HifiZine
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The Mini Convertible active loudspeaker: design

One of the drawbacks of building active speakers is the plethora of cables and boxes that result. Somehow, they just seem to multiply. One way of dealing with this is to put the crossovers and amps into the speakers. While I’ve always preferred “separates” since I’m an inveterate tinkerer, there is definitely something to be said for the neat, self-contained approach.

The above speaker is a prototype of a little project I’m working on using a two-way plate amp from miniDSP, which incorporates their eponymous DSP functionality together with a B&O ICEPower module. This amplifier module simplifies the electronics part of the project: instead of a separate DSP crossover with multiple amplifiers and associated wiring, a single pair of amp modules is all that’s needed.

The drivers are a perfect fit for a compact active loudspeaker and met with the design goals I had for this project. They were kindly supplied by Seas of Norway. This first article – in what I intend to be an on-going series of articles – will cover the design concept of the speaker and includes measurements of the prototype with a straightforward crossover. The next article will look into crossovers in detail, and the remaining articles will describe how the loudspeaker is constructed and explore the “convertible” aspect of the speaker.

A little theory

Imagine the perfect reproducer of sound: the point source. This source radiates sound energy equally in all directions, so no matter where you might be positioned (in front, to the side, above, behind), it would sound the same. Real speaker drivers, however, exhibit a degree of directivity as a consequence of their physical size and the fact that they are (typically) positioned on the baffle of a box. That is, the sound produced by the speaker is strongest in one particular direction – usually directly in front of the speaker or driver, referred to as on-axis – and weaker in other directions. This variation is frequency-dependent and can be shown in a number of ways; but a simple one is to show the frequency response curves at different angles relative to the on-axis position.

Figure 1 illustrates response curves of a hypothetical two-way speaker. At the top is the on-axis frequency response of the woofer in blue, and in red the off-axis response at, say, 30 degrees in the horizontal direction. At higher frequencies, the off-axis sound level drops relative to on-axis because of the woofer’s increasing directivity – the woofer is starting to “beam.” The next pair of curves are for the tweeter. Like the woofer, the off-axis output drops off as frequency increases, but at a much higher frequency. Finally, at the bottom we’ll assume that we have created a perfectly flat on-axis response with a crossover. The horizontal off-axis response shown in red, however, is not flat: because of the different off-axis outputs of the woofer and tweeter near the crossover, the combined off-axis response has a pronounced dip in the response below the crossover frequency.

Figure 1. Typical off-axis response of a two-way loudspeaker

This is fairly typical behavior for a two-way loudspeaker, and can be seen in numerous frequency response measurements posted online. See, for example, the response plots made by the Canadian NRC of the Thiel CS1.6, Seas’ measurements of the Mimir kit, the measurements on Stereophile of the Proac Response Two, and so on. (See also this explanation from Stereophile). This is not to criticise those loudspeakers, but to point out that it’s a common trade-off made for a two-way loudspeaker.

Why would we care how a speaker measures anywhere but on-axis (assuming that the speaker is pointed at the listener)? Because what you hear when you listen to a speaker in a room is not just the direct sound from the speaker, but also the sound created by reflections within the room. In Chapter 18 of Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms, Floyd Toole explains that in blind listening tests the quality rating of a loudspeaker is strongly correlated to three factors:

• Flat on-axis response
• Smoothly-varying power response
• Lower -10 dB extension frequency

The power response is the acoustic output of the loudspeaker integrated over a sphere with the speaker at its center. That is, it is the frequency response of the total sound radiated into the room, regardless of direction. (See Note 1 below.) And a smooth horizontal off-axis response is a significant factor in achieving a smooth power response. If, as illustrated in Figure 2 below, the dispersion (see Note 2 below) of the tweeter at the lower end of its range is deliberately limited so that its off-axis response is reduced at the crossover frequency, the off-axis response through the crossover region is now smoothly decreasing. (As an aside: a benefit of controlling tweeter directivity is that the off-axis response at the high end is often smoother as well.)

Figure 2. Off-axis response of a two-way loudspeaker with controlled directivity

There are other design factors that affect the power response. One is the need for baffle-step compensation for a small speaker (with typical in-room placement). Another is the fact that the two drivers will create vertical lobing around the crossover region. (See Note 3 below.) The nature of this lobing depends on the specifics of the crossover.

Driver selection

I decided early on that I wanted controlled directivity – as described above – to be a design goal of the Mini Convertible. One approach, exemplified by the Econowave family of DIY speakers, uses a compression driver combined with a horn or waveguide to limit tweeter dispersion throughout its range, typically to a 90 degree arc (measured at the -6 dB points). A fairly large (12″ or 15″) woofer is used so that its dispersion narrows to 90 degrees to match the tweeter at the crossover frequency. This is also the approach taken in Duke LeJeune’s Controlled-Pattern Offset Bipole.

In this project, I’ve taken a different route, choosing a tweeter that has relatively wide but still controlled dispersion, and a woofer that is small enough to match this tweeter at the crossover. This enables the speaker to meet the goal of smoothly-varying power response, but in a very compact size. The tweeter had to be an off-the-shelf unit – something like the custom-machined waveguide used in the Vapor Audio Aurora, for example, would not be feasible for a DIY project. There are not very many suitable candidates, but fortunately Seas of Norway makes one, the 27TBCD/GB-DXT, readily available at a very reasonable price.

Choosing a woofer is very much a matter of choosing amongst compromises. There are a vast array of choices not just in woofer size but also related to cone material, frequency response, sensitivity/low-end trade-offs, the woofer parameters that govern the type of box possible, and of course cost and quality. As a very general rule, smaller woofers have lower sensitivity, less low bass, and lower maximum output than larger woofers, but larger woofers start “beaming” at a lower frequency and require larger boxes. In the end, the woofer I chose for this speaker is the Seas U16RCY/P, a “6 inch” (99 cm²) woofer in a compact frame, which to my mind hits the “sweet spot” in terms of the various parameters including cost.

In a sealed box, f3 of this woofer is around 80 Hz, making it ideal for crossing to a subwoofer or for use in a modest HT system. Or, a Linkwitz transform in the amp’s DSP can be used to drop the f3 for use in small rooms or on a bookshelf, subject to power and excursion limitations. In a ported box, f3 will be around 40-45 Hz, subject to enclosure volume and port tuning. (Note: the f3’s given are from simulation for an “anechoic” response – actual in-room responses will likely be a little lower.)

Cabinet concept

One of the dilemmas when building a loudspeaker is whether to make it sealed or ported. In general, a sealed speaker will roll off higher but have lower group delay. For this project, I decided to come up with a design that can be either. This is illustrated in the diagram below, and is the reason for the “Convertible” part of the speaker’s name.

The sealed version is a compact monitor, with the plate amp mounted on the back in its own sub-enclosure to isolate it from vibration within the cabinet. This is shown at the left of the diagram. The base plate of the monitor can be removed and replaced with a stand, as shown at the right. This stand is hollow – thus making the cabinet larger – and has a port near the floor. Hey presto! A ported floor-standing loudspeaker.

The size of the monitor is 198 x 326 x 300 mm (width x height x depth), including the base plate. The ported stand is a little over 600 mm tall, giving a total height for the floor-standing version of around 950 mm.

A prototype loudspeaker

The photographs below show the first prototype loudspeaker. The front edges of the enclosure are cut at 45 degrees to help reduce diffraction effects from the edges of the baffle. The baffles are not glued on, but held with screws so I can experiment with different baffle edge treatments and positioning of the tweeter. Since the prototype is for making measurements and ironing out kinks in the construction plans, I made it from a quarter-sheet of “marine ply” from the local big-box hardware store, but intend later to construct another pair from good quality Baltic Birch ply.

Preliminary equalization and crossover

I performed preliminary measurements of the speaker outside, with the speaker elevated. There was some environmental noise, and a strong reflection off the ground at slightly over 5 ms causing noticeable notches in the measurements, particularly at 300, 500, and 700 Hz. The off-axis responses are all cut off at 200 Hz because of the noise, and I’ve applied 1/6-octave smoothing to the graphs. But for now, this is adequate to assess the design goal of smooth off-axis response.

Figure 3 shows the measured response of the woofer in the above enclosure. At the top in blue is the response with no equalization, below it in red is the response after applying EQ, and then the horizontal off-axis responses at 15, 30, 45, 60, 75 and 90 degrees. As can be seen, the off-axis response of the woofer decreases smoothly up to around 2800 Hz, from where it drops more sharply, suggesting this as the upper frequency limit for a crossover (bearing in mind the considerations about off-axis response above).

Figure 3. Woofer response before equalization and after at 0, 15, 30, 45, 60, 75, 90 degrees

The woofer EQ was fairly straightforward, with the largest component being a 6 dB shelving filter for baffle-step compensation. (This will most likely be reduced to 3-4 dB for in-room use.) The tweeter equalization is a little trickier. While the tweeter itself should give a reasonably well-controlled off-axis response, the baffle conspires against this, as sound at tweeter frequencies diffracts at the edges of the baffle and causes ripples in the response. This occurs even with this tweeter and the chamfered edges, and is easily visible in the measurements. It can also be predicted or confirmed with the use of simulators such as The Edge and the Baffle Diffraction Simulator.

Figure 4 shows the tweeter response at 0, 15, 30, 45, 60, 75 and 90 degrees, without any equalization. While the off-axis curves (30 degrees and above) change fairly smoothly, the on-axis curve has some noticeable ripples – in particular, a peak above 2 kHz and a dip at 3 kHz. This raises the question of exactly which curve to optimize the equalization for: if we make the on-axis response flat, then the off-axis response will tend to have a bump at 3 kHz; if we make the off-axis response flat (to optimize the power response), then the on-axis response will have a dip at 3 kHz.

Figure 4. Tweeter response before equalization at 0, 15, 30, 45, 60, 75, 90 degrees

I decided to split the difference and equalize for the average of the on-axis and 30-degree measurements up to about 10 kHz, and see what happened. Figure 5 shows the result of this equalization, on-axis and horizontally at 15, 30, 45, 60, 75 and 90 degrees. The off-axis curves vary quite smoothly, and while the on-axis curve has some lumps in it, it’s still within a 4 dB window.

Figure 5. Tweeter response after equalization at 0, 15, 30, 45, 60, 75, 90 degrees

Can the baffle be improved or altered so that we don’t have to make this compromise? There are a number of methods used to address baffle diffraction, the best being the use of a curved baffle or a large rounded edge. We don’t really have room for that here and it’s difficult to do in a home workshop. Another is to offset the tweeter slightly from the center of the baffle, so that the diffraction effects are spread in frequency; albeit at the cost or inconvenience (for measurement and equalization) of asymmetric polar responses to the left and right sides of the speaker. And another is to put wool felt on the baffle to absorb the sound wave traveling along the baffle surface.

I’ll explore some of these at a future time. For now, let’s implement the prototype crossover! Figure 6 shows the distortion measurements of the tweeter with equalization in place. The SPL here is not high, but based purely on the distortion level, the plots suggest that the tweeter will operate well down to about 1500 Hz, so we can consider this as the lower limit for the crossover frequency.

Figure 6. Distortion measurement of tweeter with equalization

Comparing Figures 3 and 5, the off-axis plots suggest that anywhere between the 1500 and 2800 Hz limits mentioned above will give an acceptable match, with around 1700 Hz looking like the optimum. At this point, I’m reluctant to “push” the tweeter too hard, so I decided on 2 kHz for this initial version. With the microphone positioned 1 m from the drivers and vertically centered between them, I measured a difference of 0.07 ms in the impulse arrival time, so this was added as a delay to the tweeter channel. The tweeter channel also needed several dB of attenuation to match the woofer level.

Setting a fourth-order Linkwitz-Riley crossover at 2 kHz resulted in the measured response shown in Figure 7 below. These curves have 1/3-octave smoothing applied to better show the trend in the off-axis response. Overall – and with regard to the goal of smoothly-varying power response – this is looking quite good already, so it will be interesting to see if the baffle tweaks discussed above can improve on it.

Figure 7. Combined response with LR4 crossover at 2 kHz, at 0, 15, 30, 45, 60, 75 and 90 degrees

Programming the DSP

Programming the equalization curves into the miniDSP plate amp is simplicity itself. The interface program or “plugin” (currently Windows-only) will immediately be familiar to anyone who has used miniDSP products before:

A potential hiccup is that the connection to the amp is via Ethernet and not USB, so outdoor measurements and equalization may necessitate locating a long Ethernet cable. The advantage in a typical stereo setup, though, is that you don’t have to swap cables as you do with USB in order to switch between amps – just click on the amp you want to configure in the control panel:

Programming the parametric equalizers for each output channel can be done either by setting each filter manually, or by importing a file generated by the REW auto-EQ function. I used the REW auto-EQ with a bit of manual tweaking to generate correction curves for both drivers. The woofer EQ is straightforward and consists mostly of the baffle-step compensation, plus a few mild notch filters. (Note: the notch just below 200 Hz is a bit suspicious, and is probably compensating for the ground reflection mentioned above. I expect the final EQ will not have this notch.)

The EQ for the tweeter implements the correction discussed above:

Concluding remarks

You may be wondering at this point how DSP and controlling directivity are related. The answer is that they aren’t, I just wanted controlled directivity to be a design goal of this speaker. The directivity of a speaker is determined by physical properties – driver cone/dome shape and size, driver faceplate or waveguide, baffle size and shape, and so on. The advantage of DSP is the ability it has to flexibly assert overall control over the frequency response. It enables different crossovers to be easily auditioned, and it enables the speaker’s response to be readily optimized for (for example) on-axis response or a few degrees off-axis.

Additional notes

1. The power response would require hundreds of measurements to measure directly, and so is typically computed mathematically. Toole also provides related responses that can be measured more easily. For example, the listening window response is the average of the nine frequency response measurements at angles of +/- 30 degrees horizontally and +/- 10 degrees vertically. Another, the early reflections curve, is an average of 26 measurements at angles that mimic the directions of radiation that will result in first reflections in a typical listening room. Toole shows that the early reflections curve is in fact a good predictor of a loudspeaker’s measured in-room response.
2. The terms “dispersion” and “directivity” are often used almost interchangeably, as in “controlled dispersion” and “controlled directivity”. They tend to have opposite meanings, with “wide dispersion” and “low directivity” meaning roughly the same thing. I’ve not found a formal definition of “dispersion” as it relates to loudspeakers, but it tends to be used to describe the pattern of or variation in acoustic radiation, sometimes in a general sense (as in “the plot shows the dispersion pattern of the speaker”) and sometimes more specifically as the angle between the -6 dB points of a beam. In contrast, the directivity index of a speaker is defined precisely as the difference (in dB) between the on-axis response and the power response, or (Toole p379) as the difference between the listening window response and the power response.
3. The term “lobing” refers to the formation of “lobes” in the acoustic response, whereby some angles have full power radiated and some have none. It is an unavoidable consequence of the use of multiple sound sources. See Figures 1 and 2 in this Rane app note for examples of vertical lobing. Lobing also occurs in open baffle speakers because of the interference effects of the acoustic radiation from the front and rear of the baffle.

Acknowledgements

HifiZine gratefully acknowledges the support of the following companies and individuals:

• miniDSP, for providing the amplifiers used in this loudspeaker project.
• Seas of Norway, for providing the loudspeaker drivers used in this project.
• Duke LeJeune (AudioKinesis), Ammar Jadusingh (Soundfield Audio), and Patrick Dillon, for reviewing and commenting on this article prior to publication.