but setting the AI to a frequency of 45 Hz does not allow full use of the potential of the bass head. It would be beneficial to increase the case volume by 15-20% and reduce the AI tuning frequency to 21-27 Hz. 75AC-001 "Corvette" - does not have a decline at a frequency of 180 Hz by 3 dB, but a rise at a frequency of 90-95 Hz by 3 dB, caused by the resulting quality factor of the speakers, equal to 1,3-1,4 due to the small volume of the case. The acoustic power of the speakers at low frequencies is provided only by a high-quality low-frequency head 100GDN-3. It is advisable to use AI and AH corrector. Thus, if the resulting quality factor of the speaker is 1,1 ... 2, i.e. on AX AU there is a rise of +1 ... 6 dB in the region of 60-110 Hz (obvious signs of "mumbling"), and the volume of the AU is at least 2-3 times less than the equivalent volume of the low-frequency head Vas, that is, it makes sense to apply the AX correction on active filters according to the Linkwitz Transform Circuit, an example of the circuit is shown in fig. 10 (excluding R4C4R5).
Simultaneously with the AX correction, the circuit provides local correction of the signal phase in the region below the resonant frequency, which reduces the phase distortion of the speakers. AH and PFC of the corrector are shown in fig. 11 and fig. 12. Characteristics are calculated for the quality factor of a speaker with a volume of 32 liters, equal to 1,8 at a frequency of 98 Hz to obtain horizontal acoustical characteristics in terms of sound pressure from 500 to 32 Hz (-3 dB) with a resulting quality factor equal to 0,71 (woofer head 6GD-2 , Qts=0,62, Fр=31 Hz). The AX of the corrector has a rise of 12 dB per octave in the low-frequency region to compensate for the similar decline in AX of a closed speaker. But just at these frequencies, the overload capacity of a closed AS is low. Therefore, it is optimal to use such an AH correction for an AU with AI tuned to a frequency Ffi min. Determining this for a finished (or under construction) nuclear power plant is quite simple. First, we close and seal the opening of the phase inverter and measure the resistance module of the low-frequency head in the closed speaker cabinet. By the maximum value of the resistance modulus, we determine the resonant frequency of the low-frequency head Fs in the speaker cabinet. Then we open the AI hole and again measure the resistance module of the head. We determine the resonant frequency of AI Ff by the minimum of the resistance modulus. Usually, at frequencies above and below the found minimum, the head impedance modulus has pronounced peaks. If Ff is higher than or equal to Fs, then AI AS is configured incorrectly in any case. If Ff is higher than Ffi min, then increase the length of the AI pipe in proportion to the square of the desired decrease in Ff and tune the AI to the frequency Ffi min. In the case when the AI pipe of the calculated length cannot physically be installed in the AU case, a pipe of a smaller diameter is used. There is an opinion that the installation of another AI in the AU, similar to the existing one, lowers the AI tuning frequency. This opinion is wrong. In fact, the AI tuning frequency increases by a factor of sqrt2 with a simultaneous decrease in the air velocity inside the AI, which is useful in some cases (besides, a smaller diameter pipe is stiffer). In other words, installing two identical MTs is equivalent to using one MT of the same length with an inner diameter sqrt2 times larger than the pipe diameter of one of the MTs of the pair. Now it is necessary to determine the resulting quality factor of the woofer at the frequency Fs in the AU with AI tuned to the frequency Ffi min. At home, it is almost impossible to do this through direct measurement of the frequency response of the speakers by sound pressure. It is much easier and more accurate to obtain the AC value by calculation on a PC using specialized software. However, any methods of mathematical modeling involve up to 10-30 known parameters of a particular dynamic head, which, again, are difficult to measure at home. I propose a very simple way to determine the quality factor of the speakers with an accuracy of about 10-15%, which will additionally require any electret microphone (IEC-3) and a preamplifier for it with a flat frequency response from 10 to 10000 Hz. Re-close and seal the FI AS hole (if any). After that, the microphone is placed in the immediate vicinity of 2-5 mm from the diffuser of the low-frequency head at a distance of 2/3 of the radius of the diffuser from its center. An AC voltmeter is connected to the output of the microphone amplifier and a signal from the AF generator is fed to the head (through the PA with a flat frequency response). The power supplied to the head should not exceed 0,1-0,5 W. By changing the frequency of the generator from 500 to 20 Hz, the frequency response of the speaker is built. They are convinced of the presence of a “hump” in the Fs region and a frequency response slope of 12 dB / octave below this frequency. Find the ratio of the maximum output voltage at a frequency close to or slightly above Fs to the output voltage at a frequency of 500 Hz. The resulting value is squared. The result will be equal to the value of the quality factor of the speakers with FI. Adherents of any methods of reducing the quality factor of the woofer (PAS, negative output impedance of the PA, etc.) at this stage can choose the amount of sound-absorbing material in the case of a closed speaker (PAS design, Rout PA value) to obtain the desired value of the quality factor. When using a significant amount of sound-absorbing material, but not more than 15 ... 23 g / liter [7], it is desirable to "organize" a free space of 3-5 liters using a wire frame between the FI and the low-frequency head. For those who can calculate or determine the quality factor of a low-frequency driver (with known measured parameters) installed in a specific speaker cabinet, the existing standard methods are preferable. The results of measurements of the quality factor and resonant frequency of the head in a closed AS (Fs) can be used to select the corrector ratings (Fig. 10) only for the case when the FI is tuned to the frequency Fphi min, at least 2 times lower than the frequency Fs. We proceed to determine the ratings of the RC corrective stage. The operational amplifier is recommended 157UD2 (for the stereo version of the corrector, the op amp correction circuit is for unity gain). Since the calculation of the elements of the corrector is rather complicated, the results of computer calculation of the RC values are shown in Table 1 for various values of the quality factor of the speaker and the frequency Fs=80 Hz. For other values of the frequency Fs, the capacitance ratings of the capacitors are simply recalculated according to the formula: C1'= 80 C1/P'z.
Similarly, the capacitances of capacitors C2 and C3 are recalculated. You can leave the capacitances of the capacitors unchanged, and recalculate the resistances V1-VZ in the same way. The only limitation is that the resistance of the resistor B2 should not be less than 2 kOhm, because. is the main load of the op-amp at high frequencies. When the corrector is turned on before the PA (before the timbre block), the actual frequency response of the system in terms of sound pressure will be horizontal with a tolerance of ± 2 dB to the lower operating frequency (indicated in the table, subject to Fphi min < F (-ZdB)), and the equivalent quality factor of the speaker is 0,71, 1. RC ratings must be selected with an accuracy of 1,6%. With AC values equal to 4 and higher (5-6-7-1 rows of Table 30), the corrector has a significant rise in frequency response at frequencies of 20-13 Hz (16-20-24-XNUMX dB). To prevent obvious overload of the MIND and AS with a real signal taken from the output of the corrector, it is advisable to use a first-order high-pass filter with a cutoff frequency of 30-35 Hz at the input of the MIND (or tone block). This can be done by replacing (or installing) a capacitor at the input of the PA, the capacitance of which in nF is calculated using the formula 5000 / Vin., Where Rin. - input impedance of the PA (or tone block), kOhm. The sound of speakers, the frequency response of which is corrected in the two indicated ways, will not only please you - it will amaze you. You will finally feel the complete absence of sound coloration in the low frequency range - there will be no "mumbling" as such. The bass tone control of the amplifier will finally work as it should - effectively. Quite sufficient will be the depth of the bass tone control ± 3-5 dB. The return on sound pressure at the lower operating frequency of the speakers will be the maximum possible for the applied low-frequency dynamic driver.
Modeling and direct measurement of the characteristics of heads and speakers (to confirm the results of calculations) was carried out using an Intel Pentium III class multimedia PC with a calibrated sound card (frequency response 15...17000 Hz ±0,2 dB). Various free software was used, including demo versions of programs from JBL, Blaupunkt and Peerless (signal generator emulators, white noise frequency response meters, 1/2-1/12 octave pink noise spectrum analyzers, programs to calculate the parameters of closed speakers, speakers with FI, etc.) The software settings set the frequency resolution to less than 0,3 Hz. Additionally, we used: PA 60 W with slight distortion in the range of 10-40000 Hz and an electret microphone (complete with a preamplifier) with a known frequency response in the range of 30-15000 Hz ±1,0 dB. The correctness of the conclusions was verified experimentally as follows. Acquired "on the occasion" closed speakers "Bifrons" (Hungary, Budapest, plant "BEA6", 1975 onwards, volume 36 liters, multi-layer body made of solid wood filled with cotton wool 12 g / liter, 9 (!) broadband heads of BEA6 HX-125-8 type with a nominal power of 12 W each and a resonant frequency of 68-71 Hz, Qts = 1,02 ... 1,08) perfectly reproduced classical music, jazz. As soon as it came to listening to rock or modern electronic music, the speakers immediately "lost" their positions (this is at 108 W of rated power and a sensitivity of 88 dB / W * m). Measuring the parameters of the HX-125-8 heads and modeling the speakers on a PC showed all the disadvantages of the factory design. With a closed design, these speakers practically could not even give out the power that 10MAS-1 develops at a frequency of 60 Hz (the frequency response began to decline from 110 Hz). Replacing one of the 9 speakers with a FI (see photo) tuned to 38 Hz gave amazing results. The speakers sounded. It is not so important to compare the results of measuring the frequency response of the speakers before and after the alteration (the frequency response has not practically changed), as the change in the nature of the sound of the speakers - they have become "omnivorous". Even on the recordings of the chamber orchestra and the choir, an airiness, depth and clarity that did not exist before appeared. Additionally, the frequency response of the system in the region of 35-200 Hz was corrected by the described active filter, which is switched on at the PA input. Thanks to the correction of the frequency response and, most importantly, the phase response, the speakers began to reproduce the bass register with really high fidelity. In describing the sound of the speakers, it became possible to use such epithets as "correctness", "elasticity", "power", "emotionality". For example, when playing the sound of an incoming helicopter in the Pink Floyd album The Wall, everything in the room began to vibrate that could. This was "created" by honest 10 watts at frequencies from 40 Hz. After these improvements, the speakers took a worthy "leading" place in the home theater system (believe me, the subwoofer has become irrelevant). Attention! If the maximum output power of your PA exceeds the rated power of the low-frequency head of the speaker by three or more times, I recommend protecting the speaker from overload with a fuse for a current that can be calculated using the formula: head, Rg - head resistance to direct current. Publication: cxem.net
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