Electronics Design in a Passive Speaker System

Teemu Jortikka Electronics Design in a Passive Speaker System

Metropolia University of Applied Sciences Bachelor of Engineering Electronics Bachelor’s Thesis 15 May 2021

Abstract

Author Teemu Jortikka Title Electronics Design in a Passive Speaker System

Number of Pages 57 pages Date 15 May 2021

Degree Bachelor of Engineering

Degree Programme Electrical and Automation Engineering

Professional Major Electronics

Instructors Hannes Nieminen, Project Manager Heikki Valmu, Senior Lecturer

The goal of this thesis project was to start the research and development of the electronics of a passive loudspeaker system. The project being started from scratch, many of the topics included in speaker design are not limited to electronics engineering. The project was not ordered by any company but is rather a passion project of two audio engineers.

The project started with the research of the proper speaker drivers. Once the drivers were chosen, the enclosure was next in line for the design. Once the drivers and enclosure were brought to physical reality, the frequency responses from different combinations of elements were measured. From these measurements, with the help of a little DSP, the requirements for the passive circuitry of the speaker were discovered.

The circuit was to consist of a simple crossover circuit and a delay. The crossover is simple due to it just being a high pass filter and a low pass filter, but the delay is a much more tricky subject. The delay was chosen to be implemented using an all-pass filter topology. All the circuitry was simulated, but due to the limitations of the software and the nature of sound design in general, most decisions and opinions had to be made by ear.

After the circuit was simulated, numerous PCB:s were designed. These consisted of two versions of the crossover circuit, and one PCB containing one order of the all-pass filter. These orders were to be stacked in order to find the optimal amount of delay.

The end results of this project are a little inconclusive. The delay was found to be too costly and large for the benefit it brought to the sound of the speaker. The crossover worked well, and further development of the speaker continues outside the limits of this thesis project.

Keywords Loudspeaker, passive circuitry, audio, PA speakers

Tiivistelmä

Tekijä Teemu Jortikka Otsikko Electronics design in a passive speaker system

Sivumäärä 57 sivua Päivämäärä 15 Toukokuu 2021

Tutkinto Insinööri (AMK)

Tutkinto-ohjelma Sähkö- ja Automaatiotekniikka

Ammatillinen päänimike Elektroniikka

Ohjaajat Hannes Nieminen, projektipäällikkö Heikki Valmu, yliopettaja

Tämän insinöörityön tarkoitus ja päämäärä oli aloittaa kaiuttimen tutkimus- ja kehitystyö. Koska kyseessä on tyhjästä aloitettu projekti, monet käsitellyt aiheet eivät rajoitu pelkästään elektroniikkasuunnitteluun. Insinöörityötä ei ole tilattu minkään firman toimesta, vaan on enemmänkin luonteeltaan kahden äänisuunnittelijan mieltymyksiin perustuva projekti.

Projekti alkoi tarkoitukseen sopivien kaiutinelementtien tutkimuksella. Kun elementit olivat valittu, oli seuraavana vuorossa kotelosuunnittelu. Kun elementit ja kotelo olivat tuotu fyysi- seen todellisuuteen, erilaisten elementti- ja koteloyhdistelmien taajuusvasteet mitattiin. Näi- den mittaustilausten pohjalta,pienen DSP:n avustuksella, passiivipiirien vaatimukset saatiin selville.

Piiri koostuu yksinkertaisesta jakosuodattimesta ja viiveestä. Jakosuodin on yksinkertainen, sillä se on vain yksi ylipäästö- ja yksi alipäästösuodin. Viive on paljon mutkikkaampi asia suunnitella. Viiveen toteutustavaksi valittiin kaikkipäästösuodin. Kaikki piirit simuloitiin, mutta simulointiohjelman ja äänisuunnittelun luonteen vuoksi suurin osa päätöksistä piti tehdä korvakuuloon perustuen.

Sen jälkeen kun piiri simuloitiin, lukuisia piirilevyjä suunniteltiin. Nämä koostuivat kahdesta eri versiosta jakosuotimesta ja yhdestä piirilevystä ensimmäisen asteen kaikkipäästösuoti- melle. Asteita on tarkoitus kasata, ja lopullinen ratkaisu asteiden määrästä tullaan tekemään korvakuuloon perustuen.

Projektin lopputulema oli vähän tulokseton. Viive todettiin liian kalliiksi ja suurikokoiseksi suhteessa sen tuomaan sointihyötyyn. Jakosuodin toimi hyvin, ja projektin kehitystä tullaan jatkamaan tämän insinöörityön ulkopuolella.

Avainsanat Kaiutinsuunnittelu, kaiuttimet, PA, passiivielektroniikka

Contents

List of Abbreviations

1 Introduction 1

2 Loudspeaker Operation 2

2.1 The driver 3 2.2 The enclosure 5

3 PA Systems In General 7

3.1 Point source vs line array 7 3.2 Active speaker design 9 3.3 Passive speaker design 11

4 n-Array Design 13

4.1 Small size and the drivers of choice 13 4.2 Enclosure design 17 4.3 Passive electronics 20 4.4 One channel per unit 21

5 Acoustic Measurements 22

5.1 Mark 1 SMAART measurements 23 5.1.1 PTMini-6 measurement 24 5.1.2 PT816-8 measurements 25 5.2 Mark 2 SMAART measurements 29 5.3 Crossover, delay and EQ requirements 31

6 Electronics Design 32

6.1 Parallel or series connection 32 6.2 Crossover design 34 6.2.1 The Butterworth filters 35 6.2.2 Component choices 37 6.3 Delay design 38 6.3.1 All-pass filter design 39 6.4 Circuit simulation 40

7 PCB Design 44

7.1 Logic 45 7.2 Layout 47

8 Assembly & Measurements 50

8.1 Crossover 51 8.2 Delay 52

9 Conclusions 54

References 56

List of Abbreviations

AC Alternating current.

AV Audiovisual. A blanket term compassing all media consisting of visual and audio components. dBFS Decibel Full Scale. A digital audio measurement scale, from -¥ to 0. Any- thing above 0 leads to digital distortion of the signal.

DSP Digital signal processing.

EQ Equalization. A term used in audio production referring to applying different filters to affect the spectrum of a signal.

PA Public address system.

SMD Surface mount devices.

SPL Sound pressure level.

1 Introduction

Ever since the first loudspeaker was installed in a telephone by a scientist by the name of Johann Philipp Reis in 1861 [1], engineers have been coming up with different implementations and installation locations for them. In our modern era the most familiar applications for loudspeakers include (but are not limited to) the speakers on smartphones, televisions, reference monitors and the big sound systems at live music venues. While speakers are a very familiar sight for most, not many are aware that they do not come “one size fits all”. For example, a terrific speaker for replicating the sound of one’s favorite song with authenticity and excitement may be a horrendous choice for replicating the sound of minimally processed human speech.

The idea for this bachelor’s thesis came from years of combined experience in the field of audio engineering. Multiple live shows, conferences, studio sessions and lately streamed webinars combined with the experience of an AV integrator gave rise to a need for a specifically tailored speaker for a specific purpose.

Many venues where speakers are installed are increasingly conscious of their visual appearance. With the rise of globalism and the internet the world has become an increasingly smaller place, and people are generally more aware of different kinds of products and implementations on the market. This has led to the gradual decline of the traditional speaker, a wooden box suspended from a ceiling or mounted on a wall and given rise to a need for innovation. One famous Finnish company manufactures very aesthetically pleasing speakers, which sound phenomenal. However, the average customer is not aware, that these said speakers are designed to be reference studio monitors with an optimal listening distance measured in meters (depending on the model). This may not be a huge issue when finished music products (mastered to be close to 0dBFS, which means a very compressed and loud signal), but when these speakers are assigned the task of reproducing the waveform of human speech things become more difficult. There simply is not enough strength in the dispersion of the high frequencies at longer dis- tances than for example three meters. Add to this problem the tendency of amateur speakers to talk too quietly to the microphone and the habit of holding the microphone at a bad place (too far from the sound source, this time being the mouth of the speaker) and the sound technician has a big problem on his hands.

All this had led us to the desire to design and produce a speaker, which is pleasant to look at, very small and thus easy to conceal, powerful at reproducing sound in the speech spectrum and easy to install. The project name for this speaker is n-Array.

2 Loudspeaker Operation

It is beneficial to know the basics of the operation of loudspeakers before diving any deeper into the design of the n-Array. Loudspeakers can be classified into many different categories depending either on the frequency bandwidth of operation, the speakers tar- geted application, the speaker’s operational functionalities or the design of the frequency dispersion inside the speaker.

Generally, one is familiar with the classification of active-and passive speakers, the for- mer being powered by its own power source and the latter requiring a separate amplifier in order to function. Both methods of powering a speaker are used widely on both professional and consumer applications. Things become a bit more complicated when the frequency dispersion is added to the mix, resulting in the categorization of one-way, two- way and three-way speakers. One-way speakers are speakers which have only one speaker element responsible for the whole sound output of the speaker. Usually this type of speakers are specialized on the low end of the sound spectrum and are called subwoofers. Two-way speakers are speakers with internal filters (known as crossover filters) which divide the audio signal from the input into two different speaker elements, one being responsible for the lower end of the sound spectrum and the other for the higher end. These speaker elements are called the woofer and the tweeter. A three-way speaker is logically very similar to the two-way speaker with an added woofer responsible for the mid-range sound reproduction. In figure 1 we can see a good example of a typical high-end active two-way speaker.

Figure 1. Genelec 8040B active two-way speaker. [2]

These are the rough categories which can be used to classify types of speakers. A further categorization method is to categorize by designed application. These can be for example loudspeakers designed to be mounted in cars, in different materials (ceilings for example) and speakers which only work properly when placed in an array of the designer’s other products.

2.1 The driver

A loudspeaker driver can be used synonymously with a loudspeaker, but usually when talking about a driver one means a speaker element responsible for reproducing a specific frequency band of the input signal. As stated before, these drivers are called subwoofers, woofers, midranges, tweeters and super-tweeters. The larger the surface area of the loudspeaker cone, the better it is at producing sound at long wavelengths (which is synonymous with lower frequencies). This is the reason why subwoofers usually come in bigger and bulkier enclosures than other types of speakers; a large driver is required for the efficient production of low signals. When building a speaker, it is the designers job to make sure that the sound is divided optimally for all the different drivers. The manufacturers give in the datasheets limits for the lowest sound their driver can produce. It is very easy to break a driver if one is not careful.

A loudspeaker driver consists of three working parts: the cone (with its suspension), the magnet and the voice coil [3,17-18]. In figure 2 we see a cross-section of a loudspeaker driver. Note that in this figure the cone is called the diaphragm.

Figure 2. A cross-section of a loudspeaker driver [4].

The operation of a loudspeaker driver is quite simple and mechanical in nature. If one is to move a magnet inside a coil of copper wire, a current will be induced in said wire. This phenomenon is described by the physicist Michael Faraday in his law of induction [5]. When electricity flows through a wire (or a copper coil in our case), it creates a magnetic field with field lines which circle the wire.

Figure 3. The operation of an electric magnet [6].

In the case of loudspeaker drivers, two wires from an audio amplifier are connected to the voice coil. The amplifier feeds an alternating current (AC) signal into the voice coil. In figure 3 the resulting magnetic field is shown, with the battery being the amplifier gen- erating the AC signal. The voice coil in the driver is placed in the gap in the middle of the permanent magnet. When the AC signal from the amplifier is applied in the voice coil, the resulting electromagnetic force causes the voice coil to move [7,3-4]. AC signals are sinusoidal in nature, which means that the signal has both positive and negative

5 components, and therefore the ever-changing phase causes the reaction with the permanent magnet with fixed magnetic poles. Now the signal is converted to a magnetic field, but still no sound is audible, so therefore something else is needed. The conversion to changes in air pressure (which our ears and brain perceive as sound) is achieved by attaching the other end of the voice coil to a speaker cone. By doing this the AC signal, which is fed to the voice coil, which then causes the changes in the magnetic field of the voice coil, which then interacts with the permanent magnets around the voice coil causing the movement of the coil is finally converted into sound waves by the attached speaker cone. The cone must be suspended (the spider in figure 2) to prevent movement in other than the desired direction.

2.2 The enclosure

It is extremely rare to see loudspeakers in public with just their drivers suspended in free space. The reason for this is obvious; loudspeaker design triumphs or fades into obscu- rity based on the merits of its enclosure design. One can have a spectacular high end 3- way system, with the best DSP available and the most expensive drivers money can buy, but if the enclosure that they are placed in is sub-par, there is little joy to be had from the other top shelf components. The enclosure resonates, and therefore is an integral part of the sound of the speaker. This bachelor’s thesis does not focus on the enclosure and Its design, but it is vital to understand the basic principles behind the design process.

In general use there are four types of enclosure designs: closed boxes, ported boxes, labyrinths and horns [3,47]. Most of the speakers one generally encounters are of the first two categories. The designer is attempting to manipulate the frequency and phase response of the speaker by tweaking with the box design. For example, if one is planning on an amazing low-end response for a speaker, low frequencies move a lot more air than higher ones, and therefore a larger box volume is required. Directivity is also a trait, which can be manipulated with clever enclosure design. The basic physics which govern the behavior of soundwaves dictate, that the lower the frequency the less directivity there is. Therefore there are usually problems with speakers resonating too much low end from the back of the speaker. In order to tackle this problem, one can use end-fire design (the addition of another driver element inside the box in the rear) [8], which can be used to cause a phase difference between the two elements, or the designer can use port designs of varying complexity.

Figure 4. An example of a labyrinth port design [3,60].

In figure 4 there is an example of a labyrinth port design. The nearly omni-directional soundwaves are trapped in the labyrinth, being bounced around inside the box and con- stantly absorbed by the damping material, and what makes it to the end of the labyrinth has been carefully designed and calculated to be l , a quarter wavelength, effectively damping the speaker’s resonance frequency.

As is the case with most things regarding audio, most of the problems arise when dealing with the lower frequencies. High frequencies are by nature easier to handle due to their natural directivity, but it is the low end which causes most of the issues. Therefore it is only natural, that there have been parameters developed in order to tackle the issues in the design of the low end resonance of a speaker. These are the so-called Thiele/Small parameters, based on the work of both Neville Thiele and Richard H. Small. The widely accepted Thiele/Small parameters are [9,193-195]:

• � , the resonance frequency of the driver in free air.

• � , compliance of the acoustic suspension.

• �, driver electrical ratio of resistance to reactance.

• �, driver mechanical ratio of resistance to reactance.

• �, total driver ratio resistance to reactance.

These and more parameters are given in the datasheets of the drivers. These are however very useful tools in the design of the enclosure. The parameters cover different variables in acoustic, mechanical and electrical domains, which essentially the domains in which speakers operate.

3 PA Systems In General

The intended application for the final product of the development started with this thesis project, is a line-array PA system. A PA system, or a public address system, is a blanket term for every part of a system used to reproduce and amplify a human voice. This in- cludes the speakers, the amplifiers, the microphones used and the other signal processing equipment. It is however commonplace among professionals, that when one is talking about the PA system, the subject matter is the speakers and the associated amplifiers. PA systems are larger in size than the average stereo speaker sets, some PA systems even being the size of small buildings. They come in many shapes and forms, but there are some dividing lines with which one can dive deeper into the subject.

3.1 Point source vs line array

A point source PA system is almost self-explanatory; all the frequencies of the signal originate from a single point of origin. Most of the PA systems a typical person encounters are like this. In order to expand the field of the soundscape, multiple speakers can be placed at different locations. A very small PA system could be entirely sufficient as just one single loudspeaker mounted at the end of a pole. The signal would be mono, but if that is not an issue then all is well.

Figure 5. An example of the speakers of a point source PA system [10].

Technically there are no point source loudspeakers which really originate the sound from a single point of origin, because most speakers consist of multiple speaker drivers, which interact with each other forming the sound of the loudspeaker. It is beneficial to think of the speaker as a whole as the point of origin for the sound. The PA set in figure 5 is also point source, even with the addition of the subwoofer.

Point source is one method of implementing a PA system, and for many cases it is sufficient and maybe even optimal. There are, however cases, where such a method of distributing sound is either very inconvenient or insufficient. This is where the line array steps in.

Figure 6. A large suspended line array PA system [11].

In figure 6 we see a sight that is most likely familiar to many, an example of a large scale line array system. These kinds of systems can often be found in large music festivals, concert halls, stadiums and other large scale venues. A properly calculated, rigged and configured line array system can outperform almost any point source system in terms of reach and power.

Figure 7. The operation of a line array [12].

In figure 7 the basic idea of a line array is visualized. The goal is to achieve an equal field for every member of the audience in terms of sound intensity, phase and colorization. This is achieved by placing specifically designed speakers from a same manufacturer in an array, where each speaker is responsible for a certain area of the audience.

The speakers are designed in a way, that their overlapping sections interact with each other in a positive way, causing minimal negative phase or sound differences. The manufacturers of line array systems usually provide their own gear for rigging their systems (with fixed relational angles between the speakers) and their own amplifiers with specific digital signal processing (or DSP) for each array combination. Line array systems usually consist of different kinds of loudspeakers for different purposes. It is not uncommon to combine multiple different speakers in one array, for example 12 units of speakers specialized in midrange and high frequency playback, 2 units of subwoofers specialized in low mids and bass and 2 units of subwoofers specialized in the playback of “infrasound”, which means the lowest end of the spectrum of audible sound.

3.2 Active speaker design

As has been stated before, there are two methods of creating a loudspeaker in terms of power: an active speaker design and a passive design. An active speaker requires a

10 separate power source and is therefore not powered by the audio signal input.

Figure 8. A schematic for an active speaker [13].

In figure 8 we see on the right side of the schematic the power source. The circuit is connected to the AC mains via a switch, a transformer and a bridge rectifier circuit. It is not clear from this schematic to which voltage level the AC mains (230V in Finland) is converted, but it is most likely a voltage level that is optimal for the operational amplifiers used in the design. The bridge rectifier uses the four diodes to convert the AC into +DC and -DC, which is a requirement for operational amplifiers to function. If the operational amplifiers were to be powered using only a positive DC voltage, the amplifier would not be able to perform with AC signals.

There are many advantages to doing speaker design the active way. There is no need for an external expensive amplifier because of the integrated power source. This makes active speakers easy to install anywhere where there is an AC outlet. An active speaker can also boast a variety of different kinds of input connectors, due to the signal not also being the source of power. With good active circuit design the need for outside processing is reduced or eliminated completely. This is due to the very low signal levels being fed to the input, professional audio line level signals being between +4dBu and

+10dBu, which in terms of voltage is between 1.228� and 2.449� . This makes it possible to use very small components (even the SMD ones) due to the power ratings required for the components being very low. This in turn removes limitations from the design, and complex circuits impacting the frequency response and phase response are possible. In most high-level products on the market there are switches which enable different sorts of filters to help with the frequency response in different situations.

There are drawbacks to active loudspeakers as well. The biggest issue is with the power source. An active speaker requires its own connection to mains, and therefore to build a large setup for live or installation use, the need for cables is doubled compared to a passive speaker system. In installation use this is a significant extra cost because the cable and the work of the electrician is never free. It is wise to use one power source to power the whole audio signal chain, due to the possibility of differences in the AC supply and even noise. This can be a problem with active speaker system, due to the need for long extension cords.

3.3 Passive speaker design

A passive speaker is in terms of circuit design very easy to implement. A passive speaker can be as easy as simply connecting the positive and negative wires from the amplifier to a single speaker element and calling it a day. If the driver that one is plugging into is a full-range driver then everything might be okay. Speaker systems with only one full range element are rare however, and therefore some more components are required.

Figure 9. An example of a passive speaker circuit [14].

In figure 9 we see an example of passive loudspeaker circuit in all its simplicity. The circuit in this figure consists of merely a capacitor acting as a low-pass filter limiting the input of low frequencies for the tweeter and an inductor limiting the input of high frequencies for the woofer. These sorts of filters are required not only because of frequency dispersion but also to protect the drivers. Driver manufacturers specify in the datasheets for their products the minimum requirements for the crossover filters. Tweeters can not handle low frequencies; they will rupture if they are forced to resonate at lower frequencies than they are designed.

In the active design realm, the crossover filters are implemented with RC or CR circuits followed by an operational amplifier [15]. This is feasible because of the presence of amplifiers, and one need not worry too much about attenuating the signal level in the circuit as it can be amplified again with relative ease. In a passive system however, we do not want to use resistors in our crossovers, because they attenuate our signal at all frequencies resulting in reduced output levels. In passive crossover circuits capacitors and inductors are used.

The successful use of capacitors and inductors in crossover filters is based on their behavior in relation to frequency. A capacitors impedance is higher at low frequencies and smaller at high frequencies. This is called the capacitive reactance of a capacitor, which put in equation form is as follows:

1 � = (1) 2 � � �

This behavior makes capacitors the optimal choice for high pass filters in a passive system. The capacitor alone acts as a frequency dependent resistor of sorts. The logical conclusion is that the inductor acts in a same fashion, only in an opposite fashion. An inductor’s impedance behavior is that it offers much higher resistances at high frequencies and low resistances at low frequencies. This behavior is called the inductive reactance of an inductor, which put in equation form is such:

� = 2 � � � (2)

Based on this equation, it is logical to use inductors as low pass filters in passive systems. The inductor in itself already offers higher resistances to high frequencies, effectively filtering them out.

The problem with the use of crossover filters consisting merely of inductors and capacitors in a passive system is their voltage rating. In a passive system the voltage being fed into the input can be as high as 100V, which would effectively burn to crisp the

13 components used in an active crossover network. It is also wise to prepare for the unfor- tunate event of AC leaking into the amplifier channels (which is in itself a very bad situ- ation). Therefore, the voltage ratings for the components of the crossover have to be between 100V-250V. Components rated this high can take the high power levels produced by the amplifier, but they come at large physical sizes. This sets limits and re- strictions on the design of passive crossovers, because large components occupy a large space inside the enclosure, which leads to a smaller volume of air inside the enclosure, which affects the speaker’s frequency of resonance. It is also difficult to fit many big components on a PCB, which places limitations on the orders of filters (the higher the order, the more components are required). The absence of powered components also makes all manner of delay and phase manipulation much more difficult. It is also noteworthy, that passive components with high voltage ratings cost a lot of money when compared to the components in an active system.

4 n-Array Design

With the basics of speaker design fresh in mind, it is more feasible to dive into the design of the n-Array. As was previously established, the goal of this project is to build a small passive loudspeaker for install use, which is easy on the eyes due to its small size and is able to produce adequate levels of dBSPL. The best scenario would include the speaker being directive (a cardioid polar pattern) A complete set of n-Array would include six speakers in a line array and possibly a LF extension. Without the LF extension the n- Array would not be a spectacular PA system for music use.

4.1 Small size and the drivers of choice

The “n” in n-Array stands for nano, so it is meant to be a very compact product. This sets its own limits on every aspect of the design of the loudspeaker. It was decided that one speaker element will consist of two small full-range drivers and ribbon drivers performing the part of the tweeter. Extensive research was done to find the optimal choices for the drivers. Some criteria were:

• Cost. The manufacturing price per loudspeaker had to be kept as low as possible.

• The frequency response, both on-axis and off-axis.

• The sensitivity. How loud the driver is in terms of SPL when fed 1W of power and measured at a distance of 1m.

• Size. To keep the design small, the full range driver can not be too large.

With all these factors in mind, it was decided that the full-range driver at this early prototyping stage will be FaitalPro 3FE25. With its 3” diameter it still packs a considerable amount of power, the manufacturers promising a sensitivity of 91dB (1W, 1m distance).

Figure 10. The frequency response of the 3FE25 as presented in the datasheet [16].

In figure 10 we see the measured frequency response of the 3FE25 driver. It looks standard and decent for a driver of such small size. What is interesting to note is that the off- axis response drops as expected when the frequencies are high, but around 14kHz there is a significant bump, while the on-axis response drops a little at the same frequency. This is a result of some design choice (or lack thereof) in the manufacturing of the driver. The low frequency response is not too great, but it is to be expected with a driver of this size. It is also indicated in the datasheet, that the driver takes up a net air volume of 0.125d�, which is quite ok in terms of enclosure design and the reference frequency.

The design of the n-Array is a coaxial loudspeaker, which means that the elements are placed on top of each other on the horizontal plane. This gives rise to questions of what kind of drivers can be installed in such a configuration, and what happens to the output

15 of the full range driver when a tweeter is installed on top of it? Once again extensive research was made, and the drivers of choice were implemented with ribbon technology. A ribbon element is a so-called planar element, all the audio reproduction happens across a single plane without the familiar cone structure of other drivers [17]. The working principles of a ribbon driver are based on the effects of a magnetic field. An aluminum diaphragm supports a planar coil, which is usually made out of aluminum vapor, and the coil is suspended in a magnetic field. Similarly to the operation of other drivers, the magnetic field is manipulated by the addition of an AC signal from the amplifier causing the coil to vibrate. The light weight and design of a ribbon tweeter makes them excellent choices for high frequency elements. Their downside is that they are relatively easy to break, they vibrate at almost an omnidirectional pattern, and it is rare to find one with a low crossover frequency option.

Figure 11. PTMini-6 Planar ribbon tweeter [18].

In figure 11 is pictured the other of tweeters of choice. This small tweeter is a good choice for the n-Array because it is very small, only 23 mm * 74 mm and it has a solid back, so there is no sound being emitted back to the full range element. In a design with these tweeters, the n-Array would have required two of these, one on top of each full range driver. The downside to this driver is the nominal impedance of 6 Ω, which would have been a poor match with our 8 Ω full range drivers.

Figure 12. The frequency response of the PTMini-6 [18].

The crossover frequency given in the datasheet is also set at 4kHz, which is quite high and could have caused problems with achieving the desired sound (leaving too much of the higher frequencies for the full range unit to produce). In figure 12 the frequency response of the driver is shown, and it does not seem too optimal. There is a considerable dip in the high frequency representation after 10kHz, and the notch in 5kHz is also a bad thing, it being a harmonic of a typical feedback frequency around 2.5kHZ. However, with the enclosure affecting the sound in pretty much every way possible and the addition of two drivers like this, this is no great cause of concern.

Figure 13. The GRS PT618-8 Planar tweeter [19].

The other driver that passed the qualifications is also a ribbon driver. This one however is almost six times the size of the PTMini-6, so it would cover almost the entirety of the

17 faces of the two full range drivers. The size difference is not so clear from figure 13, but the dimensions of that element are 65 mm * 200 mm.

Figure 14. The frequency response of the GRS PT816-8 driver [19].

Figure 14 makes visible the spectral response of the larger ribbon driver. Compared to the smaller driver, it is clearly visible that this driver packs more punch in terms of dBSPL and low frequency playback. The off-axis response also seems to drop in a similar curve as does the on-axis, so the sound of the speaker would not change too much in the off- axis area.

4.2 Enclosure design

The objective of the design of the shape and size of the enclosure is to achieve the best sound with the minimal required space. In the first version of the enclosure (Mark 1), there is an internal tunnel structure with the objective of achieving phase cancellation at certain frequencies at the rear of the enclosure. This is based on the wavelength of soundwaves in air at 20ºC.

Figure 15. The drivers embedded in the enclosure of n-Array.

In figure 15 there are no measurements visible, but the distance from the front of the enclosure to the back is 215mm. In order to achieve some directivity, the sound emanat- ing from the front of the enclosure and circling to the back would have to interact with an off-phase (ideally inverted phase) soundwave of the same frequency. This would lead to partial rejection of the frequency band in question and therefore more directivity for the loudspeaker. The crossover frequency is set to 400Hz, and the wavelength at 400Hz in 20ºC air is calculated using the formula:

� 343 �/� � = = = 0.8575 � � 400�� (3)

Where � is the wavelength, v is the wave velocity and f is the frequency. With the enclosure being roughly 20cm long, there is no chance of total rejection via inverted phase cancellation. However, there is a chance of at least some rejection happening because a quarter wavelength of the crossover frequency is very close to the length of the enclosure.

� 0.8575� = = 0.2144� (4) 4 4

This gives an indication that partial rejection at the crossover frequency may be possible. Frequencies below 400Hz cannot be affected due to the small size of the enclosure. They are not too great a concern, because most of the feedback issues with microphones happen above 400Hz, the region around 500Hz being especially troublesome often.

Figure 16. A cross-section of the lower half of the n-Array.

In figure 16 the internal labyrinth structure leading to the open back port is shown. The length of the labyrinth is calculated to be the same, as the quarter wavelength of a 400Hz soundwave circling around the front of the enclosure to the back. When the speaker moves forward with the change of the magnetic field induced by the AC signal from the amplifier, a soundwave in a certain phase is produced and propagates through the air. When the speaker moves backwards due to the same phenomenon, a soundwave with an inverted phase is produced and is forced to go through the labyrinth inside the enclosure. After passing the labyrinth the two soundwaves interact and their difference in phase should result in at least some directivity. This can be enhanced by adding passive radiators to the ports, which resonate the same as any speaker cone. However, soundwaves do not follow a linear path through the center of the labyrinth, as they bounce and reflect off every surface they encounter (and absorb and pass through some), making the approximation of the distance of travel a much more demanding task. There is a high probability of this design not working as intended.

4.3 Passive electronics

Since the n-Array came to as an answer to a real-life problem regarding the installation of loudspeakers for a specific purpose, it was always the goal in terms of electronics design that the speaker be a passive speaker. The idea is that the customer or av integrator can flip a switch depending on the size of the n-Array (4,8,12 or 12 with an LF extension) and the signal will be routed accordingly. This would make the cabling of the speaker very easy, because one need only cable one NL8 Speacon (a speaker cable with eight hot and cold pairs) and choose the position of the switch in accordance with the size of the array.

The main part of a loudspeakers circuit is the crossover. The drivers’ manufacturers give limits for the minimums of the crossover frequencies, and the rest is up to the designer to achieve the desired sound. The first decision regarding the crossover design is the crossover frequency. It was a simple decision to use the lowest possible crossover frequencies as given in the datasheets of the ribbon drivers, these being 4kHz for the PTMini-6 and 400Hz for the PT618-8. The manufacturers also provided information about the order of the filter, which in both cases was -12dB, which correlates with a second order filter since an addition of a filter order adds 6dB to the slope of the cutoff.

Figure 17. Different filters and their envelopes [20].

The designer must also make a choice of which filter topology to implement. In figure 17 the different slopes of different topologies are shown, and it is up to the engineer to decide which one is the best for the application in question. In the case of n-Array, it was the Butterworth topology which was chosen. The reasoning behind this was that the notch at the cutoff frequency is not too pronounced as is in the Chebyshev. The Bessel and the Linkwitz-Riley filter topologies are not flat enough before the crossover frequency. Butterworth filters are designed to be as flat as possible on the passband, which

21 is good for audio use. The gain of a Butterworth low-pass filter with an order of n is in transfer function form [25]:

� (�) = |�(��)| = ( ) (5)

, where

• � = gain at zero frequency (DC Gain).

• � = cutoff frequency.

• n = the order of the filter.

The transfer function for a Butterworth high-pass filter is:

� |�(��)| = (6) √1 + �

In the case of passive loudspeaker design, both the Butterworth filters will be implemented using only inductors and capacitors.

4.4 One channel per unit

One of the goals of the design of the n-Array is to create a system, which can be effectively operated using only one channel from an amplifier. With said one channel in the finished product the user should be able to power and effectively use at least four n- Array loudspeakers. By succeeding in this design, the user will be able to create impres- sive sized line-array systems by using only one Speacon NL8 cable. Up to 32 loudspeakers could be powered with one cable if the design is a success. Mostly this is a question of the functions between the impedance of the loudspeaker (are the drivers connected

22 to each other in parallel or serial or both?) and the optimum output impedance of the amplifier channel.

5 Acoustic Measurements

Once the mark 1 -version of the enclosure was 3D printed, the measurement process was able to begin. The goal of the measurement process is to establish a general feel of the cooperation between the different combinations of the enclosure and the drivers and to use a DSP processor to discover the requirements of the passive electronic circuits (the crossover, equalization, and the delay).

The measurement setup was sufficient in terms of the equipment used, but somewhat lacking in terms of the space. Loudspeaker measurements should be conducted in a space with minimal other sources of noise (these usually being traffic, air conditioning and other living -related noise) and the space should have significant damping and ab- sorption present in order to prevent reflections. Even completely anechoic spaces are used. The measurements of the n-Array were conducted in a warehouse of a company. In the measurement space there are many sources of interference, the AC and the other companies in the office building being some. Also, in terms of reflections the space is not optimal, there being the standard shelves and pallets that one might expect in a warehouse. These sub-par conditions are not of great concern due to the R&D nature of the work, the prior experience of the engineers with measurement of PA systems in noisy environments and the very short measurement distance of 1m.

Our measurement signal chain was as follows:

• The pink ( ) noise used as the test signal was generated by a MacBook Pro running SMAART v8 audio analyzement software.

• The signal was routed through a RME UFX audio interface to a Lake LM44 processor.

• The pink noise was fed as a line level signal from the Lake LM44 processor into the input of a Crown CTS 4200 power amplifier.

• The pink noise was amplified to speaker levels by the Crown power amplifier and fed into the n-Array using two separate amplifier channels, one for the LF and one for the HF.

• The signal as dBSPL was picked up by a ISECOM 750 omnidirectional measurement microphone.

• The microphone-level signal was fed back into the MacBook Pro running the SMAART v8 via the RME audio interface.

The whole of the measurement signal chain is visualized in figure 18.

Figure 18. The measurement signal chain represented as a block chart.

To achieve a representation of the polar pattern of the loudspeaker, the measurements were taken with the loudspeaker being angled differently in relation to the measurement microphone with increments of 15º. The change in degrees was measured with a special 3D printed baseplate.

5.1 Mark 1 SMAART measurements

The Mark 1 version of the enclosure was a 3D printed ported model with the internal labyrinth structure. The ports at the rear of the enclosure were designed to be left open, shut with plastic and to be made into vibrating elements with passive radiators. The measurement process began with the verification of the drivers. After everything was satisfactory, the first measurements were taken of the two full range elements and the smaller PTMini-6 elements. The Lake LM44 processors DSP was used to create three filters, one Butterworth second order LPF at 4kHz (the crossover frequency), one Butter- worth second order HPF at 80Hz (this was done to merely filter out the unneeded frequencies that our 3FE25 driver could not produce efficiently) and a Butterworth second order HPF at 4kHZ for the ribbon drivers (the crossover filter).

5.1.1 PTMini-6 measurement

The first verification tests were conducted mostly by ear, because a machine can not really tell an answer to such a subjective question as “does this sound at all reasona- ble?”. It was very shortly concluded that the n-Array will comprise of two full range 3FE25 drivers and the larger PT6816-8 ribbon driver placed coaxially on top of the two full range drivers. Due to this reason sadly some documentation of the responses with the smaller PTMini-6 ribbon drivers were lost, but in figure 19 we get a crude idea of what it was like. In SMAART v8 software in the top there is the delay between different sound sources (in our case this is the difference in time between the full range elements and the ribbon elements), the graph in the middle is the phase of the captured signal and in the bottom there is the frequency response. The red graph above the frequency response repre- sents the coherence of the signal. If the red graph is close to the top of the graph, then everything is well and the measurement results can be trusted. Dips in the red graph indicate some sort of issue with discerning the measured signal from atmospheric noise, this is usually due to some sort of reflections.

Figure 19. A crude screenshot of the initial frequency response with the PTMini-6.

As can be seen from the frequency spectrum in the bottom of figure 19, due to the difference in the nominal impedance between the speakers (the FaitalPro 3FE25 being 8Ω and the PTMini-6 being 6Ω), the high frequencies radically overpower the lower

25 frequencies. This could be remedied through various ways, for example using an impedance equalizer circuit or simply using a resistor to soak up some excess power to equal- ize the responses. However, in the quest for the n-Array to be very power efficient, con- verting precious watts into heat with a resistor is not an option.

Due to the physical distance between the flight time of the drivers (because of the coaxial positioning), there must be some sort of delay for the ribbon elements. The difference between the surfaces of the drivers is roughly 4cm, so that in terms of milliseconds would be 0.12ms. The drivers are from two different manufacturers, and the material choices and other design choices also affect the amount of delay the driver produces, so the correct amount based on the principle of trial and error was 0.22ms.

Otherwise, the frequency response from this configuration sounded very nice. As can be expected from the manufacturer’s graphs, the on-axis and the off-axis response sounded remarkably similar. The outward appearance of the loudspeaker was also very pleasing, but after installing the larger ribbon driver PT816-8 the last of the doubt which element to use was evaporated. The PTMini-6 did not simply have as much power in it due to the physically small size of the driver.

5.1.2 PT816-8 measurements

After swapping the small ribbon drivers for the large driver, the next step in the measurement process was to compare the response in front of the loudspeaker and behind it. Between the measurements the ports on the back were either open, closed or had passive radiators in them. The hope was that the enclosure would perform well and be directive with the ports open, and the directiveness would only improve with the closing of the ports and the addition of the radiators.

Figure 20. Mark 1 response with the reflex ports open.

In figure 20 both the response from the front and the back of the speaker are shown. The response itself does not look that great with a very large peak at the 1kHz area, and another one around 14kHz. At this stage of the measurements, it is not a concern that the response is anything but flat, but the interest lies solely with the behavior of the different setups of the reflex port. When both the graphs are compared, they seem nearly identical at the 250Hz – 500Hz region, which is exactly where some directivity is desired. It would seem, that the internal labyrinth structure does not do what it was designed to. Other than that, the graph seems to be as expected, with the response measured from 135º off axis being emphasized on the low end of the spectrum.

Figure 21. Mark 1 response with the reflex ports closed.

Comparing the graphs in figures 21 and 20, it can be clearly seen that the closing of the reflex ports helped the response. The peak at around 300Hz practically vanishes, and the low-end response of the loudspeaker is a lot better. On the downside, the low-end

27 response is also “better” when measured from the back of the speaker, putting further emphasis on the simple fact that the labyrinth structure does not perform as was desired. There are also some issues with the coherence in the measurement in both figures around the 1kHz – 2kHz region, which causes some doubt as to the presence of the big peak in that frequency band.

Figure 22. Mark 1 response with the passive radiators installed.

Figure 22 could be a copy of figure 21, it is so identical. Upon observation of the results, a manual test was performed to see if the passive radiators were indeed doing anything. They were vibrating as they should be, so it can be concluded that the difference between a closed port and a port with radiators on it is negligible. With different sort of radiators, one might naturally get different results, but with these one there was no significant difference.

Figure 23. The DSP flattened polar response of the Mark 1 n-Array.

Figure 23 shows the polar response of the Mark 1 version of the loudspeaker. The frequency response of the speaker was processed with the DSP from the Lake LM44. A delay was added to the ribbon drivers channel with a value of 0.4ms, this was done by observing the changes in the phase response and modifying the amount of delay accordingly. The frequency response was also made as flat as possible. This was achieved by placing various filters with the Lake LM44 in order to smooth out the response a rea- sonable amount. Technically one could make the frequency response extremely flat with a huge number of DSP filters, but every extra filter manipulates the phase response and therefore can cause unwanted distortion or colorization of the sound. The saying “less is more” is very applicable in this case.

The polar response of the enclosure does not look bad at all. The idea behind the measurement of the polar response of the speaker is to ensure, that the loudspeaker resonates in an optimal and uniform manner all around it’s axis. These measurements were only taken of the horizontal pattern, but in the future with the measurements of more loudspeakers in an array form the vertical pattern should also be measured.

An audible problem that is not visible from the measurement graphs is the behavior of the large ribbon driver when playback is at a higher volume. As has been stated before, the driver vibrates at almost an omnidirectional pattern, which means that there has to be some sort of protective enclosure for the driver. This protective enclosure came in the form of a back cup, and the reflections from said cup caused some unwanted phase colorization in the midrange area, somewhere around 2kHz.

5.2 Mark 2 SMAART measurements

With the disappointment regarding the internal labyrinth structure with the Mark 1 enclosure, it was decided that the Mark 2 enclosure be just a empty box with no special structures inside. Mark 2 measurements are taken only with the larger PT816-8 driver. This was also 3D printed, and the variables between the measurements were with the enclosure being filled with absorbent material or not and the variations of the back cup for the ribbon driver. It is noteworthy, that the material of the enclosure at this stage is also 3D printed plastic, but it could as well be wood. 3D printing was chosen mainly due to the internal labyrinth structures, but the testing of different materials for the enclosure would also be a future task as the R&D process advances.

Figure 24. Mark 2 measurements with the reflex ports open.

The graph seen in figure 24 differs from the Mark 1 measurements with a significant drop in the low end response of the loudspeaker. The on-axis response is also a lot smoother, the large peak at the 1kHz – 2kHz area being considerably flattened. Please notice that the only thing that has changed is the internal design of the enclosure, proving the point that in loudspeaker design the magic is done in the design of the enclosure. A remarkable improvement over the Mark 1.

Figure 25. Mark 2 response with the reflex ports closed.

Again in figure 25 the difference between the Mark 1 and the Mark 2 versions is mainly in the 1kHz and 2kHz area. It is becoming more and more clear, that the empty enclosure works better than the previous one. This is most likely due to some sort of out of phase soundwaves escaping the enclosure in Mark 1 and interacting badly with the actual response.

Figure 26. Mark 2 response with passive radiators.

When comparing the graph from figure 26 from the corresponding one from the Mark 1 measurements, it is obvious that something has changed with the 135º response at around 4kHz. There seems to be some sort of dip which was not present before. This is most likely once again bad phase behavior due to the internal structures. Other than that, there is not such a great difference between the two. The same taming of the 4kHz area is the most significant difference.

Figure 27. The DSP flattened Mark 2 polar response.

Finally figure 27 shows us the flattened polar response of the Mark 2 enclosure. The polar response seems to be fine in most parts. The behavior of the enclosure at around 10kHz is a little worrisome. At angles of around 90º the 10kHz part of the spectrum is noticeably enhanced when compared to the surrounding frequency bands. The most likely cause for this anomality is a reflection from the ribbon drivers backcup due to the omnidirectional radiation pattern of the driver.

5.3 Crossover, delay and EQ requirements

The frequency responses were processed with the Lake LM44 processor to achieve a flat response from which it is easier to make observations about the polar behavior of the enclosure. These DSP filters and delays are used as the guidelines for what is required from the passive components. Since DSP is the thing of today and the future, it would be most foolish to stick to using analog electronics out of sheer stubbornness, so it is likely that the EQ filters will be applied via DSP from a good amplifier, but the delay and the crossover have to made from passive components.

The requirements for the crossover, delay and EQ are:

• The crossover frequency at 400Hz, Butterworth LPF with a -12dB slope and a Butterworth HPF with a -12dB slope (which makes both of these filters second order).

• Tweeter delay 0.35ms. This amount of delay produced the optimal phase response for the loudspeaker.

• Contour EQ filters; -10dB at 1.26kHz with a Q of 1.1 octaves, -6dB at 6.5kHz with a Q of 2 octaves, -2.5dB at 8.5kHz with a Q of 0.3 octaves and -7dB at 12kHz with a Q of 0.5 octaves.

These guidelines are to be treated as such, guidelines. It is difficult to tell what happens to the requirements when the signal chain is stripped of almost all DSP and replaced with mostly passive electronics. However, every designer needs a place from where to start and these requirements will do just fine.

6 Electronics Design

The main guidelines for the design of the electronics of the n-Array are passive implementations of the filters, space constraints and power efficiency. All the electronics simulations were performed with a software called VituixCAD, a Finnish speaker simulation software by an acclaimed speaker designer engineer called Kimmo Saunio.

6.1 Parallel or series connection

There is also a choice of doing the drivers’ connections in a parallel or serial fashion. While the subject is crossovers and the impedance of the drivers, the required variable is the � , which is the driver’s DC resistance. Driver DC resistances connected in series are defined by the equation:

� = � + � + � … + � (7)

While different resistances connected in series are defined by the equation:

1 1 1 1 1 = + + … + (8) � � � � �

The manufacturers have provided the nominal impedances for their drivers in the datasheets. These are an approximation of the impedance at the audio spectrum, which is categorized by the theoretical limits of human hearing being 20Hz – 20kHz. Using the nominal impedance values the total impedance of the drivers connected in series amounts to 24 Ω. The total impedance resulting from a parallel connection is 2.67 Ω.

In order to achieve the largest amount of power from our system, we need to compare the two connections. Let’s assume that we are feeding 1V worth of AC signal into our system. The power generated by the series connected drivers can be calculated by applying Ohm’s Law with our known connection impedances and assumed value for voltage into the equation for power:

1� � = 1� ∗ = 0.042W (9) 24Ω

The power for the drivers’ parallel connection is:

1� � = 1� ∗ = 0.375� (10) 2.67Ω

Judging by the results from the equations 10 and 11, the parallel impedance network can produce almost ten times more power than the series one. When the array aspect is kept in mind, the series impedance might also be manageable if the different n-Array elements were connected to each other in parallel. However, it is the decision at this phase of the design to implement the drivers in a parallel fashion, because it allows the user to use more combinations with the number of loudspeakers. A user can use only one cabinet if one wishes.

6.2 Crossover design

The first design choice the engineer must make when implementing a loudspeaker crossover is the crossover frequency. Determining the crossover frequency can be done in a relatively arbitrary manner or by following the minimum requirements for the filters specified in the datasheets. It is noteworthy, that if the design is a passive one, inductor power losses become a real problem when the crossover frequency is approaching as low as 300Hz. The crossover frequency for the n-Array is however 400Hz, so the inductor power loss should not be too dramatic.

As impedance is an AC variable, the amount of resistance a coil or a capacitor has changes with frequency. Therefore, a designer can not simply take the nominal impedance of a speaker driver given by the manufacturer and designing a crossover filter for any frequencies using it.

Figure 28. The impedance graph of the 3FE25 [16].

Judging from the graph visible at figure 28, the nominal impedance of 8 Ω as given by the manufacturer would have resulted in the crossover frequency of 400Hz not working correctly, as the impedance at 400Hz is closer to 6.5 Ω.

Figure 29. The impedance graph of the PT816-8 [19].

In figure 29 both the impedance and the phase response of the PT618-8 are shown. Interestingly for this driver the nominal impedance of 8 Ω is found at our given crossover frequency. To be exact, the impedance value at 400Hz is 8.7 Ω.

6.2.1 The Butterworth filters

The filter implementation for the crossover filters was decided to be a second order But- terworth filter. The quality factor, or “Q”, of a Butterworth filter is 0.707. The quality factor is relational to the bandwidth of the filter, with a lower Q value being a wider bandwidth and vice versa a higher Q value being a narrower bandwidth. The quality factor of 0.707 was designed for the filter to have a maximally flat response [21].

Finding the mathematical equations for the component values of a passive crossover filter proved to be a difficult task. The internet is filled with all sorts of different calculators and graphs for the component values in a passive crossover, but it is very rare to find the equations used attached to them. The equations for the component values can be found in all sorts of material regarding speaker design, but what is not usually present ia the mathematical proof for the equations. The equations nevertheless produce the correct values.

Figure 30. A two-way second order Butterworth crossover diagram [3,207].

In figure 30 the names for the components are the same ones used in the equations. C1&L1 being the components used for the high pass filter for the tweeter, and L2&C2 the components for the low pass filter for the woofers. The equation for the component values for the high pass filter are:

0.1125 0.1125 � = = = 32.33 �� (11) � ∗ � 8.7Ω ∗ 400��

0.2251 ∗ � 0.2251 ∗ 8.7Ω � = = = 4.896 �� (12) � 400��

The corresponding equations for the components of the low pass filter are:

0.1125 0.1125 � = = = 43.27 �� (13) � ∗ � 6.5Ω ∗ 400��

0.2251 ∗ � 0.2251 ∗ 6.5Ω � = = = 3.658 �� (14) � 400��

With the design consisting of one ribbon tweeter covering two full range drivers, the design choice of the implementation of the low pass filter must be decided. It was decided that both the woofers should have their own discrete filters in the first variant of the crossover filters. This was rationalized by this enabling separate processing for the discrete woofers. It is entirely possible, that the simple limitations of the space the PCB can occupy may cause this design to be changed. It should not affect the response of the speaker.

6.2.2 Component choices

The component values required for the crossover filter are two capacitors with the values of 32.33�� and 43.27��. The required values for the inductors are 4.896mH and 3.658mH. Theoretically one could design a clever network of parallel and series components to achieve the exact component values, but the addition of more components in- creases the cost of one unit, the space occupied on the PCB and the risk of crosstalk and other issues between the components. Therefore, it is more feasible to approximate the values for the component to the nearest values available on the market as single units.

In the interest of comparing the sound differences between components, two types of different capacitors were ordered. The 32.33 �� capacitor was rounded to a component with the value of 33 �� with a voltage rating of 250V. The same capacitor was also brought to being with a 100V voltage rated 33�� capacitor. The 43.27 �� was approxi- mated to 40 �� with a 250V voltage rating, and two 100V rated capacitors with the values of 33 �� and 6.8 ��. These two capacitors must be connected in parallel in order to achieve the required capacitance. The required inductance value 4.896mH is approxi- mated to an existing product with the value of 4.7mH and the 3.658mH is rounded to a value of 3.5mH.

The capacitors will most likely be implemented in the final product with the 100V rated components due to the dire need for each cubic centimeter. The inductors are a different story, because due to the physical characteristics of inductors the size can not be

38 reduced. To achieve a certain amount of inductance there needs to be a specific number of rounds for the copper wire, and to withstand higher power levels the wire can not be too thin.

6.3 Delay design

Since the first day of the design of the n-Array, the requirement of a delay has been known. The coaxial positioning of the drivers makes a delay a necessity. The delay could be implemented by some sort of mechanical structure, DSP, or passive electronics. Thanks to the modern era and the immense DSP capabilities available to even the consumer level, the correct amount of delay was relatively easy to determine.

The implementation of a passive delay network is not a very simple subject. The amount of data that can be found on them is relatively scarce. The reason for this is that the implementation of a passive delay network is a costly effort. The cost of components for an effective passive delay network can easily add up to 200€, which makes the cost-per- unit skyrocket. It is nevertheless the intention of this project to at least find out if the passive delay is at all feasible. The first idea was to implement the delay using a passive delay line. Plenty of equations and good material is found on the internet related to this subject [22]. Upon further study it was found that this implementation at our frequencies of operation would be highly inefficient, so other methods had to be discovered.

The widely used method of implementing a small delay in an audio circuit is by using an all-pass filter. An all-pass filter is a strange member of the world of filters. The more familiar filters are the high pass filters, low pass filters, bandpass filters, and notch filters. One is accustomed to thinking of filters as attenuating a specific frequency band and simultaneously doing different things with the phase (most of which are non-desirable artefacts). The all-pass filter in accordance with its name let’s all frequencies pass unat- tenuated. The function of the all-pass filter is to give the engineer control over phase and therefore the time domain [23]. All-pass filters are frequently made in active speaker design, while the passive ones are rarer. The transfer function of an all-pass filter is:

� − � + � �(�) = (15) � + � + �

The all-pass filter is also known by the name delay equalizer [24]. An all-pass filter is the only sensible method of implementing an internal delay in a passive speaker.

6.3.1 All-pass filter design

As was stated before, the internet is filled to the brim with equations and different implementations for the all-pass filter in active systems. The math required for the passive implementation of an all-pass filter is simply too complex for the purposes of this docu- ment, so an internet calculator will be used instead. The design will be based in a process of simulation in addition to trial and error. The whole implementation of the all-pass filter in the final product is a question mark due to the advantages it provides compared to the cost of the components.

Figure 31. The lattice phase equalizer circuit [25].

The all-pass filter seen in figure 31 is called a lattice phase equalizer. The idea of the network is that it is a constant-resistance network. The input resistance of a constant- resistance network does not change with frequency when it is correctly terminated [26]. In our case the network is terminated to the ribbon driver, and its DC resistance is 6.4 Ω.

The requirement for the time delay for the ribbon driver in our system is 0.35ms, and after the input of these values to an internet calculator (listed in the references) we get the following component values:

• The inductor value: 1.12mH.

• The capacitor value: 27.34 ��.

It is virtually impossible to find components with these values. For that reason, the component values were rounded to the closest available option. These were 27 �� for the capacitors and 1.2mH for the inductors. The disadvantage of the design of the all-pass filter is that a large time delay implies a small frequency bandwidth for the delay. Vice versa a small time delay implies a larger frequency bandwidth for the delay [27]. The addition of more orders of the all-pass filter helps correct this issue, but if one order of the filter consists of four large components rated for higher voltages, the cost for the addition of orders quickly ramps up.

6.4 Circuit simulation

All in all, the electronics of the n-Array consist of the simple crossover circuit, being the Butterworth filters for the woofer and the tweeter, and the lattice phase equalizer network for the tweeter. The simulation software VituixCAD gives plenty of simulated graphs to marvel at, the most important ones in our case being the SPL, the filter, and the phase. VituixCAD is a loudspeaker design software, therefore the effects of the enclosure on the design are also simulated. However, with the n-Array being (at first draft) too complex to accurately represent with the software, the effects of the enclosure are not simulated. There is no possibility of drawing the enclosure and its internal structures by hand, one can only input the dimensions and the internal volume measured in liters. This is the reason, why the following graphs do not look much like the measured graphs from before. The software assumes our drivers to be mounted on the same level on an infinite surface. Due to the absence of the enclosure and the coaxial positioning, the following graphs should be taken as guidelines. The impedance and frequency responses of both the drivers were imported to the software as provided by the manufacturers.

Figure 32. The SPL and the phase of the circuit without the all-pass filter.

In figure 32 the simulated responses of the loudspeaker are shown. The graph in red is the response from the 3FE25 and the blue one is the PT816-8. The grey graph is the overall response. When compared to the measured responses with the actual enclosure, the trends seem to be similar. The simulated response has much more low-end due to the woofers not being constrained to a space of limited volume. The crossover filter when simulated does exactly what was required of it. It is however interesting to note, that even with the orders of the filters being equal, the high-pass filter seems to have a steeper slope than the low-pass filter. The probable reason for this is the impedance responses of the drivers being only the calculated value at the crossover frequency and something totally else for the other frequencies.

Figure 33. The SPL and the phase response of the circuit with the all-pass network.

Figure 33 shows the responses with the all-pass network connected. There are interesting things going on with the phase of the system, and the group delay is noticeably different (pictured in gray on the right picture). The SPL response however looks quite similar, and there are no issues that can not be corrected using DSP EQ.

As was previously mentioned, the all-pass network needs additional orders to cover a large frequency range. Due to the simulation results being inconclusive, and the nature of loudspeakers being devices which produce sound (which is meant to be pleasant for

42 the listener), the SPL graph was taken as the primary guideline. The idea is to construct the delay as a module and test it out. Whichever order of the modules sounds best, that is the one the design goes with. In the following figures the effect of the increase of modules to the SPL is shown.

Figure 34. The first order all-pass filter.

Figure 35. The second order all-pass filter.

Figure 36. The third order all-pass filter.

Figure 37. The fourth order all-pass filter.

Figure 38. The fifth order all-pass filter.

As can be seen from the previous figures, in order to have a SPL graph with minimal harmful phenomena around the crossover frequency, at least five orders are needed. Five orders of an all-pass filter consist of 20 components, and that amount in itself is quite expensive to bring to reality. Simulations were concluded with ten orders of all- pass, but the results were not noticeably different from the ones with the five orders. In figures 34 and 35 the SPL response is very poor. With the addition of four orders of all- pass, the response shown in figure 38 is achieved. The group delay also does some weird things in figures 35 and 36, for there seems to be a group delay of 12ms at the crossover frequency.

With these perplexing simulation results in mind, the solution of testing the implementations in real application with real components seems ever more plausible. With the reality of everything affecting everything, the decision has to be based on the subjective opinion of the designers as to which implementation sounds best. Measured from an arbitrary frequency of 1980Hz, the five orders of all-pass seem to provide 0.3ms of delay, which is very close to the desired amount.

In figure 39 the circuit of the n-Array mark 2 is visible. The huge extended circuit at the top of the figure is the five orders of all-pass filter. In this version of the circuit, both the

44 woofers had their individual crossover filters. This design decision was later revoked, due to no different processing being planned for the woofers individually. Stripping the design down to just one filter also makes the PCB area required much smaller.

Figure 39. The final schematic with the fifth order all-pass filter.

7 PCB Design

After the circuit simulations and other design steps were completed, it was time to move on to PCB design. Compared to other electronics applications (which are usually low current applications), the PCB for the passive crossover must endure higher levels of current. If our summed driver impedance per unit with the parallel connection is 2.67 Ω and the voltage per unit is limited to 15 V, by Ohms law this would imply 5.62 A of current. The traces on our PCB need to be able to handle this sort of current, so the trace width required must be calculated. The calculations for the trace width are done by first calcu- lating the trace area using the formula [28]:

� 5.62� . . �� (�� ) = ( . ) = ( .) � ∗ ��℃ 0.048 ∗ 10℃ (16) = 176.4383 ��

The k is a constant for external traces. The result is inserted into the actual formula for the trace width:

�� (��) 176.4383 �� ℎ (��) = = �ℎ��(��) ∗ 1.378( ) 2 �� ∗ 1.378 (17) = 64.0197 mils

The thickness of the copper was decided to be 70 �m, which converted to the American measurement system is 2 oz. The resulting trace width in mils is converted to mm by multiplying it by 0.0254 which results in:

64.0197 ∗ 0.0254 = 1.626 �� (18)

With the trace width calculated, the real design process can begin.

7.1 Logic

The PCB design was made using the PADs software. In terms of logic design, the circuit itself was not hard to implement. Due to the nature of the components being so large, none of them where found in the factory libraries as is. The components had to be cre- ated by hand. The component manufacturers provided adequate datasheets, so this was not too big of an issue.

Figure 40. The Logic design of the crossover circuit with the larger components.

For the purposes of finding the best sounding components, the crossover PCB was designed and implemented with two different sorts of capacitors. In figure 40 the design of the crossover with large components is visible. The design itself is quite self-explanatory, the only thing worth opening is the presence of the SIP connectors. At this early stage of prototyping, nearly no thought at all has been put to the connectivity and the terminals of the n-Array. SIP connectors were placed as placeholders, while the actual prototyping will be done by soldering 2.25� wires to in place of the connectors.

Figure 41. The crossover logic with the smaller capacitors.

In figure 41 the alternative crossover logic is shown. The only exception logic-wise is the addition of another capacitor in parallel to the other for the low-pass filter.

Figure 42. The logic of the all-pass filter module.

The all-pass filter is shown in figure 42. The idea is, that the output from the crossover is soldered to the input of one of these modules, and then the testing process moves by listening to the sound of the speaker with the specified number of all-pass modules connected and then inserting the next one. The combination of all-pass orders with the best sound wins. It is entirely possible though, that none of these end up in the final design.

7.2 Layout

The goals and guidelines for the PCB layouts are compact size, minimal crosstalk, and logical routing. These can sometimes be at odds with each other, as is the case with inductors. When placing inductors on a PCB, it is advisable to place them at a 90º angle in relation to each other to avoid the signals from interacting via the magnetic fields. This is not always optimal, as components of equal physical dimensions usually take up the least amount of space when placed next to each other. None of the PCB’s here are the final design, as the final design will likely include the crossover and the possible delay on the same board. In the event of the delay not being required, the PCB may have to be redesigned anyway when the decisions about the connectors are made, especially with the idea of the one Speacon NL8 cable and the switch corresponding to the size of the array. Due to PADs as a software not always seeing things eye to eye with the designer, the component side varies in the design, sometimes the components being

48 mounted on the bottom and sometimes on the top. With our two-layered PCB this makes absolutely no difference.

Figure 43. The layout of the crossover PCB with the larger components.

In figure 43 the layout for the larger crossover is visible. Its dimensions are 130.9mm * 113.2mm. The layout could be squeezed into a slightly smaller size by placing the input connectors next to the other connectors. However, this choice was made simply due to the ease of use in connecting the input from the amplifier.

Figure 44. The crossover PCB layout with the small capacitors.

Figure 44 shows the amount of space saved with the implementation of the smaller in size capacitors. The dimensions of the board are 90.1mm * 92.6mm, which is roughly a 4cm reduction in length on both sides. The reduction would have been smaller, if the inductors were placed in a 90º angle in relation to each other. If there is no significant crosstalk, the layout with the smaller PCB footprint is the design of choice.

It is good practice in PCB design, if one has access to multilayered boards, to include different planes. If for example a design has multiple reference voltages and a ground, each one of those could be assigned to its own plane. This simplifies the connections to the reference voltages and the ground, due to the erasure of the need for traces, resulting in a lessened space requirement. The addition of a ground plane in these designs would not have lessened the required space, as the components themselves are the main causes for the large PCB area.

Figure 45. The PCB design of one all-pass module.

Finally in figure 45 one module of the all-pass PCB is shown. In contrast to the crossover PCBs, the inductors in the all-pass filter are cylindrical. This results in unutilized space in the corners of the board due to the small number of components. The rounding of the PCB is not of any use in this case and placing the capacitors vertically in between inductors would result in the increase of width. The measurements of one module of all-pass filter are 93.3mm * 57.9mm, so one can imagine that all the five orders would be a virtually impossible fit inside the small enclosure of the n-Array.

After the PCB layouts have been successfully designed, the next step is to mill them or pay someone else to do that for you. The choice in this project is the latter.

8 Assembly & Measurements

The PCBs were manufactured in China. This implies a significant delay in the delivery of the possible fixed versions of the PCBs. In an ideal case, the project resources would have included 24/7 open access to a PCB milling machine, but it was not the case. The PCBs arrived from China relatively fast. Upon first inspection things seemed to be ok, so the next step was to solder the components to the boards.

8.1 Crossover

The crossover was designed to be on two different boards with different sized components. This was done to make decisions of which sounds better based on the sound of each crossover circuit. Before the PCBs were designed and milled, the crossover circuit was assembled on a breadboard. The results from the breadboard crossover showed immense promise, as the sound was solid and natural. The response seemed to be better especially at the crossover frequency when compared to the DSP crossover.

Figure 46. The assembled crossover with the large components visible.

In figure 46 the crossover with the larger components is shown. The connections are made using 0.75�� JAMAC cables. JAMAC cable is not thick enough to handle large amounts of current, but with the low power required by one unit of n-Array these cables will do fine.

Figure 47. The initial response of the crossover PCB.

In figure 47 the response of the crossover is shown. Immediately attention is drawn to the worrying notch at the 250Hz area. The low-pass filter does not seem to work correctly, which is extremely weird, when the same components were used in the breadboard version of the PCB, and that variant worked more than fine. The disappointing first results from this measurement led to a test, in which the PCB was eliminated from the equation completely. The response was not better. After this the signal from the amplifier was fed directly to the full-range woofers, and the woofers worked as they are supposed to. This leads one to conclude that the fault must be with the components used. In a real R&D department this issue would be remedied by swapping the PCB and the components in it, but in this case the resources are thin, and time is limited, so replacing the components was not an option.

It is the suspicion of the designer that the fault lies with the low-pass filters inductor. The wire is too easy to detach from the coil, and this would lead to different amounts of inductance than the circuit is designed for. This should cause only a miniature difference, and the huge difference in the (partial) cutoff frequency is not accounted for with some copper unraveling. The fault will be found and dealt with in future development, but it is sadly not within the scope of this thesis project anymore. The response from the smaller crossover capacitors was not different from the large ones, so the results from that test are at this stage irrelevant.

8.2 Delay

With the disappointment from the crossover components not functioning as they were supposed to fresh in mind, the next step was to test the operation of the all-pass filter. Based on the simulations, the response should look fine with five orders of all-pass filter.

Figure 48. The response with the first order all-pass filter.

In figure 48 the response with one order of all-pass is visible. There seems to be a significant decrease in the response at around 1.3kHz. This does not bode good for the operation of the circuit, as the simulations indicated that the hole in the response should be at 500Hz. With the faulty operation of the crossover circuit added to the mix, the interpretation of the results becomes increasingly more difficult. The first order adds also about 130º of phase shift when compared to the phase response without the all-pass.

Figure 49. The response with two orders of all-pass filter.

In figure 49 the results of the addition of another all-pass order are shown. The notch at 1.3kHz is a little less pronounced, but the frequency band from 600Hz to 900Hz is virtually nonexistent. The all-pass filter is not behaving as expected.

Figure 50. The response with five orders of all-pass filter.

The addition of the third and fourth orders of all-pass filter did more or less the same things as the addition of the second. In figure 50 the response with all the five orders of all-pass is visible, and the effect it has on the response is horrible. It is nothing like the simulated filter response. The reason for this is most likely that the designer forgot one simple fact when constructing the PCBs for this project: everything is a resistor. This

54 means, that in order for the network to be a constant resistance network, all the resistances have to be equal. All the traces have an impedance of their own, and if their lengths are not exactly the same, the signal will always choose the path of least resistance. In addition to the possible difference in impedance resulting from the traces, the components themselves may not be optimal for this use. Tolerances in terms of DCR may be crucial in all-pass filter applications. It is only natural that when one is engaged in research & development, issues will come up that need resolving. Many different combinations of components and boards will be tested in hopes of finding the optimal choice for every piece. With the limited resources of the two-man R&D team in this project, the interval between the error and the next trial is too long to be documented within the confines of this thesis project.

9 Conclusions

The results from the research done in regards to the n-Array come in many forms. The loudspeaker does indeed seem to have great potential, as it does produce an adequate amount of SPL with a uniform sound all across the polar pattern. The loudspeaker driver choices are quite good, because the large size of the planar ribbon driver enables the low frequency of the crossover, which in turn brings the coaxial positioning to the realm of possibility. In addition to these the speaker in its enclosure looks aesthetically pleasing and is very compact in size.

The downsides uncovered with the research are also numerous. The difficulties regarding the directivity (cardioid pattern) give rise to questions of total redesign of the enclosure. The poor operation of the all-pass filter at this stage could lead to the scrapping of that idea completely. This could lead to the delay being simply left out of the final design in hopes that the speaker would sound good without it (the low crossover frequency helps in this regard), or to a new positioning of the drivers (meaning the placement of all the drivers on the same plane).

All in all, there seems to be quite a lot of work still to be done. This thesis project has given a lot of answers to the questions asked by the designers, but also a whole lot of new questions and issues have surfaced. This thesis project has enabled the team to deepen their understanding of speaker design and its different implementations. How- ever, as is the case with the increase of knowledge in general, in terms of passive loudspeaker design: the more you know, the more you realize you do not know. With the

55 rapid speed at which technology and DSP develops, there may arrive whole new solu- tions to the issues encountered within the confines of this project. The design work will continue, and hopefully one day the n-Array will emit soundwaves at a cardioid pattern to the earlobes of happy customers.

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