Carole Sautereau

Raphael Azria

Winnie Chan

Victoria Bacigalupo

Mariem Filali

Valentin Minter

Nicolas Delabaere

Alain Szadel

Conclusion d'un parcours de vie initié en septembre 2013, ce mémoire traitant d'électroacoustique me permet non sans émotion de revenir à mes toutes premières passions.

Nourri par la richesse des diverses rencontres faites tout au long de cette période, je garderai une admiration pour Eric Bavu, qui fut à mon égard un enseignant transmettant la connaissance de manière captivante, avant d'être le tuteur académique pour ce mémoire. Comment pourraisje ne pas citer Manuel Melon, de qui j'ai reçu mes premiers enseignements d'électroacoustique, et qui m'a à plusieurs reprises soutenu dans les recherches autour de ce document.

Intégrant la société Seltech et ses marchés de l'audio en 2018, je remercie très chaleureusement Giulio Di Capua qui en m'accordant sa confiance, aura donné carte blanche quant au développement du pôle acoustique de la société, permettant ainsi de donner lieu avec l'appui indispensable de Jin Leng, à des sujets d'investigations tels que celui-ci.

I. Introduction I.I. Global context

In an electronic market where multimedia devices are increasingly versatile, recent statistics published on the Voicebot.ai website and reported in Figure 1 highlight that wireless speaker systems are widely used for streaming music, in front of functions such as asking questions or checking the weather. Also, although the camera performance of a smartphone is often a predominant criterion for the choice of model, recent measurements from the Dxomark.com website (Figure 2) illustrate that consumers of smartphones actually use their device more for listening to music than for recording videos. It is so within this context that we understand the low frequency (LF) sound reproduction of devices, which remain compact in size, to be a noticeable interest for designers in this market.

Figure 1 -"Smart speaker use case frequency. January 2020" [START_REF] Kinsella | Streaming Music, Questions, Weather, Timers and Alarms Remain Smart Speaker Killer Apps, Third-Party Voice App Usage Not Growing[END_REF] Figure 2 -"What do you use your smartphone for?" September 2020 [START_REF] De Hillerin | Audio matters in smartphones and here's why[END_REF] Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 2 / 100

In example, considering smartphone companies as popular as Nokia and Xiaomi, Figure 3 illustrates the LF performance gap between two different generations of devices: the Nokia N95 (released in 2006) and the Xiaomi Black Shark 4 Pro (released in 2021). From this graphic, which show normalized sound pressure levels (SPL) from the mid-range, we observe that the Black Shark 4 Pro extends the nominal level from about 700 Hz to 480 Hz, subsequently with a smoother SPL decay slope. Graph recreated from [START_REF] De Hillerin | 2000 to 2021: The evolution of smartphone audio playback[END_REF] Also, from the Bluetooth speaker market, the example in Figure 4 From the above two examples as well as from the previously reported statistics, we therefore understand the interest for the audio industry to continuously improve the low frequency sound reproduction of multimedia devices which remain compact as they evolve on other aspects.

Figure 4 -SPL comparison: JBL Go 2 / JBL Go 3. Graph recreated from [START_REF] De Hillerin | Test Enceinte Go 2 : JBL améliore son best-seller ultra-nomade[END_REF] and [START_REF] Paillat | Test Enceinte ultra-portable JBL Go 3 : une brique de savon aux performances sonores étonnantes[END_REF] Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 3 / 100

I.II. Audio electronics market trends

By looking at recent developments in the Bluetooth and Smart speaker market, we observe that when a LF improvement is achieved, it most often relies on the Passive Radiator principle [START_REF]What Are Passive Radiators In Speakers?[END_REF] [7] [START_REF] Martins | The First Smart Speaker from Apple: A Strong Design and How It Is Perceived[END_REF], so that only a few of the largest devices use Bass-Reflex conceptions [START_REF] Débutant | Xiaomi Smart Speaker | Test De L'Enceinte Ok Google[END_REF] [10] [START_REF] Stemmelin | Harman/Kardon Aura : enceinte transparente sans-fil qui a du coffre[END_REF]. The operating principle of these two systems being described a little later in part II.II, Figures 5 and 6 respectively illustrate a market example for each of the two solutions.

However, in 2015 a Bass-Reflex design had been found in the small JBL Go Bluetooth speaker [START_REF] Soomal | JBL GO Smart Portable Speaker: Tear Down[END_REF], but it was then replaced by a Passive Radiator system in both the version 2 and 3, maybe both for reasons of mechanical simplicity and waterproof requirements.

Figure 5 -Apple HomePod mini split view [START_REF] Martins | The First Smart Speaker from Apple: A Strong Design and How It Is Perceived[END_REF] Figure 6 -Anker Rave split view [START_REF] Anker | Rave portable speaker: production description[END_REF] Also, in the domain of speakers designed for tablets and smartphones the work from Jiang et al. (illustrated on Figure 7) is an example that show the interest in Passive Radiators for improving the LF response of such a small system [START_REF] Jiang | Analysis and Optimization of Micro Speaker-Box Using a Passive Radiator in portable Device[END_REF]. But overall, we understand that most of these speaker systems rely on audio processors, often used to reshape the sound signature [START_REF] Patil | Smart Speakers With Smart Processors[END_REF] [15] [16] [START_REF]Smartphone audio is important, and here's what it takes to build the best[END_REF] In 2006-2007, Samsung researchers published two articles [START_REF] Arora | Low Complexity Virtual Bass Enhancement Algorithm[END_REF] [19] on the so-called "missing fundamental" technique, adapted for small transducers in portable multimedia devices. A brief description of this technique consists in creating the illusion of a fundamental frequency which cannot be physically generated by a speaker, by regenerating particular harmonics, as illustrated in Figure 8. An example of application on the market was seen in 2016 with the MaxxBass algorithm from the Waves company integrated into the SHARKK Wave Bluetooth speaker. But this device does not seem to be manufactured anymore, and it is possible that today most of the popular designers on the market developed their own algorithms to improve the bass response of their systems.

I.III. Objectives of the study and presentation of the Seltech company

The scope of this document is to investigate three well-known methods from the audio industry for the low frequency improvement of relatively small speaker enclosures designed by the company Seltech (www.seltech-international.com). Also, as the word "improvement" can lead to many different subjective interpretations, another objective of this study is to acquire knowledge about the perceptual evaluation of the improved enclosures, and thus, to relate the subjective criteria to the measurement of each of these enclosures.

Seltech is a medium-sized company (about 50 salaries), with a worldwide presence on diverse markets of the audio electronics, such as mobiles phones, Internet of Things (IoT), home automation, wearables, multimedia, telecom, toys, and others. Created in 1989, Figure 9 illustrates at today the different offices over the world, the headquarters being in Paris.

As Field Application Engineer in Acoustics for the company, my function is to support Seltech customers in the development of their application, everywhere where electroacoustics components are needed. My work is mainly founded on 3D and prototypes reviews, acoustics calculations, predictions, and measurements. Another part of my function is to continuously support and train the Seltech sales team into the challenges of the acoustics domain, as well as around the new technologies from the electroacoustics market.

Speakers of interest and their sealed enclosure

The investigations intend to focus on two electro-dynamic speakers from the Seltech portfolio:

one round shaped speaker of 40 mm outer diameter and of 18 mm height.

The reason for this choice is that this type of speaker is commonly used when looking at the compact Bluetooth / Smart speaker system market.

one rectangular shaped speaker of (L x w) 15 x 11 mm dimensions and of 3.5 mm height.

Although too thick to remain of interest in modern smartphones, this speaker is historically popular in the mobile phone market and is still a high runner in many Seltech customer applications.

Description of the speaker N ° 1 and its enclosure Composed as per illustrated on Figure 10, its main characteristics are summarized in the Table I. The typical electric impedance as well as the SPL at 0.1 m for the baffled speaker are illustrated in Appendix A. The enclosure designed for this speaker is presented and detailed on Figures 11 and12. It is made from 3D printed ABS plastic, with a fixed thickness for the walls = 2 mm. Being rectangular, this enclosure brings a rear acoustic volume (the volume seen by the rear side of the speaker diaphragm) = 165e-6 m 3 . The electric impedance as well as the SPL for the sealed enclosure at 0.3 m are respectively illustrated on Figures 14 and15, and the setup for this measurement is detailed on Figure 13. The reason for this measurement distance is that we want the microphone to measure both the speaker diaphragm and any additional source (coming from the improvement) as a unique acoustic source. Composed as per illustrated on Figure 16, its main characteristics are summarized in the Table II. The typical electric impedance as well as the SPL at 0.1 m for the baffled speaker are illustrated in Appendix A.

Illustrated on Figures 17 and18, the 3D printed enclosure for this speaker is made in two parts, and the thickness of its walls is = 1.5 mm. The rear acoustic volume so created is = 2e-6 m 3 .

The electric impedance as well as the SPL at 0.1 m for this sealed enclosure are respectively illustrated on Figures 20 and21. The setup for this measurement is detailed on Figure 19.

II.II. Studied methods for the improvement

As briefly discussed into the introduction section, this document focuses on three improvement methods well-known from the industry. This part of the document intends to describe the working principle of each of the three methods.

Improvement method N ° 1: Bass Reflex Invented by Albert L. Thuras in 1932 [START_REF] Thuras | Sound Translating Device[END_REF], a Bass-Reflex system is described as a speaker enclosure into which an opening has been made, to insert a tube (also called "vent" or "port"), as per illustrated on Figure 22. This port, in combination with the residual volume of air inside the enclosure, will so form a resonator (Helmholtz type), which once its fundamental resonance well-adjusted, will contribute to extend the LF response when compared to the original sealed enclosure design (Figure 23)

Figure 22 -Bass-Reflex principle drawing [START_REF] Thuras | Sound Translating Device[END_REF] Figure 23 -Bass-Reflex response against sealed enclosure response [START_REF] Thuras | Sound Translating Device[END_REF] Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 12 / 100 Improvement method N ° 2: Passive Radiator Harry Olson is the inventor of the Passive Radiator system. Patented in 1935 [START_REF] Olson | Loudspeaker and method of propagating sound[END_REF], this system is composed of an enclosure both containing a speaker and at least one diaphragm. This last element being often called "passive radiator" itself by confusion. Acting in a similar way than a Bass-Reflex system, the diaphragm, in combination with the residual volume of air inside the enclosure, will also form a resonator which will contribute to extend the LF response when compared to the original sealed design (Figure 25)

Figure [START_REF] Rice | Notes on the Development of a New Type of Hornless Loud Speaker[END_REF] -Passive Radiator principle drawing [START_REF] Olson | Loudspeaker and method of propagating sound[END_REF] Figure 25 -Passive Radiator response against sealed enclosure response [START_REF] Olson | Loudspeaker and method of propagating sound[END_REF] Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 13 / 100

Improvement method N ° 3: Active Equalization Unlike for the two previously described methods, the audio equalization does not really have a particular inventor but is more inspired from the acoustic telegraph and telecom domains [START_REF] Välimäki | All About Audio Equalization: Solutions[END_REF].

An example of persons having used the equalization to extend the LF response of a sealed enclosure is W. Marshall Leach, JR. into his article Active Equalization of Closed-Box

Loudspeaker Systems [START_REF] Leach | Active Equalization of closed box loudspeaker systems[END_REF]. From this work, a particular assembly of 2 nd order active high-pass filters (as per illustrated on Figure 26) is used to transform the sealed enclosure response "a"

from Figure 27 into the response "b" from this same Figure . A basic functional description of this filtering network is that it receives a voltage signal constant in frequencies at its input and transform it into a signal having the shape of the curve "c" of Figure 27. The increase of energy we can see on this curve (at around 0.6, from the x-axis) will so lead the speaker to radiate more sound in this same frequency region. -𝑅 𝑒 , the electrical resistive part of the voice coil, in ohms.

-B. l, the product of magnet field strength in the voice coil gap and the length of wire in the magnetic field, in tesla-meters -𝑀 𝑀𝐷 , the mass of the assembly "diaphragm / voice coil" and the mass of half of the outer suspension, in kilograms.

-𝑅 𝑀𝑆 , the mechanical resistance of suspensions, in Newton-second per meters -𝐶 𝑀𝑆 , the total mechanical compliance of suspensions, in meter per Newton -𝑆 𝐷 (mentioned in the form of the radius "a" in the Beranek's book), the projected area of the speaker diaphragm Based on these parameters, Leo Beranek then illustrated in the chapter "Loudspeaker enclosures" of his book, an acoustical analogous circuit for a sealed enclosure system (Figure 28). From this circuit, the current is considered analogous to an acoustic flow rate. The different components for this circuit are defined as below:

-𝑅 𝑔 , the output resistance of the electric source (ignored in the scope of this document)

- 𝑀 𝐴𝐷 = 𝑀 𝑀𝐷 𝑆 𝐷 2 ⁄
, the acoustic mass of the diaphragm assembly , where:

- 𝐶 𝐴𝑆 = 𝐶 𝑀𝑆 * 𝑆 𝐷 2 ,
𝑀 𝐴𝐵 , is the acoustic mass given by the enclosure dimensions and geometry. For both previously described sealed enclosures, this term is entirely assumed negligeable when compared to 𝑀 𝐴𝐷 , To measure the previously listed parameters, we can use a method called "Known Volume" as per described by R. Elliott into his web article [START_REF] Elliott | Measuring Loudspeaker Parameters[END_REF]. This method consists of two measurements of the speaker electric impedance, when mounted into a baffle: one without any acoustic load around it, and one with a known and sealed volume often added to the front side of it. The parameters are then calculated from the two recorded impedance curves, into the measurement software Audiomatica Clio, and using a procedure described by A. N. Thiele in one of its seminal papers [28] [29] But since the measurement of these parameters cannot be performed in vacuum, we observe the value of 𝑀 𝑀𝐷 to be affected by the mass of air particles located around the speaker diaphragm.

𝐶 𝐴𝐵 = 𝑉 𝑏 𝜌 0 𝑐 2 ,
This phenomenon therefore defines a new parameter named 𝑀 𝑀𝑆 = 𝑀 𝑀𝐷 + 𝑎𝑖𝑟 𝑙𝑜𝑎𝑑 A theoretical formula to estimate the value of this load term can be 2[

8 3 𝜌 0 𝑟 3 ]
where 𝑟 is the projected radius of the speaker diaphragm.

Measurement of the parameters for the speaker N ° 1

The parameter 𝑆 𝐷 reflecting the area of the speaker which pushes the air particles, it is often admitted that half of the outer suspension also contribute together with the diaphragm to generate the acoustic wave. Therefore, considering the diameter illustrated on Figure 30, we calculate the value of 𝑆 𝐷 = 1.02e-3 m 2 . From this table, we can observe the value of 𝑅 𝑒 to remain the same within the available measurement accuracy. On the other hand, as we observe the rest of parameters to change over the measurements, the coefficient of variation is calculated (both from the average and from the standard deviation) to briefly status on the importance of these variations from the each of average. Despite the calculated percentages are all reasonably low (the parameter 𝐶 𝑀𝑆 showing the highest variation with 1.89 %), we decide to consider the averaged values for the construction of the acoustic model. As for the speaker N ° 1, the value of 𝑅 𝑒 remains the same within the available measurement accuracy. From the calculation of the coefficients of variation, we see the parameter 𝐶 𝑀𝑆 to show the highest variation with 2.94 %. This value being a little higher than for the speaker N ° 1, we might understand that this speaker heats a bit more the air trapped inside the volume used for the measurement. This phenomenon would so start to significantly affect the correct quantification of 𝐶 𝑀𝑆 . As for the speaker N ° 1, we decide to consider the averaged values for the construction of the acoustic model.

Once all the parameters measured, we can build the acoustical circuit for each of the sealed enclosure and compare predictions against measurements, to verify the validity of our models.

As previously stated, the electric current of the circuit being equivalent to an acoustic flow rate, a separated network is built to transform the final output voltage into a quantity analogous to an acoustic pressure from a monopole type source.

Illustrated on Figure 36, this additional circuit consists of:

-A current source, reflecting the measured acoustic flow rate (𝑞) at the diaphragm point -An inductor, being equal to

Z 4πrc * 1 𝑃 0 = 𝜌 0 4𝜋𝑟 * 1 2𝑒-5
, where 𝑟 is the distance from the source When computed, the output voltage is frequency dependent and takes the following form:

𝑢(𝑓) = 1 2𝑒-5 * 𝜌 0 4𝜋𝑟 * 2𝜋𝑓 * 𝑞(𝑓)
By finally calculating 20 * log [𝑢(𝑓)] we so obtain a quantity representative of the SPL at a certain distance from the sealed enclosure, in a free field. Also, both because the models we use are linear and because this type of small speaker can rapidly behave in a non-linear way, we intend to verify that the SPL behavior of the enclosure remains the same for three arbitrary defined input voltages: 0.5 𝑢 𝑅𝑀𝑆 , 1 𝑢 𝑅𝑀𝑆 and 2 𝑢 𝑅𝑀𝑆 .

Figure 37 exposes the comparison for the electric impedance. This comparison gives a good correlation for most of the frequency band, until 2000 Hz, where the inductive behavior of the speaker voice coil starts to dominate the shape of the curve. This discrepancy can be explained by the fact that our acoustic model does not contain any inductance term for the voice coil. But this is by far acceptable since our investigations focus on the LF part of the spectrum. Within this range, we can observe the resonance peak as well as the damping for this peak to well be reproduced by the model. result signifies that above this frequency the motion of the diaphragm will break up in resonances and will so not move as a rigid piston anymore. The calculated value being close to the correlation limit we found; it might be a good explanation for the difference we see from 1500-2000 Hz.

-Another cause for this discrepancy, might be that at 0.3 m of distance from the enclosure, the microphone sees additional acoustic sources coming from the diffraction of the generated waves at the edges of the enclosure. As for the enclosure N ° 1, a comparison is performed for both the electric impedance and the SPL, and we intend to verify the linear behavior of the enclosure at the three following voltages: 0.1 𝑢 𝑅𝑀𝑆 , 0.5 𝑢 𝑅𝑀𝑆 and 1 𝑢 𝑅𝑀𝑆 .

Figure 40 compares the electric impedance. In this second design where the inductive contribution of the voice coil starts higher in frequencies, we observe an almost perfect correlation of the curves until 6000 Hz. The resonance peak recreated by the model is a bit shifted (few Hz higher), but the damping for this peak is perfectly reproduced.

II.IV. Protocol for the perceptual evaluation of each of the improvement

As introduced within the scope of the study, a listening test is intended to be carried out on the prototypes resulting from the various improvements. This type of test allows the objective performance to be linked to the subjective performance, and thus, to decide on the relevance of each of these improvements. The protocol established for this test is inspired from two articles by E. Parizet et al. [30] [31], from an article by G. Lorho [START_REF] Lorho | Perceptual Evaluation of Mobile Multimedia Loudspeakers[END_REF] and from an article by G. Liu et al. [START_REF] Liu | Evaluation of Portable Loudspeakers Using Virtual Listening Test[END_REF].

Subjects number and description

The four introduced articles respectively describe a number of 72, 64, 16, and 9 subjects. Even if we understand a small number to only give a tendency for the results, our experience can only rely on 10 subjects (5 men and 5 women), for which the age repartition is from 20 up to 55 years old.

Setup of the listening test

The test is based on paired comparisons, and similarly to the protocol described in [START_REF] Parizet | Multi-dimensional listening test: selection of sound descriptors and design of the experiment[END_REF], a square matrix is built with each of the improvement to test as inputs. From this matrix, the diagonal is removed, and a further analysis is performed to determine the relevant pairs to submit for the test. Among the improvements, a Bluetooth speaker JBL Go 3 is intended to be considered for the comparisons around the speaker N ° 1, and a smartphone Oneplus 6 will also be considered for the comparisons around the speaker N ° 2. A brief description of these devices as well as their acoustic signature (measured from our acquisition software) are reported in appendix B.

For each subject, the pairs order is randomly set by means of a combination generator tool available on the website generatormix.com. Questions asked between each pair listened to

Inspired from [START_REF] Parizet | Multi-dimensional listening test: selection of sound descriptors and design of the experiment[END_REF], the first task requested to the subject is to freely speak and comment about what he just listened to. This open talk allows to collect some words (also called "descriptors"), which once put in common from all the subjects, may help to explain a tendency or a discrepancy between the subjective and the objective performance. This task is then followed by two closed questions:

-"Which of the two systems brings more low frequencies to the sound?" -"Which of the two systems do you prefer?"

This type of forced choice procedure is directly inspired from the "Test 3" described in [START_REF] Parizet | Comparison of some listening test methods : a case study[END_REF],

but with the possibility here to answer: "I don't see the difference" or "I don't have any preference". This additional possibility avoids blocking the test or looping into many listening repeats. It therefore ensures to keep the test duration reasonably short. Audio signals used for the test Music songs are used in both [START_REF] Lorho | Perceptual Evaluation of Mobile Multimedia Loudspeakers[END_REF] and [START_REF] Liu | Evaluation of Portable Loudspeakers Using Virtual Listening Test[END_REF], but only this last article deals with short extracts of about 20 -30 seconds. Using extracts instead of entire songs is a predominant criterion for our test since we cannot retain each subject more than 30 minutes. As a compromise between the time and the number of extracts to be played, it was decided to submit two extracts of 15 seconds each, the first of which is played on a first half of combinations, before playing the other on the second half of combinations.

The selected music styles for improvements around the speaker N ° 1, are pop and jazz, both chosen loud in bass. The selected styles for improvements around the speaker N ° 2, are rock and jazz, both soft in bass, as the distortion for this type of transducer can increase rapidly when used out of its typical range.

Results exploitation

From the analysis of the results, the objectives will be:

-

To correlate the subjective attribution of LF to the measurements and explain any discrepancy with the help of collected words from the open talks.

-To compare the preferences to the LF attribution, and to also rely on the collected words to justify on the preference attribution when not due to the extended presence of LF. Although early Bass-Reflex (BR) systems were described in [START_REF] Thuras | Sound Translating Device[END_REF] and [25], the investigations carried out in this chapter mainly rely on the articles from A. N. Thiele [START_REF] Thiele | Loudspeakers in Vented Boxes: Parts I and II[END_REF] and R. H. Small [START_REF] Small | Vented-Box Loudspeaker Systems Part I: Small-Signal Analysis, and Part II: Large-Signal Analysis[END_REF]. According to this last author, the acoustical analogous circuit of a BR system has the form of the one illustrated on Figure 44.

Figure 44 -Acoustical analogous circuit of a BR system [START_REF] Small | Vented-Box Loudspeaker Systems Part I: Small-Signal Analysis, and Part II: Large-Signal Analysis[END_REF] From this circuit:

-𝑅 𝐴𝑃 represents the losses created into the port. We choose to neglect this term at a first design step,

- 𝑀 𝐴𝑃 = 𝜌 0 * 𝑝𝑜𝑟𝑡 𝑙𝑒𝑛𝑔𝑡ℎ 𝑝𝑜𝑟𝑡 𝑎𝑟𝑒𝑎
is the equivalent moving mass for the air particles into the port. The value for the port length containing some end corrections, -𝑅 𝐴𝐿 represents leakages caused by the port into the enclosure. This last parameter being difficult to estimate, it is decided to not consider it within the scope of our investigations.

Estimation of the shape for the extension

A proposed starting point for the design of a BR system, is to estimate the shape (also called "alignment") that can be reached for the extended portion of the response curve. At a time when IT was not as developed as it is today, A. defined for the x-axis, typical response curves for the three alignments, using the same speaker but different sizes for the enclosure. Depending on the alignment, we observe a noticeable difference in the SPL shape for the extension, the C4 type giving the most irregular shape, but also a difference in the frequency amount, the QB3 type showing the smallest extension. From the page 15, we calculated 𝐶 𝐴𝐵 = 1.16e-09 m 5 /N and listed the formula for the calculation of 𝐶 𝐴𝑆 . Considering the measured value for 𝐶 𝑀𝑆 and 𝑆 𝐷 , we calculate 𝐶 𝐴𝑆 = 5.51e-10 m 5 /N and the ratio 𝐶 𝐴𝑆 𝐶 𝐴𝐵 = 0.48. This value reports an alignment close to the shape of the C4 one. We therefore expect to get a considerable amount of extension in our design but with an irregular shape for the SPL in this region.

Design of the port

Once this first step reviewed, we need to estimate more accurately the quantity of LF we can bring in our design. In their respective articles [START_REF] Thiele | Loudspeakers in Vented Boxes: Parts I and II[END_REF] [34], A. Thiele and R. Small explained that the key frequencies for a BR system can fully be studied from the electric impedance curve of the speaker. The typical shape of such a curve is illustrated on Figure 46.

Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 29 / 100

Figure 46 -Typical electric impedance of a BR system [START_REF] Small | Vented-Box Loudspeaker Systems Part I: Small-Signal Analysis, and Part II: Large-Signal Analysis[END_REF] From this Figure:

-𝑓 𝐻 is often understood as the shifted resonance of the original sealed enclosure, -𝑓 𝐿 is the low frequency roll-off (LFRO) for the extension. Defined as the -3 dB point from the nominal SPL (considered at 1000 Hz in this section), -𝑓 𝑀 is the Helmholtz resonance, assuming a lossless system. Its value corresponds to the minimum of impedance in between 𝑓 𝐿 and 𝑓 𝐻 .

Although 𝑓 𝐿 is the frequency that interests us for the calculation of the extension, the design approach is made by determining 𝑓 𝑀 , the three frequencies being intimately linked and possible to compute through our acoustic model thereafter [28] [34].

From the Helmholtz resonator principle, we find the link between 𝑓 𝑀 and the port dimensions in the following formula:

𝑓 𝑀 = 𝑐 2𝜋 √ 𝐴 𝑉𝑙
, where:

-𝑉, is the inner volume of the enclosure -𝑙, is the length of the port (including end corrections) -𝐴, is the area of the port But when designing BR systems, this formula is not the only one to consider for the dimensions of the port. To avoid the generation of noise caused by aerodynamic turbulences at the ends of the port, R. Small [START_REF] Small | Vented-Box Loudspeaker Systems Part I: Small-Signal Analysis, and Part II: Large-Signal Analysis[END_REF] recommends adjusting the port area so that the velocity of air particles inside will not exceed 5% of the sound velocity. This condition can be satisfied with the following formula: 𝐴 ≥ 0.8𝑓 𝑀 𝑆 𝐷 𝑥 𝑚𝑎𝑥 (𝑥 𝑚𝑎𝑥 being the peak linear displacement of the speaker diaphragm, equal to 3.5 mm in our case)

Considering the resonance of the sealed enclosure (𝑓 𝐵 ) to be = 200 Hz and a small target for 𝑓 𝑀 fixed = 150 Hz, the above condition would require:

-A port area 𝐴 ≥ 4.28 cm 2 -A port length 𝑙 = 34 cm (end corrections included) By far, this port is too long and so not technically feasible in regards with the dimensions of our system. Moreover, in our estimations, we do not consider that the port goes inside the enclosure.

Resulting both from mechanical constraints and acoustical targets, the design proposed on As this design does not respect the above condition for the minimum area, it becomes relevant to study the noise added by the turbulences at the ends of the port. To quantify this phenomenon, we propose to design an alternative BR system relying on the article from N. Roozen et al. [START_REF] Roozen | Reduction of bass-reflex port nonlinearities by optimizing the port geometry[END_REF] In this publication the authors summarize different terminations for the port of a BR system, from which the proposed design called "Port C" appears as a good compromise between mechanics and acoustics for being considered in our system. The curvature radius for the ends of this port is related to the port inner radius by a factor 2. This leads us to design the alternative

Acoustic prediction

The below section reports only about the expected electric impedance and SPL for both the original and horn port design. The impact of turbulences for the original port design will be quantified by measuring the prototypes.

The analogous circuit for the BR system is built as per illustrated on Figure 49, with 𝑀 𝐴𝑃 ,the added moving mass term for the air particles into the port and calculated according to the formula listed in page 27. Also, the value for the term 𝐶 𝐴𝐵 is reduced from the volume taken by the port into the enclosure. To compute the global SPL of the system, the acoustic flow rate for the port section is measured similarly to the one for the diaphragm section, and then, the two flows are simply mixed into the additional circuit illustrated on Figure 50. From this comparison, we first confirm the shape for the extension to be close to a C4 alignment, as per studied in the beginning of this section. Then, with a LFRO around 80 Hz we confirm the expected extension. The sharp drop observed below this frequency, and well described in [START_REF] Thuras | Sound Translating Device[END_REF] [25] [28] [START_REF] Small | Vented-Box Loudspeaker Systems Part I: Small-Signal Analysis, and Part II: Large-Signal Analysis[END_REF], is often attributed to destructive interferences between the speaker and the port. Finally, according to the prediction we conclude that we should improve the LF of our enclosure with a slightly fluctuating SPL (± 3 dB) until 80 Hz.

Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 33 / 100 On the next page, Figure 57 compares the SPL for the original BR against the sealed enclosure at 1 𝑢 𝑅𝑀𝑆 . Looking at some points on this graph, we observe that the BR amplifies the SPL by about 3-4 dB at 150 Hz, and by about 5 dB at 100 Hz. However, we observe a LF extension that drops quickly in frequencies, far above the predicted LFRO of 80 Hz. Indeed, this point is seen at around 110 Hz, or 30 Hz above the predicted value. An explanation for this might be that the system brings some losses while our model is lossless. From this comparison, we can observe few dBs of difference between the curves in the LF region below 100 Hz. Since the strongest attenuation is shown from the curve obtained for 2

𝑢 𝑅𝑀𝑆 , we might understand a phenomenon related to non-linearities in the port when it receives strong energy. But considering this small difference of SPL, we simply conclude that this attenuation should not really be perceived when listening to this design within the voltage range considered in this study. As an aside, it might be interesting to analyze this non-linearity at higher voltages. But it would also be necessary to verify that the speaker itself remains linear in this range.

Comparison of measurements against predictions

Figure 59 compares the electric impedance of the system, while Figure 60 compares the SPL for 1 𝑢 𝑅𝑀𝑆 . As briefly discussed in the previous section, we understand both from the impedance and from the SPL that our simulated system does not predict the losses that are measured over the prototypes. Indeed, from the impedance curve we see the predicted damping for 𝑓 𝐿 being far lower than the measured one, while the predicted damping for 𝑓 𝐻 is closer to the reality. This leads to a good correlation of predicted and measured SPLs until around 120 Hz.

A way to introduce the losses in our model is to consider the resistive term 𝑅 𝐴𝑃 which was intentionally neglected at a first design step (page 27). But as this term is frequency dependent, it cannot be recreated through a pure resistance component. To calculate it, we decide to rely on both the section "Intermediate-sized Tube-Mixed Mass-Resistance" from [25] and on an application note from the company Knowles regarding microphone simulation models [START_REF] Knowles | Application Note 20: Getting started with Knowles Sisonic simulation models[END_REF]. As described in [START_REF] Knowles | Application Note 20: Getting started with Knowles Sisonic simulation models[END_REF], we create the term 𝑅 𝐴𝑃 using a voltage dependent current source, into which a Laplace transform is computed as follow:

𝐿𝑎𝑝𝑙𝑎𝑐𝑒 = 1/[( 𝜌 0 𝜋𝑟 2 ) √2𝑠𝜇 0 * [( 1 𝑟 + 2)]],

Qualification of turbulences created by the original port design

As a first step, we need to confirm that both BR systems behave identically. To proceed, a measurement comparison is performed for both the electric impedance and the SPL at 1 𝑢 𝑅𝑀𝑆 .

From the measurements reported in Appendix C, we rapidly conclude that the two systems behave identically. Only a small difference on the frequency 𝑓 𝐿 is observed, probably due to an error in adjusted length for the horn port. To quantify the aerodynamic turbulences, we rely on the work from Garcia-Alcaide et al. [START_REF] Garcia-Alcaide | The aerodynamics phenomena of a particular bass-reflex port[END_REF]. The procedure consists of measuring the near field response of the port (0.02 m fixed in our case), when excited by a pure sine equal to its resonance 𝑓 𝑀 . The setup for this measurement is illustrated on Figure 64, and the responses for the two BR are illustrated in the figures after. a broadband noise attributed to the turbulences under study, but also, the first harmonics of the pure tone increasing accordingly to the voltage and for which the responsible is more probably the speaker itself than the port.

From the two first comparisons, we clearly see the benefice of using the horn port, as it transmits the tone with much less noise than the original port. On the other hand, when applying 2 𝑢 𝑅𝑀𝑆 Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 40 / 100 the benefice of this second port is less visible. Indeed, besides still attenuating the noise above 1000 Hz by 10 dB, this port produces more turbulences in the region 100 -200 Hz. This last observation appears in total concordance with what is commented in the part "5 Experimental investigation" of [START_REF] Roozen | Reduction of bass-reflex port nonlinearities by optimizing the port geometry[END_REF]: "[…] at low levels a cylindrical port with a large curvature radius produces less blowing sound than a cylindrical port with a small curvature radius, while at higher levels it is the other way around. "

By concluding that not only the turbulences are important to consider, but also the radiation efficiency and the quality factor of the port fundamental resonance (open ends tube resonance), the authors suggested a diverging geometry as per illustrated on Figure 68. But in the end, as this shape is more complex than the design we considered (compared again on Figure 69), it might be a challenge to realize it from a manufacturing and cost aspect for Seltech. In conclusion, for reasonable SPLs, we understand the port design considered in our investigations to remain a good option against a port with sharp terminations.

Conclusion

From this first improvement method, we learned the basics of Bass-Reflex designs and how complex it can be to get a good radiating port in enclosures as small as those considered here.

But even if the LF extension we get from the prototypes is smaller than what the models predict, we get a solution that amplifies the sound by around 5dB at 100Hz, and with a -3dB point extended from 150 Hz for the sealed enclosure, to about 110 Hz. In addition, for small to middle-range SPLs, a horn shape for the port terminations can significantly reduce the noise caused by aerodynamic turbulences in this type of small tube. But in the end, one could understand that this type of small port introduces heavy losses into the system, and therefore decreases the expected SPL in the LF region. A more reasonable target for 𝑓 𝑀 would allow to increase the port area again, and therefore lead to a smaller LF region, but louder and flatter.

III.II. Improvement method N ° 2 (Passive Radiator)

The investigations carried out in this section are both inspired from the work of Jiang et al. [START_REF] Jiang | Analysis and Optimization of Micro Speaker-Box Using a Passive Radiator in portable Device[END_REF] and of R. H. Small [START_REF] Small | Passive-Radiator Loudspeaker systems, Part I: Analysis and Part II: Synthesis[END_REF]. Despite we understood in the part II.II of this document that a Passive Radiator (PR) system is composed both of a speaker and of a diaphragm, we do not have the measurement capabilities to properly qualify this last element. Therefore, relying on the following phrase from [START_REF] Small | Passive-Radiator Loudspeaker systems, Part I: Analysis and Part II: Synthesis[END_REF] "[...] the passive radiator is often made from the same frame and suspension as the driver […]", we decide to simply consider a secondary speaker identical to the first one, but non-wired, to design our system. For the rest of the section, this transducer will be called "passive element" (PE). As already discussed, 𝑅 𝐴𝐵 is neglected and 𝑅 𝐴𝐿 is not considered in our models.

Figure 70 -Acoustical analogous circuit of a PR system [START_REF] Small | Passive-Radiator Loudspeaker systems, Part I: Analysis and Part II: Synthesis[END_REF] From this Figure, we can observe similarities with a BR system. Indeed, the circuit is extended by an additional loop on the right of the 𝐶 𝐴𝐵 term, containing so the acoustical properties of the PE (instead of the properties of a port).

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Qualification of the passive element, and estimation of the shape for the extension Applying the same method than described in the part II.III, the Table VI on the next page summarizes the measured values only for the mechanical parameters of this element. Also, proceeding as in [START_REF] Small | Passive-Radiator Loudspeaker systems, Part I: Analysis and Part II: Synthesis[END_REF], we think relevant to compare these values with the ones of the speaker.

This, to assess whether the two elements will behave similarly in the design. -The first one, already introduced on page 28, is the System compliance ratio (called α in [START_REF] Small | Passive-Radiator Loudspeaker systems, Part I: Analysis and Part II: Synthesis[END_REF]), and defined =

𝐶 𝐴𝑆 𝐶 𝐴𝐵 , -
The second one is the PR compliance ratio (called δ in [START_REF] Small | Passive-Radiator Loudspeaker systems, Part I: Analysis and Part II: Synthesis[END_REF]) and defined = Figure 71 -"Responses obtainable from passive-radiator system for the condition δ = α" [START_REF] Small | Passive-Radiator Loudspeaker systems, Part I: Analysis and Part II: Synthesis[END_REF] Acoustic prediction

Once the PE qualified, the circuit illustrated on Figure 72 is built with the term 𝐶 𝐴𝑅 containing the previously calculated value and the terms 𝑅 𝐴𝑅 and 𝑀 𝐴𝑅 calculated using the formulas from the page 15.

The 𝐶 𝐴𝐵 term is reduced from the volume taken by the PE in the enclosure.

At this design step, only the SPL from the system is relevant to compare with the sealed enclosure. The curves are illustrated on Figure 73 for a comparison at 0.3 m and for 1 𝑢 𝑅𝑀𝑆 .

From this graphic, we observe that the system as it is does not improve the LF region but degrades it. In more detail, the "notch" we see on the As previously introduced, this section will discuss the adjustment of the PE 𝑓 𝑆 , for extending the LF response. And as mentioned also, this adjustment will consist of increasing the value of Mar. But to determine the optimal value, we decide to rely on the method described in the part "4. Optimization" of [START_REF] Jiang | Analysis and Optimization of Micro Speaker-Box Using a Passive Radiator in portable Device[END_REF]. The procedure described in this section consists of resolving an integral function (𝐹) from the sealed SPL to the tuned PR SPL, and thus between two arbitrary defined frequencies. The formula for this integral is given here below:

𝐹 = ∫ [𝑆𝑃𝐿 𝑃𝑅 (𝑓) 𝑓 2 𝑓 1 -𝑆𝑃𝐿 𝑆𝑒𝑎𝑙𝑒𝑑 (𝑓)] 𝑑𝑓
By then comparing the result for different 𝑀 𝐴𝑅 values, we are so able to status on the optimal configuration for getting the heaviest and largest LF extension.

To proceed, the first evaluation to do is to theoretically estimate from what 𝑀 𝐴𝑅 value the PR solution starts to extend the LF response, instead of degrading it.

Proceeding by step of 0.5x 𝑀 𝐴𝑅 , Figure 79 compares the simulated SPL for the sealed enclosure against different scenarios for the PR system. a dynamic of 10 dB (instead of 3 dB for the BR) to define the two frequencies between which we intend to solve the integral function. The reason for this choice is that 10 dB corresponds to a loudness perceived as half as loud for a human.

Starting again from 1000 Hz on the sealed enclosure curve, the -10 dB point is found at about 100 Hz. Therefore, the integral will be solved for SPLs between 100 and 1000 Hz.

The Table VII After analyzing these predictions, we observe from both the results of the integrals and the shape of the curves that the optimal configuration must be given for 𝑀 𝐴𝑅 ′ = 3.5x 𝑀 𝐴𝑅

Prototype customization

Now we have determined the optimal 𝑀 𝐴𝑅 ′ term in our system, we need to find the corresponding amount of mass to add on the PE diaphragm. From the page 15, we know that 𝑀 𝐴𝑅 ′ is linked to 𝑀 𝑀𝑅 ′ by the constant value of 𝑆 𝐷 2 . To avoid calculation errors due to rounding, we directly rely on the term 𝑀 𝑀𝑅 which comes from a direct measurement and transpose 𝑀 𝑀𝑅 ′ = 3.5x 𝑀 𝑀𝑅 .

From the page 16 we learned that the mass 𝑀 𝑀𝐷 ′ of the moving part for the PE can be found from the formula 𝑀 𝑀𝐷 ′ = 𝑀 𝑀𝑅 ′ -2[ Five measurements over the scale are performed to confirm its weight (reported on Table IX), and the additional part is then mounted over the prototype as per illustrated on Figure 84

Prototype qualification

As for the BR system, we first quantify the improvement realized by the tuned PR design prior to compare measurements against predictions. The setup for this qualification remains the same as the one for the initial system verification (Figure 65). On the next page, Figure 85 compares the SPL for the tuned design against the sealed enclosure, at 1 𝑢 𝑅𝑀𝑆 .

A first observation is that the LF extension is much less significant than for the BR system.

However, we can still quantify a frequency improvement by looking at the 75 dB SPL point:

for the sealed enclosure this point is at 140 Hz, while for the PR solution it is extended to 120 Hz. From a global point of view which also takes the dB amplification into account, we doubt that this improvement can be perceived when listening to this design. Remaining on a zoomed dynamic of -20 to + 20 dB, we see a perfect match of the three curves, and therefore simply conclude that our system remains linear within the defined voltage range.

Comparison of measurements against predictions

Figure 87 compares the electric impedance of the system, while Figure 88 compares the SPL at 1 𝑢 𝑅𝑀𝑆 . As explained in [START_REF] Small | Passive-Radiator Loudspeaker systems, Part I: Analysis and Part II: Synthesis[END_REF], the form of the impedance curve is identical to the one of a Bass-Reflex system. Therefore, we expect to get on the curve the three key frequencies𝑓 𝐿 , 𝑓 𝑀 and 𝑓 𝐻 which describe the same phenomenon than for a BR system (the mass term in the resonance 𝑓 𝑀 being the moving mass of the PE). Analyzing the curve on Figure 87, we can see a perfect match between measured and predicted values for the frequencies. Only the damping at 𝑓 𝐿 is a bit underestimated by the model. We so conclude that our model perfectly approaches mechanical behavior of the system. From the SPL curves illustrated on Figure 88 also, we see our model perfectly recreating the measurement tendency. As for the electric impedance, the damping at the notch is underestimated but we globally get a good correlation of the curves.

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Conclusion

Unlike the Bass-Reflex design, we conclude that we well approach the mechanical and acoustical behavior of this Passive Radiator design. However, we understand that using a speaker as passive element instead of a diaphragm is not optimized regarding the range of compliance values. Indeed, with a calculated δ ratio of 0.4, we can only achieve non-flat alignments with small extensions. In the end, even if we know that with equivalent systems, a

Passive-Radiator is less efficient than a Bass-Reflex [START_REF] Tanasescu | Passive radiator speaker design -Box calculation example[END_REF], we could continue the investigations by developing a PE specifically on this subject, as this design is very popular in the market. But that would require acquiring the necessary measurement capabilities, as per described in Appendix D.

III.III. Improvement method N ° 3 (Active Equalization)

As introduced in the part II.II, we intend to follow the technique used in [START_REF] Leach | Active Equalization of closed box loudspeaker systems[END_REF], but with designing only one 2 nd order active high-pass filter (HPF). However, both because we do not have the capabilities to achieve this filter in the analog domain and because we have seen from part I.II the tendency of the market to use audio processors, we intend to configure this HPF in the digital domain, on a processor as popular as those from Analog Devices.

Presentation of the audio processor

The component selected for our investigations is the codec ADAU1772 integrating an audio processing engine. Its functional diagram reported in Appendix E embeds analog-to-digital converters (and vice versa) so that users can easily deal with the analog chain of a speaker system.

This hardware solution comes with a graphical programming software called SigmaStudio. Its interface allows to connect graphics blocks together to design the signal flow and route it to the various available input and output ports. From the software libraries, the section "General 2 nd

Order" delivers a variety of filter algorithms among which we can find a HPF showing a transfer function identical to the elementary filters used for the network designed in [START_REF] Leach | Active Equalization of closed box loudspeaker systems[END_REF]:

𝐻(𝑠) = 1 𝑠 2 + 𝑠 𝑄 +1
, where 𝑠 is the complex frequency and 𝑄 is the filter quality factor [START_REF]General Filters[END_REF].

Illustrated in Figure 89, the software menu for the settings of this HPF features:

-A field for entering the center frequency 𝑓 𝐻𝑃𝐹 -A field for setting the quality factor 𝑄 -A field for setting an output gain (in dB)

This last parameter acting on the global output gain (as per shown by the example in Figure 90) our intention is to let this parameter set to "0". And so similarly to [START_REF] Leach | Active Equalization of closed box loudspeaker systems[END_REF], we target to only amplify the signal around the center frequency by means of the Q factor.

Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 54 / 100 From this last figure, the values for the components are defined as below:

-𝑅 arbitrary set to 1

-𝑅 2 = 𝑅 2 = 0.5 -𝑅 1 = 𝑅 2 * [( 3𝑄-1 𝑄 ) -1] -𝐶 = 1 2𝜋𝑅𝑓 𝐻𝑃𝐹
In this configuration, we can drive the network by only setting a value for value for 𝑄 and 𝑓 𝐻𝑃𝐹 . The second parameter of interest is 𝐼 𝑚𝑎𝑥 , the maximum peak current consumable by the speaker before damaging it. This data being unknown from the speaker manufacturer, we propose to check the theoretical fusing current of a wire identical both in diameter and in material to the one used in the speaker voice coil. Considering a copper wire of diameter = 0.13 mm, the found value is around 3.6 A.

For sure, our intention is to stay far below this theoretical limit which could (if not correctly estimated) seriously damage the speaker. To proceed, we decide to investigate this equalization solution with two parallel scenarios:

-One design in which we rule on a maximum current in the center frequency region corresponding to twice the current in the mid-frequency band, -An alternative design in which we allow the current in the center frequency region to correspond to three times the current in the mid-frequency band.

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The prediction of the current consumption is realized using the same reversed circuit than for the displacement, and by simply computing the current in the electric loop illustrated in Figure 94. From the previous graphs, we confirm to remain under the excursion limit of 3.5 mm in both scenarios for which the defined current limit is reached at each of the HPF frequency. Finally, predicted SPLs at 1 𝑢 𝑅𝑀𝑆 are compared on Figure 97 to the sealed solution. A first observation is that this EQ technique alone does not make it possible to achieve a flat extension. Also, it is not surprising to see the EQ N ° 2 extending the response lower in frequencies (LFRO estimated at 75 Hz), but we observe the two scenarios to be equivalent in the range 120 -200 Hz. which is above the predicted value (75 Hz). We therefore understand that we may have reached a limit in the speaker behavior with respect to the energy injected. When looking at the SPL behavior according to the voltage input, we observe for both solutions a decrease of SPL at 2 𝑢 𝑅𝑀𝑆 , in the range 75-150 Hz. However, the EQ N ° 2 showing a marked variation at both at 1 and 2 𝑢 𝑅𝑀𝑆 , we suspect this second solution to strongly behave in a nonlinear manner. A way to detect that we reach a limit of linearity in our system is by evaluating the Total amount of Harmonic Distortion (THD). This parameter, expressed in %, is defined as the ratio between all the harmonic components of a signal and the overall signal itself.

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Conclusion

As for the Passive Radiator design, we conclude that we well approach the behavior of this solution. And by showing large LF extensions, this design could be a good alternative to Bass-Reflex designs. However, depending on the filter network configuration, we learned that nonlinearities can quickly appear with increasing energy. This first results in a distorted sound of the solution, but also leads to a risk of damaging the speaker itself and therefore reducing its lifetime. Additionally, the increase in current consumption caused by this design remains important to consider in the context of battery-operated applications.

In the end, a solution which monitors the current consumption in real-time to activate / deactivate the equalizer according to the required energy to deliver could be a good way to deal with such a design.

III.IV. Perceptual evaluation of each of the improvement

As introduced in part II.IV, the objective of this section is to discuss the results of the listening tests carried out for each of the improvements, and thus to correlate the subjective perception of LF with the performed measurements. Also, this section intends to analyze the link between the LF sensation and the global sound preference.

However, as discussed in the PR section, although we master the system behavior, the use of a speaker as PE does not really improve the LF response. We so decided not to select this improvement for tests.

Inspired from [START_REF] Parizet | Multi-dimensional listening test: selection of sound descriptors and design of the experiment[END_REF], a square matrix is built (Table X) with each of the improvements to test as inputs. The different pairs come from the intersections, and a row reading determines a test direction while a column reading determines the reverse direction. In addition to these pairs, we submitted the original BR port to compare against the horn port. But for this additional test,

we only asked subjects to freely speak with no questions about LF and preferences.

Finally, as described in the test protocol, the pairs order is randomly set for each subject, so that hearing fatigue does not occur at the same time.

Table X -Listening test N ° 1 -Matrix of improvements to test

Sealed EQ BR (Horn port) JBL Go 3 Sealed X X X EQ X X X BR (Horn port) X X X JBL Go 3 X X X
Subjects seated at approximately 70 cm from the speaker enclosures hidden by a tissue. The SPL measured in this condition, and for a music type signal is = 70 dB SPL (global 𝐿 𝑒𝑞 over 15 seconds of music extract). This value giving 77 dB SPL when recalculated at 30 cm, we understand this energy to be close to our sinusoidal measurements performed at 1 𝑢 𝑅𝑀𝑆 . We will therefore consider these measurements for the comparisons.

Music extracts presentation

As defined in the protocol, we played two extracts of 15 seconds each per half of combinations to be submitted. The first comes from the jazz song "It Ain't Necessarily So" by artist Jamie

Cullum. The second is from the pop song "Billie Jean" by artist Michael Jackson.

Spectra of these extracts are compared in Figure 104. A first observation is that the global energy repartition looks similar to the shape of a pink noise.

Indeed, relying on articles like the one written by E. Bazil [START_REF] Bazil | Mixing To A Pink Noise Reference[END_REF], mixing a song with a pink noise spectrum as target would "sounds naturally 'balanced'.". Also, by showing 5 dB more in LF and 10 dB more in HF, the extract from Michael Jackson seems to bring more energy overall.

The two sound samples are equivalent in the mid frequency range. Table XII reports collected words which was pronounced more than one time over all the comparisons. By looking first at the LF attribution, we remark from the averaged values that for both pairs a large majority of subjects attributed more LF to the improvements. This correlates well with what we measured and so confirm the success of our developments.

Looking then at the preferences, a large majority voted for the improvements as well.

Considering so the words collected, we can verify if the reason for preference is driven by the LF extension. Table basically split in two categories: words which more refer to a positive qualification, and those which more refer to a negative qualification. Among the descriptors used, we observe that the expression "more powerful" was pronounced 7x times in regards with the BR system. However, from Figure 105, the only gain of energy we see is in the LF region.

We therefore conclude on a feeling which might be related to this LF improvement.

On the EQ solution side, the positive word "wider" was pronounced 2x times against a feeling of "dry", "closed" and "noisy" sound for the sealed solution in comparison. Here also, the word "wider" used for the EQ against the word "closed" used for the sealed solution might relates to the LF improvement from the EQ, as only this region is amplified by the solution.

Finally, for both solutions we conclude on preferences which are related to the LF extension they provide. Comparison between the improvements Figure 106 illustrates the subtractions 𝐵𝑅 𝑆𝑃𝐿 -𝐸𝑄 𝑆𝑃𝐿 , so that we can see how much the BR solution extend the LF region compared to the EQ one.

Figure 106 -Listening test N ° 1 -SPL comparison between improvements

From the Table XIII we see that the BR system is preferred at 50 % while only 30 % of the subjects attribute more LF to it. Unlike the previous comparisons, the collected words will this time help us to better understand the reason for the preference. Table XIV on the next page classifies the words in the same way as for the previous section.

From these collected words, we notice the expression "more powerful" pronounced 4x times as well as the word "deeper" pronounced 2x times, both with respect to the BR solution. As discussed in the previous section, these feelings could relate to the LF amplification created by the BR system. However, with the expressions "more balanced" and "clearer" pronounced 4x and 2x times in favor of EQ, we understand that if the LFs are amplified too much, it can lead to a feeling of speaker system wrongly balanced.

But that does not explain why the BR system is preferred over the EQ one. An explanation for this maybe that the BR is perceived twice as "more precise". It is possible that this latter sensation describes artifacts introduced by the processor into the EQ solution, making the sound reproduction less precise than that of the BR. But in this context, an SPL curve is not sufficient to try to explain this feeling. Comparisons against a solution from the market As both introduced in part II.IV and in the beginning of this section, the Bluetooth speaker JBL Go 3 was part of the listening tests, mainly for evaluating the improvements from this study against a solution (equivalent in size) from the market.

Figure 107 reports about normalized SPLs at 500 Hz for all the systems, while the Table XV on the next page summarizes all the answers for the LF and preference questions.

A quick observation from the SPL graph is that the LF performance of the JBL Go 3 is quite similar to the one of our improvements, except for the peak around enclosures resonance, where the JBL brings a flatter response. By analyzing the average percentages for the LF attribution, we see that the JBL is seen to provide more bass except when compared to the BR system, for which an equality of performance is found. Looking more in detail between the two directions of test: the subjects attribute more LF to the JBL (60%) for the direction BR → JBL, while they attribute more LF to the BR (also 60%) for the other direction: JBL → BR. This observation is interesting to analyze, both because the two solutions do not really perform differently in LF, and because listening to the two solutions during the test is spaced a few seconds apart, it could reveal a bias induced by the auditory memory.

One method to overcome this bias would be to immediately switch from speaker A to speaker B (and vice versa) during continuous playback.

Also, the JBL spectral response being flatter, it is possible that the overall sound balance benefits the JBL for LF attribution.

From the results on the preference, we can discuss the three cases separately. Table XIV summarizes the words collected for all comparisons.

Firstly, the JBL compared to the sealed enclosure is preferred at 60%. Considering the percentage for the LF attribution, it would make sense for the preference to correlate with this parameter. Indeed, by using the term "more powerful" again, we understand that the subjects refer to the improved LFs of this speaker system. But by expressing 3x times that the JBL is "more balanced", the preference could also be linked to the overall spectral balance of the sound, with a system amplifying less HF compared to LF. An equality is found in the preference between the EQ solution and the JBL. However, the latter system is perceived 7x times as "muffled" against an EQ perceived 5x times as "clearer". But in the end, it seems the subjects noticed that the EQ produces some distortion. This therefore answers our question of whether the distortion measured previously was going to be perceived when listening.

Finally, when our BR solution is compared to the JBL, 75% prefer the BR system. With 4x times the word "muffled" pronounced for the JBL against the word "clearer" pronounced for the BR, it confirms that the overall sound balance counts for a lot in the preference. However, we notice here again that the expression "more powerful" is used 5x times to describe the sound signature BR.

As an aside, it is interesting to note that the JBL is perceived twice as "less reactive" than the BR system. As we know that the JBL Go 3 contains a PR system, it is possible that this feeling refers to a well-known property of PRs in the industry: a poor restitution of the transient response [START_REF] Tanasescu | Passive radiator speaker design -Box calculation example[END_REF] Additional comparison: original BR port against horn BR port This additional comparison intends to determine whether the subjects perceive a difference in the sound created by the two port models.

To proceed, a third musical sample was selected from the song "Latch" by artist Disclosure. From Table XVII, we first see that half of the subjects did not perceive any difference between the two conceptions. For the other half, the horn design is perceived as "more powerful", while the original port produces a "more balanced" sound. The SPL of the two solutions being identical, it is not possible for us to comment on these feelings.

On the other hand, with a new feeling collected on the "attacks" of the drum kicks, it is possible that one of the two models reproduces the transients less well. One way to quantify this sensation is to measure the impulse response of each of the systems, at a distance equivalent to the listening point during the tests.

But unfortunately, having not a sufficiently low background noise to measure at this distance, Figure 108 proposes an evaluation of this response at ports output.

A brief observation of this graph is that the horn solution shows a little less damping on the time response than what the original port illustrates.

Therefore, although this measurement is not representative of what the subjects listened to, we still conclude on a new benefit of this alternative port solution, which better reproduces the transients of a sound.

Table XVII -Listening test N ° 1 -Additional comparison: collected words

Conclusion

From these perceptual tests, we first learn that the improvements investigated in this study work well and are seen to provide more LF, even when this extension is not directly noticed.

Compared to the EQ solution, the BR system remains preferred and perceived to be more powerful. But from this comparison as well as comparisons with a market solution, we learn how important a sound must be well balanced to be appreciated. Indeed, although the BR and JBL solutions are judged to be almost equivalent in terms of bass, the BR remains 75% preferred for its overall sound signature. For information, by conducting these tests on a population with an age range of 20 to 55 years, we did not focus specifically on a young audience who could give more importance to the reproduction of bass.

In addition, this listening test taught us how important it is to have a good design when integrating an audio processor. Indeed, the slightest distortion resulting from too much solicitation of the speaker can be perceived by the audience, when compared to another system as efficient in LF. This reminds us of the relevance of relying on a processor allowing to monitor speaker behavior in real time, so that it remains in its linear domain.

From the side comparison performed between the two BR designs, although we cannot really conclude anything about the perceptual assessment, an additional measurement will have enabled us to learn that a horn-shaped port would help to increase system responsiveness to transients, when compared to a straight port.

Finally, we learn from this first part of investigations that a traditional Bass-Reflex design on this type of small speaker system seems to work, but also remains at today the best performance / cost ratio for Seltech, with however an attention point to be paid to potential high losses in such a small port.

Also, given the LF performance of the JBL Go 3 and market trends, we confirm the relevance for Seltech to continue developing PR solutions using a PE optimized for this purpose.

From the conclusions around this first speaker, we now propose to study again these three improvement methods around the second speaker selected in the scope of our study. This section follows the same method as that applied for the design around the speaker N ° 1 (part III.I). But given the small size of this second enclosure, we build a model that directly integrates potential losses into the port. The circuit for that system is illustrated on Figure 109. = 0.56). We therefore expect to get a noticeable extension but with an irregular shape for the SPL.

Design of the port

Following the guidance in [START_REF] Small | Vented-Box Loudspeaker Systems Part I: Small-Signal Analysis, and Part II: Large-Signal Analysis[END_REF], and with 𝑥 𝑚𝑎𝑥 = 0.25 mm and a target for 𝑓 𝑀 = 700 Hz (or 50

Hz below the sealed enclosure 𝑓 𝐵 ), we define the following requirements for the port:

-An area 𝐴 ≥ 0. In this design also, the proposed port respecting the condition from [START_REF] Small | Vented-Box Loudspeaker Systems Part I: Small-Signal Analysis, and Part II: Large-Signal Analysis[END_REF] is too long and so not technically feasible in regards with the dimensions of our system. We therefore understand that it is necessary to considerably reduce the diameter of the port for getting a reasonable length, integrable in our design. However, with a dimension range becoming noticeably small, we are reaching a technical limit about the dimensional accuracy attainable by the 3D printing technique.

To continue our investigations from this point and try to achieve a BR design for this enclosure, we decide to rely on existing tubes from the market that are manufactured using the plastic injection technique: a well-known process for mass production of plastic components, which allows great precision in view of our needs.

Figure 110 illustrates a 90-degree tube from the Aquarium market (a tube network connector that supplies oxygen to fishes) with an opening area 𝐴 = 0.03 cm 2 (2 mm of diameter) and a total length = 3.4 cm. Once shorted to 1 cm (Figure 111), the calculated resonance 𝑓 𝑀 for the tube integrated into the enclosure is = 670 Hz. Although this extremely small port design could lead to high losses in the acoustic radiation, we decide to continue our investigation and estimate the amount of LF extension that this system could provide.

Acoustic prediction

Figure 112 on the next page illustrates the computed electric impedance for the system. From this simulation, we almost approach the previously calculated resonance by finding Here also, the first step is to quantify the improvement realized by the proposed design prior to compare against prediction. The setup for the measurement is detailed on Figure 116.

Figure 117 compares the SPL for the original BR against the sealed enclosure at 0.5 𝑢 𝑅𝑀𝑆 . An immediate comment from the BR qualification is that we well find the predicted peak at 𝑓 𝐻 , but we do not observe any LF extension, when compared to the sealed solution.

To better understand what phenomenon is happening, we propose to compare the SPL as well as further parameters against predictions. A first observation from the SPL graph is that the overall shape of the curve is well reproduced by the model. This confirms that the prototyped port radiates energy. But in the region around 𝑓 𝐿 , it is not surprising to observe a model that predicts a high and undamped SPL, while the measurement on the prototype shows a strongly damped curve, even causing the slope to change below 𝑓 𝐿 . From this observation, we conclude that the port seems to be functioning, but with too high losses in its acoustic radiation. The latter being probably the result of a too small opening size.

Conclusion

Although this first method does not bring any LF extension, we observe that we correctly approach the behavior of the system, and therefore validate a prediction method remaining valid in enclosures as small as the one considered here. In the end, as this improvement method remains very inexpensive, it could be relevant to continue our investigations but only with ports much larger than the one built here. The risk of such large ports is that it could lead to the inability to mechanically build the system. Additionally, given the low resonance damping of the enclosure, a porous material should be implemented to attenuate the peak at 𝑓 𝐻 . In the end, ratios between mechanical complexity and acoustic efficiency will have to be evaluated to decide whether this solution in such small enclosures is interesting to consider. From the difference in percentage reported by Table , we understand the speaker used as PE to behave a bit differently (around 10 % of difference) from the original speaker, while they are supposed to be identical. This difference of behavior is assumed to reflect the variation in production of this transducer. When looking at α and δ ratios, we calculate:

- α = 𝐶 𝐴𝑆 𝐶 𝐴𝐵 = 0.63 - δ = 𝐶 𝐴𝑅 𝐶 𝐴𝐵 = 0.71
With almost equal ratios (δ ≈ α), we first finally conclude on a similar behavior of the two elements when integrated into the enclosure, but we also understand that we can only achieve a non-flat and small extension.

Acoustic prediction

The circuit from Figure 122 is built, and the SPL at 0.1 m and for 0.5 𝑢 𝑅𝑀𝑆 is illustrated on Figure 125. From this graphic, we observe here also that the system as it is does not improve the LF region but degrades it. As discussed in part III.II, this degradation is due to a too high PE resonance frequency.

Verification of the initial prediction

The PR prototype is so built as per illustrated on Figure 126, simply with a second aperture for the PE, identical to the first one. The setup for the measurement is illustrated on Figure 127. The comparison for the electric impedance is illustrated on Figure 128, and the one for the SPL at 0.5 𝑢 𝑅𝑀𝑆 is illustrated on Figure 129.

From the impedance comparison the different peaks are correctly reproduced by the model.

Only a small difference on both 𝑓 𝐿 and 𝑓 𝐻 . Also, as discussed on previous cases, the global damping is a bit underestimated by the model.

We also find this underestimation on the SPL comparison: the simulated amount of energy at 𝑓 𝐻 being higher than what measured over the prototype.

Finally, we still conclude on a global validity of our model regarding the behavior of the prototype. Still relying on the method described in [START_REF] Jiang | Analysis and Optimization of Micro Speaker-Box Using a Passive Radiator in portable Device[END_REF], we intend to solve an integral function of SPLs between two defined frequencies. Starting from 4000 Hz on the sealed enclosure curve, the -10 dB point is found around 350-375 Hz. We will so solve the integral between 350 and 4000 Hz.

From a first analysis, we determine 𝑀 𝐴𝑅 ′ ≥ 2.5x 𝑀 𝐴𝑅 for extending the LF response. The Table XIX and Figure 130 respectively report the integral results and the curves for 2.5x 𝑀 𝐴𝑅 ≤ 𝑀 𝐴𝑅 ′ ≤ 4x 𝑀 𝐴𝑅 . From these predictions, we observe the optimal configuration to be given for 𝑀 𝐴𝑅 ′ = 3x 𝑀 𝐴𝑅

Table XIX -PR system N ° 2 -F function integral result for different added masses

Prototype customization

The procedure described on page 49 is applied to calculate 𝑀 𝑀𝐷 , and the result is verified on a scale using another PE sample. After verification the considered values are:

-𝑀 𝑀𝐷 = 87.4e-3 g Five measurements over the scale are performed to confirm its weight (reported on Table XX), and the additional part is then mounted over the prototype as per illustrated on Figure 133.

- 𝑀 𝑀𝐷 ′ = 3x 𝑀 𝑀𝐷 =

Prototype qualification

The setup for the qualification remains the same as the one for the initial system verification (Figure 127). On the next page, Figure 134 compares the SPL for the tuned design against the sealed enclosure, at 0.5 𝑢 𝑅𝑀𝑆 . As discussed for the design around the speaker N ° 1, the LF extension is observed to be very small: only a few dB of amplification is seen near the 60 dB line, and in the 350-400 Hz region. Here also, the use of a speaker as PE makes it possible to study PR designs, but we doubt that this observed improvement can be perceived when listening to this solution.

Comparison of measurements against predictions

Figure 136 compares the electric impedance of the system. A first observation is that the model well recreates 𝑓 𝐻 . However, 𝑓 𝑀 is not reproduced due to an underestimation of the damping in this region, and 𝑓 𝐿 is reproduced in value only, its damping being also wrong. However, here also, using a speaker as PE instead of a diaphragm cannot lead to wide and flat LF extensions. If we want to continue our investigations around this design, we must develop a diaphragm that is both optimized in losses and in compliance. Such an element could result from joint work between Seltech and its speaker manufacturers.

IV.III. Improvement method N ° 3 (Active Equalization)

Following the technique used in [START_REF] Leach | Active Equalization of closed box loudspeaker systems[END_REF], but with designing only one 2 nd order HPF, the networks used for the prediction are respectively reminded on Figure 139 for the acoustical circuit, and on Figure 140 for the HPF. This last element is controlled by its quality factor 𝑄 and its center frequency 𝑓, as defined on page 54.

Acoustic prediction

The upper limit in the behavior of this second speaker is defined as follow:

-𝑥 𝑚𝑎𝑥 = 0.25 mm -𝐼 𝑚𝑎𝑥 = 2x 𝐼 in the frequency band where the HPF does not operate. From the above graphs, we confirm to remain under the excursion limit of 0.25 mm in a scenario for which the defined current limit is reached at the HPF center frequency.

The SPL predicted at 0.5 𝑢 𝑅𝑀𝑆 is compared to the sealed solution on Figure 143. A quick and first observation is that the -3 dB point is extended from 515 to 390 Hz by the solution. But also, as for enclosure n ° 1 we notice that this HPF alone does not allow a flat extension to be made. The resonance peak for this second enclosure being much less damped than for the previous speaker, it may be relevant to try to attenuate it by means of a parametric equalizer available in the libraries of the processor. In this way we should learn about the possibility to achieve a flat extension. Finally, as for the design around the speaker N ° 1, we observe a very good correlation between predicted and measured current consumption at 1 𝑢 𝑅𝑀𝑆 (Figure 150). Only a small difference in low and mid frequencies can be explained by a phenomenon related to the increase of the voice coil resistance, with both the temperature and the energy it receives.

IV.IV. Perceptual evaluation of each of the improvement

As for the enclosure N ° 1, this section presents the results of listening tests performed for improvements around the second enclosure, with the same objective of correlating subjective criteria with acoustic measurements.

Here too, even if the PR system is approached well, using a speaker diaphragm as PE does not really improve the LF response. We therefore do not retain this solution for our tests.

The matrix giving the pairs to be tested is constructed in accordance with Table XXI, with some of the comparisons planned against the OnePlus 6 smartphone.

Table XXI -Listening test N ° 2 -Matrix of improvements to test

Sealed EQ N °1 (HPF) EQ N ° 2 (HPF + Parametric) OnePlus 6 Sealed X X X EQ N ° 1 X X X EQ N ° 2 X X X OnePlus 6 X X X
With a measured SPL at 70 cm giving 83 dB SPL when recalculated at 10 cm, we are in higher conditions than the maximum measured over the prototypes (79 dB SPL at 2 kHz, 1 𝑢 𝑅𝑀𝑆 ). We will therefore still consider the measurements at 1 𝑢 𝑅𝑀𝑆 for comparisons but noting that the curves may not perfectly reflect the behavior of the speakers during the tests.

Signals presentation

The first extract is from the jazz song "Whatever" by artist China Moses. The second is taken from the pop-rock song "Next to you" by artist Lake House. Spectra of these extracts are compared in Figure 151.

When analyzed between 0.2 and 20 kHz, the two songs bring similar energy despite their difference in musical style. Indeed, this type of speaker distorting quickly when excited out of its range, both songs have been chosen soft on bass and drums, explaining the similarities that we see in the LF region. Table XXII on the following page summarizes the results for the LF and preference questions.

A first observation is that the gain in LF is much more perceived for EQ N ° 1 than for EQ N ° 2. We therefore understand that part of the LF could have been interpreted as a low medium by the subjects. Indeed, by using the word "LF" in the question instead of the word "bass", it is possible that we have biased the answers. With a preference for EQ n ° 1 (at 65%) compared to the sealed, and for the sealed (at 55%) compared to the EQ n ° 2, the words collected during the tests will help us to explain these results. From Table XXIII, we observe that EQ N ° 1 is mainly perceived as "more powerful" compared to the sealed solution, but also "closer". As in the previous analysis, we interpret these words as being effectively related to the physical improvement of LF.

On the other hand, when EQ N ° 2 is submitted for comparison, it is a feeling of clarity in favour of the sealed solution that leads the audience (with other arguments) to prefer this solution to the EQ. Unlike the comment on the previous page, it is possible that the non-attenuation of the low mediums in the sealed solution contributes this time more to the notion of clarity instead of LF presence.

Finally, only a comparison between the two EQs should allow us to study the interest of flattening the LF extension. From Table XXIV, we see most of non-response to the questions on LF and preference. We therefore fully rely on the words collected from Table XXV to try to explain this situation.

For people who noticed a difference, EQ N ° 2 was first perceived 3x times as "more balanced".

Although we cannot conclude anything from a feeling expressed at 30%, we still understand that a system providing a flat sound signature can better reproduce the spectral balance of an audio mix compared to a system with a non-flat signature.

On the other hand, the EQ N ° 1 being perceived 2x as "more powerful", this may explain why this solution is preferred against the other one.

In the end, as this comparison only gives trends, it would be relevant to test this solution both on various prototypes and on a larger number of subjects, to confirm the interest in such a sound signature. Comparisons against a solution from the market Figure 154 shows the SPLs normalized to 2000 Hz, both for the studied solutions and for the OnePlus 6 speaker system. Given the sound signature of the latter system, the choice of frequency for normalization can be submitted to discussion. But in the end, this way of proceeding still allows us to judge the relative presence of LF and HF compared to the energy present at 2 kHz (where this type of enclosure is supposed to behave like a perfect piston).

Therefore, this graph still allows us to link the subjective perception to the measured SPLs. Table XXVI reports the responses to the LF and preference questions. From a first analysis, our EQ solutions are both perceived as containing more bass and preferred by the subjects in front of the OnePlus smartphone. Although we are less on a one-to-one comparison than for the previous chapter, we still conclude on a successful sound signature when compared to a solution from the market similar in size.

However, when compared to the sealed enclosure, the OnePlus is generally perceived to offer more LF, although relative SPLs show the opposite. We could explain this feeling by the fact that the SPL slope of the OnePlus below 2 kHz is smoother than for the sealed solution, which increases in energy first until resonance, and then drop rapidly. It is therefore possible that the OnePlus is perceived as bringing more bass, from an overall spectral balance point of view.

But finally, when the preference is requested, the sealed solution is chosen in majority at 55%. A quick observation is that in all comparisons our solutions are far seen as bringing more clarity to the sound. As a possible opposite feeling, the OnePlus is often perceived as "filtered" and "muffled". With the word "clearer" pronounced 16x in total over the three comparisons, we understand that this feeling was very important in the choice of preference.

Looking at the other words in descending order, the expression "more powerful" appears 5x times with respect to the OnePlus when compared to the sealed solution. Considering both the shape of the SPL and the sensitivity of the human ear in mid frequencies, we understand this time that this sensation more refers to the energy present in mid frequencies than in LF. Other

Conclusion

At the end of this second listening test, we confirm the good functioning of our improvements which are distinctly noticed when listening to them. However, we cannot confirm the interest of designing a flat LF extension. Indeed, when the two EQ solutions are compared with each other, most of the audience does not notice any difference. As commented during this comparison, it would be relevant to conduct another measurement campaign on both diverse prototypes and a larger number of subjects, to confirm or not the interest in such a design.

Finally, when we compare our solutions to a similar sized product from the market, these firsts are initially perceived to be stronger in bass, but above all we understand that the preferences towards these solutions are mainly driven by their HF signature.

One thing that we must consider about this last property, is that our devices radiate directly into space while the speaker system built into the OnePlus first radiates into a front volume (made of a tubing network) to then lead to the outside.

We therefore conclude without surprise from this last observation that the way of integrating a speaker system into a product is at least as important as the design of the system itself. V. Summary of the investigations and conclusion

V.I. Synthesis

Reviewing the methods considered in this study, we understand that a traditional Bass-Reflex design remains the most efficient at low frequency, both in terms of measurement and perception. Also, by not involving anything other than a plastic tube, this system remains the simplest to design against the other two methods. However, from these investigations we will also have learned to what extent a small port size can cause large losses in the radiation, thus leading our models to overestimate the performances.

On the other hand, further investigation has taught us that a port with horn terminations can help reduce noise from aerodynamic turbulence, but also potentially increase the responsiveness of the system to transients.

Then, providing as much LF as a Bass-Reflex, but being totally possible to design in both speaker systems, the Active Equalization technique is still a method that Seltech does not know much about. And although our models perfectly approximate the performance of this solution, we will have come up against non-linearities that both appear and are perceived as a function of the requested input energy.

By relying on processors to program such a type of EQ, we realized how easy it is to tune a wide and flat extension over the original system response. But when we asked our test subjects to compare this flat extension against a non-flat design, we could not confirm the benefits of designing such a shape of sound signature.

Finally, even if not retained for our listening tests, the investigations around Passive Radiators will have made it possible to understand the behavior of systems very popular on the market.

Indeed, by integrating a speaker as passive element, we have been then able to fully model the solution and confirm that we can predict its performance well.

On the other hand, as we know that the use of a speaker like PE is not suitable for this kind of design, we were only able to obtain non-flat and narrow extensions.

In the end, whatever the extension method considered, we will also have learned from this study, that within a population aged from 20 to 55 years, the LF presence in a sound is appreciated, but the overall spectral balance of this sound is even more so.

Part V -Summary of the investigations and conclusion

Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 99 / 100

V.II. Industrial feasibility and cost point of view

Under the assumption that the three improvements give comparable performances, this study will have proved to us the potential difficulties for the integration of a BR port in a system as compact as those we considered. Indeed, when these ports are designed curved, this can sometimes lead to an impossibility of manufacturing the solution as it has been imagined in regards with constraints of mass production processes such as plastic injection.

On the other hand, when compared to the other two solutions, a Bass-Reflex design remains by far the cheapest, and this cost aspect is important to consider for applications where the budget of the audio function is not a priority. In the end about this method, as soon as the space available for the audio part of a device becomes drastically small, it will be relevant to set up evaluation indicators such as ratios between mechanical complexity and expected acoustic efficiency, to be able to decide whether to opt for this solution or not.

Otherwise, we will have fully understood that a Passive Radiator system can replace a Bass-Reflex when the enclosure becomes too small. However, this system using a diaphragm instead of a port, it is first a more expensive solution but also a more sensitive one to performances variation within production. Indeed, where a Bass-Reflex just needs to be controlled on its port dimensions, a diaphragm must be controlled on its three mechanical parameters 𝑅 𝑀𝑅 , 𝐶 𝑀𝑅 and 𝑀 𝑀𝑅 . In addition, by adding a secondary vibrating element to the system, there will be a point of attention to be paid on both a good insulation from vibrations and a good overall balance of the system. Finally, active equalization could appear as the simplest design to handle, in front of a Bass-Reflex. But that is without count on the fact that this design involves a processor as well as an amplifier in the audio chain. If not a problem for the industrial side, it could be an issue for the cost aspect. Indeed, apart relying on customer capabilities, this solution would require Seltech to develop and supply all the electronics around the speaker enclosure. In addition, apart from the risk of not being competitive in terms of cost in this second scenario, this design consumes energy compared to the other two. And this remains important to consider in the context of battery-operated applications.

Ultimately, since all the methods reviewed in this document modify the behavior of the speaker itself, it may be necessary to requalify its power supply capability each time a LF extension is designed. This qualification being done both in regards with the maximum possible excursion for the diaphragm and the current consumption capacity.

Part V -Summary of the investigations and conclusion

Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 100 / 100

V.III. Future work proposals

As this document only reflects one year of investigations, it cannot cover all the ideas and open questions around the reviewed methods. In this context, the aim of this section is to offer some open ideas for further work following this study.

A first obvious proposal is to equip ourselves with a diaphragm measurement equipment, as described in Appendix D. Indeed, from our investigations around Passive Radiators designs, we understood how important it is to master the behavior of a PE to properly adjust its resonant frequency, and thus achieve the targeted extension.

However, knowing the properties of a diaphragm is not the only aspect to consider in PR designs. Indeed, although we can act on the moving mass of this element to adjust our alignment, we can in no way modify the loss and compliance properties of an already manufactured object.

Therefore, given the competition of PR designs in the market, only joint work between Seltech and its manufacturing partners could lead to competitive membranes giving wide and flat extensions.

As for Bass-Reflex designs, as the listening tests carried out have led us to conclude that a big bass peak is not necessarily what the public prefers, faced with a feeling of global spectral balance, we could launch new investigations on larger ports with a more reasonable target for the Helmholtz frequency, thus leading to a smaller, but flatter LF region.

An additional idea to help flatten the SPL at the speaker resonance would be to add a piece of porous material into the enclosure.

Finally, we could as well design an EQ alone, as combine it with BR / PR systems (to correct the artifacts of such systems), but in the end we will have to improve our knowledge on a solution to monitor the current consumption in real time in the speaker. Thus, to automatically activate / deactivate the equalizer, or even to modify its properties according to the required input energy.

All the above ideas remain purely proposals, in a constantly evolving market with recurring innovations.

List of Figures

Figure 3 -

 3 Figure 3 -SPL comparison: Nokia N95 / Xiaomi Black Shark 4.Graph recreated from[START_REF] De Hillerin | 2000 to 2021: The evolution of smartphone audio playback[END_REF]

  illustrates how JBL improved the LF region of its Go version 3 (released in 2020) compared to its Go version 2 (released in 2018). The graphic illustrates normalized SPLs from 1000 Hz. In addition of having a flatter sound signature, the Go version 3 bring a flat extension of about 60 Hz.

Figure 7 -

 7 Figure 7 -Micro Passive Radiator prototypes[START_REF]What Are Passive Radiators In Speakers?[END_REF]

Figure 8 -

 8 Figure8-Pitch perception of a complex tone (Missing fundamental effect)[START_REF] Young | Dedicated Audio Processors at the Edge are the Future. Here are the Reasons Why[END_REF]

Figure 9 -

 9 Figure 9 -Geographical distribution of Seltech offices

Figure 10 -

 10 Figure 10 -Speaker N ° 1 -Detailed composition

Figure 11 -Figure 13 -

 1113 Figure 11 -Sealed enclosure N ° 1 -Assembly elements Figure 12 -Sealed enclosure N ° 1 -Assembled system

Figure 14 -Figure 15 -

 1415 Figure 14 -Sealed enclosure N ° 1 -Typical electric impedance

Figure 16 -

 16 Figure 16 -Speaker N ° 2 -Detailed description

Figure 17 -Figure 19 -

 1719 Figure 17 -Sealed enclosure N ° 2 -Assembly elements Figure 18 -Sealed enclosure N ° 2 -Assembled system

Figure 20 -Figure 21 -

 2021 Figure 20 -Sealed enclosure N ° 2 -Typical electric impedance

Figure 26 -Figure 27 -

 2627 Figure26-" Possible three-operational-amplifier realization of the active equalizer"[START_REF] Leach | Active Equalization of closed box loudspeaker systems[END_REF]

Figure 28 -

 28 Figure28-Acoustical analogous circuit for a sealed enclosure system[25]

  is the acoustic compliance of the air volume into the enclosure For the enclosure designed around the speaker N ° 1: 𝐶 𝐴𝐵 = 1.16e-09 m 5 /N For the enclosure designed around the speaker N ° 2: 𝐶 𝐴𝐵 = 1.41e-11 m 5 /N Also, regarding the size of the considered systems, it is assumed that the damping behavior of the air trapped inside the box is quite low, or non-existing. This leads us to neglect the term 𝑅 𝐴𝐵 from the circuit as well. Therefore, the analogous circuit for the sealed enclosure becomes as per illustrated on Figure29.

Figure 29 -

 29 Figure 29 -Simplified analogous circuit for a sealed enclosure

Figure 30 -

 30 Figure 30 -Speaker N ° 1 -Diameter considered for the calculation of SD

Figure 31 -

 31 Figure 31 -Speaker N ° 1 -Parameters measurements 1/2 Figure 32 -Speaker N ° 1 -Parameters measurements 2/2

  Scope of the investigations: Approach used for prediction Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 18 / 100 Measurement of the parameters for the speaker N ° 2Considering the small dimensions for the diaphragm of this speaker, Figure33illustrates the two lengths which are considered to approximate 𝑆 𝐷 into a rectangular area of 1e-04 m 2 .

Figure 33 -

 33 Figure 33 -Speaker N ° 2 -Dimensions considered for the calculation of SD

Figure 34 - 2 Figure 35 -

 34235 Figure 34 -Speaker N ° 2 -Parameters measurements 1/2 Figure 35 -Speaker N ° 2 -Parameters measurements 2/2

Figure 36 -

 36 Figure 36 -Additional electric network for the SPL calculation

Figure 37 --

 37 Figure 37 -Sealed enclosure N ° 1 -Model / Measurement electric impedance comparison

Figure 38 -

 38 Figure 38 -Sealed enclosure N ° 1 -Model / Measurement SPL comparison

Figure 39 -

 39 Figure 39 -Sealed enclosure N ° 1 -SPL behavior over the voltage

Figure 40 -

 40 Figure 40 -Sealed enclosure N ° 2 -Model / Measurement electric impedance comparison

Figure 41 -

 41 Figure 41 -Sealed enclosure N ° 2 -Model / Measurement SPL comparison

Figure 42 -

 42 Figure 42 -Sealed enclosure N ° 2 -SPL behavior over the voltage

Figure 43

 43 Figure43describes the listening test environment. Each subject seats at about 70 cm from the pairs to listen to. The solutions are installed on a stand, over a decoupling foam pad, and are hidden to the subject by means of an acoustically transparent tissue. A microphone is installed on the side to record all comments and answers from the subject to different questions asked between each pair listened.

Figure 43 -

 43 Figure 43 -Listening tests environment

  Part II -Scope of the investigations: Protocol for the perceptual evaluation Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 26 / 100

Figure 45 -

 45 Figure45-Illustration of alignments C4, B4, and QB3 (n ° 8, 5, and 3)[START_REF] Thiele | Loudspeakers in Vented Boxes: Parts I and II[END_REF]

Figure 47

 47 Figure 47 illustrates a curved port with an area 𝐴 fixed = 0.5 cm 2 (8 mm diameter), a total length of 8 cm and a theoretical resonance 𝑓 𝑀 calculated = 106 Hz, considering the ends correction term = 0.614 * 𝑃𝑜𝑟𝑡 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟

  Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 31 / 100 system illustrated on Figure48featuring horn shaped ends. In this design, the port length is adjusted considering its effective value at half of the horns.

Figure 48 -

 48 Figure 48 -BR system N ° 1 -Horn port prototype drawings

Figure 49 -

 49 Figure 49 -Simplified acoustical circuit of a BR system (lossless)

Figure 50 -

 50 Figure 50 -Electric network for the SPL calculation of a BR system

Figure 51 -

 51 Figure 51 -BR system N ° 1 -Simulated electric impedance

Figure 52 -

 52 Figure 52 -BR system N ° 1 -Simulated SPL comparison: BR / Sealed

Figure 53 -

 53 Figure 53 -BR system N ° 1 -Original prototype Figure 54 -BR system N ° 1 -Horn port prototype

0. 3

 3 m center axis between speaker and port Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 35 / 100

Figure 58 -

 58 Figure 58 -BR system N ° 1 -Measured SPL comparison for the 3 voltages

Figure 61

 61 Figure 61 on the next page illustrates only the port portion of the circuit with this term.

Figure 59 -

 59 Figure 59 -BR system N ° 1 -Electric impedance comparison: Simulation / Measurement

  where 𝜇 0 is the dynamic air viscosity, and 𝑠 the Laplace operator. The newly predicted electric impedance as well the SPL at 1 𝑢 𝑅𝑀𝑆 are compared again, respectively on Figures62 and 63. As brief comments, we observe that the impedance curve is better recreated by this new model, but on the other hand, only a small Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 37 / 100 attenuation is observed in the LFRO region with a SPL still far above what we measure over the prototype. We conclude that we face much more losses than what we can predict. And this might be a side effect of a port too narrow.

Figure 62 -

 62 Figure 62 -BR system N ° 1 -Electric Impedance comparison: Measurement/Simulation w/ and w/o losses

Figure 64 -

 64 Figure 64 -BR system N ° 1 -Setup for qualification of turbulences created by ports designs

Figure 66 -

 66 Figure 66 -BR system N ° 1 -Qualification of turbulences created by ports at 1 uRMS

Figure 68 -

 68 Figure68-BR port designs : Port E geometry[START_REF] Roozen | Reduction of bass-reflex port nonlinearities by optimizing the port geometry[END_REF]

  Part III -Investigations around the speaker enclosure N ° 1: Passive-Radiator Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 42 / 100

  Figure 70 illustrates the circuit for the PR, where: -𝑅 𝐴𝑃 (named 𝑅 𝐴𝑅 for this document) represents the losses created by the energy dissipation in the moving part of the PE, -𝑀 𝐴𝑃 (named 𝑀 𝐴𝑅 for this document) is the mass for both the moving part of the PE and the air particles around its diaphragm, -𝐶 𝐴𝑃 (named 𝐶 𝐴𝑅 for this document) represents the compliance for the moving part of the PE.

  Figure 71 to estimate the shape of extension we might get in our design. Showing a normalized x-axis equivalent to f 𝑓 𝑠 , this graphic illustrates possible alignments, according to the value of α,

1 2𝜋 √ 1 𝑀

 11 PR curve is caused by the resonance frequency (𝑓 𝑆 ) of the PE. As by definition 𝑓 𝑆 = 𝐴𝑅 𝐶 𝐴𝑅 , we understand that this frequency can either be controlled by 𝑀 𝐴𝑅 or 𝐶 𝐴𝑅 . Therefore, if we want to decrease 𝑓 𝑆 for extending the LF response, the only change we can do on a manufactured PE is on 𝑀 𝐴𝑅 . More concretely, to affect this term in the right direction, we simply need to add additional mass over the diaphragm, paying attention on keeping a good balance of it.

Figure 72 -

 72 Figure 72 -Simplified acoustical circuit of a PR system

Figure 74 -

 74 Figure 74 -PR system N ° 1 -Prototype elements Figure 75 -PR system N ° 1 -Assembled prototype

Figure 77 -

 77 Figure 77 -PR system N ° 1 -Electric impedance comparison: Measurement / Simulation

Figure 79 -

 79 Figure 79 -PR system N ° 1 -Simulated SPLs for determining the minimum mass to add

  Part III -Investigations around the speaker enclosure N ° 1: Passive-Radiator Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 49 / 100

8 3𝜌 0

 80 𝑟 3 ]. Following this relationship, it would give: -𝑀 𝑀𝐷 = 1.83 g -𝑀 𝑀𝐷 ′ = 3.5x 𝑀 𝑀𝐷 = 6.40 g, and the mass to add = 6.40 -1.83 = 4.57 g -Trying to verify this theoretical value for 𝑀 𝑀𝐷 by weighing the moving part from another sample of this PE (as shown in Figure 81 and Table VIII), we found a mass approximately equal to half of the calculated value, or 𝑀 𝑀𝐷 = 1.83 / 2 = 0.915 gBecause both the scale used is well calibrated and the above calculation remains theoretical, we therefore decide to rely on the measured value and consider the mass to add to be = 2.290 g.

Figure 81 -

 81 Figure 81 -PR system N ° 1 -PE moving mass weighing

Figure 82 -

 82 Figure 82 -PR system N ° 1 -PE additional radiating element

Figure 85 -

 85 Figure 85 -Tuned PR system N ° 1 -Measured SPL comparison: PR / Sealed

Figure 86 -

 86 Figure 86 -Tuned PR system N ° 1 -Measured SPL comparison for the 3 voltages

Figure 87 -

 87 Figure 87 -Tuned PR system N ° 1 -Electric impedance comparison: Measurement / Simulation

  Part III -Investigations around the speaker enclosure N ° 1: Active Equalization Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 53 / 100

Figure 89 -

 89 Figure 89 -Menu Settings for the SigmaStudio 2 nd order HPF

Figure 91 -

 91 Figure 91 -Active EQ N ° 1 -Analogous circuit Figure 92 -Active EQ N ° 1 -HPF circuit

  Part III -Investigations around the speaker enclosure N ° 1: Active Equalization Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 55 / 100 Acoustic prediction Without programmed function from the processor to monitor the speaker behavior and set a upper limit for Q, we propose to rely on two parameters. The first one being 𝑥 𝑚𝑎𝑥 , the maximum possible peak excursion for the speaker diaphragm, already mentioned = 3.5 mm on page 30. A way to predict the diaphragm displacement is to work with the original speaker model involving both the electrical and mechanical domains additionally to the acoustical one ( [25]: Chapter 3: Part IX). As illustrated on Figure 93, by regenerating the predicted acoustic flow toward the mechanical domain, we can get the velocity at the diaphragm point, which once integrated trough a capacitor leads to a value representative of the diaphragm displacement.

Figure 93 -

 93 Figure 93 -Active EQ N ° 1 -Additional loop for computing the speaker diaphragm excursion

Figure 94 -

 94 Figure 94 -Active EQ N ° 1 -Additional loop for computing the current consumption

Figure 97 -

 97 Figure 97 -Active EQ N ° 1simulated SPL comparison: EQs N ° 1 and 2 / sealed

Figure 98 reports measured SPLs at 1

 1 Figure 98 reports measured SPLs at 1 𝑢 𝑅𝑀𝑆 while Figures 99 and 100 on the next page respectively summarize the SPL behavior according to the voltage input. As predicted by the models, the two solutions identically extend the LF response until about 120 Hz. Below this frequency, the EQ N ° 2 continues to amplify the sound but with a LFRO observed at 105 Hz,

Figure 98 -

 98 Figure 98 -Active EQ N ° 1 -Measured SPL comparison: EQs N ° 1 and 2 / sealed

Figure 99 -

 99 Figure 99 -Active EQ N ° 1 -SPL comparison for the EQN ° 1 over the 3 voltages

Figure 101 -

 101 Figure 101 -Active EQ N ° 1 -Measured distortion comparison at 2 uRMS: Sealed / EQs / BRs

Figure 102 -

 102 Figure 102 -Active EQ N ° 1 -SPL comparison for the EQ N ° 1: Measurement / Simulation

Figure 103 -

 103 Figure 103 -Active EQ N ° 1 -Current consumption comparison for the EQ N ° 1: Measurement / Simulation

  Part III -Investigations around the speaker enclosure N ° 1: Listening test Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 63 / 100

Figure 104 -

 104 Figure 104 -Listening test N ° 1 -Music spectra comparison Comparison of the improvements against the sealed solution

Figure 105 -

 105 Figure 105 -Listening test N ° 1 -SPL comparison: Improvements / SealedThe Table XI summarizes the test results (in percentage) for the questions on the LF attribution and on the preference.

  Part III -Investigations around the speaker enclosure N ° 1: Listening test Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 66 / 100

Figure 107 -

 107 Figure 107 -Listening test N ° 1 -SPL comparison: Improvements / Sealed / JBL Go 3

  Part III -Investigations around the speaker enclosure N ° 1: Listening test Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 68 / 100

Figure

  Figure in Appendix G shows the spectrum of this extract, which looks similar in all points to the other ones, apart a little more of energy in LF. Most importantly, this song contains frequent pronounced drum kicks compared to other extracts.

Figure 108 -

 108 Figure 108 -Listening test N ° 1 -Impulse response comparison: Original BR port output / Horn BR port output

2 IV

 2 Part IV -Investigations around the speaker enclosure N ° 2: Bass-Reflex Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 71 / 100 IV. Investigations around the speaker enclosure N °

Figure 109 -

 109 Figure 109 -Simplified acoustical circuit of a BR system

Figure 110 -

 110 Figure 110 -BR system N ° 2 -Presentation of a tube sourced from the market

  Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 73 / 100 𝑓 𝑀 = 680 Hz. The frequency 𝑓 𝐻 is found = 960 Hz, and 𝑓 𝐿 is found = 425 Hz. We so understand that the designed system should extend the enclosure response down to about 425 Hz.

Figure 112 -

 112 Figure 112 -BR system N ° 2 -Electric impedance simulation

Figure 113 -

 113 Figure 113 -BR system N ° 2 -Simulated SPL comparison: BR / Sealed

Figure 114 -

 114 Figure 114 -BR system N ° 2 -Prototype bottom casing Figure 115 -BR system N ° 2 -Assembled prototype

Figure 117 -

 117 Figure 117 -BR system N ° 2 -Measured SPL comparison: BR / Sealed

Figure 118 -

 118 Figure 118 -BR system N ° 2 -Electric impedance comparison: Measurement / Simulation

Figure 119 -

 119 Figure 119 -BR system N ° 2 -SPL comparison: Measurement / Simulation

Figure 120 -

 120 Figure 120 -BR system N ° 2 -Setup for measuring the SPL at port output

  Part IV -Investigations around the speaker enclosure N ° 2: Passive-Radiator Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 78 / 100 IV.II. Improvement method N ° 2 (Passive Radiator)PR designs around this small enclosure are approached using the same acoustical circuit than the one built for the enclosure N ° 1. Its network reminded on Figure122features the three terms 𝑅 𝐴𝑅 , 𝐶 𝐴𝑅 , and 𝑀 𝐴𝑅 that reflect the mechanical behaviour of the PE and must be properly qualified.

Figure 122 -

 122 Figure 122 -PR system N ° 2 -Simplified analogous circuit for a PR system

Figure 123 -

 123 Figure 123 -PR system N ° 2 -PE presentation Figure 124 -PR system N ° 2 -PE bottom view

  Part IV -Investigations around the speaker enclosure N ° 2: Passive-Radiator Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 79 / 100

Figure 125 -

 125 Figure 125 -PR system N ° 2 -Simulated SPL comparison: PR / Sealed

  Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 80 / 100

Figure 126 -

 126 Figure 126 -PR system N ° 2 -Assembled prototype

Figure 128 -

 128 Figure 128 -PR system N ° 2 -Electric impedance comparison: Measurement / Simulation

  Figure 130 -PR system N ° 2 -Simulated SPLs for different added masses

  262.3e-3 g, and the mass to add = approx. 175e-3 g To constitute this mass, Figures131 and 132illustrate that we choose to extract the diaphragm from another PE sample, below which we apply some mastic, both to reach the right value of mass and for being able to stick this whole additional part onto the PE.

Figure 131 -

 131 Figure 131 -PR system N ° 2 -PE additional radiating element

Figure 133 -

 133 Figure 133 -PR system N ° 2 -Tuned prototype

Figure 134 -

 134 Figure 134 -Tuned PR system N ° 2 -Measured SPL comparison: PR / Sealed

Figure 135 -

 135 Figure 135 -Tuned PR system N ° 2 -Measured SPL comparison for the 3 voltages

Figure 136 -

 136 Figure 136 -Tuned PR system N ° 2 -Electric impedance comparison: Measurement / Simulation

Figure 137 -

 137 Figure 137 -Tuned PR system N ° 2 -SPL comparison at 0.5 uRMS: Measurement / Simulation

  Part IV -Investigations around the speaker enclosure N ° 2: Active Equalization Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 86 / 100

Figure 139 -

 139 Figure 139 -Active EQ N ° 2 -Analogous circuit Figure 140 -Active EQ N ° 2 -HPF circuit

Figures

  Figures 141 and 142 respectively illustrate the simulated diaphragm excursion and current consumption for 1 𝑢 𝑅𝑀𝑆 input, which is the highest voltage under study, and for the proposed combination 𝑄 = 2.25 and 𝑓 𝐻𝑃𝐹 = 400 Hz.

Figure 141 -

 141 Figure 141 -Active EQ N ° 2simulated diaphragm excursion

Figure 142 -

 142 Figure 142 -Active EQ N ° 2simulated current consumption

Figure 143 -

 143 Figure 143 -Active EQ N ° 1simulated SPL comparison: EQ / sealed

Figure 144 -

 144 Figure 144 -Menu Settings for the SigmaStudio Parametric filter

Figure 145 -

 145 Figure 145 -Active EQ N ° 2 -Measured SPL comparison: EQs N ° 1 and 2 / sealed

Figure 146 -

 146 Figure 146 -Active EQ N ° 2 -SPL comparison for the EQ N ° 1 over the 3 voltages Figure 147 -Active EQ N ° 2 -SPL comparison for the EQ N ° 2 over the 3 voltages

Figure 148 -

 148 Figure 148 -Active EQ N ° 2 -Measured distortion comparison at 1 uRMS: Sealed / EQs

Figure 149 -

 149 Figure 149 -Active EQ N ° 2 -SPL comparison for the EQ N ° 1: Measurement / Simulation

Figure 150 -

 150 Figure 150 -Active EQ N ° 2 -Current consumption comparison for the EQ N ° 1: Measurement / Simulation

  Figure 151 -Listening test N ° 2 -Music spectra comparison

Figure 152 -

 152 Figure 152 -Listening test N ° 2 -SPL comparison: Improvements / Sealed

Figure 153 -

 153 Figure 153 -Listening test N ° 2 -SPL comparison between improvements

  Part IV -Investigations around the speaker enclosure N ° 2: Listening test Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 95 / 100

Figure 154 -

 154 Figure 154 -Listening test N ° 2 -SPL comparison: Improvements / Sealed / OnePlus 6

  Part V -Summary of the investigations and conclusionStudy for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 98 / 100

Figure 13 -

 13 Figure 13 -Sealed enclosure N ° 1 -Measurement setup .........................................................................................................

Figure 14 -

 14 Figure 14 -Sealed enclosure N ° 1 -Typical electric impedance ..............................................................................................

Figure 15 -

 15 Figure 15 -Sealed enclosure N ° 1 -Typical SPL at 0.3 m, normalized at 500 Hz ...................................................................

Figure 16 -

 16 Figure 16 -Speaker N ° 2 -Detailed description .......................................................................................................................

Figure 17 -

 17 Figure 17 -Sealed enclosure N ° 2 -Assembly elements .........................................................................................................

Figure 18 -

 18 Figure 18 -Sealed enclosure N ° 2 -Assembled system............................................................................................................

Figure 19 -

 19 Figure 19 -Sealed enclosure N ° 2 -Measurement setup ..........................................................................................................

Figure 20 -

 20 Figure 20 -Sealed enclosure N ° 2 -Typical electric impedance ............................................................................................

Figure 21 -

 21 Figure 21 -Sealed enclosure N ° 2 -Typical SPL at 0.1 m, normalized at 2000 H .................................................................

Figure 22 -

 22 Figure 22 -Bass-Reflex principle drawing [20] ......................................................................................................................

Figure 23 -

 23 Figure 23 -Bass-Reflex response against sealed enclosure response [20] ...............................................................................

Figure 24 -

 24 Figure 24 -Passive Radiator principle drawing [21] ...............................................................................................................

Figure 25 -

 25 Figure 25 -Passive Radiator response against sealed enclosure response [21] ........................................................................

Figure 26 -

 26 Figure 26 -" Possible three-operational-amplifier realization of the active equalizer" [23] ....................................................

Figure 27 -

 27 Figure 27 -(a) system before equalization; (b) system after equalization; (c) equalizer [23] ..................................................

Figure 28 -

 28 Figure 28 -Acoustical analogous circuit for a sealed enclosure system [25] ...........................................................................

Figure 29 -

 29 Figure 29 -Simplified analogous circuit for a sealed enclosure ..............................................................................................

Figure 30 -

 30 Figure 30 -Speaker N ° 1 -Diameter considered for the calculation of SD ............................................................................

Figure 31 -

 31 Figure 31 -Speaker N ° 1 -Parameters measurements 1/2 .....................................................................................................

Figure 32 -

 32 Figure 32 -Speaker N ° 1 -Parameters measurements 2/2 ......................................................................................................

Figure 33 -

 33 Figure 33 -Speaker N ° 2 -Dimensions considered for the calculation of SD .........................................................................

Figure

  Figure 34 -Speaker N ° 2 -Parameters measurements 1/2 ......................................................................................................

Figure 48 -

 48 Figure 48 -BR system N ° 1 -Horn port prototype drawings .................................................................................................

Figure 49 -

 49 Figure 49 -Simplified acoustical circuit of a BR system (lossless) .........................................................................................

Figure 50 -

 50 Figure 50 -Electric network for the SPL calculation of a BR system .....................................................................................

Figure 51 -

 51 Figure 51 -BR system N ° 1 -Simulated electric impedance .................................................................................................

Figure 52 -

 52 Figure 52 -BR system N ° 1 -Simulated SPL comparison: BR / Sealed ................................................................................

Figure 53 -

 53 Figure 53 -BR system N ° 1 -Original prototype ...................................................................................................................

Figure 54 -

 54 Figure 54 -BR system N ° 1 -Horn port prototype .................................................................................................................

Figure 55 -

 55 Figure 55 -BR system N ° 1 -Assembled prototype ...............................................................................................................

Figure 56 -

 56 Figure 56 -BR system N ° 1 -Measurement setup ..................................................................................................................

Figure 57 -

 57 Figure 57 -BR system N ° 1 -Measured SPL comparison: BR / Sealed .................................................................................

Figure 58 -

 58 Figure 58 -BR system N ° 1 -Measured SPL comparison for the 3 voltages ..........................................................................

Figure 59 -

 59 Figure 59 -BR system N ° 1 -Electric impedance comparison: Simulation / Measurement ...................................................

Figure 60 -

 60 Figure 60 -BR system N ° 1 -SPL comparison: Simulation / Measurement ..........................................................................

Figure 61 -

 61 Figure 61 -BR system N ° 1analogous circuit for simulation of port losses ........................................................................

Figure 62 -

 62 Figure 62 -BR system N ° 1 -Electric Impedance comparison: Measurement/Simulation w/ and w/o losses .......................

Figure 63 -

 63 Figure 63 -BR system N ° 1 -SPL comparison: Measurement/Simulation w/ and w/o losses ...............................................

Figure 64 -

 64 Figure 64 -BR system N ° 1 -Setup for qualification of turbulences created by ports designs ..............................................

Figure 65 -

 65 Figure 65 -BR system N ° 1 -Qualification of turbulences created by ports at 0.5 uRMS ........................................................

Figure 66 -

 66 Figure 66 -BR system N ° 1 -Qualification of turbulences created by ports at 1 uRMS ...........................................................

Figure 67 -

 67 Figure 67 -BR system N ° 1 -Qualification of turbulences created by ports at 2 uRMS ...........................................................

Figure 68 -

 68 Figure 68 -BR port designs : Port E geometry [35] ................................................................................................................

Figure 69 -

 69 Figure 69 -BR port designs : Port C geometry [35] .................................................................................................................

Figure 70 -

 70 Figure 70 -Acoustical analogous circuit of a PR system [38] .................................................................................................

Figure 71 -

 71 Figure 71 -"Responses obtainable from passive-radiator system for the condition δ = α" [38] ..............................................

Figure 72 -

 72 Figure 72 -Simplified acoustical circuit of a PR system ..........................................................................................................

Figure 73 -

 73 Figure 73 -PR system N ° 1 -Simulated SPL comparison: PR / Sealed .................................................................................

Figure 74 -

 74 Figure 74 -PR system N ° 1 -Prototype elements ..................................................................................................................

Figure 75 -

 75 Figure 75 -PR system N ° 1 -Assembled prototype ...............................................................................................................

Figure 76 -

 76 Figure 76 -PR system N ° 1 -Measurement setup ..................................................................................................................

Figure 77 -

 77 Figure 77 -PR system N ° 1 -Electric impedance comparison: Measurement / Simulation ..................................................

Figure 78 -

 78 Figure 78 -PR system N ° 1 -SPL comparison: Measurement / Simulation ...........................................................................

Figure 79 -

 79 Figure 79 -PR system N ° 1 -Simulated SPLs for determining the minimum mass to add ....................................................

Figure 80 -

 80 Figure 80 -PR system N ° 1 -Simulated SPLs for different added masses ............................................................................

Figure 81 -

 81 Figure 81 -PR system N ° 1 -PE moving mass weighing .......................................................................................................

Figure 82 -

 82 Figure 82 -PR system N ° 1 -PE additional radiating element ...............................................................................................

Figure 83 -

 83 Figure 83 -PR system N ° 1 -PE additional radiating element weighed down .......................................................................

Figure 84 -

 84 Figure 84 -PR system N ° 1 -Tuned prototype .......................................................................................................................

Figure 85 -

 85 Figure 85 -Tuned PR system N ° 1 -Measured SPL comparison: PR / Sealed ......................................................................

Figure 86 -

 86 Figure 86 -Tuned PR system N ° 1 -Measured SPL comparison for the 3 voltages...............................................................

Figure 87 -

 87 Figure 87 -Tuned PR system N ° 1 -Electric impedance comparison: Measurement / Simulation ........................................

Figure 88 -

 88 Figure 88 -Tuned PR system N ° 1 -SPL comparison: Measurement / Simulation ................................................................

Figure 89 -

 89 Figure 89 -Menu Settings for the SigmaStudio 2 nd order HPF ...............................................................................................

Figure 90 -

 90 Figure 90 -Impact of the Gain parameter on the SigmaStudio HPF for f =200 Hz; Q 1.41; G= 0 and 6 dB ...........................

Figure 91 -

 91 Figure 91 -Active EQ N ° 1 -Analogous circuit .....................................................................................................................

Figure 92 -

 92 Figure 92 -Active EQ N ° 1 -HPF circuit...............................................................................................................................

Figure 93 -

 93 Figure 93 -Active EQ N ° 1 -Additional loop for computing the speaker diaphragm excursion ...........................................

Figure 94 -

 94 Figure 94 -Active EQ N ° 1 -Additional loop for computing the current consumption .........................................................

Figure 95 -

 95 Figure 95 -Active EQ N ° 1simulated diaphragm excursion for EQs N ° 1 and 2 ...............................................................

Figure 96 -

 96 Figure 96 -Active EQ N ° 1simulated current consumption for EQs N ° 1 and 2 ................................................................

Figure 97 -

 97 Figure 97 -Active EQ N ° 1simulated SPL comparison: EQs N ° 1 and 2 / sealed .............................................................

Figure 98 -

 98 Figure 98 -Active EQ N ° 1 -Measured SPL comparison: EQs N ° 1 and 2 / sealed ..............................................................

Figure 99 -

 99 Figure 99 -Active EQ N ° 1 -SPL comparison for the EQ N ° 1 over the 3 voltages .............................................................

Figure 100 -

 100 Figure 100 -Active EQ N ° 1 -SPL comparison for the EQ N ° 2 over the 3 voltages ...........................................................

Figure 101 -

 101 Figure 101 -Active EQ N ° 1 -Measured distortion comparison at 2 uRMS: Sealed / EQs / BRs .............................................

Figure 102 -

 102 Figure 102 -Active EQ N ° 1 -SPL comparison for the EQ N ° 1: Measurement / Simulation ..............................................

Figure 103 -

 103 Figure 103 -Active EQ N ° 1 -Current consumption comparison for the EQ N ° 1: Measurement / Simulation ...................

Figure 104 -

 104 Figure 104 -Listening test N ° 1 -Music spectra comparison ................................................................................................

Figure 105 -

 105 Figure 105 -Listening test N ° 1 -SPL comparison: Improvements / Sealed ........................................................................

Figure 106 -

 106 Figure 106 -Listening test N ° 1 -SPL comparison between improvements ..........................................................................

Figure 107 -

 107 Figure 107 -Listening test N ° 1 -SPL comparison: Improvements / Sealed / JBL Go 3 ......................................................

Figure 108 -

 108 Figure 108 -Listening test N ° 1 -Impulse response comparison: Original BR port output / Horn BR port output ...............

Figure 109 -

 109 Figure 109 -Simplified acoustical circuit of a BR system .......................................................................................................

Figure 110 -

 110 Figure 110 -BR system N ° 2 -Presentation of a tube sourced from the market ....................................................................

Figure 111 -

 111 Figure 111 -BR system N ° 2 -Shortening of the tube to constitute the Port of the system ...................................................

Figure 112 -

 112 Figure 112 -BR system N ° 2 -Electric impedance simulation ..............................................................................................

Figure 113 -

 113 Figure 113 -BR system N ° 2 -Simulated SPL comparison: BR / Sealed ..............................................................................

Figure 114 -

 114 Figure 114 -BR system N ° 2 -Prototype bottom casing ........................................................................................................

Figure 115 -

 115 Figure 115 -BR system N ° 2 -Assembled prototype .............................................................................................................

Figure 116 -

 116 Figure 116 -BR system N ° 2 -Measurement setup ................................................................................................................

Figure 117 -

 117 Figure 117 -BR system N ° 2 -Measured SPL comparison: BR / Sealed ...............................................................................

Figure 118 -

 118 Figure 118 -BR system N ° 2 -Electric impedance comparison: Measurement / Simulation .................................................

Figure 119 -

 119 Figure 119 -BR system N ° 2 -SPL comparison: Measurement / Simulation ........................................................................

Figure 120 -

 120 Figure 120 -BR system N ° 2 -Setup for measuring the SPL at port output ...........................................................................

Figure 121 -

 121 Figure 121 -BR system N ° 2 -Port output measured SPL .....................................................................................................

Figure 122 -

 122 Figure 122 -PR system N ° 2 -Simplified analogous circuit for a PR system ........................................................................

Figure 123 -

 123 Figure 123 -PR system N ° 2 -PE presentation .....................................................................................................................

Figure 124 -

 124 Figure 124 -PR system N ° 2 -PE bottom view ....................................................................................................................

Figure 125 -

 125 Figure 125 -PR system N ° 2 -Simulated SPL comparison: PR / Sealed ...............................................................................

Figure 126 -

 126 Figure 126 -PR system N ° 2 -Assembled prototype .............................................................................................................

Figure 127 -

 127 Figure 127 -PR system N ° 2 -Measurement setup ................................................................................................................

Figure 128 -

 128 Figure 128 -PR system N ° 2 -Electric impedance comparison: Measurement / Simulation .................................................

Figure 129 -

 129 Figure 129 -PR system N ° 2 -SPL comparison: Measurement / Simulation .........................................................................

Figure 130 -

 130 Figure 130 -PR system N ° 2 -Simulated SPLs for different added masses ..........................................................................

Figure 131 -

 131 Figure 131 -PR system N ° 2 -PE additional radiating element .............................................................................................

Figure 132 -

 132 Figure 132 -PR system N ° 2 -PE additional radiating element weighed down .....................................................................

Figure 133 -

 133 Figure 133 -PR system N ° 2 -Tuned prototype ....................................................................................................................

Figure 134 -

 134 Figure 134 -Tuned PR system N ° 2 -Measured SPL comparison: PR / Sealed ....................................................................

Figure 135 -

 135 Figure 135 -Tuned PR system N ° 2 -Measured SPL comparison for the 3 voltages .............................................................

Figure 136 -

 136 Figure 136 -Tuned PR system N ° 2 -Electric impedance comparison: Measurement / Simulation ......................................

Figure 137 -

 137 Figure 137 -Tuned PR system N ° 2 -SPL comparison at 0.5 uRMS: Measurement / Simulation ...........................................

Figure 138 -

 138 Figure 138 -Tuned PR system N ° 2 -SPL comparison at 0.1 uRMS: Measurement / Simulation ...........................................

Figure 139 -

 139 Figure 139 -Active EQ N ° 2 -Analogous circuit ...................................................................................................................

Figure 140 -

 140 Figure 140 -Active EQ N ° 2 -HPF circuit .............................................................................................................................

Figure 141 -

 141 Figure 141 -Active EQ N ° 2simulated diaphragm excursion .............................................................................................

Figure 142 -

 142 Figure 142 -Active EQ N ° 2simulated current consumption ..............................................................................................

Figure 143 -

 143 Figure 143 -Active EQ N ° 1simulated SPL comparison: EQ / sealed ................................................................................

Figure 144 -

 144 Figure 144 -Menu Settings for the SigmaStudio Parametric filter...........................................................................................

Figure 145 -

 145 Figure 145 -Active EQ N ° 2 -Measured SPL comparison: EQs N ° 1 and 2 / sealed ............................................................

Figure 146 -

 146 Figure 146 -Active EQ N ° 2 -SPL comparison for the EQ N ° 1 over the 3 voltages ...........................................................

Figure 147 -

 147 Figure 147 -Active EQ N ° 2 -SPL comparison for the EQ N ° 2 over the 3 voltages ...........................................................

Figure 148 -

 148 Figure 148 -Active EQ N ° 2 -Measured distortion comparison at 1 uRMS: Sealed / EQs .......................................................

Figure 149 -

 149 Figure 149 -Active EQ N ° 2 -SPL comparison for the EQ N ° 1: Measurement / Simulation ..............................................

Figure 150 -

 150 Figure 150 -Active EQ N ° 2 -Current consumption comparison for the EQ N ° 1: Measurement / Simulation ...................

Figure 151 -

 151 Figure 151 -Listening test N ° 2 -Music spectra comparison ................................................................................................

Figure 152 -

 152 Figure 152 -Listening test N ° 2 -SPL comparison: Improvements / Sealed .........................................................................

Figure 153 -

 153 Figure 153 -Listening test N ° 2 -SPL comparison between improvements ..........................................................................

Figure 154 -

 154 Figure 154 -Listening test N ° 2 -SPL comparison: Improvements / Sealed / OnePlus 6......................................................

Table I -

 I Speaker N ° 1 -Main characteristics

	Nominal Impedance [Ohms]	4 +/-15 %
	Maximum input pink noise power [Watts]	4
	Fundamental resonance (𝑓 𝑆 ) [Hz]	160 +/-25 %
	Sensitivity [dB SPL / W / m]	77 +/-3 averaged at 0.4, 0.6,0.8, 1.0 kHz

Table II -

 II Speaker N ° 2 -Main characteristics

	Nominal Impedance [Ohms]	8 +/-15 %
	Maximum input pink noise power [Watts]	0.7
	Fundamental resonance (𝑓 𝑆 ) [Hz]	550 +/-20%
	Sensitivity [dB SPL / 0.1 W / m]	62 +/-3 at 2 kHz

Table III

 III

									Coefficient
	Parameter	#1	#2	#3	#4	#5	Average	Standard Deviation	Of Variation
									[%]
	𝑅 𝑒 [Oms]*	3.62	3.62	3.62	3.62	3.62	/	/	/
	𝑅 𝑀𝑆 [N.s/m]	5.37e-01	5.30e-01	5.54e-01	5.31e-01	5.44e-01	5.39e-01	9.78e-03	1.81
	𝐶 𝑀𝑆 [m/N]	5.35e-04	5.45e-04	5.21e-04	5.29e-04	5.21e-04	5.30e-04	1.00e-05	1.89
	𝑀 𝑀𝑆 [kg]	1.78e-03	1.75e-03	1.83e-03	1.78e-03	1.82e-03	1.79e-03	3.22e-05	1.79
	B. l [T.m]	2.23	2.22	2.27	2.22	2.26	2.24	2.36e-02	1.06

-Speaker N ° 1 -Measurements of the fundamental parameters *Measured from the impedance curve without the volume

Table IV -

 IV Speaker N ° 2 -Measurements of the fundamental parameters

									Coefficien
	Parameter	#1	#2	#3	#4	#5	Average	Standard Deviation	t Of Variation
									[%]
	𝑅 𝑒 [Oms]*	7.93	7.93	7.93	7.93	7.93	/	/	/
	𝑅 𝑀𝑆 [N.s/m]	1.46e-01	1.40e-01	1.45e-01	1.45e-01	1.45e-01	1.44e-01	2.25e-03	1.56
	𝐶 𝑀𝑆 [m/N]	8.85e-04	9.21e-04	8.64e-04	8.55e-04	8.92e-04	8.83e-04	2.60e-05	2.94
	𝑀 𝑀𝑆 [kg]	8.07e-05	7.75e-05	8.15e-05	8.24e-05	8.00e-05	8.04e-05	1.86e-06	2.32
	B. l [T.m]	0.61	0.60	0.61	0.61	0.61	0.61	5.02e-03	0.83

*Measured from the impedance curve without the volume

III. Investigations around the speaker enclosure N ° 1 III.I. Improvement method N ° 1 (Bass-Reflex)

	Part III -Investigations around the speaker enclosure N ° 1: Bass-Reflex
	Study for the improvement of low frequencies in Seltech speaker enclosures	p. 27 / 100
	Frédéric Fallais -2021

  and Figure 80 respectively illustrate the integral results and the curves for 2.5x 𝑀 𝐴𝑅 ≤ 𝑀 𝐴𝑅 ′ ≤ 4.5x 𝑀 𝐴𝑅 .

	Table VII -PR system N ° 1 -F function integral result for different added masses
	PR configuration	Value for the function 𝐹, with 𝑓 1 = 100 Hz and 𝑓 2 = 1000 Hz
	𝑀

𝐴𝑅 ′ = 2.5x 𝑀 𝐴𝑅 257 𝑀 𝐴𝑅 ′ = 3x 𝑀 𝐴𝑅 577 𝑀 𝐴𝑅 ′ = 3.5x 𝑀 𝐴𝑅 792 𝑀 𝐴𝑅 ′ = 4x 𝑀 𝐴𝑅 775 𝑀 𝐴𝑅 ′ = 4.5x 𝑀 𝐴𝑅 667 Figure 80 -PR system N ° 1 -Simulated SPLs for different added masses

Table VIII

 VIII

	#1	0.912
	#2	0,910
	#3	0.908
	#4	0.908
	#5	0.909
	Average	0.909

-PR system N ° 1 -MMD weighing 𝑀 𝑀𝐷 [g]

Table IX -

 IX PR system N ° 1additional mass weighing

		Additional
		Mass [g]
	#1	2.287
	#2	2.289
	#3	2.288
	#4	2.287
	#5	2.290
	Average	2.288
		Figure 84 -PR system N ° 1 -Tuned prototype

Table XVI

 XVI

	LF Attribution	Preference	More balanced	Clearer	Closer	More accurate	More powerful	Warm	Round	Realistic	Wider	Closed	Distorted	Muffled	Less Reactive	Noisy
	(Sealed ↔ JBL): Sealed 5% 40% 2x	2x								1x	1x	2x		2x
	(Sealed ↔ JBL): JBL 85% 60% 3x	1x			2x		1x			1x		2x		1x
	(EQ ↔ JBL): EQ 40% 50% 2x	5x	1x	1x	2x				2x		5x			1x
	(EQ ↔ JBL): JBL 55% 50% 1x	1x			1x	1x			1x		2x	7x
	(BR ↔ JBL): BR 45% 75% 1x	4x	1x	1x	5x			2x	2x
	(BR ↔ JBL): JBL 45% 15% 1x				1x	1x	1x		1x	1x	1x	4x	2x

-Listening test N ° 1 -Comparisons against a market solution: Collected words

  14 cm 2 (or a diameter 𝑑 ≥ 4 mm)

-

A length 𝑙 = 4.27 cm (end corrections included) Study for the improvement of low frequencies in Seltech speaker enclosures Frédéric Fallais -2021 p. 72 / 100

Table XVIII -

 XVIII PR system N ° 2 -PE qualification

	Parameter	Speaker (1)	Passive element (2)	(2) -(1)	[(2) -(1)] / (1) [%]
	𝑅 𝑀𝑆/𝑅 [N.s/m]	1.44e-01	1.25e-01	-1.92e-02	-13.32
	𝐶 𝑀𝑆/𝑅 [m/N]	8.83e-04	1.00e-03	1.17e-04	13.20
	𝑀 𝑀𝑆/𝑅 [kg]	8.04e-05	8.86e-05	8.18e-06	10.17

Table XX -

 XX PR system N ° 2additional mass weighing

		Additional
		Mass [g]
	#1	0.175
	#2	0.178
	#3	0.177
	#4	0.178
	#5	0.178
	Average	0.177

Table XXII -

 XXII Listening test N ° 2 -Comparison Improvements / Sealed: Answers to LF and preference questions Figure 106 illustrates the subtraction 𝐸𝑄 𝑁𝑜. 2 𝑆𝑃𝐿 -𝐸𝑄 𝑁𝑜. 1 𝑆𝑃𝐿 , in order to verify that the parametric does not create any other modification on the SPL than in the region where it is supposed to operate.

	Comparison between the improvements
				LF Attribution						Preference
		Sealed	EQ N ° 1		No attr.		Sealed		EQ N ° 1		No pref.
	Sealed → EQ N ° 1	20%			80%		0%			20%		80%		0%
	EQ N ° 1 → Sealed	40%			40%		20%		40%		50%		10%
	(Sealed ↔ EQ No. 1) Average	30%		60%		10%		30%		65%		5%
		Sealed	EQ N ° 2		No attr.		Sealed		EQ N ° 2		No pref.
	Sealed → EQ N ° 2	20%			70%		10%		30%		60%		10%
	EQ N ° 2 → Sealed	60%			30%		10%		80%		10%		10%
	(Sealed ↔ EQ No. 2) Average	40%		50%		10%		55%		35%		10%
	Table XXIII -Listening test N ° 2 -Comparison Improvements / Sealed: Collected words
		LF Attribution	Preference	More balanced	More powerful	Better rendering	Wider	Clearer	Deeper	Closer	Round	Warmer	Distorted	Metallic	Echoes	Noisy
	(Sealed ↔ EQ N ° 1): Sealed 30% 30% 1x			1x 1x							1x
	(Sealed ↔ EQ N ° 1): EQ N ° 1 60% 65% 1x 5x 1x 2x 3x 1x 3x 1x		1x 1x 1x
	(Sealed ↔ EQ N ° 2): Sealed 40% 55% 1x 2x			4x						2x
	(Sealed ↔ EQ N ° 2): EQ N ° 2 50% 35%		2x 1x 1x		1x		1x 2x 1x 1x 1x 2x
	Study for the improvement of low frequencies in Seltech speaker enclosures			p. 94 / 100
	Frédéric Fallais -2021

Table XXIV -

 XXIV Listening test N ° 2 -Comparison between improvements: Answers to LF and preference questions

				LF Attribution					Preference
		EQ N ° 1	EQ N ° 2	No attr.	EQ N ° 1	EQ N ° 2	No pref.
	EQ N ° 1 → EQ N ° 2	20%		20%		60%		20%		20%		60%
	EQ N ° 2 → EQ N ° 1	20%		30%		50%		50%		20%		30%
	Average	20%		25%		55%		35%		20%		45%
	Table XXV -Listening test N ° 2 -Comparison between improvements: Collected words
	LF Attribution	Preference	No difference	More balanced	More powerful	More accurate	Clearer	Warmer	Deeper	Distorted	Muffled	Aggressive
	EQ N ° 1 20% 35%			2x		1x	1x	1x		1x
	EQ N ° 2 25% 20%		3x		1x	1x			1x
	No difference		9x					1x

Table

  XXVII of collected words on the next page could help us understand the reason for this preference.

Table XXVI -

 XXVI Listening test N ° 2 -Comparisons against a market solution: Answers to LF and preference questions

			LF Attribution			Preference
		Sealed	OnePlus	No attr.	Sealed	OnePlus	No pref.
	Sealed → OnePlus	30%	70%	0%	60%	40%	0%
	OnePlus → Sealed	50%	50%	0%	50%	40%	10%
	(Sealed ↔ OnePlus) Average	40%	60%	0%	55%	40%	5%
		EQ N ° 1	OnePlus	No attr.	EQ N ° 1	OnePlus	No pref.
	EQ N ° 1 → OnePlus	40%	60%	0%	80%	20%	0%
	OnePlus → EQ N ° 1	70%	20%	10%	40%	50%	10%
	(EQ No. 1 ↔ OnePlus) Average	55%	40%	5%	60%	35%	5%
		EQ N ° 2	OnePlus	No attr.	EQ N ° 2	OnePlus	No pref.
	EQ N ° 2 → OnePlus	50%	50%	0%	70%	30%	0%
	OnePlus → EQ N ° 2	70%	30%	0%	80%	20%	0%
	(EQ No. 2 ↔ OnePlus) Average	60%	40%	0%	75%	25%	0%

Table XXVII -

 XXVII Listening test N ° 2 -Comparisons against a market solution: Collected words

	LF Attribution	Preference	More balanced	More powerful	More accurate	Better rendering	Wider	Clearer	Deeper	Closer	Distorted	Metallic	Closed	Muffled	Filtered	Noisy
	(Sealed ↔ OnePlus): Sealed 40% 55% 1x		1x		1x 6x					2x 2x
	(Sealed ↔ OnePlus): OnePlus 60% 40%		5x 1x		2x			1x 1x 1x 1x 1x 2x 1x
	(EQ N ° 1 ↔ OnePlus): EQ N ° 1 55% 60% 1x		1x 1x 2x 6x 3x 1x 2x			2x 1x 1x
	(EQ N ° 1 ↔ OnePlus): OnePlus 40% 35% 2x 1x 1x 1x 1x 2x			1x 2x		5x 1x 1x
	(EQ N ° 2 ↔ OnePlus): EQ N ° 2 60% 75% 1x 1x				4x 2x 1x 1x		2x 3x
	(EQ N ° 2 ↔ OnePlus): OnePlus 40% 25% 2x 2x			2x 3x			2x		1x 2x 2x 3x

  Figure 1 -"Smart speaker use case frequency. January 2020" [1] .............................................................................................Figure 2 -"What do you use your smartphone for?" September 2020 [2] .................................................................................Figure 3 -SPL comparison: Nokia N95 / Xiaomi Black Shark 4. Graph recreated from [3] .....................................................Figure 4 -SPL comparison: JBL Go 2 / JBL Go 3. Graph recreated from [4] and [5] ...............................................................Figure 5 -Apple HomePod mini split view [8] ..........................................................................................................................Figure 6 -Anker Rave split view [10] .......................................................................................................................................Figure 7 -Micro Passive Radiator prototypes [6] ......................................................................................................................Figure 8 -Pitch perception of a complex tone (Missing fundamental effect) [15] .....................................................................Figure 9 -Geographical distribution of Seltech offices .............................................................................................................Figure 10 -Speaker N ° 1 -Detailed composition .....................................................................................................................Figure 11 -Sealed enclosure N ° 1 -Assembly elements ..........................................................................................................Figure 12 -Sealed enclosure N ° 1 -Assembled system ............................................................................................................

  34 -Speaker N ° 2 -Parameters measurements 1/2 ......................................................................................................Figure 35 -Speaker N ° 2 -Parameters measurements 2/2 ......................................................................................................Figure 36 -Additional electric network for the SPL calculation .............................................................................................Figure 37 -Sealed enclosure N ° 1 -Model / Measurement electric impedance comparison ..................................................Figure 38 -Sealed enclosure N ° 1 -Model / Measurement SPL comparison .........................................................................Figure 39 -Sealed enclosure N ° 1 -SPL behavior over the voltage ......................................................................................Figure 40 -Sealed enclosure N ° 2 -Model / Measurement electric impedance comparison ..................................................Figure 41 -Sealed enclosure N ° 2 -Model / Measurement SPL comparison .........................................................................Figure 42 -Sealed enclosure N ° 2 -SPL behavior over the voltage .......................................................................................Figure 43 -Listening tests environment ..................................................................................................................................Figure 44 -Acoustical analogous circuit of a BR system [34] .................................................................................................Figure 45 -Illustration of alignments C4, B4, and QB3 (n ° 8, 5, and 3) [28] ..........................................................................Figure 46 -Typical electric impedance of a BR system [34] ...................................................................................................Figure 47 -BR system N ° 1 -Prototype drawings .................................................................................................................

Remerciements

List of Tables

 Table I -