Understanding Thiel Small’s parameters. Car audio and DIY

Thiel-Small parameters allow you to understand how a speaker will sound in a particular enclosure without buying, listening or benchmarking. This is especially useful for car audio enthusiasts, because they have to deal with bare speakers that are mounted in doors and trunk racks. Someone uses these parameters to calculate the appropriate volume and type of space for a loudspeaker, someone likes to select speakers from different manufacturers and checks their compatibility with each other. This article will explain in simple language who Thiel and Small are, what parameters they came up with and what to do with them now.

Who started it all
Thiel on the left, Small on the right

Albert Neville Thiel is an Australian engineer, in his childhood, which fell in the thirties, he performed with a school choir on the radio and became interested in acoustics, received an engineering education, researched sound and picture broadcasting at the dawn of television broadcasting, rose to the rank of chief engineer in large television and video companies. In 1961, he published a scientific article in which he proposed to describe the characteristics of any speaker with one set of parameters: “resonant frequency, volume of air, equivalent acoustic flexibility of the loudspeaker, and the ratio of electrical resistance to resistance to motion at the resonant frequency.” And, referring to the companies producing acoustics, he urged “to publish these parameters as part of the basic information about their products.”
Richard Small is an electroacoustician from California, who crafted amplifiers and speakers with his pianist father as a child, and received a Master of Science degree from MIT. He worked with Till in the seventies, together they brought a set of parameters to mind. In particular, Small added the concept of mechanical quality factor. It is curious that in the future he worked for a long time at Harman-Becker as chief engineer of the automotive audio department.
What these parameters give
If you get hold of a speaker without a name and markings, but it looks good. By measuring the Thiel-Small parameters, you can learn a lot about this dynamics: at what frequencies it plays, how much bass there will be, in what volume it is better to place it, etc.
If you have a speaker system, but you don’t like the way it sounds . You can pull out the speakers from it and, by measuring, find out whether they generally correspond to the case in which they are installed. It often happens that there is no chance to make loudspeakers friends with the box in which the manufacturer placed them, and then either one or the other will have to be changed.











If you need to choose the acoustic design for the subwoofer: woofer, subwoofer, midbass. Thiel-Small parameters will tell you how to set them to get the best results.
If you need to select crossovers and adjust the filters for tweeters so that during their operation they stay away from their own resonant frequency – this way the sound will be better, and there will be less noise, hum and artifacts.
If you need to choose a subwoofer . The more low frequencies the speaker plays, the more Thiele-Small parameters need to be taken into account, since they describe, among other things, the interaction of the speaker with the environment, and it is the bass that makes the windows of neighboring houses tremble from dubstep from a passing car with two 18-inch subwoofers. …
If you need to build a subwoofer. Some people buy naked sub speakers and use Thiel-Small parameters and special calculators to calculate the appropriate acoustic design. If the saw and the hammer are not alien to skillful hands, then very decent subwoofers are obtained for ridiculous money for their quality.
If you want to craft a speaker system. Design experiments with subwoofers often inspire more serious achievements in the field of acoustic engineering. Some people start building their own home speakers and find it a new hobby, if not a craft.
The main parameters of Thiel-Small
To understand their essence, you need to remember that the speaker consists of two parts:

Fixed: rigid frame with magnet.
Movable: A coil with a winding that, when an electrical signal is applied, produces a magnetic field that interacts with a permanent magnet. This sets the coil in motion, and it pushes the diffuser attached to it, which is located on a flexible suspension. And so that this structure does not wobble left and right, it is supported by an elastic centering washer.

Thus, the movable part of the speaker only moves up and down, like a piston. This movement compresses and expands the air, creating sound waves. If you pour liquid into the speaker, you can see how these waves are formed:

It is the operation of such a piston that is described by the Thiel-Small parameters. There are three fundamental parameters.

1. Equivalent volume (Vas, m3)
The suspension and centering washer have some elasticity that prevents the entire system from moving freely. It can be thought of as a spring. If we take such a volume of air, which in its elasticity is equal to this spring, then just the equivalent volume will turn out.

The smaller the equivalent volume, the stiffer the speaker’s moving system.

This parameter refers to the desired cabinet response rather than the speaker itself. However, this is by no means the volume of the cabinet in which the speaker should be placed. If this is done, then the Q factor and the resonant frequency will increase too much. A pillow of air will raise the resonance and act like a spring, interfering with the braking of the speaker.

The equivalent volume is calculated by multiplying the stiffness of the suspension, the diameter of the diffuser (because this surface interacts with another spring – air), the density of the surrounding air and the speed of sound in it. Accordingly, the stiffer the suspension, the less will be the volume of air that will affect the speaker by the fact of its existence. Likewise with the diffuser – the larger the membrane, the more it compresses the air inside the speaker or subwoofer housing, and therefore the response force of the opposing air will be higher.

It is Vas that often plays a decisive role in choosing a speaker for a certain volume. This is especially true for subwoofers – large cones need large volumes. It is usually advised to aim at a sub with Vas in the 30-50 HP region.

2. Resonant frequency (Fs, Hz)
If flashbacks from school physics lessons have not yet begun, then they will definitely appear here. There is an oscillating system – for example, a swing. If you put them aside and let go, then they will swing with a certain natural frequency. This will be the resonant frequency. In addition, pushing the swing with it in time will allow it to swing faster and stronger than using any other frequency.

This has the most direct relation to dynamics: the moving system (first of all the suspension) is the swing, and the electricity is the guy who pushes them. If you apply a signal to the speaker at its resonant frequency, then both of these frequencies will add up and form a resonance. On the impedance graph, and even the frequency response graph, there will be a peak at this point.

The softer the suspension and the greater the mass, the lower the resonant frequency.

Fs is one of the most important parameters, since below it the sound pressure of the speaker drops noticeably. Therefore, for subwoofers, the lowest possible resonance frequency is needed, since after it there is usually a serious drop in frequency response. This means that the lower the resonant frequency, the deeper the bass will be.

It is also important to note that the resonant frequency is measured with a speaker without a case. When placing a loudspeaker in a cabinet, Fs is influenced by the volume of the latter. If you want the resonant frequency (and the total Q factor, about which below) remain the same, then you should install the speaker in such a trunk, the volume of which exceeds Vas at least three times.

The resonant frequency will help determine the role of the speaker in the speaker. For example, if Fs is more than 50 Hz, then you cannot build a subwoofer with such a speaker; the role of a midbass is best suited for it. If Fs is higher than 100 Hz, then such a speaker is best used for reproducing mid frequencies. For the sub, Fs in the region of 21–35 Hz will be suitable.

3. Total Q factor (Qts)
After the speaker cone has reproduced the sound, it returns to its original position, and not instantly, but smoothly fading out at the resonant frequency – like a swing that has stopped swinging. How quickly the diffuser returns to its place is the total Q.

The faster the diffuser returns to its original position after the signal is emitted, the lower the Q-factor.

The lower the quality factor, the better. If the diffuser takes a long time to return to its original position, due to oscillations at the resonant frequency, extraneous noise, hum and artifacts will appear.

The total Q factor consists of two “incomplete” ones:

Mechanical quality factor (Qms) , which depends on the mass of the moving system (the heavier, the longer the diffuser will stop, the higher the quality factor) and suspension rigidity (stiffer – higher).
Electrical Q-factor (Qes) . It was her that Richard Small added, having found out that the speaker coil, when returned to its original position, works like an electric generator. The movement of the winding against the magnet produces an electric current that flows through the winding and collides with the signal from the amplifier. It turns out something like a short circuit that interferes with the movement of the diffuser, and much more than Qms. The electrical figure of merit depends on the power of the magnet – the more powerful it is, the lower it is.
It is curious that the quality factor is a dimensionless parameter. For example, if it is equal to one, this means that to stop the diffuser, the latter must complete exactly one cycle of oscillations (i.e., the signal disappears, the membrane goes up and down, then stops).

It is believed that the best Q-factor for a speaker system is approximately 0.5-0.7 for normal music and 0.8-0.9 for those who like genres with a predominance of sharp bass. The lower it is, the higher the bass frequency rolloff creeps along the frequency response graph, depriving the listener of them. At large values ​​of Qts, a hump occurs in the resonance region on the frequency response graph, and the rest of the characteristics deteriorate.

The ratio of the resonant frequency to the total Q is also important. If the result of dividing both values ​​is 50, then the speaker should be used only in a closed volume. If it reaches 100, then a phase inverter can be added to the design.

Secondary parameters
The above three parameters are fundamental, but not the only ones. Sometimes in the passports for a speaker or speaker there are other characteristics, but not all of them have a meaning and applicability. Commonly found are the following:

Sd (sq. M.) – the effective area of ​​the diffuser, required to calculate the main parameters.
Mms (kg) – the mass of the moving system, when measuring which even the mass of the air moving with the membrane is taken into account. Needed to calculate the basic parameters.
Xmax (mm) – the maximum displacement of the diffuser to one of the sides, at which the linearity of the stroke is maintained (that is, there will be no sound distortion).
Bl, (T * m) – electromechanical coupling coefficient, the product of the wire length in the gap between the magnet and the magnetic flux strength. The higher Bl, the stronger the “engine” of the speaker, the better.
Sensitivity (dB) – an indicator of the speaker’s sensitivity, does not apply to the vehicle parameters, but is very important, since it shows the future loudness of the speaker. Sensitivity is the volume that a speaker outputs at a given power. Roughly speaking, if you take two speakers and apply a signal of the same power to them, then the one that yells louder will be more sensitive.
Where to find these parameters
Thiel-Small’s fundamental parameters allow simulating at least the average loudness and impedance of a future speaker system. They will also help you calculate the design and volume of the enclosure that will house the loudspeaker.

But in order to use these parameters, you need to know them first. Sometimes it’s just like the JBL STAGE3 607C. You just need to open the installation guide and voila!

Component speaker JBL STAGE3 607C 3 450 *

But they are often hidden deep under marketing slogans. For example, to find out the required characteristics of the Morel Tempo Ultra 572 speaker, you need to find a pdf with a presentation of the speaker line in the wilds of the official website and rewind to the very bottom. The reward will be a hefty table with all the parameters of all the speakers in the manufacturer’s lineup

There are other ways as well. For example, in one of the online calculators you can find a database of popular speaker models . For example, you need to find out the characteristics of the Ural AK-74. When you select the required model in the application, its profile with the main characteristics, including vehicle parameters, opens . And by clicking on the calculation of the duct, you can see the graphs of the impedance and Spl:

How to measure yourself
From under the rubble in the garage, a pair of noun-name speakers were extracted. They look good, but who made them and for what tasks is a mystery shrouded in darkness. By measuring their parameters, you can understand what kind of animals they are and what they will do. This is not difficult to do, but you will need several devices:homemade attenuator of four resistors, so as not to burn the preamp of the sound card;
weight for measuring the equivalent volume using the added mass method. You need to find out the exact weight of this load, for example, weigh a copper coin with jewelry scales – it is important that the weight is not magnetised;
Room Eq Wizard software. It is free and can be downloaded from the official website. In it, you will need to take only two measurements – with and without a weight.

The procedure is simple, but requires some preparation, so the description would take the independence of the article. Fortunately, on the official website of the Room Eq Wizard there is such an article in English, and on YouTube there are Russian-language videos with a detailed description of the process:

Thiel-Small parameters are very useful to know when working with bare speakers. They allow you to design the volume for a loudspeaker, guided not only by aesthetic preferences, but also by formulas and mathematics. A scientific approach will allow you to achieve the highest quality sound in all conditions.