The Black Dahlia
Dick Olsher offers a Do-It-Yourself Loudspeaker Kit
(Originally published in Stereophile Magazine, November 1990)
Why another two-way kit? Has DO lost confidence in the original Dahlia design or in the later update—the Dahlia-Debra? Far from it. It's been about four years since the original Dahlia design has appeared in print. Over these years, it became clear to me that there was much design scope left in even a "simple" two-way design. The Black Dahlia is an attempt to master several little-explored possibilities of such designs. It bears almost no relationship to my earlier designs, and represents a sophisticated, computer-aided design effort, of a minimonitor with excellent power handling and a natural tonal balance.
As most of you know, my wife Lesley is the featured singer of Platinum & Gold—a local Jazz Trio. I have used the Dahlia-Debra for mild sound-reinforcement at Platinum & Gold concerts. As long as the venue was a small hall or club, the results were satisfactory. However, there were times when the Dahlias were pushed hard for too long causing the Audax woofers to fail catastrophically. What Lesley wanted was improved power-handling in a smaller package yet for increased portability.
Because the speakers are normally stand-mounted during performances, one of my goals was to achieve a full-bodied tonal balance under such freestanding conditions. There's an inherent conflict between imaging and tonal balance. An easy way of beefing up the lower mids, upper bass and mid bass regions is by placing the speaker flush against a wall. This effectively increases the size of the front baffle and allows the loudspeaker to continue radiating into half-space through the lower octaves. Imaging suffers, however, as early wall reflections interfere with the direct sound. Moving the speaker away from the wall improves imaging by reducing the number and intensity of early room reflections. Away from the security blanket of a room boundary the speaker encounters what has been dubbed "diffraction loss." At frequencies whose half wavelength is larger than the effective diameter of the front baffle, the sound wraps around the front baffle. The radiation pattern changes from half space to full space with an attendant drop in on-axis sensitivity.
There is nothing mysterious about this: the same energy output is being distributed over a larger chunk of space. This is the rationale for putting a reflector behind a light source. Light that would otherwise be radiated backward and to the sides is reflected or concentrated in the forward direction resulting in a brighter beam. At much lower audio frequencies, the wavelength becomes long enough to encounter room boundaries, which again reinforce the direct radiation. As a result the SPL at the listening seat begins to rise in the deep bass. The sum total of these effects is a frequency response droop typically in the range from 200 to 300 Hz. This is right smack in the power range of an orchestra, a range rich in fundamentals. Losses here rob the music of weight and body giving the sound a lean and emaciated character. I've always appreciated a minimonitor's imaging capabilities. A wide and stable soundstage is high on my list of priorities. But so is a convincing tonal balance that lets a cello or a piano speak with full authority. The older I get, the closer aligned I've become to J. Gordon Holt's long-standing love affair with proper tonality. Gordon, for as long as I've known him, has taken a music lover's approach to reproduced music. A speaker had to reproduce the crux of the orchestra correctly; all else was of secondary importance. The "blat" of a tuba had to be just right or Gordon felt cheated. Being denied the experience of a concert hall balance was his ultimate disappointment. To paraphrase Guru Gordon: "Where's the beef?" Well, I'm raising the skull and crossbones flag right now. The Black Dahlia is all about tonal realism; the timid among you should make an early exit right about now. One of my major design goals was to properly flesh out the lower mids while maintaining a freestanding geometry.
There are three basic ways to do this in a two-way loudspeaker. One possibility is to use a dual voice-coil woofer with one coil operating over the entire passband of the woofer and use the second coil to preferentially fill-in the diffraction loss region. Another way is to equalize the woofer's response to compensate for the loss. This is difficult to do passively. It means that the response of the woofer's low-pass filter network has to be distorted to enhance output through the diffraction loss region. This may either screw up the woofer's response in the upper mids or by itself provide insufficient compensation. Finally, and this is the method I opted for, it is possible to use passive equalization in combination with a target SPL response that intersects the diffraction loss valley. This allows greater flexibility in restoring balance between the lower and upper mids, but at the expense of lower sensitivity because output through the upper range of the woofer is suppressed. The Black Dahlia's target SPL of 82 dB is a full 5 dB below the nominal 87 dB sensitivity rating of the woofer.
Another artifact of diffraction loss, is the unnatural emphasis of upper register detail in speakers so afflicted. Lightening the lower mids serves to unmask low-level detail that is normally obscured. Yes, it is possible for minimonitors to have too much detail or an etched analytical sort of presentation. Typically, the problem is exacerbated by a rising high end that further exaggerates treble transients and etches upper midrange detail. Lean lower mids together with a rising treble response is the perfect recipe for a light and airy little speaker with lots of expressly spelled out detail that so many audiophiles love. This is NOT what the Black Dahlia is all about. I've gone to extreme lengths to control the lower to upper midrange balance and the midrange to treble balance. With the hindsight of this project, I can tell you that tonal balance is an essential springboard for a natural sounding loudspeaker.
I expect that both Just Speakers and Madisound will offer the kit on the strength of the several hundred Dahlias they have sold to date and as a service to the home constructor. My sole compensation is the joy and satisfaction of creating a minimonitor more responsive to the experience of live music, and, in the process pushing the art forward.
Choice of Drivers
One of the nice things about home construction is that one need not be bound by commercial constraints of profit margins because there are no middlemen. Selection of expensive drivers may be made without worries of being able to market an expensive mini box.
To keep box size relatively small requires a small woofer with a moderate equivalent volume. After examining the specifications of a host of candidates, I settled on the Dynaudio 17W-75-XL (8 ohm version). This 6.5-inch woofer is a new design with a nearly ideal total Q for bass reflex applications. Its rated power handling is outstanding for a driver of this size being 130 watts long-term and 1000 watts for 10 ms transients. A 3-inch aluminum voice coil drives a shallow one-piece molded plastic cone. The pole piece is vented for better power handling and the high frequency rolloff is well damped.
The selection process for the tweeter was much easier. Leaf tweeters cannot handle much power and would have to be crossed over well above the comfort zone of the woofer. As a family, I avoid soft domes. Tweeters are subjected to large accelerations, and unless they are very rigid the radiating surface will break-up and resonate at a fairly low frequency. The design philosophy behind soft domes appears to be to let them break-up and then try to dampen the resonances as gracefully as possible. The best soft domes are not that bad. They obscure and smear treble transients, but at least they possess decent long-term listenability and don't actively irritate by sizzling and spitting treble information at you. Hard-domed tweeters usually break up in the lower treble and when they do, it's time to run for cover. In general, they are not as forgiving as soft domes, being less well damped. So when they begin to fall apart, the resonances have no place to hide.
This sort of tweeter is hazardous to my health; prolonged exposure has driven me screaming from the room. That leaves metal domes as a possibility. The MB Electronics 1-inch titanium dome is one that I'm intimately familiar and still comfortable with. Its first break-up mode is at 26 kHz. Transients are fast and detailed, but in its stock form the tweeter is a bit too alive with a slight metallic aftertaste.
To minimize the MB's sonic signature, I modify it as follows. First, using a pair of pliers remove the plastic grill from the face plate and discard it. For the next step you'll need to purchase a spray can of a fixative with the trade name of Tuffilm, available at art supply houses. This fixative is normally used to apply a matte coating to paintings, but in this application it serves to dampen out low-level resonances in the titanium. Mask the surround of the dome with say masking tape to protect it from the spray. Then apply a 1-second burst of the coating, wait 5 minutes for the stuff to dry and repeat the application. After another 5 minutes, repeat the application for a third and final time. The treated tweeter visually appears duller, and sounds cleaner, although its measured frequency response is no different from that of the stock version.
The MB titanium tweeter also has a rising high-frequency response on axis, which has to be dealt with in the crossover network. Unless this is equalized out, its sound is entirely too hot. Although not without problems, this tweeter really shines once its problems are catered to. Its speed and detailing are worth the effort.
The Crossover Network
In the frequency domain, the ideal filter response would possess rectangular amplitude versus frequency response and a constant group delay. There would be no attenuation at all in the pass band, and at the cutoff frequency the response would drop like a rock with no transition band to infinite attenuation in the stop band. And it would really be nice to do this with a constant group delay (which implies a linear phase characteristic). A constant group delay means that all of the frequencies that make up a transient waveform will be delayed the same amount while passing through the filter. If the various frequencies are not delayed equally, waveform distortion will occur at the output; the output and input waveforms will not be identical.
Unfortunately, Mother Nature is not so kind. With a conventional LC network it is only possible to approximate either a frequency-selective amplitude response or a flat group delay. These two parameters turn out to be mutually exclusive. The steeper the descent to the stop band, the worse is the group delay, especially in the transition band. The well-known Butterworth response offers a "maximally flat" passband with reasonably steep decent into the stop band for say a fourth order filter. The steepest decent into the stopband of any all-pole filter is given by the Chebyshev response, but at the expense of introducing magnitude ripple in the passband. A "maximally flat delay" may be had with the Bessel (also known as Thomson) family of filters, but at the expense of much poorer selectivity than a comparable Butterworth type. There are even families of transitional filters. An example of the latter would be the Thomson-Butterworth type whose performance is intermediate between that of a Butterworth and a Bessel type.
Another type of response that should be mentioned is the Gaussian response. If you want perfect behavior in the time domain with no ringing whatsoever on a step or impulse response than this is the filter for you. The descent into the stop band is gradual and slow. It can be shown mathematically that a filter whose rolloff is steeper than a Gaussian, will produce some ringing. Thus, even a Bessel or our ideal filter with a perfectly linear phase characteristic will produce ringing because its rate of attenuation is steeper than a Gaussian.
Confronted with such a wide choice of filters, it is not surprising that there is no clear-cut consensus on what is the optimum electrical filter for loudspeakers. In recent years, however, several trends or schools of thought appear to have crystallized.
Richard Small, of Thiele-Small parameter fame, was one of the very first to address this issue. Around 1970 he advocated the use of constant-voltage filters, which in essence require 6 dB/octave passive networks. For ideal loudspeakers this would indeed be the optimum electrical network. Such a network is not only "transient-perfect" but also satisfies the condition that the vector sum of voltage transfer functions for the high and low pass sections is unity. It follows that in the ideal situation, the combined SPLs of the two drivers are flat at all frequencies.
But what are the assumptions underlying this ideal loudspeaker? The first one is that the frequency and phase response of the drivers is identical in the crossover region. That is to say that the tweeter and the woofer are identical in the crossover region. That's not that difficult to achieve in practice, providing one is careful with the choice of crossover points. Marshall Leach tells a story about a three-way kit, popular with students at Georgia Tech, which used first order networks. He became involved in the design of the enclosure, and after the system was built the measured frequency response was found to have a severe dip in the crossover region between the woofer and midrange. At first, it was suspected that one of the drivers was connected to the crossover network with a reversed polarity or "out of phase." After the box was opened, it was found that the drivers were properly connected in phase. However, by reversing the phase of the midrange driver, the dip in the crossover region could be eliminated. This puzzling problem was resolved after a study of the phase response of the drivers. The crossover point was at 500 Hz, a full octave above the low-frequency resonance of the midrange. Yet, the phase lead in the acoustic response of the midrange caused by its LF resonance was the primary cause for the destructive interference of the drivers at 500 Hz.
The second assumption is that both drivers radiate essentially from the same point in space. Otherwise, phase differences are introduced by the path length differences, which become significant at crossover frequencies around 2 to 3 kHz. Small freely assumed that the drivers were mounted very close together and acknowledged that if large driver spacings are employed "there is no ideal solution to the crossover design problem." Anticipating Linkwitz to some extent he went on to offer the following advice: "In Practice, some driver spacing is unavoidable, and the resulting path length difference introduces unwanted phase shift into the acoustic addition of driver outputs. The most severe effects occur for driving signals of equal amplitude and nearly 180-degrees phase difference, because the addition in this case is very sensitive to small additional phase shifts. Any choice in the design of crossover networks should favor a solution which gives the least phase difference between outputs when the amplitudes are comparable."
The most serious defect of first order networks is that they require drivers with useful frequency ranges that overlap by about four octaves (two octaves on either side of the crossover point). There aren't many drivers out there that meet this requirement, and for a two-way design this becomes a major headache. A couple of years later, Small backed off his original first order network recommendations by considering distortion products. He pointed out that because the excursion of a driver rises at the rate of 12 dB per octave with decreasing frequency until its resonant frequency is reached, the cutoff rate of the tweeter network should be at least 12 dB per octave. This ensures that tweeter excursion, along with distortion, is well controlled. Running a tweeter fairly close to its LF resonance with a first order high-pass network has to be a classic blunder. I recollect a case several years ago where a manufacturer complained bitterly about one of my reviews. I accused his product, which featured such a tweeter/crossover combination, of possessing a gritty and harsh treble quality, but his tweeter was the same drive unit employed in a design we liked very much. He wanted to know how could Stereophile both dislike and praise the same tweeter? The answer, of course, is that the sound of a tweeter will be very dependent on how and where it is crossed over to the other drive units.
Not to be outdone, Thiele entered the fray in 1975 with his own set of optimum passive network recommendations. Implicitly assuming an ideal loudspeaker, he concluded that passive networks should be made up of complimentary pairs of odd-order Butterworth filters, with the individual drivers connected in the sense that produced the lesser phase delay error. For first and fifth order networks that means in phase, and out of phase for a third order network. His preference seemed to be for a third order network. He pointed out that such a network offers an "all-pass" response. That is, the summed amplitude response of the two filters is constant across the entire frequency spectrum but the phase delay varies with frequency. Because these type of networks present a constant resistance to its input, the resulting power response is constant with frequency, and they are known as "constant resistance" type.
How did Thiele feel then about the effect of non-constant group delay of such a network on transient response? He said, "...audible errors in transient response are much more likely to result from narrow peaks or valleys in the amplitude response." These are easily passed over in response plots, especially since they are readily ascribed, sometimes rightly sometimes wrongly, to the acoustical environment in which loudspeaker measurements are often, crudely, taken."
A major breakthrough in the art arrived in 1976 with the publication of Sigfried Linkwitz's network analysis for noncoincident drivers. For loudspeakers, where the distance between drivers is comparable to the wavelength at the crossover frequency, the phase shifts caused by the difference in path lengths to a point on the design axis can cause serious interference effects resulting in a nonsymmetrical radiation pattern. The interference between drivers will be strongest at the crossover frequency because it is here that both drivers contribute equal-amplitude signals. The radiation pattern at frequencies much higher or lower than the crossover point is determined only by the driver active in that range. Driver spacing is a problem for most loudspeakers, especially at the crossover frequency between the midrange and tweeter. For example, a third-order Butterworth network under such circumstances will produce a frequency-dependent tilt of the main radiation lobe below the listening axis, so that the acoustic axis of the loudspeaker moves as frequency changes. This is most undesirable as it significantly colors the frequency range around the crossover point. To accommodate real world loudspeakers, Linkwitz identified three desirable performance criteria for crossover networks. First, the phase difference between the tweeter and midrange/woofer signals at the crossover frequency should be zero to avoid tilting the radiation pattern. The amplitude of the low and high pass sections should be -6 dB at the crossover point so that the sum of the two is unity without peaking. And finally, the phase difference between the drivers should be the same at all frequencies to preserve the symmetry of the radiation pattern above and below the crossover frequency. Linkwitz credits Riley for pointing out that the cascade of two identical Butterworth filters will meet these criteria. Peter Garde generalized these results in 1979 to show that any all-pass, even-order crossover, must correspond to high and low-pass filters formed from two identical Butterworth filters in cascade.
It is important to keep in mind that although a Linkwitz-Riley (L-R) network is in phase around the crossover point, it exhibits a nonlinear phase response. Therefore, while an L-R network has a flat magnitude response, it is not "transient-perfect." However, providing that the phase delay variation is reasonably smooth, as it is for second and fourth order networks, transient ringing and waveform distortion should be subjectively benign.
Unfortunately, there are practical problems that stand in the way of realizing a perfect marriage between drivers and crossover networks. Drivers are very much like children; they're often not very well behaved. Their impedance response is non-flat, as is their pass band frequency response. The former is reasonably easy to correct with impedance equalization networks. However, the latter is difficult to deal with without computer-aided optimization techniques. Computer-aided design of crossover networks became popular in the late 70s, at least with some large loudspeaker manufacturers. Because these programs ran on mini or mainframe computers, and expensive test equipment was required for the input data, this technique was out of reach for the home constructor. Around 1983 Peter Schuck in Canada developed a CAD method using a fast algorithm together with clever simplifying assumptions that made optimized network design possible on a personal computer. The core of the program is the optimization routine. The target response for a filter/driver is compared to the calculated response and the network components are adjusted to minimize the SPL response error. This work led to the evolution of at least a couple of commercial PC-based, software packages for optimizing loudspeaker network design.
Having such software available to me meant that I could explore several network design possibilities without having to actually go through the pain and expense of building anything. One of my design objectives was to achieve a uniform or symmetrical polar response within a 20-degree cone centered on the listening axis. This listening window was defined by choosing five design points: one on the listening axis, two points on a horizontal plane at -10 and +10 degrees from the listening axis, and two points on a vertical plane at -10 and +10 degrees to the listening axis. For the Black Dahlia, the listening or design axis was fixed as line perpendicular to the front baffle, between the tweeter and woofer. The program was required to minimize the overall SPL error using all design points in relation to the target response. I was willing to trade some on-axis response flatness for enhanced polar response within the listening window. Too often, a loudspeaker is designed to sum flat at a single point in space. And by moving a measuring mike around the front baffle, a single point can usually be found where the amplitude response is close to perfection. But what happens when you move your head slightly off this magical point? Does the response change? If it does, you have entered the twilight zone. Expect not only the imaging to suffer, but also considerable coloration as you are subjected to what might typically be a several-dB magnitude peak or dip. So you either keep your head in a clamp or return to my notion of a listening window. At a distance of two meters from the front baffle, the diameter of the sweet spot is about 70.5 cm or 2.3 feet. So even if your head is not exactly centered on the listening axis, the head and shoulders will be comfortably within the sweet spot. Even if one is exposed only to the direct sound from a loudspeaker, reflections and diffraction from the pinnae, head and shoulders determine the soundfield inside the ear. The in-ear response to the external stimulus is a complex summation of this acoustic energy. Thus, it is proper for a designer to try and maintain as uniform coverage of the head and shoulders as possible.
Because I was determined to avoid the use of a slanted front baffle in order to align the acoustic centers of the drivers, I decided to investigate a recent technique advocated by Hillerich (see the September 1989 issue of the JAES). In the Black Dahlia, the acoustic center of tweeter is about an inch in front of that of the woofer, so that the tweeter leads the woofer by about 73 microseconds. At a crossover frequency of 3 kHz, this delay represents 22% of the period and can cause serious lobing errors. Following Hillerich's method, we would use say a second order low-pass filter on the woofer, and a fourth-order high-pass filter for the tweeter. The idea is to use the greater group delay of the higher order filter to compensate for the time lead of the tweeter. According to Hillerich, the conditions of local phase matching and complementary transfer functions which are necessary for flat summed magnitude response and good polar behavior can only be fulfilled approximately by this approach. But Hillerich feels that this should be good enough in practice. My computer simulations failed to support that view. I was able to achieve a very flat magnitude response at only a single design point, and consistently ended up with a very poor polar response within my desired listening window. Certainly, I'm in no position to generalize about the merit of Hillerich's approach, but with these particular drivers I could not achieve even a semblance of decent polar response, and I was forced to abort this approach.
Next, I tried an L-R network, and even without a sloping front baffle, I was able to achieve a very decent polar response. The L-R appeared to be a safe bet, but I decided to try a couple of other possibilities before making a final decision. And I'm sure glad I did. The real surprise turned out to be the Legendre network.
The what? Around 1958 Papoulis and Fukada independently found the answer to the following question: which filter offers the highest rate of attenuation without introducing ripple in the passband? That is, under the condition of a monotonically decreasing response, which filter produces the sharpest attenuation cutoff? The answer turned out to be a filter whose transfer function contained the Legendre polynomial of the first kind. The Chebyshev filter has better cutoff characteristics than a Butterworth. But the Chebyshev response is far from monotonic; as it introduces ripples in the passband amplitude response. Under the constraint of no ripples, the Chebyshev response degenerates into that of a Butterworth. The Legendre filter's amplitude cutoff, on the other hand, is intermediate between that of a Butterworth and a Chebyshev while maintaining a monotonic amplitude response throughout the pass and stop bands. In terms of cutoff sharpness, the Legendre filter approximates that of a Chebyshev filter with a 0.1 dB ripple. The transient behavior of the Legendre filter is slightly better than that of the 0.1 dB Chebyshev filter, but not as good as that of a similar order Butterworth. As was pointed out before, the sharper the attenuation cutoff becomes, the worse the group delay. So the Legendre filter offers much better selectivity than the corresponding Butterworth filter, without introducing response irregularities in the passband. Another practical advantage of the Legendre is that generally the required inductors are smaller in value.
The computer simulations I performed, where the crossover network was loaded by the actual impedances of the drivers, showed that within a 20-degree listening window, the polar response of a Legendre network was superior to that of a L-R network. The essential difference was along the vertical axis of the baffle, where the Legendre network produced less variation from -10 degrees to +10 degrees. At larger angles, the L-R network's polar response eclipsed that of the Legendre. It is also important to note that these results are very likely not universal, and apply specifically to these particular drivers. But nonetheless, these findings are important enough to warrant increased use of the Legendre network which has languished in obscurity till now.
Much of the crossover design work for the Black Dahlia was accomplished using CALSOD, which is an acronym for Computer-Aided Loudspeaker System Optimization and Design. This is a commercial software package designed by Witold Waldman of Audiosoft in Australia. There are two versions of CALSOD available. The professional version, CALSOD 2.00, costs AUD$349, while the standard version, CALSOD 1.20, is priced at AUD$99. These prices do include airmail postage. However, Audiosoft has recently entered into a distribution agreement with Audio Amateur Publications. Audio Amateur is now selling CALSOD 1.20 for $65, postpaid in the US, (add $5 for delivery outside the USA) through their Old Colony Sound Lab Company. The professional version of CALSOD is only available direct from Audiosoft by mail order.
The program runs on IBM PC/XT and compatible computers with at least 512K bytes of RAM and a graphics card. All of the common graphics cards are automatically detected, including CGA, EGA, VGA, and Hercules cards. An 8087 math coprocessor is supported, and is highly recommended as it greatly speeds up the calculations. In the initial version of CALSOD I received, screen graphics dumps could only be made to Epson-compatible printers. After I informed Mr. Waldman of the problem I was having with my IBM Proprinter II, he sent me an E-series version of CALSOD to replace the D-series versions in my possession. The latter version worked just fine with my IBM printer. Mr. Waldman promises that the next version of CALSOD will have printer support for a much greater variety of printers, including HP laser printers and 24-pin dot matrix printers.
After the user models the impedance and sound pressure responses of the individual drivers using curve-fitting techniques, a passive crossover network is specified with up to a maximum of 60 components. Individual driver/filter combinations can then be optimized to a particular target response. Standard filter target functions include Butterworth, L-R, and constant voltage designs. It is also possible to include user-defined transfer functions if desired. However, the real potency of CALSOD lies in its ability to optimize the summed acoustic response of the entire driver array to a particular target response—that normally being a flat sound pressure response on the design axis. Up to four different drivers can be used to simulate up to a seven-driver loudspeaker. The geometry of the driver array may be modeled pretty realistically by specifying the acoustic center of each driver in relation to the plane of the front baffle. The transfer functions of the drivers in combination with that of the crossover network are used to calculate the summed acoustic response at the design point. The network component values and crossover point are then allowed to shift in order to achieve the closest match to the target response. There are plenty of graphical displays. At each stage in the simulation, the user may inspect the magnitude and phase of the summed sound pressure response. Other displays include the impedance of each driver, the input impedance of the crossover network and driver combination, the response of each filter when it is loaded by its driver, and the filtered and unfiltered sound pressure response of each driver.
CALSOD also allows you to model bass alignments for closed-box, vented-box, passive-radiator, and filter-assisted designs using Small-Thiele parameters. Thus, it is possible to develop a complete simulation of the magnitude and phase response of a multi-way loudspeaker system.
There is also a utility program for designing air-cored inductors on the data file disk that comes with CALSOD 2.00. A simpler version of this program (called inductor) also exists on the \UTILITY subdirectory of the program disk for CALSOD 1.20. For a given inductance this program calculates the DC resistance of the inductor, required coil buildup, number of turns of wire required, number of coil layers required, and the length of wire needed. The program allows 10% for the enamel insulation in the coil buildup. I have not tried building coils using this program, so I can't tell you how close to the mark it is. But its ability to predict the DC resistance of a coil is pretty accurate, so that this feature should prove quite useful during the design stage in estimating DCR losses in the crossover network coils.
All of the above capabilities are incorporated into the standard edition of CALSOD. There are two floppy disks in the package. One disk contains the program and associated data files, while the other disk contains a copy of the user manual. At $65 it is priced to appeal to the home constructor. All of my experience with CALSOD relates to the professional version, which includes not only an outstanding 180-page user manual, but also some additional features. The most important of which is the ability to specify up to five design axes in the optimization. The crossover components are automatically varied to achieve as uniform a response as possible within the listening window defined by these axes. Using CALSOD 1.20 you could still recalculate the response at a number of other axes—one axis at a time—in order to observe the polar response of the loudspeaker. But you would lack the capability (except for trial and error) of automatically optimizing the polar response within a particular listening window.
Another feature of the professional version is the ability to model the off-axis radiation pattern of a driver by specifying an effective driver diameter. The model calculates the driver directivity assuming that it radiates as a circular piston. Thus, at a particular design or observation point, the program calculates the pressure response taking into account not only the path length from each driver but also the off-axis radiation pattern of each driver. This may be a useful embellishment for a crossover point in the lower midrange, but for a two-way design with a crossover frequency around 3 kHz its utility is rather doubtful. First of all, within a narrow listening window, the off-axis rolloff of each driver should be very small. Second, around 3 kHz very few woofers behave as piston radiators. This is breakup territory for many woofers. So it is not clear if such a model is a help or a hindrance at these frequencies. However, use of this model is not mandatory, as it can be omitted from the input file. I did use it, but in my estimation it did not play a material role in the optimization process for the Black Dahlia.
This is a mature and highly polished program, a product typical of what one would expect from a large software development house—rather than a small firm. It is logically laid out with a precision even Science Officer Spock would be proud of. The user's manual (the hard copy one that comes with the professional version of CALSOD) is extensive and worth its weight in gold. Installation, the structure of the program, and the input file format and all of the input modules are all very well explained. And there are plenty of design examples, proceeding from the simple toward the complex. It's just that you have to be patient and invest the necessary tutorial time before you can really get started.
Before you can do anything productive with CALSOD, you'll need to generate an input file. From CALSOD's main menu, invoke the Editor. This is a text editor whose command syntax is modeled after that of WordStar. Because I've been a WordStar user for many years, and actually like it as a word processor, I found this feature to be a major convenience. There are, however, several friends of mine who are former WordStar users, and who have found greener word-processing pastures. They now dislike WordStar sufficiently to never use it again. If you already own and have mastered another commercial word processor, you may want to use it for creating and later modifying the required CALSOD input files. Once you convert the files into standard ASCII, you should be able to import them into your CALSOD directory without any problems. But don't let me scare you away from the CALSOD Editor: it is really easy to use. There are pull-down menus that let you keep track of the various commands, so that you don't have to memorize any keystrokes. The Editor also lets you copy, print, and delete files.
The first required task is to model the impedance and sound pressure magnitude responses of the drivers. This is a pretty tedious process, which involves trial and error. First, the "experimental" data is entered. As a minimum, the required input consists of the impedance magnitude in ohms and the sound pressure level in dB. It is not necessary to input any phase information. The program can actually calculate the phase response using theoretical models. But if you have sophisticated test equipment that can provide phase information, then CALSOD can use the experimentally derived phase data. From the main menu, you read in the data file you have just created. And again from the main menu, you can graphically display the experimental points. You now have to model the impedance and SPL data. CALSOD's theoretical basis, as well as that of similar programs, is that the sound pressure magnitude response of a driver approximates that of a broadband band pass filter. Hence, the transfer function for the driver may be approximated by cascading second-order high and low pass filters. It is also well known by now that moving-coil loudspeaker drivers are essentially minimum phase throughout their operating range. This means that within its "pass band," the phase delay (phase shift divided by frequency) is small and decreasing with frequency. From the theory of the Hilbert Transform, it is also known that the attenuation of a minimum phase network uniquely specifies the phase delay. Thus, by taking the magnitude response of a driver and mathematically processing it through a Hilbert Transformer, the driver's phase delay may be predicted with fair accuracy. The greater the attenuation or rolloff, the greater is the change in phase delay.
To model the SPL data, you create a SOUND PRESSURE input module that consists of the driver sensitivity in dB, parameters for the appropriate high and low pass filters, and a series of MPEs or minimum phase equalizations. The entry for a single MPE consists of a frequency, a Q value, and then a magnitude value—either negative or positive. These MPEs allow you to model dips and peaks in the magnitude response of the driver. After the first cut at creating a model, you can overlay the experimental points with the model's curve and continue changing the model until good agreement is obtained between the two. This is an iterative process. You change the module in the input file, return to the main menu to plot the model and data points, and then return again to the input file for more changes, etc. The process is not difficult to execute, but rather time consuming. The impedance data is modeled similarly using an IMPEDANCE input module, which specifies the resonance frequency and impedance magnitude at resonance of the driver, the DC resistance and inductance of the voice coil, and the total Q of the driver. These parameters are tweaked, and MPEs are used until there's a satisfactory agreement between the model and the data. Using this model, the program then calculates the phase response of the impedance.
Audiosoft states that if acoustic measurement equipment is not available, that SPL data may be lifted from a manufacturer's spec sheet. Such a procedure is clearly a no-no. Drivers are normally measured by manufacturers on large IEC-specification baffles that bear no relationship to the actual box the driver will be used in. The proper procedure is to measure the in-box response of all of the drivers. I used my Neutrik System 3100 to measure each driver's on-axis frequency response at 1 meter and then input these data into CALSOD. This way one can account for the real-world frequency response of each driver and for the diffraction pattern generated by the particular box used in the design.
According to Peter Schuck, on whose early work CALSOD is based, measuring each driver at 2 meters from the front baffle on the main listening axis is an even better approach. This measurement location better approximates the far field conditions at the listening seat. A word of caution: do not attempt to model very narrow peaks and dips in the SPL response of the drivers. To do so is simply a waste of time. The crossover network cannot possibly correct for such irregularities in the driver's pass band. Any response glitches less than a third octave wide should be ignored. The moral of this story is to start with better drivers in the first place.
Next you add the filter network modules to the input file. Each driver's filter network is specified component by component. Resistors, capacitors, and inductors are allowed. The DCR value of each coil may also be entered. The location of each component in the circuit is specified by its node numbers. The input is always applied between nodes 0 and 1, where 0 is ground. The drivers are also specified by node locations and their XYZ coordinates on the front baffle are also entered. It's obviously helpful to first sketch out the starting network topology and number all of the nodes before you key everything into the input file. The XYZ coordinates of the drivers should correspond to their acoustic centers. Such data is very difficult to come by and generally speaking the acoustic center of a driver meanders about the physical location of the voice coil as a function of frequency. I've never seen such information in a manufacturer's spec sheet. As a reasonable first order approximation, however, one should take the acoustic center to coincide with the location of the driver's voice coil. If this is not a reasonable approximation, the resultant discrepancy between measurement and simulation around the crossover region will tell you so.
Finally, to complete the input file, a TARGET module is required. This module specifies the target sensitivity of the loudspeaker system and the design axes at which the summed acoustic response of the system is to be optimized. Normally, the target sensitivity would be a straight line. However, on occasion, a non-flat system response may be desired. For example, the designer may wish to implement a HF rolloff for the tweeter. And such a response characteristic may be specified in the target module.
If desired, a WEIGHTING module may also be inserted to emphasize the importance of a particular frequency range during the optimization. At last it is time for the games to begin! From the main menu change the optimizer parameters as appropriate, read in the input file, let the program calculate the system transfer functions, and then set the optimizer in motion. The choice of frequency range over which to optimize makes a difference, as does the choice of the initial crossover point. If the range is too narrow, the optimization may converge to a network that introduces serious response irregularities outside the range—just to gain a slightly lower SPL error within the range. I recommend an optimization range that's at least a couple of octaves wide—on either side of the crossover point. For the Black Dahlia I finally settled on a range of 70 Hz to 30 kHz, while weighting the crossover region. It is also important to try several crossover points on either side of what you might consider to be the optimum point. The optimization process carried out by the program is not infallible. It may very well converge to a local minimum when a much better global minimum exists. You may find that for a given optimization range, that out of several starting points, one may yield a much lower SPL error between the calculated system response and the target response. It is rarely necessary to run the optimizer beyond about a dozen or so iterations. When the SPL error starts to improve by less than a fraction of a dB, it is time to exit the optimizer. And don't be disappointed by a final error of 1 to 2 dB. The crossover network cannot perform miracles. And besides, with driver to driver variations typically being on the order of a dB, it makes little sense to try to make the optimization too perfect.
Also important is the particular target response chosen. In order to balance the Black Dahlia's lower and upper mids for freestanding conditions, I found it necessary to sacrifice several dB of upper midrange response. The optimum target response turned out to be 82 dB. I know that this is on the quiet side, but that's the price I had to pay for the full-bodied balance I sought.
It is now time to plot the calculated system response. It's always best to start at the beginning. Figure 1 shows the raw drivers' in-box frequency and phase response over the range of the optimization. The impedance of the individual drivers is shown in Figure 2 . For the final version of the crossover network, CALSOD's predicted filter transfer functions are shown in Figure 3. Notice the significant amount of treble rolloff introduced by the high-pass filter. Next, the calculated response of each filter when loaded by its driver is shown in Figure 4 for the main listening axis. This is a very important plot to examine following a system optimization run. Even though the overall summed acoustic response may end up quite flat, such a result may have been achieved at the expense of an undesirable crossover point (too low or too high) or perhaps through the use of too shallow a crossover. As you can see the actual crossover point is slightly above 3 kHz, which is about right for these drivers. The tweeter response is down about 30 dB at 2 kHz, which offers excellent protection from its LF resonance at 1 kHz. Another noteworthy feature is that both drivers are down 6dB at the crossover frequency—the telltale sign of an "in-phase" network. According to Peter Schuck, the optimization with multiple design axes naturally gravitates toward an in-phase crossover, because such a network is less sensitive to phase cancellations and produces a much smoother radiation pattern within the listening window.
The predicted system response on the main listening axis is shown in Figure 5 -- overlying the target SPL. CALSOD is saying here that nothing could be done about the narrow band dips and peaks in the woofer's response or about the tweeter's first break up mode at 26 kHz. Between 70 Hz and 20 kHz, the calculated response is within 2 dB of the target, which is also an excellent result. Of course, these calculations do not take room effects into account, and so have to be considered as "anechoic" in nature. One would expect the real-world response to be rougher, especially through the lower octaves where standing waves make quite a splash.
The system's summed acoustic response at all of the design axes is shown in Figure 6. The predicted response within the 20-degree window defined by these axes is quite tight, being within 2 dB around the crossover point. This was one of the priorities of the design, and according to CALSOD, the polar response within the listening window should be quite uniform. Finally, the predicted impedance of the system is shown in Figure 7. On the basis of these calculations, the system easily qualifies as a nominal 8-ohm load.
Armed with a large body of computer simulations, I finally set out to build a crossover network. I decided to locate the boards externally to the cabinet. This is a good idea in any event, because the interior of a loudspeaker cabinet is a pretty hostile environment for a crossover network. Or should I say a veritable hellhole, with lots of mechanical vibration and potential interference from the stray fields of the drivers' magnet assemblies. Also, from a practical standpoint, it is much easier to modify the network during the fine-tuning of the design when the boards are so readily accessible.
That moment when a new design sings for the first time, is a very special one. It is akin to an opening night when the actors and director are first exposed to public scrutiny. From its very first moments of life the Black Dahlia did not fail to impress. But, not unexpectedly, there were a couple of birth defects that needed immediate attention. Listening tests and measurements with the Neutrik system confirmed that CALSOD's predictions for system response around the crossover point were quite close to the mark. However, CALSOD overestimated the actual treble response. This was quite easy to fix by reconfiguring the tweeter's Zobel network to provide less HF shunt to ground. Yet, I was still bothered by an imbalance between the lower and upper mids. The presentation was too polite. Lesley's voice via the Lesley Test was slanted toward the lower registers; a little dark and lackluster compared with the real thing. This imbalance had to be rectified; I was not about to tolerate such timbral inexactitude. To get the Black Dahlia's voicing just right proved to be a difficult task.
An alternate crossover network aimed at boosting the upper mids by a couple of dB, designed with the aid of CALSOD merely managed to boost the range around 1 kHz and only made maters worse. The glitches around 500 Hz and 1 kHz became more audible. It was time to tweak the boards, the old fashioned way: by ear. Tweaking the high-pass filter in this fashion greatly improved matters. The midrange balance, although still not perfect, came into reasonable alignment.
The final crossover network topology is shown in Figure 8. Note that the Zobel networks for the drivers are far from standard, and serve not simply to equalize the impedance of the drivers but rather to equalize the summed acoustic response of the system. For example, the large capacitor in the tweeter's Zobel provides HF rolloff to counteract the driver's rising response. All of the caps are either polypropylene or metalized polypropylene. The network was optimized around 19-gauge coils and the DCR losses for these coils was included in the simulation.
With this project behind me, I cannot imagine tackling another speaker project without a computer-aided design tool such as CALSOD at hand. The fact that CALSOD's predictions were not perfect does not detract from the incredible savings in time and labor that it afforded me. CALSOD enabled me to narrow down the field from a bewildering array of crossover possibilities without having to spend time and money chasing down dead ends. It is a fantastic design tool that affords the home constructor flexibility and design sophistication only available previously to industry giants.
Enter XOPT. Version 3.0 is Peter Schuck's most recent commercial program for loudspeaker crossover optimization. The program has evolved since 1986 to the point where it now offers essentially the same design capabilities as those of CALSOD. XOPT can optimize the components of a given filter to obtain the best least-squares error fit between the driver/filter transfer function and the desired target response. It can also optimize the summed acoustic response of a multi-way loudspeaker taking into account the locations of the drivers on the front baffle and up to five design axes. Because CALSOD is based on Peter Schuck's early work, one might expect quite a bit of theoretical similarities between the two, and that is exactly the case. XOPT can calculate the phase of a driver's impedance by fitting a model to the measured impedance magnitude. And by assuming that the drivers' response is minimum phase, XOPT can also calculate the acoustic phase from the driver's magnitude response using a numerical Hilbert transform.
While XOPT lacks CALSOD's fancy graphics and extensive documentation, I actually found it easier to use. Input data may be entered interactively from the keyboard without the need to master the format for a data file. Another major advantage of XOPT is that unlike CALSOD it automatically models a driver's impedance and SPL magnitude from the experimental data. Whereas CALSOD requires a time-consuming trial and error fit of the data. And at $199, XOPT is quite a bit cheaper than the professional version of CALSOD. It is also much easier to make crossover changes on the fly without having to mess with data files by using a series of pop-up menus. Despite all that, I have to confess to a distinct fondness for CALSOD. Data files are easier to manipulate with the resident editor. The graphics are really addictive. And it is much easier to provide weighting instructions. In XOPT, each data point is assigned an individual weight, whereas CALSOD allows you to weight a frequency range using a functional description. For the near future I plan to use both programs. If you want quick results, however, I would recommend XOPT as it requires much less of a learning curve. XOPT arrived too late in the project to do much design work with. However, using the same experimental data, I was able to verify that XOPT's calculated system response was very similar to that of CALSOD. This is not surprising considering the similar foundations of both programs.
To paraphrase an old chess axiom about pawns being the soul of chess, I would argue that the cabinet is the soul of a loudspeaker. Often overlooked in the design equation, its quality of construction can make or break a particular design. For the sake of keeping my sanity through all of this and because I'm not a woodworker, I commissioned the cabinets from Woodstyle. Made of ¾-inch particle board, with a single H-brace, and rounded corners (see Figure 9), and naturally finished in beautiful black, these cabinets are certainly adequate for the task. They are not, however, particularly well damped, and rapping your knuckles on the enclosure does produce a distinct ring. So I would imagine that starting from scratch you could do better if you're willing to invest in more exotic technology. For starters I would recommend a sandwich construction for the enclosure walls. Two half-inch layers of particle board with a thick layer of glue in between should provide a rigid foundation for the Black Dahlia. As far as the Woodstyle enclosure is concerned, it does color the upper bass. The resultant bass quality is warmer and fuller in a pleasant euphonic way that most folks will not find objectionable. The enclosure will be available fully assembled from Just Speakers and Madisound for around $140/pair. LEAP, Chris Strahm's Loudspeaker Enclosure Analysis Program, was used for the design of the enclosure. LEAP goes beyond the simplistic Small-Thiele box analysis programs by offering more precise modeling of the loudspeaker circuit. I have found it to be an excellent tool for deep bass alignment calculations. However, it makes the inherent assumption that the woofer is radiating into half space—that it is effectively mounted in a wall. Thus, it fails to account for diffraction losses of a stand-mounted loudspeaker, by overestimating the system response through the upper bass. Having chosen a bass-reflex design to push the bass extension to around 50 Hz, I was quite concerned at the same time about providing effective damping for the woofer well into the deep bass. Maintaining the woofer excursion within reasonable limits is important for controlling distortion products. Harmonic distortion and IM and FM distortion products all increase dramatically as the woofer's suspension is pushed toward its nonlinear limits. Vented loudspeakers are especially susceptible to subsonic energy because as a rule they unload in the deep bass below the resonant frequency of the vent. Toward that end, the vent was tuned to around 40 Hz, to limit the woofer excursion in the midbass while sacrificing some low-end extension. The enclosure is stuffed with about a pound of longhair wool. The wool is draped around the brace in such a way as to ensure that the wool does not sag to the bottom of the box. The vent in the Woodstyle enclosure is made of cardboard tubing. This is an expedient way to fashion the vent. However, I do prefer, a 2-inch diameter PVC pipe as a far more rigid alternative. The net volume of the enclosure is about 0.81 cubic feet; the internal dimensions in inches being 9W x 15 3/4H x 9 3/4D. See Figure 9 for a schematic of the enclosure. If you decide to build you own cabinet, try to keep the dimensions of the front baffle the same and if necessary, increase the depth slightly to compensate for thicker walls.
The Black Dahlia was expressly designed for stand mounting, so be sure to use good quality stands to elevate them to the proper listening height. The main listening axis is the perpendicular to the front baffle between the woofer and tweeter. The speakers should be toed-in until the listening axes intersect at the listening position. The speakers do not require any tilt back, but they should be firmly anchored to the stands. Double-sided tape is a good start, but a clamp would even be better. I have been known to use a brick on top of the enclosure to tightly couple the box to the stand. Naturally, I'm pleased with the sonic results or the Black Dahlia would not have seen light of day. This is only one of a handful of speakers that does not betray the fact that it uses a metal dome tweeter. The upper octaves if anything remind me of a concert hall perspective, without that hi-fi-ish emphasis and shrillness that some audiophiles prefer as a steady diet. Side by side with the Dahlia-Debra, the Black Dahlia comes off sounding much tamer on top. There's lots of quick detail together with a dynamic bloom that'll really give you goosebumps. I'm also pleased at the tonality of the upper bass and lower midrange. The anemia so typical of many mini-monitors is absent. The ability of these speakers to throw a soundstage is also exceptional. In my opinion they're competitive with any minimonitor out there. I'll restrict my sonic assessment to just the above brief synopsis. Because there hasn't been a new father or a speaker designer who has failed to embrace his offspring, I've asked JA to provide you not only with his own unbiased opinion but also with a full set of measurements using the MLSSA and Audio Precision systems. JA's review, which is included in this issue's "Equipment Reports" section, should be construed as an independent view of the Black Dahlia, from someone removed from the sweat and tears that accompany the gestation and birth of a new loudspeaker.
Above all, this project is dedicated to the home constructor who's searching for kilobuck sound quality on a budget. Bon voyage!
Note: The Black Dahlia, as were the previous Dahlias, is a public domain design. That means that anyone, even a manufacturer, may use it for either private or commercial purpose. I have licensed no one to produce Dahlias and I do not receive royalties from the sale of these kits. I do not want any commercial ties or potential conflict of interest to evolve during my tenure at Stereophile as an audio reviewer.
Sources for Parts and Software:
Drivers, cabinets, and crossover parts are available from:
Computer-aided crossover design software is available from the following sources:
The standard version of CALSOD is priced at $65 and may be ordered from:
Old Colony Sound Lab
CALSOD 2.00, the professional version may be ordered directly from:
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* All text and figures are copyrighted to Black Dahlia Acoustics, Ltd. (Copyright 1998)
ALL RIGHTS RESERVED.