Bass in the car: non-standard solutions. Encyclopedia of radio electronics and electrical engineering

Encyclopedia of radio electronics and electrical engineering / Speakers

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How to expand the bandwidth of effectively reproducible frequencies in a car speaker system at minimal cost? The author, a repeated participant in car audio competitions and a tireless experimenter, offers original design solutions (with the application of calculation formulas) that will provide a noticeable improvement in the "bass" of the speaker system without a significant reduction in the useful volume of the trunk.

The main problem that arises when building a speaker system in a car is a weakened reproduction of the lower frequencies of the range. A ready-made or homemade subwoofer is the most radical solution to the "bass" problem. However, the box-shaped body takes up a lot of space in the trunk, and the built-in structures that repeat the complex curved surfaces of the car are very laborious to manufacture.

Therefore, boxless subwoofers, despite their inherent disadvantages, are still popular. The simplicity of the solution also plays an important role - in order to install a speaker (for motorists - a synonym for a dynamic head) in the rear shelf in the design of free air, no special qualifications are required. However, the method is suitable only for "real" sedans, the trunk of which is separated from the passenger compartment by a partition. Otherwise, the tightness of this acoustic design is very conditional, and the reproduction of low frequencies deteriorates. In addition, the size of the shelf under the rear window limits the maximum size of dynamic heads, so 6,5-8" diameter round heads or 6x9 (7x10)" elliptical heads are the limit for most common vehicles.

Hatchbacks do not have this problem; a fifteen-inch subwoofer head can easily be placed in the rear shelf there. But it is not so easy to solve the problem. A flimsy rear shelf is not so bad, the real trouble is that it is extremely difficult to isolate the trunk volume from the passenger compartment. As a result, there are more problems than gain from such a solution: it is unrealistic to seal the joints of the shelf with the sides of the luggage compartment and the back of the rear seat. The acoustic design in this case is no longer a "conditionally closed" box, but an acoustic screen. As a result, leakage losses "eat up" all the advantages of a large diffuser. Increasing the input power or correcting the frequency response will not save the situation.

Fortunately, losses are significant only at high input power at frequencies below 50 Hz. They decrease with an increase in the volume of the trunk (the degree of change in pressure decreases). Losses can be further reduced by using speakers with a small drive volume (smaller cone area and small stroke). However, their efficiency is low, so this path is of no interest.

The problem can be solved by changing the type of acoustic design. Since in hatchbacks the rear shelf for installing speakers still needs to be at least strengthened, and as a maximum - made anew, then a slight complication of its design is not such a big drawback. Further, two options for the acoustic design of low-frequency heads in a car are proposed, which have been repeatedly tested in practice [1,2].

Strip loudspeaker

From the point of view of maximum efficiency, it is most advantageous to use a bandpass loudspeaker (bandpass). First, this type of acoustic design does not reproduce out-of-band signals. Therefore, the use of electrical filters in the signal path that form the frequency response of the subwoofer is no longer strictly mandatory. Secondly, the efficiency of a bandpass loudspeaker is much higher than that of other types of acoustic design, which will allow the use of a relatively low-power amplifier. Together, these circumstances make it possible for the subwoofer to work directly from the head unit (radio). This is especially attractive for those who do not want to install an additional amplifier.

For our purposes, a fourth-order system is especially convenient, consisting of two chambers - closed and resonant, in the partition between which a dynamic head is installed. We will use the trunk as a closed chamber, and turn the shelf into a resonant chamber equipped with a phase inverter (Fig. 1).

The opposite is also possible, but it is not easy to implement, since possible leaks and in particular the variable volume of the trunk (it depends on the filling) affect the tuning of the resonant chamber to a much greater extent than the setting of a closed one. Yes, and it is almost impossible to find out the exact value of the trunk volume necessary for calculations - not a single automaker gives it with an accuracy of up to a liter. Finally, the efficiency of such a variant according to the simulation results is noticeably lower.

Bandpass allows you to flexibly control the frequency response of the speaker system. The main characteristics are determined by the resonant chamber, and the volume of the closed chamber can be considered as a tool for adjusting the resonant frequency and quality factor of the head. However, in our case, certain restrictions come into force: some design parameters are "objective reality", and they cannot be changed arbitrarily. So, the volume of the trunk, in this version playing the role of a closed acoustic chamber, is usually at least 300 liters, and it is difficult to vary it. Fortunately, with the appropriate choice of head parameters, the effect of the volume of the closed chamber on the frequency response can be minimized. Simulation of various options by the JBL Speaker Shop program made it possible to determine the main ratios of the parameters (Fig. 2):

In the proposed design, the volume of the resonant chamber and the dimensions of the phase inverter port are quite acceptable. An increase in the volume of the resonant chamber relative to the equivalent volume narrows the bandwidth, and a decrease in the volume of the resonant chamber expands the band, but the frequency response becomes double-humped. Taking into account the real volumes of the trunk and the available volumes of the resonant chamber, dynamic heads with the following parameters are best suited for such a design: total quality factor Qts = 0,7 ... 1,0; equivalent volume Vas = 10...60 l; natural resonance frequency Fb = 40...60 Hz.

These conditions are met not only by "serious" speakers, but also by most "pancakes". The simulation results of the AU "in the same trunk" are shown in fig. 3.

It can be seen here that the efficiency of a bandpass system with a dynamic head having the specified parameters in the frequency range below 50 Hz is noticeably higher than that of a closed case (at least theoretically). The cutoff frequency of a closed case at a level of -3 dB is only 42 Hz, and for a bandpass loudspeaker it is 27 Hz. At the same time, in the region of the lowest frequencies (15 ... 30 Hz), the bandpass is inferior to the phase inverter, made in the same volume of the case - while the frequency response unevenness in the passband of the phase inverter is higher. True, in the case of a phase inverter of such a volume, it will be very difficult to use the trunk for its intended purpose ...

The practical implementation of the proposed design is not difficult. Just look at a typical fortified shelf (Fig. 4).

To turn into a bandpass, it lacks only a sealed resonant chamber and a phase inverter. And despite the seemingly impressive volume of the resonant chamber, it is visually not large: for the volume obtained in the calculation of 45 liters with a panel size of 1,1x.55 m, the internal height of the chamber is only 7,5 cm! Taking into account the thickness of the walls, the total height is no more than 10 cm. And such a loss in the height of the trunk can be transferred painlessly.

Most modeling programs also calculate the phase inverter port, usually only with a circular cross section. To calculate the phase inverter without using specialized programs, you can use the well-known formula [3]

where Fb - resonance frequency, Hz; V, - chamber volume, cm3; S, - port area, cm2; l - tunnel length (panel thickness), cm; k - aspect ratio of the hole

From the position of manufacturing technology, it is most convenient to make a phase inverter port in the form of a hole in the panel, without using a pipe. Since no mathematical transformations bring the formula to a form convenient for calculating hole sizes, it is easier to use the method of successive approximations. In the first approximation, the cross section of the hole is chosen within 50 ... 70% of the diffuser area (the total area of ​​the diffusers, if there are several speakers). Then, the tuning frequency of the phase inverter is determined for a given panel thickness and the volume of the resonant chamber. Then it remains only a few iterations to refine the area of ​​the hole and drive the result into a "fork".

For the final adjustment of the tuning frequency (in the direction of increase), it is convenient to use the hole shape coefficient k: its value to the power of 0,12 grows very slowly, the elongation of the hole does not exceed 1,4 ... 1,6 even for very narrow and long slots ( 1:20...1:50). If, as a result of all calculations, the hole area still turns out to be less than 20% of the diffuser area, it is worth increasing the depth of the port, i.e. go to a short pipe or a long slot with a "side". In this case, it must be remembered that the distance from the inner cut of the pipe to the wall of the resonant chamber must be at least its "characteristic" size, equal to the square root of the area (the same root of S in the denominator). If this condition is not met, the "surplus" of the pipe will have to be taken out of the body or the geometry of the resonant chamber should be revised. Perhaps it is worth increasing the volume of the resonant chamber and completely repeating the calculations, starting with the simulation.

Let me explain with an example. For the speaker, based on the above calculation, a 25 cm diameter head with a cone area of ​​approximately 380 cm2 was used. The port must be set to 50 Hz. For a 45 l chamber with a panel thickness of 12 mm, a 300 cm2 hole gives a tuning of 104 Hz, with an area of ​​100 cm2 the tuning frequency is reduced to 77 Hz. Further reduction of the hole area is undesirable, so the depth of the port will have to be increased. With the same area of ​​100 cm2 and a depth of 48 mm, the tuning frequency is even lower - 67 Hz. Reluctantly, we reduce the hole area to 74 cm2 (pipe with an outer diameter of 100 mm, an inner diameter of 97 mm), and increase the depth to 110 mm. The hole area is 19% of the cone area, the tuning frequency is exactly 50 Hz.

The result is achieved, but not in the best way. Since the internal height of the body is 7,5 cm and the characteristic size of the tube is 8,6 cm, the entire tube must fit outside the resonant chamber. The advantage of the considered option of acoustic design is that the characteristics of the speakers are practically independent of the loading of the luggage compartment (up to about half of its volume). However, it is not possible to implement a phase inverter without a pipe with all types of heads, which is a definite disadvantage. And the pipe sticking out of the rear shelf is downright avant-garde aesthetics. However, art (including music) requires sacrifice...

Acoustic load in speakers (flat resonator)

And if you approach the problem from the other side - take out the resonant chamber on top of the shelf? Naturally, dynamic heads must meet the requirements already given earlier: full quality factor in the range of 0,7 ... 1, moderately rigid suspension, low frequency of the main resonance.

The simplest version of the resonant chamber is a flat acoustic screen placed in close proximity to the diffuser. The mass of air under the screen will behave in the same way as in the phase inverter pipe - it will oscillate. And the role of the port will be played by a slot around the perimeter of the screen. In the first approximation, this design can be considered a variant of the Helmholtz resonator, and the same formula (1) can be used for the calculation, but in a transformed form - for the "without pipe" variant:

where Fb - resonance frequency, Hz; Vc - chamber volume, cm; Sb - port area, cm2; k - hole shape factor (k = 1-1,25).

However, for calculating the screen, the formula in this form is extremely inconvenient, since all the quantities on the right side are interconnected. In addition, the degree and even the direction of the influence of certain parameters is not clear. Therefore, convenient formulas for calculating the screen were derived (formula derivation and analysis at the end of the article).

For a preliminary calculation of the screen area, we apply the following formula:

where S is the screen area, cm2.

As can be seen, only the screen area appears in formula (3). Where did the rest of the settings go? Careful analysis showed that the tuning frequency is weakly dependent on the shape of the screen and the height of its installation (tuning within 10% of the average value). Therefore, for a preliminary calculation, it is sufficient to take into account the average values ​​of these parameters by the value of the coefficient in the numerator. And for the final calculation, apply the exact formula (4), which is given below.

It is easy to calculate that for frequencies below 120 Hz, the screen area above the shelf exceeds 1,2 m2, and further reduction in the tuning frequency is limited by the size of the vehicle...

The exact tuning frequency is determined by the formula

where h - screen installation height, cm; j - coefficient of the screen shape, equal to: 2,03 - for a round screen; 2,17 - for a square screen; 2,25 - for a rectangular screen with an extension of 2:1.

For experimental verification, a screen with dimensions of 0,99x0,46 m was installed on the reinforced rear shelf of the IZH-2126 "Oda" car. The design tuning frequency for calculation by formula (3) was chosen as 200 Hz, refined by formula (4) - 215 Hz. In the process of adjustment and listening, it turned out that the optimal screen installation height lies within 25 ... 40 mm. This measure made it possible to eliminate the "failure" of the frequency response in the mid-bass region and to smooth out the resonant peak characteristic of the applied heads.

Sketches of the shelf parts are not given, because for cars of other brands, the dimensions will be different. The screen is made of plywood with a thickness of 9 mm; to increase the rigidity, an duralumin corner 20x20 mm is installed on the bottom side of the screen. The screen is attached to the shelf with six long bolts with flange nuts, which allows you to adjust the height of the installation (Fig. 5).

It is clear that such a design cannot replace a subwoofer, but it can improve bass reproduction below 200 Hz even from the most inexpensive speakers. That is why the author's idea was picked up, and in a number of Russian cities, car services even launched small-scale production of shielded acoustic shelves for common cars. In addition to improving low-frequency performance, it is also important for consumers that the speakers in such a shelf are not visible and the car does not attract the attention of intruders. And you can put something on top without blocking the diffuser.

Explanations and comments with the derivation of formulas (3) and (4)

For phase inverters of a relatively large area (when the characteristic size of the port is much greater than its depth) in formula (1), the term I can be taken equal to zero:

where Fb - resonance frequency, Hz; Vc - chamber volume, cm3; Sb - port area, cm2; k is the aspect ratio of the hole.

Usually in the literature this formula is given in a slightly different form (2), where k (already without a degree!) Is called the shape factor of the hole and its boundary values ​​are given: 1 for round and square holes and 1,25 for a long slot. The essence of the calculation does not change from this; indication of boundary values ​​is convenient for practical purposes, but hides the physical meaning of this coefficient. For the formula in the traditional representation, the case of a flat screen is not considered at all; accordingly, the value of the coefficient for such a configuration is not indicated in the reference books, which complicates the analysis. In the original publication [2], this circumstance contributed to an error and false conclusions (which, in fact, none of the readers delved into - practice was more convincing than theory).

For the convenience of further analysis, we introduce the "ideal" coefficient of the screen shape i:

where P is the perimeter of the screen: S is the area of ​​the screen.

For a circle, it is minimal and equal to 3,54, for a square - 4, for a rectangle with an aspect ratio of 2:1 - 4,24. Further elongation of the screen does not make sense even for layout reasons.

The square root of the screen area is nothing more than its "characteristic" size:

The port in this acoustic design is not a hole, it is the boundary between the volume of air under the screen and the surrounding space. Therefore, the area of ​​this "ring" port is the product of the perimeter of the screen and the height of its installation. At the same time, the volume under the screen is the product of its area and the installation height. Let us express the port area in terms of the screen perimeter and its installation height h, and the chamber volume in terms of the screen area and the same installation height. The aspect ratio of a hole is the ratio of the perimeter to the height. Passing to the "effective" size and coefficient, we get

Substituting expression (6) for the "characteristic" size, we finally obtain

Influence of screen shape and size

Depending on the shape of the screen, the numerator of formula (7) will take the following values: round screen - 2,03; square screen - 2,17; rectangular screen with elongation - 2:1 - 2.25.

Thus, with the same area, a round screen will provide the minimum tuning frequency. In general, the influence of the screen shape is insignificant - when moving from a circle to a square of the same area, the tuning frequency increases by only 7%.

The influence of the installation height is also insignificant - when it changes from 3 to 15 cm, the tuning frequency decreases by 7%. A further increase in the height of the screen installation is pointless.

Screen area proves to be the most effective adjustment mechanism

Substituting the average installation height and form factor, we get a convenient formula for preliminary calculation

where Fb - resonance frequency, Hz; S - screen area, cm2.

Literature

1. Shikhatov A. Bandpass in the regiment. - Master 12 volts, 2002, No. 41.
2. Shikhatov A. Dynamics and regiment. - Master 12 volts, 2003, No. 48.
3. Reference book for a radio amateur designer. Ed. M. M. Chistyakova. MRB, vol. 1195. - M.: Radio and communication, 1993.

Author: A. Shikhatov, Moscow

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