29.06.2020

Parameters of the small subwoofer style. Thiel-Small parameters: let's use them. Magazine "Avtozvuk". Fs - speaker resonant frequency

Fundamental Mechanical Parameters

Fs(Hz) - natural resonance frequency of the loudspeaker head in open space. At this point its impedance is maximum.

Fc(Hz) - resonance frequency of the speaker system for a closed enclosure.

Facebook(Hz) - bass reflex resonance frequency.

F3(Hz) - cutoff frequency at which the head output decreases by 3 dB.

Vas(cub.m) - equivalent volume. This is a closed volume of air excited by the head, which has a flexibility equal to the flexibility Cms of the movable system of the head.

D(m) is the effective diameter of the diffuser.

Sd(sq.m) - effective diffuser area (approximately 50-60% of the design area).

Xmax(m) - maximum diffuser displacement.

Vd(cub.m) - excited volume (product of Sd by Xmax).

Re(Ohm) - head winding resistance DC.

Rg(Ohm) - output impedance of the amplifier, taking into account the influence of connecting wires and filters.

Qms(dimensionless value) - mechanical quality factor of the loudspeaker head at the resonant frequency (Fs), takes into account mechanical losses.

Qes(dimensionless quantity) - the electrical quality factor of the loudspeaker head at the resonant frequency (Fs), takes into account electrical losses.

Qts(dimensionless value) - the total quality factor of the loudspeaker head at the resonant frequency (Fs), takes into account all losses.

Qmc(dimensionless value) - mechanical quality factor of the acoustic system at the resonant frequency (Fs), takes into account mechanical losses.

Qec(dimensionless quantity) - the electrical quality factor of the acoustic system at the resonant frequency (Fs), takes into account electrical losses.

Qtc(dimensionless value) - the total quality factor of the acoustic system at the resonant frequency (Fs), takes into account all losses.

Ql(dimensionless quantity) - the quality factor of the acoustic system at frequency (Fb), taking into account leakage losses.

Qa(dimensionless quantity) - the quality factor of the acoustic system at frequency (Fb), taking into account absorption losses.

Qp(dimensionless quantity) - the quality factor of the acoustic system at frequency (Fb), taking into account other losses.

n0(dimensionless quantity, sometimes %) - relative efficiency (efficiency) of the system.

Cms(m/N) - flexibility of the moving system of the loudspeaker head (displacement under the influence of mechanical load).

mms(kg) - effective mass of the moving system (includes the mass of the diffuser and the air oscillating with it).

Rms(kg/s) - active mechanical resistance of the head.

B(T) - induction in the gap.

l(m) - length of the voice coil conductor.

Bl(m/N) - magnetic induction coefficient.

Pa- acoustic power.

Pe- electric power.

c=342 m/s- speed of sound in air under normal conditions.

p=1.18 kg/m^3- air density under normal conditions.

Le- coil inductance.

B.L.– value of magnetic flux density multiplied by the length of the coil.

Spl– sound pressure level in dB.

Thiel–Small parameters: three acoustic maps

We will talk about what is really important to know about acoustics. Namely, about the famous Thiel-Smol parameters.

Who had the honor of bearing the names of Thiel and Small's parameters? Let's remember this too. First in the bunch is Albert Neville Thiel(in the original A. Neville Thiele, “A” is almost never deciphered). Both by age and bibliography. Thiel is now 89 years old, and when he was 40, he published a landmark paper that pioneered the ability to calculate loudspeaker performance using a single set of parameters in a convenient and repeatable manner.

There, in the work of 1961, it was said, in particular: “ Area Loudspeaker Characteristics low frequencies can be adequately described by three parameters: the resonant frequency, the volume of air equivalent to the acoustic flexibility of the loudspeaker, and the ratio of electrical resistance to resistance to motion at the resonant frequency. The same parameters are used to determine electroacoustic efficiency. I encourage loudspeaker manufacturers to publish these parameters as part of the basic information about their products».

Neville Thiel's request was heard by the industry only a decade later, at which time Thiel was already working with Richard Small, a native of California. Richard Small is spelled in Californian, but for some reason the respected doctor prefers the German pronunciation of his own name. Small turns 75 this year, which, by the way, is a more important anniversary than most. In the early seventies, Thiel and Small finally finalized their proposed approach to calculating loudspeakers.

Neville Thiel is now a professor emeritus at a university in his home country of Australia, and Dr. Small's last professional position that we were able to track was chief engineer of the Harman-Becker automotive audio department. Well, of course, both are part of the leadership international society acoustic engineers (Audio Engineering Society). In general, both are alive and well.

CARD ONE, MEASURED IN HERTZ

So: Thiel - Small parameter No. 1 - natural resonant frequency of the speaker. Always indicated Fs, regardless of the language of publication. The physical meaning is extremely simple: since the speaker is an oscillatory system, it means there must be a frequency at which the diffuser will oscillate when left to its own devices. Like a bell after being struck or a string after being plucked. This means that the speaker is absolutely “naked”, not installed in any housing, as if hanging in space. This is important because we are interested in the parameters of the speaker itself, and not of what surrounds it.

The frequency range around the resonant one, two octaves up, two octaves down - this is the area where the Thiel-Small parameters operate. For subwoofer heads not yet installed in the housing, Fs can range from 20 to 50 Hz, for midbass speakers from 50 (bass “sixes”) to 100 - 120 (“fours”). For diffuser mid-frequencies - 100 - 200 Hz, for domes - 400 - 800, for tweeters - 1000 - 2000 Hz (there are exceptions, very rare).

How is the natural resonant frequency of a speaker determined? No, as is most often defined - clearly, read in the accompanying documentation or in the test report. Well, how was she initially recognized? It would be easier with a bell: hit it with something and measure the frequency of the buzz produced. The speaker will not hum explicitly at any frequency. That is, he wants to, but the damping of diffuser vibrations inherent in his design does not allow him to do so. In this sense, the speaker is very similar to a car suspension, and I have used this analogy more than once and will continue to do so. What happens if you rock a car with empty shock absorbers? It will swing at least a few times at its own resonant frequency (where there is a spring, there will be a frequency). Shock absorbers that are only partially dead will stop the oscillations after one or two periods, while those that are in good working order will stop after the first swing. In dynamics, the shock absorber is more important than the spring, and here there are even two of them.

The first, weaker one, works due to the fact that energy is lost in the suspension. It is no coincidence that the corrugation is made from special types of rubber; a ball made of such material will hardly bounce off the floor; a special impregnation with high internal friction is also chosen for the centering washer. This is like a mechanical brake of diffuser vibrations. The second, much more powerful, is electric.

Here's how it works. The speaker's voice coil is its motor. An alternating current flows in it from the amplifier, and the coil, located in a magnetic field, begins to move with the frequency of the supplied signal, moving, of course, the entire moving system, then it is here. But a coil moving in a magnetic field is a generator. Which will generate more electricity the more the coil moves. And when the frequency begins to approach the resonant one, at which the diffuser “wants” to oscillate, the amplitude of the oscillations will increase, and the voltage produced by the voice coil will increase. Reaching a maximum exactly at the resonant frequency. What does this have to do with braking? None yet. But imagine that the coil leads are connected to each other. Now a current will flow through it and a force will arise, which, according to Lenz’s school rule, will impede the movement that generated it. But the voice coil in real life shorted to the amplifier output impedance, close to zero. It turns out like an electric brake that adapts to the situation: the more the diffuser tries to move back and forth, the more the counter current in the voice coil prevents this. The bell has no brakes, except for the damping of vibrations in its walls, and in bronze - what damping...

SECOND MAP, NOT MEASURED IN ANYTHING

The brake power of the speaker is numerically expressed in the second Thiel-Small parameter. This - full speaker quality factor, denoted Qts. Expressed numerically, but not literally. In the sense that the more powerful the brakes, the smaller the value Qts. Hence the name “quality factor” in Russian (or quality factor in English, from which the designation of this quantity originated), which is, as it were, an assessment of the quality of the oscillatory system. Physically, the quality factor is the ratio of elastic forces in a system to viscous forces, otherwise - to friction forces. Elastic forces store energy in the system, alternately transferring energy from potential (a compressed or stretched spring or speaker suspension) to kinetic (the energy of a moving diffuser). Viscous ones strive to turn the energy of any movement into heat and irrevocably dissipate. A high quality factor (and for the same bell it will be measured in tens of thousands) means that there are much more elastic forces than frictional forces (viscous, these are the same thing). This also means that for each oscillation only a small part of the energy stored in the system will be converted into heat. Therefore, by the way, quality factor is the only value in the three Thiel-Small parameters that does not have a dimension; it is the ratio of one force to another. How does a bell dissipate energy? Through internal friction in bronze, mainly slowly. How does a speaker do this, whose quality factor is much lower, and therefore the rate of energy loss is much higher? In two ways, depending on the number of “brakes”. Some is dissipated through internal losses in elastic elements suspension, and this share of losses can be estimated by a separate value of the quality factor, it is called mechanical, denoted Qms. The second, larger part is dissipated in the form of heat from the current passing through the voice coil. The current produced by her. This is the electrical quality factor Qes. The total effect of the brakes would be determined very easily if it were not the values of the quality factor, but, on the contrary, the values of losses that were used. We would just fold them. And since we are dealing with reciprocals of losses, we will have to add the reciprocals, so it turns out that 1/Qts = 1/Qms + 1/Qes.

Typical values of quality factor: mechanical - from 5 to 10. Electrical - from 0.2 to 1. Since inverse quantities are involved, it turns out that we sum up the mechanical contribution to losses of the order of 0.1 - 0.2 with the electrical contribution, which is from 1 to 5. It is clear that the result will be determined mainly by the electrical quality factor, that is, the main brake of the speaker is electric.

So how do you snatch names from the speaker? three cards"? Well, at least the first two, we'll get to the third. The same voice coil, the fiery speaker motor, comes to the rescue. After all, we have already realized: a flame motor also works as a flame generator. And in this capacity, it seems to be sneaking about the amplitude of vibrations of the diffuser. The greater the voltage appears on the voice coil as a result of its oscillations together with the diffuser, the greater the range of oscillations, which means the closer we are to the resonant frequency.

How to measure this voltage, given that a signal from the amplifier is connected to the voice coil? That is, how to separate what is supplied to the motor from what is generated by the generator, is it on the same terminals? You don’t need to divide, you need to measure the resulting amount.

This is why they do this. The speaker is connected to an amplifier with the highest possible output impedance; in real life, this means: a resistor with a value of much, one hundred, at least, times the nominal resistance of the speaker is connected in series with the speaker. Let's say 1000 ohms. Now, when the speaker is operating, the voice coil will produce a back-EMF, sort of like for an electric brake to operate, but braking will not occur: the coil terminals are connected to each other through a very high resistance, the current is negligible, the brake is useless. But the voltage, according to Lenz’s rule, is opposite in polarity to the supplied one (“generating movement”), will be in antiphase with it, and if at this moment you measure the apparent resistance of the voice coil, it will seem that it is very large. In fact, in this case, the back-EMF does not allow the current from the amplifier to flow unhindered through the coil, the device interprets this as increased resistance, but what else?

We will discuss exactly how the required values are determined from the impedance curve another time, when we talk about methods for measuring parameters. Now we will assume that someone (the speaker manufacturer or the associates of your humble servant) did this for you. But I will note this. There are two misconceptions associated with attempts to expressly analyze the Thiel-Small parameters based on the shape of the impedance curve. The first is completely bogus, we will now dispel it without a trace. This is when they look at the impedance curve with a huge hump at resonance and exclaim: “Wow, good quality!” Kind of high. And looking at the small bump on the curve, they conclude: since the impedance peak is smoothed out so much, it means that the speaker has high damping, that is, a low quality factor.

So here it is: in fact simple version it's exactly the opposite. What does a high impedance peak at resonance frequency mean? That the voice coil produces a lot of back-EMF, designed to electrically brake the oscillations of the cone. Only with this connection, through a large resistance, the current necessary for the operation of the brake does not flow. And when such a speaker is turned on not for measurements, but normally, directly from the amplifier, the braking current will flow, be healthy, the coil will become a powerful obstacle to the excessive oscillations of the diffuser at its favorite frequency.

All other things being equal, you can roughly estimate the quality factor from the curve, and remembering: the height of the impedance peak characterizes the potential of the speaker's electric brake, therefore, the higher it is, the LOWER the quality factor. Will such an assessment be exhaustive? Not exactly, as was said, she will remain rude. After all, in the impedance curve, as already mentioned, information about Qes, and about Qms, which can be dug (manually or using a computer program) by analyzing not only the height, but also the “shoulder width” of the resonant hump. On this occasion, we have carried out several computational experiments here; if you are interested, take a look.

And how does the quality factor affect the shape of the speaker’s frequency response? This is what interests us, isn’t it? How it affects - it has a decisive impact. The lower the quality factor, that is, the more powerful the internal brakes of the speaker at the resonant frequency, the lower and more smoothly the curve will pass near the resonance, characterizing the sound pressure created by the speaker. The minimum unevenness in this frequency band will be at Qts, equal to 0.707, which is commonly called the Butterworth characteristic. At high Q values, the sound pressure curve will begin to “hump” near resonance, it’s clear why: the brakes are weak.

Is there a “good” or a “bad” total quality factor? By itself, no, because when the speaker is installed in an acoustic design, which we will now consider only a closed box, both its resonance frequency and the overall quality factor will become different. Why? Because both depend on the elasticity of the speaker suspension. The resonant frequency depends only on the mass of the moving system and the rigidity of the suspension. With increasing hardness Fs grows, with increasing mass it falls. When the speaker is installed in a closed box, the air in it, which has elasticity, begins to act as an additional spring in the suspension, the overall rigidity increases, Fs growing. The total quality factor also increases, since it is the ratio of elastic forces to braking forces. The brake capabilities of the speaker will not change from installing it to a certain volume (why would it?), but the total elasticity will increase, the quality factor will inevitably increase. And it will never become lower than the “naked” dynamics. Never, that's the bottom limit. How much will all this increase? And this depends on how rigid the speaker’s own suspension is. Look: the same value of Fs can be obtained with a light diffuser on a soft suspension or with a heavy one on a hard suspension; mass and stiffness act in opposite directions, and the result may turn out to be numerically equal. Now if we place a speaker with a rigid suspension in some volume (which has the elasticity required for this volume), then it will not notice a slight increase in the total rigidity, the magnitude Fs And Qts won't change much. Let's put a speaker with a soft suspension there, in comparison with the rigidity of which the “air spring” will already be significant, and we will see that the total rigidity has changed significantly, which means Fs And Qts, initially the same as that of the first speaker, will change significantly.

In the dark “pre-Tile” times, to calculate new values resonance frequencies And quality factor(to avoid confusion with the parameters of the “naked” speaker, they are designated as Fc And Qtc) it was necessary to know (or measure) directly the elasticity of the suspension, in millimeters per newton of applied force, to know the mass of the moving system, and then play tricks with calculation programs. Thiel proposed the concept of “equivalent volume,” that is, a volume of air in a closed box whose elasticity is equal to the elasticity of the speaker suspension. This quantity, denoted Vas, and there is a third magic card.

CARD THIRD, VOLUMERIAN

How to measure Vas- the story is separate, there are funny twists. For practice, it is important to understand two things. First: the extremely Lokhovian delusion (alas, which nevertheless occurs) that given in accompanying documents to speaker value Vas- this is the volume in which the speaker should be placed. And this is just a characteristic of the speaker, depending only on two quantities: the rigidity of the suspension and the diameter of the diffuser. If you place a speaker in a box with a volume equal to Vas, the resonant frequency and total quality factor will increase by 1.4 times (this is Square root of two). If in a volume equal to half Vas- 1.7 times (root of three). If you make a box with a volume of one third of Vas, everything else will double (the root of four, the logic should already be clear without formulas).

As a result, indeed, the smaller, other things being equal, the value Vas the speaker, the more compact design you can count on, maintaining the planned indicators for Fc And Qtc. Compactness, however, does not come for free. There is no such thing as free in acoustics. Low value Vas at the same resonant frequency, the dynamics are the result of a combination of a rigid suspension with a heavy moving system. And the sensitivity most decisively depends on the mass of the “movement”. Therefore, all subwoofer heads, distinguished by the ability to work in compact closed housings, are also characterized by low sensitivity compared to colleagues with lightweight diffusers, but higher values Vas. So there are no good or bad Vas values either, everything has its own price.

TO HANG OR NOT TO HANG?

Figurative definition of measurement conditions Fs as the resonant frequency of a speaker hanging in the air, gave rise to the misconception that this is how this frequency should be measured, and enthusiasts really strove to hang speakers on wires and ropes. In competent laboratories, speakers are clamped in a vice during measurements, and not suspended from a chandelier.

The results of a computational experiment that will help those wishing to understand how the values of electrical and mechanical quality factor are expressed in impedance curves. We took the full set of electromechanical parameters of a real-life speaker, and then began to change some of them. First, the mechanical quality, as if the material of the corrugation and the centering washer had been replaced. Then - electric, for this it was necessary to change the characteristics of the drive and the moving system. Here's what happened:

Qts received by change Qes. The top four curves are exactly the same in shape as when we changed Qms, their shape is determined by the values Qts, but they remained the same. Lower, red curves obtained for Qts more than 0.5, of course, others, and a hump begins to grow on them, due to the increased quality factor.

But now pay attention: the point is not only that at high Qts a hump appears on the characteristic, and the sensitivity of the speaker decreases at frequencies above the resonant one. The explanation is simple: all other things being equal Qes can increase only with increasing mass of the moving system or with decreasing magnet power. Both lead to a decrease in sensitivity at mid frequencies. So the hump at the resonant frequency is, rather, a consequence of the dip at frequencies above the resonant one. There is nothing free in acoustics...

CONTRIBUTION OF THE JUNIOR PARTNER

By the way: the founder of the method A.N. Til intended to take into account only the electrical quality factor in the calculations, believing (fairly for his time) that the share of mechanical losses was negligible compared to the losses caused by the operation of the “electric brake” of the speaker. The junior partner’s contribution, however, was not the only one, was in accounting Qms, now this has become important: modern drivers use materials with increased losses that were not available in the early 60s, and we have come across speakers where the value Qms was only 2 - 3, with an electric one under one. In such cases, it would be a mistake not to take mechanical losses into account. And this became especially important with the introduction of ferrofluid cooling in RF heads, where, due to the damping effect of the liquid, the share Qms in full quality factor becomes decisive, and the impedance peak at the resonance frequency becomes almost invisible, as in the first graph of our computational experiment.

THREE CARDS DISCOVERED BY THILE AND SMALL

1. Fs- the frequency of the main resonance of the speaker without any housing. Characterizes only the speaker itself, and not the finished speaker system based on it. When installed in any volume it can only increase.

2.Qts- total quality factor of the speaker, a dimensionless quantity characterizing the relative losses in the dynamics. The lower it is, the more the radiation resonance is suppressed and the higher the resistance peak on the impedance curve. Increases when installed in a closed box.

3. Vas- equivalent speaker volume. Equal to the volume of air with the same rigidity as the suspension. The stiffer the suspension, the less Vas. At the same hardness Vas increases with increasing diffuser area.

TWO HALVES THAT CONSTITUTE CARD No. 2

1. Qes- the electrical component of the total quality factor characterizes the power of the electric brake, which prevents the diffuser from swinging near the resonant frequency. Typically, the more powerful the magnetic system, the stronger the “brake” and the smaller the numerical value Qes

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

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

[Q] I found a large speaker with no markings on occasion. 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 low frequency design.

[Q] What are T/S parameters?

[A] The minimum set of parameters for calculating low-frequency design, proposed by Till and Small.

Fs - resonant frequency of the speaker without design
Qts - total quality factor of the speaker
Vas is the equivalent volume of the speaker.

[Q] How to measure T/S parameters?

[A] To do this, you need to assemble a circuit from a generator, a voltmeter, a resistor and the speaker under study. The speaker is connected to the output of the generator with an output voltage of several volts through a resistor with a resistance of about 1 kOhm.

1. We remove V(F) = frequency response of the speaker resistance in the resonance area. The speaker must be in free space (away from reflective surfaces) during this measurement. We find the resistance of the speaker on direct current (useful), write down the resonance frequency in the air Fs (this is the frequency at which the voltmeter readings are maximum:), the voltmeter readings Uo at the minimum frequency (well, for example, 10 Hz) and Um at the resonance frequency Fs.

2. Find the frequencies F1 and F2 at which the V(F) curve intersects with the level V=SQRT(Vo*Vm).

3. Find Qts=SQRT(F1*F2)*SQRT(Uo/Um) / (F2-F1) This is the total quality factor of the speaker, one might say, the most important value.

4. To find Vas, you need to take a small closed box of volume Vc, with a hole slightly smaller than the diameter of the diffuser. Place the speaker firmly against the hole and repeat the measurements. These measurements will require the resonant frequency of the speaker in the Fc enclosure. We find Vas=Vc*((Fc/Fs)^2-1).

This technique was written in Audio Store 4 in 1999. I haven’t tested it.. There are others where the mechanical parameters of the head, mass, flexibility, etc. are measured.

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

[A] Each speaker is designed for a specific type of acoustic design. To find out what exactly it is for, let's look at the quality factor.

Qts > 1.2 are heads for open boxes, optimally 2.4
Qts< 0.8-1.0 - головки для закрытых ящиков, оптимально 0,7
Qts<0.6 - для фазоинверторов, оптимум - 0,39
Qts<0.4 - для рупоров

It would be more correct to sort heads not by quality factor, but by Fs/Qts value. I’ll quote from memory, I don’t feel like calculating the formulas.

Fs/Qts >30 (?) screen and open case
Fs/Qts >50 closed housing
Fs/Qts >85 bass reflexes
Fs/Qts >105 Bandpasses (bandpass 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, low-frequency design and environment. In order for this system to avoid overshoot in the impulse response, its quality factor must be less than 0.7 for systems with radiation from one side of the speaker (closed and bass reflex) and 1.93 for two-way systems (screen and open box design)

[A] Open drawers and screens - the simplest type registration Advantages: ease 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 front panel size. Quite competent and simple calculations for this type of design can be found in VC. Ioffe, M.V. Lizunkov. Household acoustic systems, M., Radio and communications. 1984. Yes, and in old Radios there are probably primitive amateur radio calculations.

[A] The closed box design comes in two types, infinity screen and compression gimbal. Getting into one category or another depends on the ratio of the flexibility of the speaker suspension and the air in the box, designated alpha (by the way, the first can be measured, and the second can be calculated and changed using filling). For an infinite screen, the flexibility ratio is less than 3, for a compression suspension it is more than 3-4. As a first approximation, we can assume that the heads are sharpened with a higher quality factor for an infinite screen, and with a lower quality factor, for a compression suspension. For a pre-installed speaker, a closed enclosure like an infinity screen has a larger volume than a compression box. (Generally speaking, when there is a speaker, the optimal housing for it has a uniquely defined volume. Errors that arise during parameter measurements and calculations can be corrected within small limits by filling). Closed box speakers have powerful magnets and soft surrounds, unlike open box speakers. Formula for the resonant frequency of a speaker in volume V designFс=Fs*SQRT(1+Vas/V), and an approximate formula connecting the resonant frequencies and quality factors of the head in the housing (index “c”) and in open space (index “s”)Fc/Qtc=Fs/Qts

In other words, it is possible to realize the required quality factor of the acoustic system in the only way, namely by choosing the volume of a closed box. Which quality factor should I choose? People who have not heard the sound of natural musical instruments, usually choose speakers with a quality factor of more than 1.0. Speakers with such a quality factor (=1.0) have the least uneven frequency response in the low-frequency region (what does sound have to do with it?), achieved at the cost of a small overshoot in the transient response. The smoothest frequency response is obtained at Q=0.7, and a completely aperiodic impulse response at Q=0.5. Nomograms for calculations can be taken from the above book.

[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. A filter can be described by a transfer characteristic. The transfer characteristic can always be adjusted to a known function. In filter theory, several types of power functions are used, named after the mathematicians who were the first to understand 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 a second order) and a set of coefficients a and b (from these coefficients you can then move on to the values of real elements of the electric filter, or electromechanical parameters.) Further, when it comes to approximating the transfer characteristic with a 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 housing (or capacitances and inductances in an electrical filter) is such that the frequency and phase characteristics can be adjusted to one or another polynomial with the greatest accuracy. The smoothest frequency response is obtained if it can be approximated by a Butterworth polynomial. The Chebyshev approximation is characterized by a wave-like frequency response, and greater length working area (according to GOST up to -14 dB) in the region of lower frequencies.

[Q] What type of approximation should I choose for the bass reflex?

[A] So, before building a simple bass reflex, you need to know the volume of the box and the tuning frequency of the bass reflex (pipe, hole, passive radiator). If we choose the smoothest frequency response as a criterion (and this is not the only possible criterion), we will get the following table A) Qts< 0,3 -наиболее гладкой будет кривая квазитретьего порядка Б) Qts = 0,4- лучше описывается баттервортовскими кривыми В) Qts>0.5 - you will have to allow waves on the frequency response, according to Chebyshev. In case A) the bass reflex is tuned 40-80% above the resonance frequency. In case B) - to the resonance frequency. In case C) below the resonance frequency. In addition, in these cases there will be a different volume of the case. In order to find the exact tuning frequencies, you need to take the original formulas, which are cumbersome enough to present them here. Therefore, I refer those interested to the Audio Store for 1999, after this educational program it will be possible to figure it out there, or to Aldoshina’s books. And even Ephrussi’s articles in Radio for ’69 will do.

Conclusion

If, after reading all this, you still have a desire to rivet something yourself, then you can take some kind of program on the Internet and calculate it all yourself, remembering that you can’t make candy out of G.. You should not get carried away with reducing the cutoff frequency; in no case should you try to compensate for the decline in the frequency response with an amplifier. The frequency response may even out a little, but the sound will be enriched with a mass of harmonics and subharmonics. On the contrary, the best results, in terms of pleasantness to the ear, can be achieved by forcibly losing the lowest frequencies at the PA input, i.e. frequencies below the cutoff frequency of the woofer. Another note regarding bass reflexes: an error in setting the bass reflex resonance frequency of 20% leads to a surge or drop in the frequency response of 3 dB.

Yes, I almost forgot to say about subwoofers, which are actually bandpass resonators. The quality factor of the speakers for them should be even lower. The simplest bandpass can also be calculated, but that’s where my courtesy ends.

So I decided to write an article myself, which is very important for acousticians. In this article I want to describe ways to measure the most important parameters of dynamic heads - the Thiel-Small parameters.

Remember! The technique below is only effective for measuring the Thiel-Small parameters of speakers with resonant frequencies below 100 Hz (i.e. woofers), the error increases at higher frequencies.

The most basic parameters Tilya-Smolla, by which it is possible to calculate and produce an acoustic design (in other words, a box) are:

Speaker resonant frequency F s (Hertz)
Equivalent volume V as (liters or cubic feet)
Total quality factor Q ts
DC resistance R e (Ohm)

For a more serious approach, you will also need to know:

Mechanical quality factor Q ms
Electrical quality factor Q es
Diffuser area S d (m 2) or its diameter Dia (cm)
Sensitivity SPL (dB)
Inductance L e (Henry)
Impedance Z (Ohm)
Peak power Pe (Watt)
Mass of the moving system M ms (g)
Relative stiffness (mechanical flexibility) C ms (meters/newton)
Mechanical resistance R ms (kg/sec)
Motor power (product of induction in the magnetic gap by the length of the voice coil wire) BL (Tesla*m)

Most of these parameters can be measured or calculated at home using not particularly sophisticated measuring instruments and a computer or calculator that can extract roots and exponentiate. For an even more serious approach to designing acoustic design and taking into account the characteristics of speakers, I recommend reading more serious literature. The author of this “work” does not claim any special knowledge in the field of theory, and everything stated here is a compilation from various sources - both foreign and Russian.

Measurement of Thiel-Small parameters R e, F s, F c, Q es, Q ms, Q ts, Q tc, V as, C ms, S d, M ms.

To measure these parameters you will need the following equipment:

Voltmeter
Signal generator audio frequency. Generator programs that generate the necessary frequencies are suitable. Like Marchand Function Generator or NCH tone generator. Since it is not always possible to find a frequency meter at home, you can completely trust these programs and your sound card installed on your computer.
Powerful (at least 5 watts) resistor with a resistance of 1000 ohms
Accurate (+- 1%) 10 ohm resistor
Wires, clamps and other rubbish to connect it all into a single circuit.

Scheme for measurements

Calibration:

First you need to calibrate the voltmeter. To do this, instead of a speaker, a 10 Ohm resistance is connected and by selecting the voltage supplied by the generator, it is necessary to achieve a voltage of 0.01 volts. If the resistor is of a different value, then the voltage should correspond to 1/1000 of the resistance value in Ohms. For example, for a 4 ohm calibration resistance, the voltage should be 0.004 volts. Remember! After calibration, the generator output voltage cannot be adjusted until all measurements are completed.

Finding R e

Now, by connecting a speaker instead of a calibration resistance and setting the frequency on the generator to close to 0 hertz, we can determine its resistance to direct current Re. It will be the voltmeter reading multiplied by 1000. However, Re can be measured directly with an ohmmeter.

Finding Fs and Rmax

The speaker during this and all subsequent measurements must be in free space. The resonant frequency of a speaker is found at the peak of its impedance (Z-characteristic). To find it, smoothly change the frequency of the generator and look at the voltmeter readings. The frequency at which the voltage on the voltmeter will be maximum (a further change in frequency will lead to a voltage drop) will be the main resonance frequency for this speaker. For speakers with a diameter greater than 16cm, this frequency should be below 100Hz. Don't forget to record not only the frequency, but also the voltmeter readings. Multiplied by 1000, they will give the speaker resistance at the resonant frequency Rmax, necessary for calculating other parameters.

Finding Q ms , Q es and Q ts

These parameters are found using the following formulas:

As you can see, this is a sequential finding of additional parameters R o, R x and measurement of previously unknown frequencies F 1 and F 2. These are the frequencies at which the speaker impedance is equal to Rx. Since Rx is always less than Rmax, there will be two frequencies - one is slightly less than Fs, and the other is slightly more. You can check the accuracy of your measurements with the following formula:

If the calculated result differs from the previously found one by more than 1 hertz, then you need to repeat everything all over again and more carefully. So, we have found and calculated several basic parameters and can draw some conclusions based on them:

If the resonant frequency of the speaker is above 50Hz, then it has the right to claim to work, at best, as a midbass. You can immediately forget about the subwoofer on such a speaker.
If the resonant frequency of the speaker is above 100Hz, then it is not a woofer at all. You can use it to reproduce mid frequencies in three-way systems.
If the F s /Q ts ratio of a speaker is less than 50, then this speaker is intended to operate exclusively in closed boxes. If more than 100 - exclusively for working with a bass reflex or in bandpasses. If the value is between 50 and 100, then you need to carefully look at other parameters - what type of acoustic design the speaker gravitates towards. It is best to use special computer programs for this that can graphically simulate the acoustic output of such a speaker in different acoustic designs. True, one cannot do without other, no less important parameters - V as, S d, C ms and L.

Finding Sd

This is the so-called effective radiating surface of the diffuser. For the lowest frequencies (in the zone of piston action) it coincides with the design one and is equal to:

The radius R in this case will be half the distance from the middle of the width of the rubber suspension on one side to the middle of the rubber suspension on the opposite side. This is due to the fact that half the width of the rubber suspension is also a radiating surface. Please note that the unit of measurement for this area is square meters. Accordingly, the radius must be substituted into it in meters.

Finding the inductance of the speaker coil L

To do this, you need the results of one of the readings from the very first test. You will need an impedance (impedance) of the voice coil at a frequency of about 1000 Hz. Since the reactive component (X L) is separated from the active R e by an angle of 900, we can use the Pythagorean theorem:

Since Z (coil impedance at a certain frequency) and R e (coil DC resistance) are known, the formula converts to:

Having found the reactance X L at frequency F, you can calculate the inductance itself using the formula:

V as measurements

There are several ways to measure equivalent volume, but at home it is easier to use two: the “additional mass” method and the “additional volume” method. The first of them requires several weights of known weight from materials. You can use a set of weights from pharmacy scales or use old copper coins of 1,2,3 and 5 kopecks, since the weight of such a coin in grams corresponds to the face value. The second method requires a sealed box of a known volume with a corresponding hole for the speaker.(mospagebreak)

Finding V as using the added mass method

First you need to evenly load the diffuser with weights and measure its resonant frequency again, writing it down as F" s. It should be lower than F s. It is better if the new resonant frequency is 30% -50% less. The weight of the weights is approximately 10 grams for every inch of diffuser diameter. That is, for a 12" head you need a load weighing about 120 grams.

where M is the mass of added weights in kilograms.

Based on the results obtained, V as (m 3) is calculated using the formula:

Finding V as by the additional volume method

It is necessary to seal the speaker in the measuring box. It is best to do this with the magnet facing out, since the speaker does not care which side it has volume on, and it will be easier for you to connect the wires. And there are fewer extra holes. The volume of the box is designated as V b.

Then you need to measure Fc (the resonant frequency of the speaker in a closed box) and, accordingly, calculate Q mc, Q ec and Q tc. The measurement technique is completely similar to that described above. Then the equivalent volume is found using the formula:

The data obtained as a result of all these measurements is sufficient for further calculation of the acoustic design of a low-frequency link of a sufficiently high class. But how it is calculated is a completely different story.

Determination of mechanical flexibility C ms

Where S d is the effective area of the diffuser with a nominal diameter D. How to calculate is written earlier.

Determination of the mass of the mobile system Mms

It is easily calculated using the formula:

Motor power (product of induction in the magnetic gap and the length of the voice coil wire) BL

Most importantly, do not forget that for more accurate measurement values of the Thiel-Small parameters, it is necessary to conduct the experiment several times, and then obtain more accurate values by averaging.

- How! Do you have a grandmother who guesses three cards in a row, and you still haven’t learned her cabalistics from her?
A.S. Pushkin, "The Queen of Spades"

Today we will talk about what is really important to know about acoustics. Namely, about the famous Thiel-Small parameters, knowledge of which is the key to winning in the gambling game of car audio. Without defamation and cabalism.

One outstanding mathematician, according to legend, while lecturing to students, said: “And now we will begin to prove the theorem whose name I have the honor to bear.” Who had the honor of bearing the names of Thiel and Small's parameters? Let's remember this too. The first in the bunch is Albert Neville Thiele (in the original A. Neville Thiele, “A” is almost never deciphered). Both by age and bibliography. Thiel is now 84 years old, and when he was 40, he published a landmark paper that pioneered loudspeaker performance calculations based on a single set of parameters, in a convenient and repeatable manner.

There, in a 1961 paper, it was said, in part, “The low-frequency performance of a loudspeaker can be adequately described by three parameters: the resonant frequency, the volume of air equivalent to the acoustic flexibility of the loudspeaker, and the ratio of electrical resistance to resistance to movement at the resonant frequency The same parameters are used to determine electroacoustic efficiency. I encourage loudspeaker manufacturers to publish these parameters as part of the basic information about their products."

Neville Thiel's request was heard by the industry only a decade later, at which time Thiel was already working with Richard Small, a native of California. Richard Small is spelled in Californian, but for some reason the respected doctor prefers the German pronunciation of his own name. Small turns 70 this year, which, by the way, is a more important anniversary than most. In the early seventies, Thiel and Small finally finalized their proposed approach to calculating loudspeakers.

Neville Thiel is now a professor emeritus at a university in his home country of Australia, and Dr. Small's last professional position that we were able to track was chief engineer of the Harman-Becker automotive audio department. And, of course, both are members of the leadership of the International Society of Acoustic Engineers (Audio Engineering Society). In general, both are alive and well.

On the left is Thiel, on the right is Small, in order of contribution to electroacoustics. By the way, the photo is rare, the masters did not like to be photographed

To hang or not to hang?

The figurative definition of the conditions for measuring Fs as the resonant frequency of a speaker hanging in the air gave rise to the misconception that this is how this frequency should be measured, and enthusiasts actually tried to hang speakers on wires and ropes. A separate issue of “BB”, or even more than one, will be devoted to measuring acoustic parameters, but I’ll note here: in competent laboratories, speakers are clamped in a vice during measurements, and not suspended from a chandelier.

Real impedance curve of a woofer. It calculates two of three main parameters

Impedance curves for different meanings total quality factor, while the electrical Qes is the same, equal to 0.5, and the mechanical one varies from 1 to 8. The total quality factor Qts does not seem to change much, but the height of the hump on the impedance graph varies greatly, and the less Qms, the sharper it becomes

Dependence of sound pressure on frequency at the same Qts values. When measuring sound pressure, only the total quality factor Qts is important, so completely different impedance curves correspond to not so different sound pressure curves versus frequency

The same Qts values, but now Qms = 4 everywhere, and Qes changes so as to reach the same Qts values. The Qts values are the same, but the curves are completely different and differ much less from each other. The lower, red curves were obtained for those values that could not be obtained in the first experiment at a fixed Qes = 0.5

Sound pressure curves for different Qts obtained by changing Qes. The four upper curves are exactly the same in shape as when we changed Qms, their shape is determined by the Qts values, but they remain the same. The lower, red curves obtained for Qts greater than 0.5 are, of course, different, and a hump begins to grow on them due to the increased quality factor.

Now pay attention: the point is not only that at high Qts a hump appears on the characteristic, and the sensitivity of the speaker at frequencies above the resonant one decreases. The explanation is simple: other things being equal, Qes can only increase with an increase in the mass of the moving system or with a decrease in the magnet power. Both lead to a decrease in sensitivity at mid frequencies. So the hump at the resonant frequency is, rather, a consequence of the dip at frequencies above the resonant one. There is nothing free in acoustics...

Junior partner contribution

By the way: the founder of the method A.N. Thiel intended to take into account only the electrical quality factor in the calculations, believing (correctly for his time) that the share of mechanical losses was negligible compared to the losses caused by the operation of the “electric brake” of the speaker. The junior partner's contribution, however, was not the only one, however, was taking into account Qms, this has now become important: modern drivers use materials with increased losses that did not exist in the early 60s, and we came across speakers where the Qms value was only 2 - 3, with electric under unit. In such cases, it would be a mistake not to take mechanical losses into account. And this became especially important with the introduction of ferrofluid cooling in RF heads, where, due to the damping effect of the liquid, the Qms share in the total quality factor becomes decisive, and the impedance peak at the resonance frequency becomes almost invisible, as in the first graph of our computational experiment.

Three cards revealed by Thiel and Small

1. Fs - the main resonance frequency of the speaker without any housing. Characterizes only the speaker itself, and not the finished speaker system based on it. When installed in any volume it can only increase.

2. Qts - total quality factor of the speaker, a dimensionless quantity characterizing the relative losses in the dynamics. The lower it is, the more the radiation resonance is suppressed and the higher the resistance peak on the impedance curve. Increases when installed in a closed box.

3. Vas - equivalent speaker volume. Equal to the volume of air with the same rigidity as the suspension. The stiffer the suspension, the less Vas. At the same stiffness, Vas increases with increasing diffuser area.

Two halves making up card No. 2

1. Qes - the electrical component of the total quality factor, characterizes the power of the electric brake, which prevents the diffuser from swinging near the resonant frequency. Typically, the more powerful the magnetic system, the stronger the “brake” and the smaller the numerical value of Qes.

2. Qms - the mechanical component of the total quality factor, characterizes losses in the elastic elements of the suspension. The losses here are much smaller than in the electrical component, and Qms is numerically much larger than Qes.

How long does the bell ring?

What do a bell and a loudspeaker have in common? Well, the fact that both sound is obvious. More importantly, both are oscillatory systems. What's the difference? The bell, no matter how you strike it, will sound at the only frequency prescribed by the canon. And outwardly, the speaker is not so different from it - in a wide range of frequencies, and can, if desired, simultaneously depict both the ringing of a bell and the puffing of a bell-ringer. So: two of the three Thiel-Small parameters precisely describe this difference quantitatively.

You just need to firmly remember, or better yet, re-read the quote from the founder in the historical and biographical note. It says “at low frequencies.” Thiel, Small and their parameters have nothing to do with how the speaker behaves at higher frequencies and do not bear any responsibility for this. Which speaker frequencies are low and which are not? And this is what the first of the three parameters speaks about.

Map one, measured in hertz

So: Thiel-Small parameter No. 1 is the speaker’s own resonant frequency. It is always designated Fs, regardless of the language of publication. The physical meaning is extremely simple: since the speaker is an oscillatory system, it means there must be a frequency at which the diffuser will oscillate when left to its own devices. Like a bell after being struck or a string after being plucked. This means that the speaker is absolutely “naked”, not installed in any housing, as if hanging in space. This is important because we are interested in the parameters of the speaker itself, and not of what surrounds it.

The frequency range around the resonant one, two octaves up, two octaves down - this is the area where the Thiel-Small parameters operate. For subwoofer heads that have not yet been installed in the housing, Fs can range from 20 to 50 Hz, for midbass speakers from 50 (bass “sixes”) to 100 - 120 (“fours”). For diffuser mid-frequencies - 100 - 200 Hz, for domes - 400 - 800, for tweeters - 1000 - 2000 Hz (there are exceptions, very rare).

Here's how it works. The speaker's voice coil is its motor. An alternating current flows through it from the amplifier, and the coil, located in a magnetic field, begins to move with the frequency of the supplied signal, moving, of course, the entire moving system, then it is here. But a coil moving in a magnetic field is a generator. Which will generate more electricity the more the coil moves. And when the frequency begins to approach the resonant one, at which the diffuser “wants” to oscillate, the amplitude of the oscillations will increase, and the voltage produced by the voice coil will increase. Reaching a maximum exactly at the resonant frequency. What does this have to do with braking? None yet. But imagine that the coil leads are connected to each other. Now a current will flow through it and a force will arise, which, according to Lenz’s school rule, will impede the movement that generated it. But in real life the voice coil is closed to the output impedance of the amplifier, which is close to zero. It turns out like an electric brake that adapts to the situation: the more the diffuser tries to move back and forth, the more the counter current in the voice coil prevents this. The bell has no brakes, except for the damping of vibrations in its walls, and in bronze - what damping...

The second map, not measured in anything

The brake power of the speaker is numerically expressed in the second Thiel-Small parameter. This is the total quality factor of the speaker, denoted Qts. Expressed numerically, but not literally. I mean, the more powerful the brakes, the lower the Qts value. Hence the name “quality factor” in Russian (or quality factor in English, from which the designation of this quantity originated), which is, as it were, an assessment of the quality of the oscillatory system. Physically, the quality factor is the ratio of elastic forces in a system to viscous forces, otherwise - to friction forces. Elastic forces store energy in the system, alternately transferring energy from potential (a compressed or stretched spring or speaker suspension) to kinetic (the energy of a moving diffuser). Viscous ones strive to turn the energy of any movement into heat and irrevocably dissipate. A high quality factor (and for the same bell it will be measured in tens of thousands) means that there are much more elastic forces than frictional forces (viscous, these are the same thing). This also means that for each oscillation only a small part of the energy stored in the system will be converted into heat. Therefore, by the way, quality factor is the only value in the three Thiel-Small parameters that does not have a dimension; it is the ratio of one force to another. How does a bell dissipate energy? Through internal friction in bronze, mainly slowly. How does a speaker do this, whose quality factor is much lower, and therefore the rate of energy loss is much higher? In two ways, depending on the number of “brakes”. Part is dissipated through internal losses in the elastic elements of the suspension, and this share of losses can be estimated by a separate value of the quality factor, it is called mechanical, denoted Qms. The second, larger part is dissipated in the form of heat from the current passing through the voice coil. The current produced by her. This is the electrical quality factor Qes. The total effect of the brakes would be determined very easily if it were not the values of the quality factor, but, on the contrary, the values of losses that were used. We would just fold them. And since we are dealing with quantities that are the reciprocals of losses, then we will have to add the reciprocal quantities, which is why it turns out that 1/Qts = 1/Qms + 1/Qes.

So how do you snatch the names of the “three cards” from the speaker? Well, at least the first two, we'll get to the third. It is useless to threaten with a pistol, like Hermann, the speaker is not an old woman. The same voice coil, the fiery speaker motor, comes to the rescue. After all, we have already realized: a flame motor also works as a flame generator. And in this capacity, it seems to be sneaking about the amplitude of vibrations of the diffuser. The greater the voltage appears on the voice coil as a result of its oscillations together with the diffuser, the greater the range of oscillations, which means the closer we are to the resonant frequency.

This is why they do this. The speaker is connected to an amplifier with the highest possible output impedance; in real life, this means: a resistor with a value of much, one hundred, at least, times the nominal resistance of the speaker is connected in series with the speaker. Let's say 1000 ohms. Now, when the speaker is operating, the voice coil will generate a back-EMF, sort of like for the operation of an electric brake, but braking will not occur: the coil leads are closed to each other through a very high resistance, the current is negligible, the brake is useless. But the voltage, according to Lenz’s rule, is opposite in polarity to the supplied one (“generating movement”), will be in antiphase with it, and if at this moment you measure the apparent resistance of the voice coil, it will seem that it is very large. In fact, in this case, the back-EMF does not allow the current from the amplifier to flow unhindered through the coil, the device interprets this as increased resistance, but what else?

By measuring the impedance, that same “apparent” (but in fact complex, with all sorts of active and reactive components, now is not the time to talk about this) resistance, two cards out of three are revealed. The impedance curve of any cone speaker, from Kellogg and Rice to the present day, looks, in principle, the same, it even appears in the logo of some electroacoustic scientific community, now I forget which one. The hump at low (for this speaker) frequencies indicates the frequency of its fundamental resonance. Where there is a maximum, there is the coveted Fs. It couldn't be more elementary. Above resonance there is a minimum impedance, which is usually taken as the nominal impedance of the speaker, although, as you can see, it remains this way only in a small frequency band. Higher up, the total resistance begins to increase again, now due to the fact that the voice coil is not only a motor, but also an inductance, the resistance of which increases with frequency. But we won’t go there now; the parameters that interest us don’t live there.

It is much more complicated with the value of the quality factor, but, nevertheless, comprehensive information about the “second card” is also contained in the impedance curve. Comprehensive, because from one curve you can calculate both the electrical Qes and the mechanical quality factor Qms, separately. We already know how to then make a complete Qts out of them, which is really necessary when calculating the design; it’s a simple matter, not a Newton binomial.

So: in the simplest version, it’s exactly the opposite. What does a high impedance peak at resonance frequency mean? That the voice coil produces a lot of back-EMF, designed to electrically brake the oscillations of the cone. Only with this connection, through a large resistance, the current necessary for the operation of the brake does not flow. And when such a speaker is turned on not for measurements, but normally, directly from the amplifier, the braking current will flow, be healthy, the coil will become a powerful obstacle to the excessive oscillations of the diffuser at its favorite frequency.

All other things being equal, you can roughly estimate the quality factor from the curve, and remembering: the height of the impedance peak characterizes the potential of the speaker's electric brake, therefore, the higher it is, the LOWER the quality factor. Will such an assessment be exhaustive? Not exactly, as was said, she will remain rude. Indeed, in the impedance curve, as already mentioned, information about both Qes and Qms is buried, which can be dug out (manually or using a computer program) by analyzing not only the height, but also the “shoulder width” of the resonant hump.

And how does the quality factor affect the shape of the speaker’s frequency response? This is what interests us, isn’t it? How it affects - it has a decisive impact. The lower the quality factor, that is, the more powerful the internal brakes of the speaker at the resonant frequency, the lower and more smoothly the curve will pass near the resonance, characterizing the sound pressure created by the speaker. The minimum ripple in this frequency band will be at Qts equal to 0.707, which is commonly called the Butterworth characteristic. At high Q values, the sound pressure curve will begin to “hump” near resonance, it’s clear why: the brakes are weak.

Is there a “good” or a “bad” total quality factor? By itself, no, because when the speaker is installed in an acoustic design, which we will now consider only a closed box, both its resonance frequency and overall quality factor will become different. Why? Because both depend on the elasticity of the speaker suspension. The resonant frequency depends only on the mass of the moving system and the rigidity of the suspension. As stiffness increases, Fs increases, and as mass increases, it decreases. When the speaker is installed in a closed box, the air in it, which has elasticity, begins to work as an additional spring in the suspension, the overall rigidity increases, Fs increases. The total quality factor also increases, since it is the ratio of elastic forces to braking forces. The brake capabilities of the speaker will not change from installing it to a certain volume (why would it?), but the total elasticity will increase, the quality factor will inevitably increase. And it will never become lower than the “naked” dynamics. Never, that's the bottom limit. How much will all this increase? And this depends on how rigid the speaker’s own suspension is. Look: the same value of Fs can be obtained with a light diffuser on a soft suspension or with a heavy one on a hard suspension; mass and stiffness act in opposite directions, and the result may turn out to be numerically equal. Now if we place a speaker with a rigid suspension in some volume (which has the elasticity required for this volume), then it will not notice a slight increase in the total stiffness, the values of Fs and Qts will not change much. Let’s put a speaker with a soft suspension there, in comparison with the stiffness of which the “air spring” will already be significant, and we will see that the total stiffness has changed significantly, which means that Fs and Qts, initially the same as those of the first speaker, will change significantly.

In the dark “pre-Tile” times, in order to calculate new values of the resonance frequency and quality factor (they, in order not to be confused with the parameters of the “bare” speaker, are designated as Fc and Qtc), it was necessary to know (or measure) directly the elasticity of the suspension, in millimeters per newton of applied force , know the mass of the moving system, and then play tricks with calculation programs. Thiel proposed the concept of “equivalent volume,” that is, a volume of air in a closed box whose elasticity is equal to the elasticity of the speaker suspension. This value, designated Vas, is the third magic card.

Map three, three-dimensional

How Vas is measured is a separate story, there are funny twists, and this, as I’m saying for the third time, will be in a special issue of the series. For practice, it is important to understand two things. First: an extremely Lokhov’s misconception (alas, nevertheless encountered) that the Vas value given in the accompanying documents for the speaker is the volume in which the speaker should be placed. And this is just a characteristic of the speaker, depending only on two quantities: the rigidity of the suspension and the diameter of the diffuser. If you put a speaker in a box with a volume equal to Vas, the resonant frequency and overall quality factor will increase by a factor of 1.4 (this is the square root of two). If in a volume equal to half Vas - 1.7 times (root of three). If you make a box with a volume of one third of Vas, everything else will double (the root of four, the logic should already be clear without formulas).

As a result, indeed, the smaller, other things being equal, the Vas value of the speaker, the more compact design you can count on, while maintaining the planned indicators for Fc and Qtc. Compactness, however, does not come for free. There is no such thing as free in acoustics. The low Vas value at the same resonant frequency of the speaker is the result of a combination of a rigid suspension with a heavy moving system. And the sensitivity most decisively depends on the mass of the “movement”. Therefore, all subwoofer heads, distinguished by the ability to operate in compact closed enclosures, are also characterized by low sensitivity compared to colleagues with lightweight diffusers but high Vas values. So there are no good or bad Vas values either, everything has its own price.

Prepared based on materials from the magazine "Avtozvuk", March 2005.www.avtozvuk.com

Attention! The methods given below are only effective for measuring the parameters of speakers with resonant frequencies below 100Hz; at higher frequencies the error increases.
To obtain the most reliable results, it is recommended to carry out all measurements several times (3-5 times), then the arithmetic mean value is taken as the result.

Before measuring parameters, the speaker must be “stretched”. The fact is that a speaker that has been idle for a certain time or a new speaker will have different parameters from those that we will measure after the speaker has played for a certain time and is working regularly. Therefore, the point of stretching the speaker is to obtain reliable measurement parameters. There are many opinions on how and how much to warm up: just with music, with a sinusoidal signal (sine) at the resonance frequency of the speaker Fs, with a sine at 1000 Hz, with a sine at different frequencies, with white and pink noise, with test disks.

How to warm up is up to you - it’s a matter of your capabilities and time, but you definitely need to warm up.

On my own behalf, I advise you to warm up during the day in various combinations of the above methods, you should start with the sine of the self-resonance frequency Fs (taken from the speaker’s passport) to maximum amount time, then use other methods. You can use test discs, preferably those that contain both musical and technical tracks, i.e. generated signals various shapes, frequency and power, and it’s better to start with technical tracks. It is advisable to warm up the speaker by 50-100% of the rated power, it all depends on your conditions, ears and nerves.

The most basic parameters by which acoustic design (case, box) can be calculated and manufactured are the Thiel-Small parameters.

Measurement of resonant frequency Fs, speaker quality factor Qts and its components electrical and mechanical quality factor Qes, Qms.

Method 1

To measure these parameters you will need the following equipment:

* Voltmeter
*Audio signal generator
*Frequency meter
* Powerful (at least 2 watts) resistor with a resistance of 1000 ohms
*Precise (+- 1%) 10 ohm resistor
* Wires, clamps and other rubbish to connect it all into a single circuit.

Of course, this list is subject to change. For example, most generators have their own frequency scale and a frequency meter is not necessary in this case. Instead of a generator, you can also use a computer sound card and appropriate software (for example, this one) capable of generating sine waves from 0 to 200 Hz of the required power. Or I also had to do this when there was no computer nearby: I cut tracks with frequencies from 20-120 Hz onto a disk, then played it on a DVD connected to an amplifier, and then connected a suspended speaker through a resistor.

Calibration
First you need to calibrate the voltmeter. To do this, instead of the speaker, a resistance of 10 Ohms is connected and by selecting the voltage supplied by the generator, it is necessary to achieve a voltage of 0.01 volts. If the resistor is of a different value, then the voltage should correspond to 1/1000 of the resistance value in Ohms. For example, for a calibration resistance of 4 ohms, the voltage should be 0.004 volts.
Remember! After calibration, it is NOT possible to adjust the output voltage of the generator (amplifier) until all measurements are completed.

Determination of Fs and Rmax.
The speaker in this and all subsequent measurements must be in free space; usually it is suspended (usually on a chandelier) away from walls and various objects. The resonant frequency of a speaker is found at the peak of its impedance (Z-characteristic). To find it, gradually increase the generator frequency, starting from about 20 Hz, and look at the voltmeter readings. The frequency at which the voltage on the voltmeter will be maximum (a further change in frequency will lead to a voltage drop) will be the main resonance frequency for this speaker. For speakers with a diameter greater than 16cm, this frequency should be below 100Hz. Don't forget to record not only the frequency, but also the voltmeter readings. Multiplied by 1000, they will give the speaker resistance at the resonant frequency Rmax, necessary for calculating other parameters.

Definition of Qms, Qes and Qts.
These parameters are determined using the following formulas.

As you can see, this is a sequential search for additional parameters Ro, Rx and measurement of previously unknown frequencies F1 And F2. These are the frequencies at which the speaker impedance is equal to Rx. Because the Rx always less Rmax, then there will be two frequencies - one is slightly less Fs, and the other is slightly larger.

Determination of head winding resistance to direct current Re.
Now, by connecting a speaker instead of a calibration resistance and setting the frequency on the generator to close to 0 hertz, we can determine its resistance to direct current Re. It will be the voltmeter reading multiplied by 1000. However, Re You can measure it directly with an ohmmeter.

Method 2

The measurement scheme is the same as in the first method, the elements are the same: a 1 kOhm resistor and a generator - either an audio frequency generator capable of producing a voltage of 10-20V, or a generator-amplifier combination that meets the same requirement. We place the speaker away from the walls, ceiling and floor (it is often recommended to hang it). We connect a voltmeter to points A and C (i.e. to the amplifier output), and set the voltage to 10-20 V at a frequency of 500-1000 Hz.
We connect the voltmeter to points B and C (i.e. directly to the speaker contacts) and by changing the frequency of the generator we find the frequency at which the voltmeter readings are maximum (as shown in the figure below). This is the frequency of the speaker's own resonance Fs. Let's write it down Fs And Us-voltmeter readings.

By changing the frequency up relative to Fs, we find the frequencies at which the voltmeter readings are constant and significantly less Us(with a further increase in frequency, the voltage will begin to increase again, in proportion to the increase in speaker impedance). Let's write down this value, Um.

A graph of the impedance of a speaker in free space and in a closed box looks something like this.

Calculate the voltage U12 according to the formula:

By changing the frequency, we achieve readings on the voltmeter corresponding to the voltage U12, find the frequencies F1 and F2.

We calculate the acoustic or mechanical quality factor using the formula:

Electrical quality factor:

And finally, the full quality factor:

Method 3 - Measuring till-small parameters using a bass reflex

The measurement scheme is the same as in the first method, the elements are the same: a calibration resistor Rk with a nominal value of 10 Ohms and an active resistance R, which sets the current in the circuit, with a nominal value of 1 kOhm. You can take resistances Rk and R of other values, fulfilling the conditions:

Rk - can be anything, but close to Re

R/Re > 200

Where Re is the DC resistance of the voice coil.
Measurements start from the most precise definition DC resistance of the voice coil Re and calibration resistor Rk using digital voltmeter or multimeter.
Then, instead of the speaker, we turn on the calibration resistor Rk and measure the voltage Uk on it. The voltage corresponding to the voice coil resistance to direct current is found using the formula:

Where: Sd- effective radiating surface of the diffuser, m2; Cms- relative rigidity.

The radiating surface of the diffuser for the lowest frequencies (in the zone of piston action) coincides with the structural one and is equal to: Radius R in this case, it will be half the distance from the middle of the width of the rubber suspension on one side to the middle of the rubber suspension on the opposite side. This is due to the fact that half the width of the rubber suspension is also a radiating surface. Please note that the unit of measurement for this area is square meters. Accordingly, the radius must be substituted into it in meters.

We calculate the relative stiffness Cms based on the results obtained using the formula:

M/N (meters/Newton), where M- mass of added weights in kilograms.

Determination of equivalent volume using the additional volume method

To determine the equivalent volume of a speaker using the additional volume method, use a sealed measuring box with a round hole that matches the diameter of the speaker cone. It is better to choose the volume of the box closer to the one in which we are then going to listen to this speaker. It is necessary to seal the speaker in the measuring box. It is best to do this with the magnet facing out, since the speaker does not care which side it has volume on, and it will be easier for you to connect the wires. And there are fewer extra holes. seal all cracks.

Then you need to take measurements Fс(resonant frequency of the speaker in a closed box) and, accordingly, calculate the mechanical and electrical quality factor Qmc And Qec and the quality factor of the speaker in the measuring box Qts" (Qtс). After which we calculate the equivalent volume using the formula:

With almost the same results you can use more simple formula:

Where: Vb- volume of the measuring box, m3.

Let's check: calculate and if measured in a box Qts'=Qtc, well, or almost equal, which means everything has been done correctly, and you can move on to designing the acoustic system.

conclusions

So, we have found and calculated several basic parameters and can draw some conclusions based on them:

*1. If the resonant frequency of the speaker is above 50Hz, then it has the right to claim to work, at best, as a midbass. You can immediately forget about the subwoofer on such a speaker.
*2. If the resonant frequency of the speaker is above 100Hz, then it is not a woofer at all. You can use it to reproduce mid frequencies in three-way systems.
*3. If the ratio Fs/Qts the speaker is less than 50, then this speaker is intended to work exclusively in closed boxes. If more than 100 - exclusively for working with a bass reflex or in bandpasses. If the value is between 50 and 100, then you need to carefully look at other parameters - what type of acoustic design the speaker gravitates towards.

It is best to use special computer programs for this that can graphically simulate the acoustic output of such a speaker in different acoustic designs. True, one cannot do without other, no less important parameters - Sd, Cms And Le.
The data obtained as a result of all these measurements is sufficient for further calculation of the acoustic design of a low-frequency link of a sufficiently high class.

Leisure

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