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Created on 03/05/2007 19:59.

Updated 04.17.2020 08:58.

Author: Unknown.

In connection with the multiple questions of how to calculate the enclosures for the speakers, I am posting several articles related to the calculation of the acoustic design for subwoofers. Don’t forget that acoustic design is important for woofers. And so we begin ….

Recently, a lot of questions have been heard about speakers and subwoofers. The vast majority of answers can be found on the first three pages of any book written by professionals. The material is addressed primarily to beginners, lazy;) and rural home-builders, prepared on the basis of books by I.A. Aldoschina, V.K. Joffe, partly Ephrussi, magazine publications at Wireless World, AM and (some) personal experience. Information from the Internet and FidoNet was not used.

The material in no way pretends to be complete coverage of the problem, but is an attempt to explain the basics of acoustics on the fingers.

Most often, the question sounds something like this: “found a speaker, what to do with it?”, Or “Comrade, but they say there are such subwoofers …”. Here we will consider only one option for solving this problem: According to the available dynamics, make a box with optimal parameters at HF, as far as possible. This option is very different from the task of the factory designer – to pull the lower frequency of the system to the value required by the technical specifications.

## [Q] Found on the occasion a large unmarked speaker. How do you know if you can make a subwoofer out of it?

[A] You need to measure its T / S parameters. Based on these data, make a decision on the type of HF design.

## [Q] What are T / S parameters?

[A] The minimum set of parameters for calculating the HF design proposed by Till and Small.

- F
_{s}– resonant frequency of the speaker without decoration - Q
_{ts}– full Q-factor of the speaker - V
_{as}– equivalent speaker volume.

## [Q] How to measure T / S parameters?

[A] We read the article “Measurement of Thiel-Small parameters at home”

## [Q] I now have speaker parameters, what should I do with them?

[A] When designing, each speaker is sharpened for a specific type of acoustic design. To find out for what exactly, let’s look at the quality factor.

- Q
_{ts}> 1.2 these are heads for open boxes, 2.4 is optimal - Q
_{ts}<0.8-1.0 - heads for closed boxes, optimally 0.7 - Q
_{ts}<0.6 – for phase inverters, optimum – 0.39 - Q
_{ts}<0.4 – for horns

It would be more correct to sort the heads not by the quality factor, but by the value of F_{s}/ Q_{ts}… Let me cite from memory, reluctance to calculate the formula.

- F
_{s}/ Q_{ts}> 30 (?) Screen and open case - F
_{s}/ Q_{ts}> 50 closed housing - F
_{s}/ Q_{ts}> 85 bass reflexes - F
_{s}/ Q_{ts}> 105 Bandpasses (band pass resonators)

Elasticity, meatiness, dryness and other similar characteristics of the sound emitted by a bass speaker are largely determined by the transient response of the system formed by the speaker, bass design and the environment.

To ensure that this system does not have an overshoot on the impulse response, its Q-factor should be less than 0.7 for systems with radiation on one side of the speaker (closed and bass reflexes) and 1.93 for two-way systems (design such as a screen and an open box)

## [Q] Where to read about open design?

[A] Open boxes and screens are the simplest type of decoration. Advantages: simplicity of calculation, no increase in resonant frequency (only the type of frequency response depends on the size of the screen), almost constant quality factor. Disadvantages: large size of the front panel.

Fairly competent and simple calculations of this type of design can be found in V.K. Ioffe, M. V. Lizunkov. Household acoustic systems, M., Radio and communication. 1984. Yes, and in the old Radios there are probably primitive amateur radio calculations.

## [Q] How to calculate a closed box?

[A] The closed box design comes in two types, infinite screen and compression gimbal. Getting into a particular category depends on the ratio of the flexibility of the speaker suspension and the air in the box, alpha is indicated (by the way, the first can be measured, and the second can be calculated and changed by filling).

For an infinite screen, the flex ratio is less than 3, for a compression gimbal it is more than 3-4. As a first approximation, we can assume that the heads with a high Q factor are sharpened for an infinite screen, with a smaller one for a compression suspension.

For a pre-assembled speaker, an endless-screen enclosure has a larger volume than a compression box. (Generally speaking, when there is a speaker, the optimal housing for it has an unambiguously defined volume. Errors arising in the measurement of parameters and calculations can be corrected within small limits by filling).

Closed box speakers have powerful magnets and soft suspension, unlike open drawer heads. Formula for the resonant frequency of a speaker in a volume V design

F_{with}= F_{s}* SQRT (1 + V_{as}/ V)

, and an approximate formula connecting the resonant frequencies and Q-factors of the head in the housing (index “c”) and in open space (index “s”) F_{c}/ Q_{tc}= F_{s}/ Q_{ts}

In other words, it is possible to realize the required quality factor of the speaker system in a single way, namely by choosing the volume of a closed box. Which Q factor should you choose? People who have not heard the sound of natural musical instruments usually choose speakers with a Q factor greater than 1.0.

Loudspeakers with such a Q factor (= 1.0) have the smallest uneven frequency response in the low-frequency region (and what does sound have to do with it?), Achieved at the cost of a small overshoot on the transient response. The most smooth frequency response is obtained at Q = 0.7, and a completely aperiodic impulse response at Q = 0.5. Homograms for calculations can be found in the above book.

More details and a calculator can be found in the article “Calculation of a closed box”.

## [Q] In articles about columns, words like “approximation according to Chebyshev, Butterworth”, etc. are often found. What does this have to do with speakers?

[A] The speaker system is a high-pass filter. The filter can be described by a transfer characteristic. The transfer characteristic can always be matched to a known function. In filter theory, several types of power functions are used, named after the mathematicians who were the first to suck on this or that function.

The function is determined by the order (maximum exponent, i.e. H (s) = a * S ^ 2 / (b2 * S ^ 2 + b1 * S + b0) has the second order) and a set of coefficients a and b (from these coefficients you can then go to the values of the real elements of the electric filter, or electromechanical parameters.)

Further, when it comes to approximating the transfer characteristic by the Butterworth or Chebyshev polynomial or something else, this must be understood in such a way that the combination of the properties of the speaker and the case (or capacitance and inductance in an electric filter) turned out to be such that, with the greatest accuracy, the frequency and phase characteristics can be adjusted to fit a particular polynomial.

The smoothest frequency response is obtained if it can be approximated by the Butterworth polynomial. The Chebyshev approximation is characterized by a wave-like frequency characteristic, and a greater length of the working section (according to GOST up to -14 dB) into the low-frequency region.

## [Q] What kind of approximation …

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