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Design of the Esquire
By Scott C. Blaier
10 Apr 1996
Crossover Design
The crossover described here is not a cookbook design whose values were determined by plugging a nominal driver impedance value into a formula. All of the component values were optimized using the CALSOD computer program and later "tweaked" after listening tests. I choose these two drivers specifically for their smooth amplitude response, rolloff characteristics (especially the P13WH which is ruler flat with an almost perfect 2nd order rolloff), resonance control, off-axis dispersion, etc. to ease in crossover design; the effort paid off handsomely. Although the final crossover is complicated, I feel it is justified, and exploits the best features of the drivers in this system. I designed and experimented with many other types (Bessel, Chebychev, Butterworth) of filters of different orders (1st, 2nd, and 3rd) at many frequencies. But in the end, I found that a fourth order Linkwitz-Riley network at 3.0 kHz. looked the best on paper, and more importantly, sounded the best. Although the tweeter's excellent damping and low resonance suggest a lower crossover frequency could be used with a shallower rolloff, I found that such an approach often unbalanced the driver's bottom to top frequency response and resulted in audible distortion. The choice of a Linkwitz-Riley fourth order filter, with a crossover frequency located more than 2 octaves above the tweeter's resonance may seem a bit conservative. But listening tests indicate that this is a solution that allows the tweeter operate at its best. Fortunately, the relatively high crossover frequency poses no problem for the P13WH, because its off-axis performance is down only -1.0 dB 30 degrees off-axis below 3.0 kHz.
The graph Fig. 2. Modelled SPL response of The Esquire show a near theoretically perfect fourth order Linkwitz-Riley response centered around 3.0 kHz. The power response dips - 3.0 dB around the crossover frequency, as it should, and total amplitude response is flat through the crossover region. Also note the near perfect symmetry and smoothness of the each driver's rolloff curve around the crossover. The electrical filters' response exactly compliment each driver's acoustic rolloff to strictly maintain a 4th order Linkwitz-Riley transfer function well above and below the crossover point. Please note that the drivers are operating in phase, and reversing the polarity of the tweeter will produce a severe response null of - 25.0 dB centered around the crossover frequency of 3.0 kHz.
Both drivers have outstanding off axis response, and coupled with Linkwitz-Riley's absence of frequency dependent polar tilt, superior damping, and minimum driver interaction, provide excellent stereo imaging.
The cost of the complicated 4th order Linkwitz-Riley network is somewhat compromised phase and transient response. These design compromises are unacceptable to some listeners; however, my ears are less sensitive to these shortcomings then to the many problems solved by using a high order crossover. Loudspeaker design is an exercise in comprise, and it is these compromises that determine the overall "sound" of any loudspeaker system. The nice part about building your own loudspeaker is that you can choose what to compromise on, based on personal listening preferences. I did not use the crossover to compensate for the response step because these loudspeakers are to be used on a bookshelf against the wall, which will reinforce bass response.
A diagram of the crossover schematic is included with the article Fig. 3. Crossover Schematic. I used quality Mylar capacitors in the tweeter circuit and quality electrolytics in the woofer circuit. Both circuits use quality air core inductors whose parasitic d.c. resistance is considered throughout the design. Certainly tweaks such as buying expensive polypropylene capacitors and exotic inductors are possible. But these tweaks can double the overall project budget for perhaps a modest overall increase in performance per dollar spent. I purchased a surplus of Mylar capacitors and precision matched each capacitor to 1% of the theoretical CALSOD value. Finally, if you wish to improve inductor quality, please note that it will effect each driver's Qts by changing its Qes, and overall crossover performance. Replacing the inductors in series with the woofer with lower d.c. resistance "exotic" inductors may improve overall sound. But the d.c. resistance in the tweeter circuit inductors contribute to each legs total damping resistance, and should not be changed; if you insist on using low resistance "exotic" inductors, you must make up the lost resistance by using a larger value series resistors.
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