Räv-L, a two-way speaker project from 2022 based on sb17cac/nbac and sb26cdc/adc

[Maartenovic]

Introduction​

Behind this cryptic headline comes a series of posts concerning the development and design of a speaker, called the Räv-L. The slightly childish or playful name is a pastiche of Revel (the speaker brand, which alludes to the verb 'to reveal'), as the Räv-L has similar low-distortion drivers (SB Acoustics metal drivers) as some of Revel's better speakers.

The purpose of the article series is partly to illustrate an iterative development process, and partly to hopefully stimulate your own tests, builds or just increased understanding in the area of loudspeakers. Another purpose is to provide an understanding of what greatly affects the sound experience.

HiFi is an area where it is relatively easy to achieve something pretty good, especially when it comes to loudspeakers, as today there are good drivers and free or affordable measurement and simulation tools. It can be fun to pick low-hanging fruit that has become increasingly rare in our optimized world and where the great achievements were in many cases made decades or centuries ago.

There are other benefits too: Understanding of sound reproduction and what affects the sound experience is increased manifold by trying out a design process, rather than, for example, testing equipment and above all, reading articles, reviews or commenting. It is also a creative process that (if methodically carried out and according to the principles below) counteracts learned helplessness.

Although there are many aspects that need to be taken into account in order to design a good-sounding loudspeaker, according to experience gained from this simple development work, few of them now require a deeper understanding of physics and mathematics. There are both free tools and good principles to reuse, which take care of the significantly more complicated areas such as analog and digital signal processing, Fourier analysis, fluid mechanics, wave propagation in various materials, which of course affect the electroacoustic systems that loudspeakers are. Since the development of loudspeaker elements in recent years has also meant that distortion has been significantly reduced, all the necessary parts are available to create loudspeakers yourself for a small amount of money that can actually compete with the best on the market. These necessary parts are 1) low-distortion elements, 2) free/cheap measuring tools, 3) principles that guide design.

The posts will to some extent follow a chronological order as it was developed on one of Sweden's HiFi forums, but will also be restructured and supplemented to provide a more comprehensive picture. The text will contain many quotes from a gentleman who calls himself "I-or" (short name for Isidor, where I-or happens to be the name given to Eeyore). He is an extremely skilled technical consultant in acoustics and audio technology, as his very initiated, well-read and factual posts on a HiFi forum have been an indispensable enabler in the development process. These contributions relate primarily to the above-mentioned principles for guidance in design.

Frequency response, dispersion and distortion​

So what are these guiding principles?

I-or has repeatedly mentioned three factors; 1; frequency response, 2; dispersion and 3; distortion. These three factors are (according to I-or) the ones that studies have found to mainly affect the listening experience for speakers.

In-depth quotes I-or​

By frequency response it is understood that one means a suitable reference axis, which can vary somewhat, but is usually fairly close to the zero-degree direction. The list (1; frequency response, 2; dispersion and 3; distortion) is in order of priority. It is not entirely obvious what the dispersion should look like (since this largely depends on the setup and the acoustic environment), only that it is an advantage that it lacks more severe irregularities in the frequency direction. A spherical dispersion is not recommended, however, because you get far too large a proportion of room contribution and therefore easily get too "swampy" reproduction. Speakers with too high horizontal directivity, on the other hand, often sound a bit "trapped" because they do not utilize lateral reflections to create a wider and more homogeneous soundscape. The points in the list are generally valid for typical setups and are where consensus science has stood for almost 40 years.

Spinorama​

Spinorama is a way to measure and visualize frequency response and dispersion, an outcome of research by Toole et al. which has also become an ANSI standard: CTA-2034-A R-2020. The following image shows a self-performed Spinorama measurement of Räv-L with different curves exported from the free tool VituixCAD:

In-depth quotes I-or​

As for the frequency dependence of the dispersion, I am not so sure that it is optimal with a fairly constant decrease towards higher frequencies, since this property is only a side effect of how conventional speakers are constructed. The mostly rather odd designs that have had clearly deviating dispersion during Harman's listening sessions have probably had many other weaknesses, but above all the dispersion has not been particularly suitable either. Olive's formula was developed in Harman's listening room, which differs a lot acoustically from many modern and sparsely furnished (i.e. undamped) Swedish homes. For example, if you place the speakers relatively close to the side walls in a room with an open plan and high ceiling height (i.e. long reverberation time), high directivity will already be crucial at relatively low frequencies. However, the correspondence for typical Swedish listening rooms and setups will probably be quite good.

How wide dispersion?​

In-depth quotes I-or​

Without going into details, I would say that the Carlsson speakers spread too much and the (Earl) Geddes speakers too little in a fairly typical room. In the former case it sounds somewhat swampy and in the latter case it feels confined. I am also convinced that the Carlsson speakers sound considerably better than the Geddes speakers for standing listeners. I base this on good listening experience with Carlsson speakers and experience with "constant directivity" designs from manufacturers other than Geddes. Interestingly, this is completely in line with the Tooles/Olives research results. The above applies generally even though the different Carlsson models show quite large differences between themselves.

​

Vertical dispersion​

Directivity index (DI) does not distinguish between horizontal and vertical dispersion. For conventional loudspeakers with physically separated elements and filters with limited slope, what is loosely called 'lobing' occurs. This means that there is interference between the elements in the crossover area and these interferences will sometimes amplify and sometimes weaken the level at different vertical angles. Or to put it another way, the sound will be clearly colored in the vertical direction and also differently colored at different vertical angles.

With Svante Granqvist's software Xdir you can easily play with the effects of lobing:

Now you only listen indirectly to the vertical dispersion (as well as the horizontal dispersion) and the question is what impact does this have? According to I-or, uneven vertical frequency response primarily causes timbre coloration.

In-depth quotes I-or​

The first thing you should do is to completely forget about the influence of the first floor reflection, other than the frequency response influence for lower frequencies. This is of course almost always there in real sound events regardless of the acoustic environment in general, but perhaps above all because at higher frequencies it is almost always attenuated by a carpet or shielded by a coffee table. Various studies have shown that the first floor reflection does not pose a problem in practice. The first ceiling reflection is a different matter, however, since it is not attenuated/shielded to any great extent and arrives considerably later (around 3 ms after the direct sound) and for higher frequencies can therefore be reasonably well separated from the direct sound. For typical speakers, the ceiling reflection affects the height of the soundscape to a lesser extent, but mainly has a timbre influence. It is therefore advantageous to ensure that the frequency response at a vertical angle of around 40-45 degrees does not deviate too much from the direct sound as far as possible. This is not particularly difficult to achieve in itself, but if you also want a smooth frequency response for the direct sound for standing listeners at the listening chair (about 15 degrees vertical angle), lots of difficulties arise. To achieve this, you have to work with steep filters with the right characteristics and in addition, the positions of the acoustic centers for the tweeter and the midrange/bass element must be optimized, which is certainly easily solved in an active design by delaying the signal to the tweeter. MTM configurations naturally do not work at all in terms of smooth vertical dispersion (the separation between the M elements already causes this well below the crossover frequency), but neither do MT configurations on the market meet all the conditions, except possibly in extreme exceptional cases. Note the valley centered at about 700 Hz (about 1/5 of the crossover frequency) in the measurement: Image: Dunlavy Audio Labs SC-I measured by Stereophile The above naturally applies to radiators that can be broadly characterized as point sources, but for line sources, completely different conditions are obtained. Here, the limiting surfaces from both the floor and ceiling can be utilized via reflection effects to provide an overall almost infinitely long line source. This has major positive effects because the listener is always in the radiators near field and the frequency response is therefore not affected by the distance to the source, which is the case for a finite line source. As for vertical directivity, it can sometimes be allowed to be relatively high as long as a reasonable frequency response is obtained for standing listeners. This may seem contradictory since the first ceiling reflection should ideally have a frequency response that is as close as possible to the direct sound. However, the recommendation applies to fairly typical dispersive designs and if the radiation is clearly vertically directed, the first ceiling reflection will be so weak that it does not have much of an impact. However, one should be aware that the soundscape is projected slightly lower in that case and that in practice one easily obtains too large variations in the directivity index to avoid problems with the sound balance in the listening position that are not related to the first ceiling reflection. For direct field listening, dispersion is less important, but this is not very common in a home environment. Personal preferences do not have much of an impact, and listeners tend to have relatively similar opinions for setups in typical rooms, even if more unusual acoustic environments may, for example, require more directivity due to long reverberation times or other acoustic difficulties. As for the 15-degree vertical angle, I am at least very annoyed by speakers that clearly change the sound balance when you stand up. This is very common because it is the case with typical element and filter configurations and in 9 cases out of 10 you get a proper valley around the crossover frequency. As recently discussed in another thread, this also does not provide any advantages for the projection of the soundscape via HRTF effects, which has been put forward as a reason why this would be desirable.

Is Spinorama enough?​

Does Spinorama show everything that matters? Although the correlation between results from Spinorama measurements and rankings of perceived sound quality in the blind studies Toole and Olive have conducted is extremely high, they exclude a third important factor, namely distortion. I-or has repeatedly pointed out the Harman group's neglect of the influence of distortion. Therefore, Spinorama only shows some (but still most) of what is important.

In-depth quotes I-or​

Toole and Olive seem to have never bothered to design/select/correct a low-distortion loudspeaker with good frequency response and dispersion to isolate the distortion, but have had the effect of the distortion obscured by the more potent effects of frequency response and dispersion when looking for correlation between different parameters. In addition, the situation has been worsened by taking psychoacoustically weighted distortion measurements quite lightly. It is also my experience that distortion of "normal" magnitude at medium sound pressure levels is something that the average listener values as quite unimportant, while for sensitive individuals it is absolutely crucial in some cases (compare, for example, with color flicker for DLP projectors). Finally, Olive's formula is of course "middle of the road" in all respects, since Harman really only wants to sell speakers and is therefore mostly interested in what listener Joe Schmoe (and possibly his richer brother Jonathan Schmoe Jr.) will buy. This means that, above all, the significance of deviations in acoustic environment and program material relative to the test setup is not reflected in the results.

 

[Maartenovic]

Distortion​

Distortion, as quoted from Wikipedia, means; “distortion or incorrect reproduction of a signal”. Which is a concept that should of course be highly relevant in sound reproduction.

Distortion can be measured in different ways, for example by sending in a sine signal (pure tone) and measuring the degree of harmonics in relation to the input signal. The summation measure is called Total Harmonic Distortion (THD). Another measure is Intermodulation Distortion (IMD), where for example you send in two or more sine tones and measure the mixed products that nonlinearities create.

Note that these are just two different ways of measuring distortion created by (the same) nonlinearities.

Occasionally one reads that THD is not an important measure. Although the correlation to perceived sound quality is not as great as for Spinorama measurements, it is far from insignificant. One can also increase the correlation by weighting the higher-order partial tones (harmonics) more, as the auditory masking effects decrease the more the harmonics differ in frequency, in relation to the fundamental.

The importance of low distortion​

To emphasize the importance of low distortion, I begin with some descriptive quotes from I-or to give the reader an idea of the effects of distortion:

" I don't know if it's anyone else but me who is always struck by the incredible power and purity that cymbals, hi-hats, glockenspiels, triangles, etc. exhibit in reality, which is never reproduced even remotely correctly by normal speakers that sound powerless, strained and thin. In reality you can clearly hear that these are vibrating metal structures, when reproduced it partly sounds like some kind of shaped noise.

Very few listeners have ever owned a speaker with a THD of around 0.05%, but once you get used to it you become very sensitive to distortion. The immediate reaction when you hear a well-known recording with almost no distortion is usually something like "of course that's how it's supposed to sound". Soft yet incredibly distinct is perhaps the best description of the subjective impression. More like real instruments and voices, simply put.

Although piano music is effective in revealing distortion, distortion can often be heard with virtually all program material, as typical loudspeakers exhibit a THD of about 0.2 – 0.5% at medium sound pressure levels, i.e. well above the detection limit.

My guess is that the audibility threshold with the right (or perhaps rather wrong) program material goes down to a THD somewhere around 0.01% for typical loudspeaker distortion that is clearly dominated by the second tone and sometimes even the third tone. However, this area is quite unexplored and sometimes one can read hair-raising reports where listeners have failed to detect a THD of 10%.

THD correlates fairly well with subjective evaluation. Sometimes you might get the impression that there is no correlation at all, which is completely wrong. There are quite a few relatively cheap, active speakers today that have good frequency response and dispersion, but still sound pretty bad. If you measure the distortion, you can see why, even if you lump it together as THD.

It is also the case that speakers with low THD should definitely be prioritized by listeners who know that they are sensitive to distortion. There are no speakers on the market that exhibit such low distortion that they would even approach the detection limit for sensitive/trained listeners. It all becomes so incredibly clear when you hear a speaker with perhaps 0.05 % THD and realize how much distortion you normally have to put up with.”

THD, a useful concept?​

In-depth discussion​

There seems to be a dearth of studies investigating the impact of distortion on the audio experience. A Danish study; Perception & Thresholds of Nonlinear Distortion using Complex Signals, shows how difficult it is to emulate perception and quantify subjective experience. A quote from the results section of the study summarizes the following: It was found that both conventional metrics were not well correlated with subjective perception of distortion with correlations of -0.4845 and -0.4466, respectively. Both of the newly developed metrics, on the other hand, were found to be well correlated with subjective data obtained with overall correlations of -0.9486 and 0.9547, respectively. A correlation of about 0.45 – 0.5 between THD and subjective estimate is close to the limit of high correlation (0.5) and corresponds to an effect size (Cohen's-d) of about 1 – 1.15, which in turn corresponds to an NNT (Numbers Needed to Treat) of about 2.5. The lower the value, the better. This can be compared with drugs that often have an NNT of about 5 – 200. Placebo effects often result in an NNT of 10 or lower, which means that placebo effects are relatively large, which is why double-blind studies are necessary. Of course, placebos also affect HiFi. Placebo is a power or ability that people possess, which is sometimes mistakenly confused with imagination. The effects are as real as they can be, but the causes of experiences or impressions in these cases are the human's suggestibility and not an external factor such as a cable, new gadget or pill. In addition to this, there are problems with habituation, adaptation, habituation and sensitization (which are to some extent related perception and cognitive psychology concepts that concern non-associative learning and which, in short, deal with how, for example, nerve cells or senses gradually reduce or increase their receptivity depending on previous stimuli. A simple example is that if you turn the bass control to max, the bass sounds exaggerated. If you listen for a while, you get used to it to a certain extent and then turn it back to neutral position, the sound is perceived as weak in bass. Sensitization works in the opposite way to habituation, where the sensitivity of nerve cells or senses to a specific stimulus increases the more the nerve cell or sense is exposed to the specific stimulus. These basic mechanisms of course also play a role in listening evaluation of HiFi equipment. Group and social psychological processes can also play a role in evaluation. Subjective impressions in uncontrolled forms are therefore of very dubious value and not infrequently directly incorrect or not reproducible. As far as I could see, the Danish study seems to deal with at least the majority of these influencing factors and sources of error, in addition to the signal processing sources of error that they probably have a very good grasp of. Criticisms raised against their use of ordinal scale levels are not relevant. In psychometrics, of course, understanding the scales is fundamental, but if there is not too much skewness etc. (deviation from normal distribution), parametric as well as non-parametric statistical methods often work quite equally well. The small objection I noted (if I didn't read it wrong) is that they classified a correlation of about 0.45 between THD and subjective assessment as low. In a psychometric context, it would be on the verge of high correlation. But of course they got a much higher correlation with their method and it certainly looks interesting. I perceive the content to be in line with what I-or has written many times, - THD is a relevant although somewhat rough measure (known since the 50s) and reflects the nonlinearities that a system exhibits. In addition to the above study, the amateur study BLIND TEST RESULTS Part II: "Is high Harmonic Distortion in music audible?" Respondent Results points out that very low distortion levels are audible. If you exclude the worse listeners, it may be possible to distinguish distortion of 0.02% or -75 dB from, for example, 0.3% (-50 dB). The person who set up and analyzed the blind study uses the Chi-square test (a method of hypothesis testing used when you want to investigate whether there is a relationship between two categorical variables) to test for significance, which means that the study is really not bad despite being done in 'free time'. It would have been nice to have a higher response rate to get higher significance, but otherwise it seems to be well done at a quick glance. The following quote shows that the limit for audibility of distortion may possibly be lower than 0.02%: Under more controlled "lab" conditions with very high-fidelity systems, it's possible (likely) that the absolute threshold of audibility for harmonic distortion would be even lower. I also expect audibility of THD would be easier with test tones rather than real music. ​ I have my own experience that there is a clear audible difference between speakers that distort about 0.1% compared to about 0.5% at 85 dB @ 1 m. Should I put it blindly? Yes, I think so. Have I tested blindly? Well, that requires careful equalization. How can I then believe that it is distortion that makes the difference? Because it sounds cloudier, gritty, etc. with higher (measured) distortion and not as tone curve changes.

Speaker distortion​

In-depth quotes I-or​

Loudspeakers exhibit, up to severe overdrive, a clear dominance of lower-order distortion products because the nonlinearities mainly depend on the displacement (Bl(x), Le(x), Kms(x) etc.) while the sound pressure depends on the acceleration. Another way of looking at it is that loudspeakers, being the sluggish electromechanical things they are, like to flatten or round off the signal, but usually have difficulty creating sharp discontinuities in the time plane, while electronics have no problem with this and like to send out slightly "angular" signals even when the input signal is a rounded and nice sine. However, there are exceptions for loudspeakers, e.g. in the case of so-called rub & buzz, severe overdrive or even "bottoming", where all problems create "angular" output signals and thus sound extremely bad. However, a picture says more than a thousand words (input signal consisting of two sinusoids, 400 and 500 Hz with 0.1% andrathon distortion and 0.1% fifth-tone distortion respectively): Image: IM-dist It is the same THD in both cases (-60 dB or 0.1 %), but the fifth-tone distortion creates a lot more garbage, also with a higher amplitude, and therefore sounds significantly worse. The IMD is of course higher in the fifth-tone case, however. Some of the components are masked by the input signal, so perceptually it becomes somewhat more complicated than above. It is clear, however, that higher-order distortion products are significantly more unpleasant-sounding than lower-order ones.

Gradation of distortion​

I-or has proposed a grading of distortion:

"A rough classification can look like this, without taking into account the structure of the harmonic components and the frequency dependence, which will greatly affect the subjective impression.

Hi-fi speakers of a fairly decent size and priced at over 10 thousand SEK per pair, THD at 85 dB, 1 m, free field, f >200 Hz

Very poor result: >1 %
Poor result: 0.5 –1%
Ordinary result: 0.2 –0.5%
Good result: 0.1 –0.2%
Very good result: 0.05 –0.1%
Top class: <0.05 %"

Perhaps we can use this scale, here reversed for wasps and other things, considering that the fairy tale character I-or (Eyeore) is quite pessimistic and that we are looking at negative effects here :

 

[Maartenovic]

Brief construction description and construction pictures​

Before the article series continues with distortion, element selection, tests with baffle and filter, and results, here are some construction pictures and simple construction instructions.

Simple box without bracing and with a slotted port on the outside to minimize the audibility of organ pipe resonances, and to be able to place the box close to the wall. Height and depth can be varied, the important thing is that the volume is about 17–19 liters (depending on the selected tuning in the port), and that the baffle width is kept within 22–26 cm. It is advantageous to make the box floor-standing and shallow. Strongly rounded edges on the baffle, and profiling of the baffle according to the pictures below (the latter is not necessary but improves the frequency response on-axis). The placement of the elements is relatively important, the tweeter is placed 85 mm from the top and the bass a further 170–180 mm down (i.e. 265 mm from the top).

The box is filled to approximately 40–50% with mineral wool, placed at least 5 cm from the inner door opening and base elements so that these are not damped.



Number: What

• 2 pcs SB-Acoustics SB17NBAC35-4 or SB17CAC35-4
• 2 pcs SB-Acoustics SB26ADC-C000-4 or SB26CDC-C000-4
• 2 pcs 8.2 µ u F
• 2 pcs 0.2 mH , wire thickness between 0.6–0.8 mm
• 2 pcs 18 µ u F
• 4 pcs 1 mH wire thickness between 1.2–1.4 mm
• 2 pcs 10 µ u F
• 2 pcs 15 µF
• 2 pcs 5.6 µF
• 2 pcs 3.3 ohms, 5 watts
• 2 pcs 4.7 ohms or 5.6 ohms depending on treble level (choices possible between 4–6 ohms)
• 2 pcs 1 ohm (if you choose 4.7 ohm above and want to be able to adjust) , 5 watts
• 2 connection terminals

Measurements of different filters​

4.7 ohm series resistor for tweeter​

5.6 ohm series resistor for tweeter​

Dimensions:

 

[Maartenovic]

Räv-L part 2: Distortion and element selection​

In the first part of the article series, we went over the first two of the three factors; 1) frequency response, 2) dispersion characteristics and 3) distortion, which are the factors that (according to I-or) have been found in studies to mainly affect the listening experience for loudspeakers. This part will focus on the third factor, distortion.

As mentioned in the first part, distortion is generally considered to have less impact on the listening experience but is also thought to be more dependent on the listener's sensitivity to distortion. Since the impact on the listening experience is highly individual-dependent, and since loudspeaker distortion is generally about 100 times higher in level than what well-designed electronics contribute (albeit often with different spectral distribution), this can be an argument for trying to minimize distortion in loudspeakers as far as possible. Another argument is that it is not possible to influence distortion through design to the same extent as for frequency response and dispersion properties. In short, the choice of loudspeaker elements is decisive when it comes to minimizing distortion. For this reason, it may be appropriate to start a design process by looking for loudspeaker elements that provide as little distortion as possible but also meet the requirements for sound pressure level that you want. Here, you should also consider the working range of the elements and roughly have an idea of suitable crossover frequencies with regard to distortion and dispersion. The latter is largely determined by the diameter of the elements (if waveguides or horns are not used).

Distortion mechanisms in loudspeaker drivers​

There are several factors that cause distortion in electrodynamic speaker drivers of the type that have been around for about 100 years.

Distortion occurs due to nonlinearities in the suspension, cone and motor system. Nonlinearities are when the output signal does not linearly follow the input signal by a certain factor (constant).

The image below from speaker measurement company Klippel shows common causes of distortion in speaker drivers and the frequency range within which they normally operate.

• k ms (x): Stiffness in suspension depending on the cone deflection
• Bl (x): So-called power factor in the motor system depending on the deflection of the voice coil (and cone)
• L (x): Inductance depending on the deflection of the voice coil (and cone)
• L (i): Inductance dependent on current variations
• Doppler distortion depending on the cone movement
• Cone breaks depending on the movement of the cone

New manufacturers; Purifi and BlieSMa​

A discussion about a new speaker driver manufacturer; Purifi, resulted in the following comments about breakups and distortion, which opened my eyes to the progress that has been made in speaker driver performance, perhaps largely due to the fact that FEM simulations and Klippel tools are now commonplace:

In-depth quotes I-or​

There are no materials that even come close to damping out bending modes in the cone to the degree necessary to achieve the tulip-shaped rose that an element with no noticeable break-ups and a frequency-decreasing radiating surface could produce. This simply cannot be done, and one should be extremely skeptical of various statements that this is possible. Some manufacturers have even worked with so-called tuned attenuators in the surround with some success, but without getting rid of the problem. I would say that you see clear diaphragm distortion effects for all drivers used up to just below the first break-up frequency or higher (which is true for all full-range two-way speakers with normal cone materials and crossover frequencies). This distortion is often upwards of 1–3% (THD) at slightly higher sound pressure levels and is clearly audible. I myself have a very hard time with this distortion because the upper midrange / lower treble sounds harsch or strained. However, the combination of a stiff cone (made of graphene) and a relatively low crossover frequency can largely eliminate the problem, as for the Magico A1. To be honest, I don't think there is a single element on the market that is even close to good enough in this area. If you push it hard (105 dB / 1 m – sine in the relevant frequency range, so typically another decent bit higher total sound pressure level with music signals) you can expect peaks of about 3–30% THD around 1–3 kHz regardless of price. The reason for this is to be found in the high mechanical stresses that the cones are exposed to in the break-up area at high accelerations (sound pressure levels). In typical mechanical design work, one does not usually attach much importance to the relatively small nonlinearities that primarily polymers, but also paper materials etc. exhibit in the stress-strain diagrams because it is insignificant here and a linear approximation often works well. However, in all structural mechanical contexts, one must be very careful with excessive stresses because one easily runs into fatigue problems (compare with cone fatigue in a PA context). In a hi-fi context, cone fatigue is in principle an unknown phenomenon, but a nonlinearity of the normally negligible 3% is really bad in terms of distortion. Aluminum has great advantages compared to most other cone materials because the material behaves almost completely linearly up to the yield point. The only problems are that the internal losses are minimal and that the amplitudes at resonance are thus sky-high, and that far too many manufacturers believe that the material will solve all problems and thus switch to large cone opening angles, which of course lowers the first bending resonance frequency significantly. However, the low internal losses can be managed and, via the high material stiffness, even turned to an advantage with so-called constrained layer technology (sandwich with rigid cover layers and super high-loss material in the core), although this is unfortunately rarely done in practice, both for reasons of ignorance and cost (who cares about 10% diaphragm distortion when you can hype cool aluminum baskets, tough ventilation or hyper-stiff titanium bobbins? The best thing is to completely avoid the break-up area with rigid cones and relatively low crossover frequencies, but if you absolutely have to deal with the resonances, you often have to choose between a couple of clear, high-frequency, narrow distortion peaks with relatively low audibility (typical of rigid cones) or a generally higher membrane distortion level, which instead starts further down in frequency and is quite broadband. It is possible to say that lousy aluminum cones are worse than equally lousy plastic or paper cones, but it is a choice between the plague and cholera. Done correctly, you have greater opportunities to optimize for low membrane distortion with rigid materials.

In connection with the above exchange of words, an element was suggested, quote I-or:

"The SB Acoustics SB15NBAC30-4 is a 5" driver and therefore does not quite meet the full range requirements for a two-way solution, but if you use it in a three-way speaker, you will get something that is on par with the distortion champion Magico S5 (around $35,000) in the midrange. The reason for its enormously fine performance is, in addition to a super-linear motor, that an aluminum cone with pressed-in stiffeners has been used and of course the cone has relatively small dimensions. This is probably one of the very best 5-inch drivers on the market and the fact that the price is relatively low does not make things worse."

In-depth quotes I-or​

The Purifi driver is very good but in my opinion not worth the money. The SB drivers (5" and 6.5") discussed above are about as good, except for the lowest frequencies, at a very reasonable cost. It is only if you absolutely have to build a tiny speaker with high performance that Purifi's 6.5" element can be relevant, otherwise it is much smarter to use the money to build three-way speakers (in the same box or with bass modules). Short ribbon elements usually give quite high distortion. However, ribbon-type line sources have the potential to perform exceptionally well here. Ceiling and floor reflections with a conventional speaker are quite different phenomena because the vertical radiation angles differ greatly (horns and line sources can reduce or completely avoid the problems through high directivity). Ceiling reflection in particular can cause some strange phenomena around the crossover frequency via the radiation lobes if you’re not careful. Severe vertical dispersion problems are most effectively avoided through short distances between the elements (relative to the wavelength), small diameters (relative to the wavelength), low crossover frequencies (Maartenovic note: Not too low though with regard to distortion), stepped baffles use (Maartenovic note: Which cause reflections) and possibly waveguides. Vertical reflections primarily have a sonic impact and can be compensated for with balancing reflections from other directions or equalization and can also reduced with some absorption/diffraction (carpet/coffee table). If you want to take the step to the full, you can use a ceiling absorber or a diffusing, large, ceiling. As long as you can maintain a nearly constant frequency response on-axis, controlled dispersion and low distortion, you can choose any crossover frequency. In practice, however, high-frequency crossovers are very difficult to achieve except for coaxial elements because the wavelength is small in relation to the element spacing.

So which speaker drivers should you choose? Since distortion (non-linear) irreversibly distorts and destroys information (unlike frequency response deviations which can be corrected in various ways, – but not both frequency response deviations and dispersion at the same time), and based on inspiration from other threads and I-or's very initiated posts, below are some comparisons between different drivers.

In addition to distortion, there are of course other parameters (such as Thiele/Small parameters and frequency response) to take into account, but these can be managed with various tricks (such as equalization), which cannot be done with distortion. Although distortion is subordinate to frequency response, the distortion in drivers to a greater extent locks the limit of what is possible to achieve in a speaker.

Low-distortion element​

The distortion varies by almost a factor of ten between different elements and since there is no correlation between price and performance when comparing measurement data from Hificompass, there is a lot to be gained from comparing elements and choosing the right one.
The list below is of course not comprehensive, but a selection from available measurements. The prices are from 2021 and have gone up since then but are included to give a price indication.

Low-distortion elements:

Tweeters
SB Acoustics SB26ADC, approx. 600 SEK per piece.
Bliesma T34B-4, approx. 4000 SEK per piece..
Bliesma T25D-6, approx. 2800 SEK per piece.
Morel CAT378, approx. 600 SEK per piece.
Peerless BC25TG15, approx. 200 SEK per piece.

Upper midrange/lower treble, 1000-4000Hz
Bliesma M74A-6 with an Aluminum-Magnesium (AlMg) dome, approx. 5000 SEK per piece.
Bliesma M74B-6 with a Beryllium (Be) dome, approx. 7000 SEK per piece.
Tangband 75-1558SEEv optionally Peerless TC9FD-18 or 10F/4424 / 10F/8424

Midrange, approx. 300-3000 Hz :
Purifi, several variants 4000 SEK per piece.

Probably Visaton AL130M, but no good measurements found.

Midbass: approx. 100-3000Hz
SB Acoustics SB17CAC, 900 kronor each.
Purifi, several variants 4000 kronor each.
Seas Excel 6" W18NX003, approx. 5000 SEK per piece.
SB Acoustics SB17NBAC, 700 SEK per piece.
SB Acoustics SB15NBAC
Probably Visaton AL130, but no good measurements found
300 –1500 Hz: Wavecor WF146WA01.

Bass, approx. 100-400Hz :
SB Acoustics SB23NRXS45-8, 969 SEK per piece.
SB Acoustics SB23NACS45-8, 1048 SEK per piece.
Scan-Speak Discovery 26W/4534G00, 1132 SEK per piece.
SB Acoustics Satori WO24P-8, 2183 SEK per piece.

Subwoofer 20-80Hz:
Scan-Speak Discovery 26W/4534G00, 1132 SEK per piece.
SB Acoustics SB23MFCL45-8, 1269 kronor each.
SEAS L26ROY, 2500 kronor each.
Probably Scan-Speak Discovery 26W/4558T00, 2500 kronor each.
Scan-Speak 28w/4578, about 7000 kronor each.
Scan-Speak 32w/4778, 6500 kronor each.
BMS 18N862



In the distortion diagram below, the higher order partials are weighted higher because these tones are less masked by the music signal and are therefore more audible. For weighting, I have used the following formula where the weighting coefficients are 1, 3, 5 and 7:



= Total harmonic distortion, = second partial or harmonic, = third harmonic, = fourth harmonic and = fifth harmonic.

The correlation to experience or audibility should therefore be higher than in psychometric contexts the relatively high 0.45 that the previously referenced Danish study found for the THD measure (NB, correlation lacks unity and can vary between -1 and 1, where 0 is no correlation, -1 full negative correlation and +1 full positive correlation).

Treble distortion​

In the graph above you can see that the SB Acoustics SB26CDC/ADC, which cost about 500 Swedish kronor, are very affordable tweeters. The Peerless BC26TG15 is even more affordable but has slightly worse performance. BlieSMa's models perform very well but are significantly more expensive. The different colors in the table summarize the distortion for a few more tweeters. Note that the selection above includes the lowest-distorting elements. As can be seen, the SB26CDC/ADC is among the very best regardless of price, even in this illustrious company. An old faithful servant like the Scanspeakt 2905-9700 performs significantly worse than the SB26ADC/CDC and BlieSMa's tweeters.

Note that the distortion in the diagram above is chosen with different input levels. This is to compensate for the different voltage sensitivities of the tweeters and thus approximate approximately similar sound pressure levels.

Distortion midrange​

These three elements (including variants) are the best that can be found today in terms of low distortion in the midrange:

Below is a comparison of how much worse but commonly used elements in, for example, old Carlsson speakers (SC-165-V) and many other speakers perform. We are talking about a factor of 5–20 times higher distortion than the best in the previous diagram above:

Distortion bass​

Below is the distortion for a selection of the lowest distortion woofers. The SB Acoustics Satori Wo24p-4 has the lowest distortion in the 100–500 Hz range, followed by the SB Acoustics SB23NRXS. The BMS 12S305 is a high-quality alternative if you accept a larger cabinet volume, as is the SB Acoustics SB34NRXL.

As a home builder or small speaker manufacturer, the standard elements of the element manufacturers are available. Larger manufacturers can produce their own elements or place orders for variants of the element manufacturers' standard range. Based on comparisons of measurements by, for example, Soundstage, the magazine Voicecoil, Audiosciencereview, or Erins Audio corner, the standard elements above exhibit such low distortion that a self-built speaker should be able to compete well with the very best commercial speakers, almost regardless of price.

Dispersion in elements?​

How will the dispersion be with hard and rigid cones?

In-depth quotes I-or​

Quote I-or:​ It is a misunderstanding that unfortunately sometimes appears (that the sound radiation is dominated by the center area near the attachment of the bobbin). When the cone increasingly breaks up for high frequencies, it is far from obvious that the sound radiation is dominated by the area near the attachment of the bobbin. This depends entirely on how the cone and surround are designed. Please study the simulation below that I made for a fairly typical mid-bass element with a plastic cone (I skipped the spider because it plays less role in this context): Higher-order modes in the surround always occur from a few hundred Hz and up depending on dimensions and material. These modes are the main cause of the small frequency response deviations seen between perhaps 200 Hz and 1500 Hz for typical speaker drivers. Similar modes in the spider also affect (you can see a mode in the spider in the animation), but to a lesser extent because they only indirectly affect the sound radiation via the movement of the cone. Without these troublemakers, the frequency response from the driver would be absolutely straight all the way up to just below the first cone mode. The influence becomes less for higher frequencies, and is ultimately overshadowed by bending modes in the cone, but remains throughout the passband. The amplitudes can be large, but the question is always how much sound radiation they lead to (the sum of the contributions from the different oscillating parts of the surround). In general, it is an advantage to have a narrow, light and stiff surround to minimize the influence of these modes, but you also need to have a certain stroke length, which requires a wider and more elastic surround. In addition, you may need to add damping to the cone. Whichever way you turn, you will have drawbacks. However, there are opportunities to improve the situation a lot, which Purifi, among others, has realized. Even though the linear influence (frequency response) may be low, large amplitudes in the surround can cause nonlinearities in the cone's movement that manifest themselves in distortion peaks. As usual, you will always encounter modes, but the fewer of these you need to handle in the passband, the better. Therefore, you should try to move as many of these modes as possible to frequencies above the passband via stiff/lightweight constructions and also break up the rotational symmetry when you can (Purifi has done this in an effective, but somewhat clumsy, way for the surround, which means that different parts around the surround have different resonant frequencies). Midwoofer mode shape Midwoofer sound pressure Midwoofer Frequency Response (0.5 m on-axis) All values and levels apply to a mid-woofer with full potential characteristics. The mode shape in the top image shows displacements that are magnified 1000 times. As can be seen, the inner part of the cone oscillates in antiphase with the outer part that dominates the sound radiation. If we continue with the example element above, it looks like this up to 2650 Hz (i.e. when the cone and surround behave well): Midwoofer soundfield And this noisy already at 3150 Hz: Midwoofer soundfield 2 As you can see, it all depends on the complexity of the source and there is also a large frequency dependence. In the example above, we have also completely neglected diffraction via the baffle in combination with the magical completely reflection-free acoustic edge, which further complicates the issue. For those who want to model effects like these, it is easy to just create a lot of point sources with source strengths and phase positions that fairly well mimic the condition that you want to describe. Then you sum all contributions in the solution space and obtain the complex-valued sound pressure (or the amplitude and phase of the sound pressure if you like). As for Klippel's NFS (Near Field Scanner), its greatest advantages lie in the low-frequency range, but it also turns out that you often see differences compared to conventional measurements carried out at 1 m quite high up in frequency, since the measurement distance in the conventional case is too short to be in the far field

Baffle simulations​

There are several different tools (Svantes Edge, VituixCad and Bagbys Excel) to choose from and they give very similar results:

In the simulations above, you can see how much impact the baffle has on the frequency response, up to about 8–9 dB at most. This is something we will return to.

Calibration, comparison with known objects​

Since I was new to measurements, I started with some comparisons with known and professionally measured objects as a reference, here sb17cac:

As can be seen, the agreement between my own measurements and factory measurements of the sb17cac is good, despite different measurement setups. The biggest deviation is below about 200 Hz where I used a much larger baffle than Sb Acoustivs uses in their factory measurements and therefore I did not get the same tap in this range.

 

[DanielT]

Hi Maarten, welcome to ASR.

I’ve read about the development and design of your RÄV speakers over at faktiskt.io. You did a really solid job with them. With the various iterations and test enclosures. You alternated between practical work, measurements, and theoretical calculations. A superb job—and the result turned out really well.

Are you thinking about adding subwoofers/ bass boxes to go with your RÄV speakers?

Two of those would be cool. Hoffman’s Iron Law applies, of course, but they have so much power that you can manage to push the frequency response lower in the "small" boxes by trading off some power. I’m particularly drawn to that aesthetically pleasing build:

Little Big 18" Subwoofer Build

I’ve been building subwoofers for years now, and I’ve always used car audio drivers. However, I recently started building speakers using pro-audio drivers, specifically mid-woofers and horn loaded compression drivers. I love how dynamic and clean-sounding these drivers are, so it was only...

www.audiosciencereview.com

Speaking of nice-looking, aesthetically pleasing builds, I like these:

My first diy speakers

Hello! This is my first try to do decent diy speakers and wanted to share some pictures. They use peerless hds 830869 woofer and sb26adc tweeter in 8" waveguide. They are still in progress so i will post more pics and info when i finish them. My plan is to try make a spinorama for these. There...

www.audiosciencereview.com

If you’re set on a two-way design with an 8-inch woofer and a 1-inch tweeter, then the
sb26adc tweeter in a waveguide is probably the way to go.

Distortion levels—and the point at which they become audible—are a favorite and recurring topic here on ASR. To a large extent, I think it comes down to training and, related to that, annoyance. Test threads pop up here and there where you can do blind tests to see how good you are at identifying distortion. Stick around ASR and you’ll see.

A few tips. On the lighter side, I recommend these threads:

Vintage Audio Advertising

Must say, the internet can sometimes be wonderful. By pure chance I landed on a discussion about vintage Empire speakers and that led me to other vintage discussions, and eventually to vintage audio advertising. Some of the ads are downright comical, at least I thought so. Lots of posing...

www.audiosciencereview.com

Funky groovy music

It’s strange—I don’t see a thread about funk music? So why not start one? :) Feel free to share what you like—artists, albums, and/or songs. Whether it’s "pure" funk à la James Brown or funk-inspired tracks with a great groov, like "Roundabout" by Yes, for example, old or new music—please feel...

www.audiosciencereview.com

 

[DanielT]

Räv-L part 2: Distortion and element selection​

In the first part of the article series, we went over the first two of the three factors; 1) frequency response, 2) dispersion characteristics and 3) distortion, which are the factors that (according to I-or) have been found in studies to mainly affect the listening experience for loudspeakers. This part will focus on the third factor, distortion.

As mentioned in the first part, distortion is generally considered to have less impact on the listening experience but is also thought to be more dependent on the listener's sensitivity to distortion. Since the impact on the listening experience is highly individual-dependent, and since loudspeaker distortion is generally about 100 times higher in level than what well-designed electronics contribute (albeit often with different spectral distribution), this can be an argument for trying to minimize distortion in loudspeakers as far as possible. Another argument is that it is not possible to influence distortion through design to the same extent as for frequency response and dispersion properties. In short, the choice of loudspeaker elements is decisive when it comes to minimizing distortion. For this reason, it may be appropriate to start a design process by looking for loudspeaker elements that provide as little distortion as possible but also meet the requirements for sound pressure level that you want. Here, you should also consider the working range of the elements and roughly have an idea of suitable crossover frequencies with regard to distortion and dispersion. The latter is largely determined by the diameter of the elements (if waveguides or horns are not used).

Distortion mechanisms in loudspeaker drivers​

There are several factors that cause distortion in electrodynamic speaker drivers of the type that have been around for about 100 years.

Distortion occurs due to nonlinearities in the suspension, cone and motor system. Nonlinearities are when the output signal does not linearly follow the input signal by a certain factor (constant).

The image below from speaker measurement company Klippel shows common causes of distortion in speaker drivers and the frequency range within which they normally operate.

• k ms (x): Stiffness in suspension depending on the cone deflection
• Bl (x): So-called power factor in the motor system depending on the deflection of the voice coil (and cone)
• L (x): Inductance depending on the deflection of the voice coil (and cone)
• L (i): Inductance dependent on current variations
• Doppler distortion depending on the cone movement
• Cone breaks depending on the movement of the cone

New manufacturers; Purifi and BlieSMa​

A discussion about a new speaker driver manufacturer; Purifi, resulted in the following comments about breakups and distortion, which opened my eyes to the progress that has been made in speaker driver performance, perhaps largely due to the fact that FEM simulations and Klippel tools are now commonplace:

In-depth quotes I-or​

There are no materials that even come close to damping out bending modes in the cone to the degree necessary to achieve the tulip-shaped rose that an element with no noticeable break-ups and a frequency-decreasing radiating surface could produce. This simply cannot be done, and one should be extremely skeptical of various statements that this is possible. Some manufacturers have even worked with so-called tuned attenuators in the surround with some success, but without getting rid of the problem. I would say that you see clear diaphragm distortion effects for all drivers used up to just below the first break-up frequency or higher (which is true for all full-range two-way speakers with normal cone materials and crossover frequencies). This distortion is often upwards of 1–3% (THD) at slightly higher sound pressure levels and is clearly audible. I myself have a very hard time with this distortion because the upper midrange / lower treble sounds harsch or strained. However, the combination of a stiff cone (made of graphene) and a relatively low crossover frequency can largely eliminate the problem, as for the Magico A1. To be honest, I don't think there is a single element on the market that is even close to good enough in this area. If you push it hard (105 dB / 1 m – sine in the relevant frequency range, so typically another decent bit higher total sound pressure level with music signals) you can expect peaks of about 3–30% THD around 1–3 kHz regardless of price. The reason for this is to be found in the high mechanical stresses that the cones are exposed to in the break-up area at high accelerations (sound pressure levels). In typical mechanical design work, one does not usually attach much importance to the relatively small nonlinearities that primarily polymers, but also paper materials etc. exhibit in the stress-strain diagrams because it is insignificant here and a linear approximation often works well. However, in all structural mechanical contexts, one must be very careful with excessive stresses because one easily runs into fatigue problems (compare with cone fatigue in a PA context). In a hi-fi context, cone fatigue is in principle an unknown phenomenon, but a nonlinearity of the normally negligible 3% is really bad in terms of distortion. Aluminum has great advantages compared to most other cone materials because the material behaves almost completely linearly up to the yield point. The only problems are that the internal losses are minimal and that the amplitudes at resonance are thus sky-high, and that far too many manufacturers believe that the material will solve all problems and thus switch to large cone opening angles, which of course lowers the first bending resonance frequency significantly. However, the low internal losses can be managed and, via the high material stiffness, even turned to an advantage with so-called constrained layer technology (sandwich with rigid cover layers and super high-loss material in the core), although this is unfortunately rarely done in practice, both for reasons of ignorance and cost (who cares about 10% diaphragm distortion when you can hype cool aluminum baskets, tough ventilation or hyper-stiff titanium bobbins? The best thing is to completely avoid the break-up area with rigid cones and relatively low crossover frequencies, but if you absolutely have to deal with the resonances, you often have to choose between a couple of clear, high-frequency, narrow distortion peaks with relatively low audibility (typical of rigid cones) or a generally higher membrane distortion level, which instead starts further down in frequency and is quite broadband. It is possible to say that lousy aluminum cones are worse than equally lousy plastic or paper cones, but it is a choice between the plague and cholera. Done correctly, you have greater opportunities to optimize for low membrane distortion with rigid materials.

In connection with the above exchange of words, an element was suggested, quote I-or:

"The SB Acoustics SB15NBAC30-4 is a 5" driver and therefore does not quite meet the full range requirements for a two-way solution, but if you use it in a three-way speaker, you will get something that is on par with the distortion champion Magico S5 (around $35,000) in the midrange. The reason for its enormously fine performance is, in addition to a super-linear motor, that an aluminum cone with pressed-in stiffeners has been used and of course the cone has relatively small dimensions. This is probably one of the very best 5-inch drivers on the market and the fact that the price is relatively low does not make things worse."

In-depth quotes I-or​

The Purifi driver is very good but in my opinion not worth the money. The SB drivers (5" and 6.5") discussed above are about as good, except for the lowest frequencies, at a very reasonable cost. It is only if you absolutely have to build a tiny speaker with high performance that Purifi's 6.5" element can be relevant, otherwise it is much smarter to use the money to build three-way speakers (in the same box or with bass modules). Short ribbon elements usually give quite high distortion. However, ribbon-type line sources have the potential to perform exceptionally well here. Ceiling and floor reflections with a conventional speaker are quite different phenomena because the vertical radiation angles differ greatly (horns and line sources can reduce or completely avoid the problems through high directivity). Ceiling reflection in particular can cause some strange phenomena around the crossover frequency via the radiation lobes if you’re not careful. Severe vertical dispersion problems are most effectively avoided through short distances between the elements (relative to the wavelength), small diameters (relative to the wavelength), low crossover frequencies (Maartenovic note: Not too low though with regard to distortion), stepped baffles use (Maartenovic note: Which cause reflections) and possibly waveguides. Vertical reflections primarily have a sonic impact and can be compensated for with balancing reflections from other directions or equalization and can also reduced with some absorption/diffraction (carpet/coffee table). If you want to take the step to the full, you can use a ceiling absorber or a diffusing, large, ceiling. As long as you can maintain a nearly constant frequency response on-axis, controlled dispersion and low distortion, you can choose any crossover frequency. In practice, however, high-frequency crossovers are very difficult to achieve except for coaxial elements because the wavelength is small in relation to the element spacing.

So which speaker drivers should you choose? Since distortion (non-linear) irreversibly distorts and destroys information (unlike frequency response deviations which can be corrected in various ways, – but not both frequency response deviations and dispersion at the same time), and based on inspiration from other threads and I-or's very initiated posts, below are some comparisons between different drivers.

In addition to distortion, there are of course other parameters (such as Thiele/Small parameters and frequency response) to take into account, but these can be managed with various tricks (such as equalization), which cannot be done with distortion. Although distortion is subordinate to frequency response, the distortion in drivers to a greater extent locks the limit of what is possible to achieve in a speaker.

Low-distortion element​

The distortion varies by almost a factor of ten between different elements and since there is no correlation between price and performance when comparing measurement data from Hificompass, there is a lot to be gained from comparing elements and choosing the right one.
The list below is of course not comprehensive, but a selection from available measurements. The prices are from 2021 and have gone up since then but are included to give a price indication.

Low-distortion elements:

Tweeters
SB Acoustics SB26ADC, approx. 600 SEK per piece.
Bliesma T34B-4, approx. 4000 SEK per piece..
Bliesma T25D-6, approx. 2800 SEK per piece.
Morel CAT378, approx. 600 SEK per piece.
Peerless BC25TG15, approx. 200 SEK per piece.

Upper midrange/lower treble, 1000-4000Hz
Bliesma M74A-6 with an Aluminum-Magnesium (AlMg) dome, approx. 5000 SEK per piece.
Bliesma M74B-6 with a Beryllium (Be) dome, approx. 7000 SEK per piece.
Tangband 75-1558SEEv optionally Peerless TC9FD-18 or 10F/4424 / 10F/8424

Midrange, approx. 300-3000 Hz :
Purifi, several variants 4000 SEK per piece.

Probably Visaton AL130M, but no good measurements found.

Midbass: approx. 100-3000Hz
SB Acoustics SB17CAC, 900 kronor each.
Purifi, several variants 4000 kronor each.
Seas Excel 6" W18NX003, approx. 5000 SEK per piece.
SB Acoustics SB17NBAC, 700 SEK per piece.
SB Acoustics SB15NBAC
Probably Visaton AL130, but no good measurements found
300 –1500 Hz: Wavecor WF146WA01.

Bass, approx. 100-400Hz :
SB Acoustics SB23NRXS45-8, 969 SEK per piece.
SB Acoustics SB23NACS45-8, 1048 SEK per piece.
Scan-Speak Discovery 26W/4534G00, 1132 SEK per piece.
SB Acoustics Satori WO24P-8, 2183 SEK per piece.

Subwoofer 20-80Hz:
Scan-Speak Discovery 26W/4534G00, 1132 SEK per piece.
SB Acoustics SB23MFCL45-8, 1269 kronor each.
SEAS L26ROY, 2500 kronor each.
Probably Scan-Speak Discovery 26W/4558T00, 2500 kronor each.
Scan-Speak 28w/4578, about 7000 kronor each.
Scan-Speak 32w/4778, 6500 kronor each.
BMS 18N862



In the distortion diagram below, the higher order partials are weighted higher because these tones are less masked by the music signal and are therefore more audible. For weighting, I have used the following formula where the weighting coefficients are 1, 3, 5 and 7:



= Total harmonic distortion, = second partial or harmonic, = third harmonic, = fourth harmonic and = fifth harmonic.

The correlation to experience or audibility should therefore be higher than in psychometric contexts the relatively high 0.45 that the previously referenced Danish study found for the THD measure (NB, correlation lacks unity and can vary between -1 and 1, where 0 is no correlation, -1 full negative correlation and +1 full positive correlation).

Treble distortion​

View attachment 547226
In the graph above you can see that the SB Acoustics SB26CDC/ADC, which cost about 500 Swedish kronor, are very affordable tweeters. The Peerless BC26TG15 is even more affordable but has slightly worse performance. BlieSMa's models perform very well but are significantly more expensive. The different colors in the table summarize the distortion for a few more tweeters. Note that the selection above includes the lowest-distorting elements. As can be seen, the SB26CDC/ADC is among the very best regardless of price, even in this illustrious company. An old faithful servant like the Scanspeakt 2905-9700 performs significantly worse than the SB26ADC/CDC and BlieSMa's tweeters.

Note that the distortion in the diagram above is chosen with different input levels. This is to compensate for the different voltage sensitivities of the tweeters and thus approximate approximately similar sound pressure levels.

Distortion midrange​

These three elements (including variants) are the best that can be found today in terms of low distortion in the midrange:

View attachment 547225



Below is a comparison of how much worse but commonly used elements in, for example, old Carlsson speakers (SC-165-V) and many other speakers perform. We are talking about a factor of 5–20 times higher distortion than the best in the previous diagram above:

View attachment 547224

Distortion bass​

Below is the distortion for a selection of the lowest distortion woofers. The SB Acoustics Satori Wo24p-4 has the lowest distortion in the 100–500 Hz range, followed by the SB Acoustics SB23NRXS. The BMS 12S305 is a high-quality alternative if you accept a larger cabinet volume, as is the SB Acoustics SB34NRXL.

View attachment 547223



As a home builder or small speaker manufacturer, the standard elements of the element manufacturers are available. Larger manufacturers can produce their own elements or place orders for variants of the element manufacturers' standard range. Based on comparisons of measurements by, for example, Soundstage, the magazine Voicecoil, Audiosciencereview, or Erins Audio corner, the standard elements above exhibit such low distortion that a self-built speaker should be able to compete well with the very best commercial speakers, almost regardless of price.

Dispersion in elements?​

How will the dispersion be with hard and rigid cones?

In-depth quotes I-or​

Quote I-or:​ It is a misunderstanding that unfortunately sometimes appears (that the sound radiation is dominated by the center area near the attachment of the bobbin). When the cone increasingly breaks up for high frequencies, it is far from obvious that the sound radiation is dominated by the area near the attachment of the bobbin. This depends entirely on how the cone and surround are designed. Please study the simulation below that I made for a fairly typical mid-bass element with a plastic cone (I skipped the spider because it plays less role in this context): Higher-order modes in the surround always occur from a few hundred Hz and up depending on dimensions and material. These modes are the main cause of the small frequency response deviations seen between perhaps 200 Hz and 1500 Hz for typical speaker drivers. Similar modes in the spider also affect (you can see a mode in the spider in the animation), but to a lesser extent because they only indirectly affect the sound radiation via the movement of the cone. Without these troublemakers, the frequency response from the driver would be absolutely straight all the way up to just below the first cone mode. The influence becomes less for higher frequencies, and is ultimately overshadowed by bending modes in the cone, but remains throughout the passband. The amplitudes can be large, but the question is always how much sound radiation they lead to (the sum of the contributions from the different oscillating parts of the surround). In general, it is an advantage to have a narrow, light and stiff surround to minimize the influence of these modes, but you also need to have a certain stroke length, which requires a wider and more elastic surround. In addition, you may need to add damping to the cone. Whichever way you turn, you will have drawbacks. However, there are opportunities to improve the situation a lot, which Purifi, among others, has realized. Even though the linear influence (frequency response) may be low, large amplitudes in the surround can cause nonlinearities in the cone's movement that manifest themselves in distortion peaks. As usual, you will always encounter modes, but the fewer of these you need to handle in the passband, the better. Therefore, you should try to move as many of these modes as possible to frequencies above the passband via stiff/lightweight constructions and also break up the rotational symmetry when you can (Purifi has done this in an effective, but somewhat clumsy, way for the surround, which means that different parts around the surround have different resonant frequencies). View attachment 547222 Midwoofer mode shape View attachment 547221 Midwoofer sound pressure View attachment 547220 Midwoofer Frequency Response (0.5 m on-axis) All values and levels apply to a mid-woofer with full potential characteristics. The mode shape in the top image shows displacements that are magnified 1000 times. As can be seen, the inner part of the cone oscillates in antiphase with the outer part that dominates the sound radiation. If we continue with the example element above, it looks like this up to 2650 Hz (i.e. when the cone and surround behave well): View attachment 547219 Midwoofer soundfield And this noisy already at 3150 Hz: View attachment 547218 Midwoofer soundfield 2 As you can see, it all depends on the complexity of the source and there is also a large frequency dependence. In the example above, we have also completely neglected diffraction via the baffle in combination with the magical completely reflection-free acoustic edge, which further complicates the issue. For those who want to model effects like these, it is easy to just create a lot of point sources with source strengths and phase positions that fairly well mimic the condition that you want to describe. Then you sum all contributions in the solution space and obtain the complex-valued sound pressure (or the amplitude and phase of the sound pressure if you like). As for Klippel's NFS (Near Field Scanner), its greatest advantages lie in the low-frequency range, but it also turns out that you often see differences compared to conventional measurements carried out at 1 m quite high up in frequency, since the measurement distance in the conventional case is too short to be in the far field

Baffle simulations​

There are several different tools (Svantes Edge, VituixCad and Bagbys Excel) to choose from and they give very similar results:

View attachment 547217

In the simulations above, you can see how much impact the baffle has on the frequency response, up to about 8–9 dB at most. This is something we will return to.

Calibration, comparison with known objects​

Since I was new to measurements, I started with some comparisons with known and professionally measured objects as a reference, here sb17cac:

View attachment 547216



As can be seen, the agreement between my own measurements and factory measurements of the sb17cac is good, despite different measurement setups. The biggest deviation is below about 200 Hz where I used a much larger baffle than Sb Acoustivs uses in their factory measurements and therefore I did not get the same tap in this range.

Superb overview. Thanks for that.

Since you refer to I-or quite a bit, perhaps you should mention that I-or describes himself as a technical consultant in acoustics and audio engineering.
So, I-or is well-versed in matters such as distortion.

 

[Maartenovic]

Thanks for the tip about Little-Big subwoofers! Looks interestring!
Right now a three-way is under construction, but maybe after that...


Yes, good clarification about I-ors background!

 

[Maartenovic]

Baffle and filter, the biggest influencing factors​

Influence from the baffle?​

Below are selected examples of simulations in VituixCad to illustrate the baffle's effect on frequency response; direct sound and dispersion.

Baffle size?​

How does the baffle affect frequency response and dispersion? Primarily through the baffle step, which is visible as an increase in the level with increasing frequency. Otherwise, minor changes to the baffle dimensions have quite a small impact, according to this picture on the next page:

FEM-simulated baffle of I-or​

Rounding the edges of the baffle significantly softens the strong effects of diffraction in the upper midrange and treble. Given that these effects are relatively large, it is somewhat surprising that the majority of HiFi speakers do not have rounded edges with large radius. The more advanced finite element simulations (FEM) below demonstrate the importance of rounding the edges with large radius of the baffle to reduce large irregularities in the frequency response. The upper image shows the large peaks and valleys in the frequency response from about 700 Hz and up, which an angular baffle provides, is illustrated at angles of 40 and 60 degrees horizontally (note that the order is reversed in the images), and vertically 45 degrees. The lower image shows the frequency response for the same angles but for a rounded baffle. As you can see, they are significantly smoother.

Tests with angular baffles in various shapes and strong edge rounding​

The following images show tests with rectangular and triangular baffles. The results show that they are basically equally bad, as can be seen in the two upper images with rectangular baffles and the lower left one with triangular baffles.

A test with a heavily bent sheet metal resulted in a very large improvement, as the fourth picture on the bottom right shows, also enlarged in the picture below. Now even the placement of the tweeter on the baffle was not critical:

Here is a comparison between a rounded and a beveled edge. The bevel was wide, about 35–40 mm:

Profiling and rounding of baffle​

To straighten the frequency response and reduce disturbances in the tweeter due to diffraction, the baffle needs to have strong edge rounding.

Below pictures showing two profiles illustrated from above. Actually, it has been good to have a 3D scanner, but at the same time it is not super critical with the exact profile, as long as it is properly and harmoniously rounded. In addition, a little asymmetry is often a good thing.

The lower grey baffle is 26 cm wide. The upper purple is 24 cm. The purple is slightly better in width and edge rounding but the grey provides better compensation for the tweeter's hump tendency peak at 5–5.7 kHz, which with this deliberately chosen profile is counteracted by diffraction. Overall, the grey profile is better.

The size of the elements has a major impact on dispersion​

Distance between elements affects

Filters have a big impact


All the images of filter simulations above are simply created. I can recommend playing around a bit with this type of software (here VituixCad) if you are even the slightest bit interested in understanding further how these things are connected.

Crossover frequency?​

For power tolerance reasons, the tweeter does well to be divided as high as possible, which also needs to be weighed against the fact that between register elements the division should be below approximately 1/3 of the frequency where the cone breaks up sharply to reduce distortion.

One aspect is the matching of the tweeter to the dispersion (Directivity Index, DI) for the midrange. The figure below shows that the dispersion in the lower tweeter becomes more even with waveguides than without:


The image below shows that you can actually divide a tweeter with waveguides somewhat higher than a tweeter without waveguides without getting too large discontinuities in the dispersion for midrange and tweeter:

According to the picture above, the crossover should be below about 2 kHz for a tweeter without a waveguide and between 2–4 kHz for a tweeter with a waveguide. The limits are not exact and in practice you can often get a crossover of around 2.2–2.5 kHz between a one-inch dome tweeter without a waveguide and a 5–7 inch element.

 

[Maartenovic]

Vertical distance between drivers​

The interference between physically separated elements and crossovers without infinitely steep filter flanks will always cause interference in the crossover area. This leads to an impact on the directivity index (DI).
My own tests show that the element spacing should be within 1.0–1.4 times the wavelength at the division frequency , preferably around 1.2. This is also the recommendation of Kimmo Sauristo (developer of VituixCad) and also what Kimmen at Faktiskt.io came up with through his own calculations.
Kimmen wrote:​

. ..came to something similar to Kimmo's (developer of VirtuixCad) result: maximum directivity at 0.7 wavelengths and minimum at 1.2 for sources in phase. However, with sources 90 degrees out of phase, DI becomes 0 dB regardless of distance. The latter was very exciting.

Kimmen's calculations of the directional index were based on the following integral with spherical coordinates:​

For a crossover of 2.4 kHz, the center distance between the elements should be between 14 to 20 cm, or ideally 17 cm. For the Räv-L, the distance was 18 cm and the crossover ended up at 2400 Hz. One should also ensure that the ceiling reflection at 45 degrees is reasonably straight in frequency response, which follows from a very simple formula that VER +45 should give a difference of one or more multiples of a wavelength at the division, that is, the center to center distance (c–c) in meters should be: The following image illustrates that normally the ceiling reflex has approximately two wavelengths of path difference between bass and treble, measured at a long distance. (However, crossover filters can affect how it turns out in reality and will likely differ from the overly simple calculations below):​

​

In-depth quotes I-or​

In addition to Kimmen's exemplary review of the properties of the directional index linked above, I would like to add that this differs somewhat from what I consider to be significantly more important, namely the frequency response in specific directions. It is not entirely unexpected that the most even dispersion in the most important vertical directions is achieved if it is possible to squeeze the elements together with a c/c distance of half a wavelength (or even less). For the crossover to the tweeter, however, this is often tricky for geometric reasons and then it becomes more advantageous to increase the distance significantly, even if you then have to compromise somewhat with the properties (standing listeners). It should also be noted that the filter characteristic naturally has a major impact here, as does how the acoustic center of the midrange/bass element is positioned (both in height and depth). In practice, the main radiation lobe should preferably point slightly upwards. The vertical dispersion is fortunately easier to handle than the horizontal one, partly because the ceiling height is more or less constant while the distance of the side walls to the speaker varies quite significantly, and partly because the ears, due to their location on the head, are much more sensitive to the influence of horizontal reflections. Below you will find results for some different filter characteristics and elements with constant frequency response but reasonably realistic dispersion. The first receiver position applies to standing listeners at a distance of 3 meters and the second applies to the ceiling reflection (B stands for Butterworth and LR for Linkwitz-Riley). Crossover frequency 2 kHz, tweeter 10 cm above and 0 cm in front of acoustic center of woofer : In this particular case, third-order Butterworth (B3) is preferable because it avoids the valley around 2 kHz for the first ceiling reflection (the lower right diagram). However, Butterworth characteristics are sensitive to phase deviations around the crossover frequency, so it is important to have control over the acoustic center of the woofer – just a centimeter here or there makes a big difference. Stepping or tilting the baffle or reversing the placement of the tweeter and woofer elements can be a good idea if you want to work with as simple filters as possible (the phase characteristics around the crossover frequency can of course be controlled both via the placement of the sources and electrically).​ Crossover frequency 2.5 kHz, tweeter 20 cm above and 0 cm in front of acoustic center of woofer:​ Fourth-order Linkwitz-Riley (LR4) works well for ceiling reflections but not for standing listeners. LR8, due to its super-steep filter flanks, gives rise to very narrow valleys but is in practice only relevant for active solutions. Note that in reality diffraction effects from the baffle will smooth out the deviations to some extent and especially the valleys are significantly limited. In addition, one must of course normally modify the theoretically ideal filters somewhat since real elements do not exhibit constant frequency response. In this context, it may also be interesting to know that Revel appears to provide the shiny phase in the characteristics of the first ceiling reflection (approximately 45 degrees vertical), despite the results from Toole/Olive's investigations on behalf of Harman.​

How well does the passive filter for Räv-L follow the above recommendations? – Quite well, as the filter functions electrically and acoustically correspond to something between the Butterworth third order (BW3) and the Linkwitz-Riley fourth order (LR4) on the next page:​

Simple visualization of Linkwitz-Riley fourth order (LR4) filter function:

​

Simple visualization of the Butterworth third order (BW3) filter function:​

Simple visualization of filter function for Räv-L passive filter:​

In the next part of the article series I will show that Räv-L provides comparatively very flat frequency response not only in the reference axis but also for ceiling reflex and floor reflex. It is only the frequency response for standing listeners that could be improved with further fine-tuning of filter functions and a slight depth shift of the tweeter.​

Bass response​

In this project, relatively little time has been spent on achieving a bass response adapted to rooms. The reasons for this decision are partly that the bass reflex box for a small 6½-inch element is difficult to tune below 30 Hz and at the same time get a reasonable level from the bass port, and partly that the influence from rooms varies greatly and that you generally need to equalize anyway .
For Räv-L, a port tuning of approximately 31 Hz was chosen in an 18 liter box.​

Slot port​

A rectangular port provides benefits. Quote I-or:​

" If you want the bass reflex port to be turbulence-optimized, you should gradually increase the port height towards the ends of the port (about a 15 degree angle up to at least double the port height works well if you want a simple shape, but you should also smooth out sharp edges). You must of course take this into account when calculating the tuning frequency (it is fine to use the average area in the calculation and reduce the port height in the central part to compensate)."
"At a height of about 7 mm, the thickness of the boundary layers begins to constitute such a large part of the total height that you lose about half a dB in sensitivity, so this can be considered a lower limit. Then you can of course not have an unlimited high flow velocity inside the port either, but this is very high and where the limit is will probably depend mostly on the surface roughness (how smooth the surface is) if the shape is smooth without discontinuities. In practice, the turbulence problems arise at the exit of the air (at both port openings), so you would prefer to reduce the maximum flow velocity in the orifices to about 20 m/s (RMS).
The equivalent gate height He:

He = (2·h1·L1+h2·L2)/Ltot


Where index 1 applies to the end sections (h1 is the average height here) and index 2 applies to the middle section).”

For Räv-L, the equivalent height for the port was:​

He = (2·2·5+1·15)/25=35/25=1,4 cm
​

In-depth quotes I-or​

The figure below shows the amount of flow velocity and the goal is to get as straight velocity contours and as low a flow velocity as possible in the port opening to avoid rotation of the flow, i.e. turbulence. With about 30 m/s in the narrowest part of the port, this is about 11 m/s in the opening. Image: Flow rate in wear port As you can see, it looks good even though the flow velocity becomes quite high around the right opening, up to just under 9 m/s (i.e. 30% of the maximum velocity). In practice, however, the flow velocity is considerably lower here, perhaps 6 m/s (i.e. 20% of the maximum velocity) because we also have openings along the sides that do not exist in this 2D model. Incidentally, the distance to the lower surface was 70 mm for some reason. Also note the very gradual curvature at the beginning of the gate end, which is optimal. The closer to this shape you can get, the better. A design according to the above will therefore work excellently. (The acoustician also realizes that the extra cavity with openings created in this way will have a Helmholtz resonance frequency that is not too far from the first pipe resonance frequency in the port and thus with maximum unluckiness can lead to a certain amplification of the port sounds, but somewhere you have to draw the line for what the 'do-it-yourselfer' should consider. If you keep the openings around 40% of the height as in the picture above, you will not have any problems in this case with a port length of 26 cm and you even have a certain advantage of the configuration compared to a port opening in free air.)

​

Detailed study of the above figure.

​

 

[Maartenovic]

Räv-L: Results and summary​

This last posts is about comparisons with other speakers, measurement procedures, dispersion properties, interferences in rooms. Maartenovic announces that work on a three- way speaker is progressing, it is called “Rävelator ”. Maartenovic is also currently working on developing a waveguide for the tweeter element

There is much to comment on in the following measurements but I will let them mostly speak for themselves. My experience after measuring and testing over a number of weekends and listening over many months, is that the correlation between subjective experience and measurements must be enormously high (I would guess close to +1). But it is important to understand the measurements. Some are obvious, such as raised treble sounds like 'raised treble' etc. Distortion sounds impure, sharp, or sometimes just like a 'haze' or 'fog' that the music is wrapped in. Freedom from distortion provides clarity, transparency and openness. Dispersion can be a little harder to connect to subjective experience (hence the many discussions in various forums) and this is where space comes in. A reasonable assumption in my opinion is that large variation in dispersion in different registers is problematic as early reflexes can affect the sound in a way that is difficult to predict, something that is supported by studies by Toole et al. (see part one of this article series).

The following image is available online and can provide an idea of how deviations from a straight frequency response can be perceived, taken from https://thenextweb.com/news/how-to-understand-speaker-measurements-and-why-they-matter and https://diyaudioheaven.wordpress.com/tutorials/perception/how-to-interpret-graphs/frequency-response/ :

Image: Example of subjective experience of frequency response variations.

Spinorama, dispersion and variation Räv-L​

The measurement procedure is described below. The result is as follows:

Comparison with other good speakers​

The image below compares the frequency response of the Räv-L to other speakers with unusually flat frequency responses. Note that the scale on the y-axis is 20 dB and not the normal 50 dB, which is why all deviations from a flat frequency response are magnified.

Distortion Räv-L​

The distortion at 3 volts is “very good”; approximately 0.07% between 300–10,000 Hz and within the midrange close to “top class” (<0.05%) according to the I-or scale:

“A rough classification can look like this, without taking into account the structure of the harmonic components and the frequency dependence, which will greatly affect the subjective impression.

Hi-fi speakers of a fairly decent size and priced at over 10 thousand SEK per pair, THD at 85 dB, 1 m, free field, f > 200 Hz

Very poor result: > 1%Poor result: 0.5-1% Ordinary result: 0.2-0.5% Good result: 0.1-0.2% Very good result: 0.05-0.1% Top class: < 0.05% ”

From: https://www.faktiskt.io/phpBB3/viewtopic.php?f=10&t=71403&p=2149612&#p2149612



At around 102 dB sound pressure level at 1 meter distance, the distortion is still only 0.4% between 300–10000 Hz. Second tones dominate, which is often considered less disturbing than higher partials, and the distortion is lowest in the registers where hearing is most sensitive. So you could say that it is a hearing-friendly speaker!

Measurement procedure​

The height of the speaker and microphone was just over 3 meters above the ground in the middle of an apple orchard and with a house about 10 meters away. The first reflection occurs about 15 milliseconds after the direct sound, which gives a frequency resolution of about 65 Hz. The stand is 4 centimeters wide and the top plate is cut diagonally (like a "V") to minimize reflections. Tests with moving the speaker a little in front of the top plate do not give any measurement difference.

Measurement software has been REW, ARTA and Sirp, all of which have given identical results. Two microphones have been used, a Line Audio CM3 (Cardioid) which was only used in the beginning before I bought a Line Audio OM1 which is supposed to have an error margin within one decibel. Tests with both microphones give equivalent results between 500–10000 Hz.
Sound card is an EMU-0404 which has been tested via loop coupling and is straight within 20–20000 Hz (can't remember exact numbers). Voltage measurements are made with a Fluke 85 TRMS with a specified inaccuracy of 0.05%. This voltmeter has been regularly professionally calibrated at an old job but that was 20 years ago.
The REW measurements have not been calibrated for level but I chose to go for voltage measurement via Fluke, which is considerably more accurate.

The measurements have been compared against factory measurements of elements and in one case against speakers measured by NRC (Soundstage) but also against measurements by others with the MiniDSP UMIK-1 microphone of their Räv-L builds. All of these are well within ±2 dB, often closer to ±1 dB, despite different measurement setups.

Settings REW (standard REW): * Measurement data measured by REW V5.20.9* Source: ASIO E-MU Audio, Analog IN A
* Format: 256k Log Swept Sine, 1 sweep at -10.0 dBFS using a loopback as a timing reference
* Dated: 2022-Aug-19 19:44:58* REW Settings:* C-weighting compensation: Off* Target level: 75 .0 dB
* Note: ; Delay 3.3647 ms (1.154 m, 3 ft 9.4 in) relative to Loopback from 2: Analog OUT to 2: Analog IN B with no timing offset* Measurement: Fox-L-two, 4.7ohm hor 0* Smoothing: None* Frequency Step: 1/24 octave* Start Frequency: 100,000 Hz

The angles for dispersion measurement are not exact, I estimate that they are within about 5 degrees but tests show that deviations in angles for measuring dispersion have little impact. However, I have been careful with the reference axis and sometimes also tested adjusting a little up and down to ensure that any deviations do not affect the result.
The reliability is good compared to professional measurements by NRC/Soundstage.​

When measuring distortion, it is desirable to have a background level below the level of distortion you want to measure, and to be able to measure relatively reflex-free in the reference axis. When measuring at a distance of 30 cm and a sound pressure level of 95 dB (which means 85 dB at 1 meter) and a background level of 35 dB, you can safely measure down to 0.01% distortion. REW keeps track of the background level and reports this separately in the distortion tab. However, it seems that REW can extrapolate the distortion well below the background level with a fairly good degree of certainty. For the above reasons, a higher input signal gives safer results (as long as over- control is avoided). Stepped sine is more accurate than log-sweep.

The latest measurements in mid-August 2022 have been reviewed by I-or, who I consider to be the given expert on measurements at Faktiskt.io where the measurements were first published. The results can be considered more than acceptable.

Listening impressions:​

The goals are achieved with Räv-L, the working hypotheses are answered. Subjectively, they also sound better in many ways than anything I've owned before, although "Circle of Confusion" always makes it worse in comparison, as does absolute level and psychology.

The Räv-L play with an openness, clarity and nuance that I am not used to. Nothing that bothers me, no register that stands out (apart from a slight emphasis in 5–6 kHz and a slightly weak level 150–300 Hz). As a bonus, the speakers create a three-dimensional sound image that made me wonder if any surround mode in the receiver was turned on, but no, “direct mode” was turned on as it usually is. The fact that the stereo effect is more tangible is fun, at the same time that moving the head affects the stereo effect more, which feels unusual and a bit tricky, as if everything has become more razor-sharp.

The shortcomings of the Foxes are partly sound pressure capacity, partly the response in bass and mid-bass and some deviations in dispersion: A 6-inch element can only handle a fraction of what a powerful 10-incher can handle. The level is about 1–2 decibels too weak between 150-400 Hz and the energy curve has about 1 decibel increase at 6–7 kHz. Equalization addresses these minor shortcomings. Finally, they have low sensitivity, I would guess at about 84–85 dB.

In-depth quotes I-or​

“I always appreciate measurement results because these, unlike listening impressions, are reliable provided that the measurements are well performed. I hope everyone understands that these are extremely ambitious measurements. Just look at the measurement setup several meters above the ground, also including the possibility of "spinorama"! In addition to this, the measurement results include information about production dispersion, which is far too rarely presented. Measurement nerds should not miss more detailed raw data, which is linked to above, but easily gets lost in the large amount of text: https://user.faktiskt.io/Maarten/Diverse_m % e4tningar/ . All audiophiles who have achieved constant frequency response, good dispersion and low distortion will soon realize that it was obvious how the music was intended to sound. Nothing in the reproduction is jarring – no sonorous accents, no "sameness", no soundscape tied to the speakers, no obvious impurities or graininess. All recordings, good or bad, of course still sound different but still significantly better than with typical speakers. The that has not ensured that the frequency response, dispersion and distortion are of a high class has not come close to what a high-performance stereo system can achieve. If you take the shortcut of releasing the frequency response, by equalizing and thereby focusing only on dispersion and distortion, even as a happy 'do-it-yourselfer' with relatively little prior knowledge and minimal work, you can build speakers that match the market's most high-performance models regardless of price. Maartenovic has, however, gone the long, hard, passive route, but has still succeeded well with results that in many respects match the best on the market"

Normalized polar diagrams, comparison with Revel et al.​

If you compare with the Revel 226be (which has received very good reviews and measures really well) and now instead normalize against frequency response, it looks like the diagram below. The result is surprisingly similar to the Räv-L!
Below is also a comparison with the Wharfedale Linton, which has received quite good reviews. As you can see, the Linton has a clearly worse polar diagram with significantly larger irregularities.

Lobing?​

Lobing is a concept that refers to the fact that the sound radiation becomes more directional in the crossover area due to the sound radiation of the elements overlapping each other and thereby interfering. This results in a greatly varying vertical dispersion. See part 1 of this article series.

To get control over the lobing and vertical dispersion, the phase response from the filter is interesting and this is what it looks like for the crossover in Räven (export from VituixCAD including the impedance of the elements). As can be seen, the bass (SB17) is between 50–70 degrees 'before' the tweeter between 300–20000 Hz (the green curve ):

This compensates by a margin for the time shift that the elements themselves contribute (and which here is about an angle of about 3–5 degrees down for the radiation lobe in the crossover area). Based on these diagrams, it can be assumed that the Räv-L's lobe in the crossover points 3–5 degrees upwards. I would like to remind you that this is not the case, but rather it points straight ahead, that is, 0 degrees measured between bass and treble. (The difference in simulated and actual phase response may be due to uncertainties in impedance measurements, etc.).
I-or's advice to let the lobe point a little upwards seems sensible considering that it is then easier to get a fairly straight frequency response both in ceiling reflex ( vertically +40 to +50 degrees upwards) and floor reflex (vertically -30 degrees downwards) and also for standing listeners (vertically +10 to +15 degrees). The Räven managed to achieve the first two but not with the last, see diagram:

This is how Räv-L measures 0, 10, 20, 30, 40, and 50 degrees horizontally off axis:

This is how Räv-L measures based on the early reflections that Spinorama groups:

The 5–8 kHz range compared to 2 kHz could possibly be made a little more balanced with a slightly lower crossover frequency, but I didn't find it worth the effort as there are still small differences. The results are basically world class and better than, for example, the Revel M106 for 26,000 SEK.
The weakness at 100–500 Hz is due to the sb17cac and I didn't want to reduce the sensitivity even more or make the filter significantly more expensive. (In 2022, the components for crossovers cost 1800 SEK and the elements around 3000 SEK). In addition, I-or commented that the area still has to be equalized for all speakers when they are placed in a listening room.
Another aspect is that it is difficult to optimize multiple directions (I would say that with conventional construction it is not possible to fully do this, but requires waveguides for both midrange and treble, as well as an optimized baffle).

I also think that it is probably more important to look at the Spinorama graphs (as seen above) than individual directions (apart from the direct sound). I have experienced that the risk of getting stuck in sub- and error-optimization loops is high otherwise. For example, optimizing these curves is more important than, for example, 30–40 degrees off-axis:

For example, a Linkwitz-Riley fourth-order filter (LR4) provides, compared to less steep filters, minimal overlap between the elements, minimal lobing, and a phase response that is followed between the elements. With appropriate values, the delay needed for the desired vertical radiation is achieved.

 

[DanielT]

Vertical distance between drivers​

The interference between physically separated elements and crossovers without infinitely steep filter flanks will always cause interference in the crossover area. This leads to an impact on the directivity index (DI).
My own tests show that the element spacing should be within 1.0–1.4 times the wavelength at the division frequency , preferably around 1.2. This is also the recommendation of Kimmo Sauristo (developer of VituixCad) and also what Kimmen at Faktiskt.io came up with through his own calculations.
Kimmen wrote:​

. ..came to something similar to Kimmo's (developer of VirtuixCad) result: maximum directivity at 0.7 wavelengths and minimum at 1.2 for sources in phase. However, with sources 90 degrees out of phase, DI becomes 0 dB regardless of distance. The latter was very exciting.

Kimmen's calculations of the directional index were based on the following integral with spherical coordinates:​

View attachment 547248

For a crossover of 2.4 kHz, the center distance between the elements should be between 14 to 20 cm, or ideally 17 cm. For the Räv-L, the distance was 18 cm and the crossover ended up at 2400 Hz. One should also ensure that the ceiling reflection at 45 degrees is reasonably straight in frequency response, which follows from a very simple formula that VER +45 should give a difference of one or more multiples of a wavelength at the division, that is, the center to center distance (c–c) in meters should be: The following image illustrates that normally the ceiling reflex has approximately two wavelengths of path difference between bass and treble, measured at a long distance. (However, crossover filters can affect how it turns out in reality and will likely differ from the overly simple calculations below):​

​ View attachment 547249

In-depth quotes I-or​

In addition to Kimmen's exemplary review of the properties of the directional index linked above, I would like to add that this differs somewhat from what I consider to be significantly more important, namely the frequency response in specific directions. It is not entirely unexpected that the most even dispersion in the most important vertical directions is achieved if it is possible to squeeze the elements together with a c/c distance of half a wavelength (or even less). For the crossover to the tweeter, however, this is often tricky for geometric reasons and then it becomes more advantageous to increase the distance significantly, even if you then have to compromise somewhat with the properties (standing listeners). It should also be noted that the filter characteristic naturally has a major impact here, as does how the acoustic center of the midrange/bass element is positioned (both in height and depth). In practice, the main radiation lobe should preferably point slightly upwards. The vertical dispersion is fortunately easier to handle than the horizontal one, partly because the ceiling height is more or less constant while the distance of the side walls to the speaker varies quite significantly, and partly because the ears, due to their location on the head, are much more sensitive to the influence of horizontal reflections. Below you will find results for some different filter characteristics and elements with constant frequency response but reasonably realistic dispersion. The first receiver position applies to standing listeners at a distance of 3 meters and the second applies to the ceiling reflection (B stands for Butterworth and LR for Linkwitz-Riley). Crossover frequency 2 kHz, tweeter 10 cm above and 0 cm in front of acoustic center of woofer : View attachment 547250 In this particular case, third-order Butterworth (B3) is preferable because it avoids the valley around 2 kHz for the first ceiling reflection (the lower right diagram). However, Butterworth characteristics are sensitive to phase deviations around the crossover frequency, so it is important to have control over the acoustic center of the woofer – just a centimeter here or there makes a big difference. Stepping or tilting the baffle or reversing the placement of the tweeter and woofer elements can be a good idea if you want to work with as simple filters as possible (the phase characteristics around the crossover frequency can of course be controlled both via the placement of the sources and electrically). Crossover frequency 2.5 kHz, tweeter 20 cm above and 0 cm in front of acoustic center of woofer:​ View attachment 547251 Fourth-order Linkwitz-Riley (LR4) works well for ceiling reflections but not for standing listeners. LR8, due to its super-steep filter flanks, gives rise to very narrow valleys but is in practice only relevant for active solutions. Note that in reality diffraction effects from the baffle will smooth out the deviations to some extent and especially the valleys are significantly limited. In addition, one must of course normally modify the theoretically ideal filters somewhat since real elements do not exhibit constant frequency response. In this context, it may also be interesting to know that Revel appears to provide the shiny phase in the characteristics of the first ceiling reflection (approximately 45 degrees vertical), despite the results from Toole/Olive's investigations on behalf of Harman.​

How well does the passive filter for Räv-L follow the above recommendations? – Quite well, as the filter functions electrically and acoustically correspond to something between the Butterworth third order (BW3) and the Linkwitz-Riley fourth order (LR4) on the next page:​

Simple visualization of Linkwitz-Riley fourth order (LR4) filter function:

View attachment 547252​

Simple visualization of the Butterworth third order (BW3) filter function:​

View attachment 547253

Simple visualization of filter function for Räv-L passive filter:​

View attachment 547254

In the next part of the article series I will show that Räv-L provides comparatively very flat frequency response not only in the reference axis but also for ceiling reflex and floor reflex. It is only the frequency response for standing listeners that could be improved with further fine-tuning of filter functions and a slight depth shift of the tweeter.​

Bass response​

In this project, relatively little time has been spent on achieving a bass response adapted to rooms. The reasons for this decision are partly that the bass reflex box for a small 6½-inch element is difficult to tune below 30 Hz and at the same time get a reasonable level from the bass port, and partly that the influence from rooms varies greatly and that you generally need to equalize anyway .
For Räv-L, a port tuning of approximately 31 Hz was chosen in an 18 liter box.​

Slot port​

A rectangular port provides benefits. Quote I-or:​

" If you want the bass reflex port to be turbulence-optimized, you should gradually increase the port height towards the ends of the port (about a 15 degree angle up to at least double the port height works well if you want a simple shape, but you should also smooth out sharp edges). You must of course take this into account when calculating the tuning frequency (it is fine to use the average area in the calculation and reduce the port height in the central part to compensate)."
"At a height of about 7 mm, the thickness of the boundary layers begins to constitute such a large part of the total height that you lose about half a dB in sensitivity, so this can be considered a lower limit. Then you can of course not have an unlimited high flow velocity inside the port either, but this is very high and where the limit is will probably depend mostly on the surface roughness (how smooth the surface is) if the shape is smooth without discontinuities. In practice, the turbulence problems arise at the exit of the air (at both port openings), so you would prefer to reduce the maximum flow velocity in the orifices to about 20 m/s (RMS).
The equivalent gate height He:

He = (2·h1·L1+h2·L2)/Ltot


Where index 1 applies to the end sections (h1 is the average height here) and index 2 applies to the middle section).”

For Räv-L, the equivalent height for the port was:

He = (2·2·5+1·15)/25=35/25=1,4 cm
​

In-depth quotes I-or​

The figure below shows the amount of flow velocity and the goal is to get as straight velocity contours and as low a flow velocity as possible in the port opening to avoid rotation of the flow, i.e. turbulence. With about 30 m/s in the narrowest part of the port, this is about 11 m/s in the opening. View attachment 547255 Image: Flow rate in wear port As you can see, it looks good even though the flow velocity becomes quite high around the right opening, up to just under 9 m/s (i.e. 30% of the maximum velocity). In practice, however, the flow velocity is considerably lower here, perhaps 6 m/s (i.e. 20% of the maximum velocity) because we also have openings along the sides that do not exist in this 2D model. Incidentally, the distance to the lower surface was 70 mm for some reason. Also note the very gradual curvature at the beginning of the gate end, which is optimal. The closer to this shape you can get, the better. A design according to the above will therefore work excellently. (The acoustician also realizes that the extra cavity with openings created in this way will have a Helmholtz resonance frequency that is not too far from the first pipe resonance frequency in the port and thus with maximum unluckiness can lead to a certain amplification of the port sounds, but somewhere you have to draw the line for what the 'do-it-yourselfer' should consider. If you keep the openings around 40% of the height as in the picture above, you will not have any problems in this case with a port length of 26 cm and you even have a certain advantage of the configuration compared to a port opening in free air.)

​

View attachment 547256​

Detailed study of the above figure.

​

You’ve put in a hell of a lot of work. Very impressive. I think many DIYers could benefit from what you (and I-or) addressed regarding "slot ports". It is quite common to see in the measurements Amir performs on ported speakers that commercial manufacturers still haven't optimized port designs to address these issues. A DIYer, however, can do just that.

Since you are addressing Kimmo Sauristo (developer of VituixCAD) regarding center-to-center (c-c) spacing, here is a thread where he discusses that, #2:

Minimum c-c is 1.0 x wave length and maximum about 1.4 x wave length at XO frequency assuming that design is conventional uni-directional box (not open baffle) with phase matching (acoustical 4th order) slopes. Good and quite flexible initial/design value for c-c is 1.2 x wave length at XO, giving smooth combination of power and early reflections i.e. balanced sound without significant power dip at XO due to bump in DI and dip in vertical early reflections. In other words, this concept aims lobe nulls to directions which are the least significant for power response and vertical early reflections - and listener sitting in sweet spot of course.

Some help with lobing

I think I understand the concept but can't figure out the solution. "Lobing occurs with any two drivers producing the same frequency range in parallel (identical signal) where the distance between the drivers is greater than 1/4 wavelength of any frequency they are reproducing." So if I am...

www.audiosciencereview.com

 

[Jonazkur]

SB26ADC/CDC are really a price to performance king tweeters. I use one with Purifi PTT8 and love it