Audio Speaker Design Calculators
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To design the enclosure and crossover circuit for optimum performance of a speaker system, one must know the parameters of the driver. From those measurements, the enclosure and port dimensions can be calculated and system performance analyzed1.
If the Efficiency Bandwidth Product (EBP) is less than 50 and the total Q of the driver (Qts) is between 0.3 and 0.8, the driver is best suited2 for a sealed enclosure. Sealed enclosures make great guitar, bass, or keyboard enclosures and will produce better musical tone quality especially when using a tube amplifier. Some guitar systems use an open back cabinet. Open back cabinets are undesirable for good fidelity3. Use speakers that are designed for guitar or bass amplifiers for the best sound.
Vented enclosures produce great high fidelity sound. These systems are designed4 to tune the enclosure resonance and port resonance to a optimum frequency. When the "tuned" port vibrates in phase with the driver, the driver becomes virtually motionless and the sound comes mostly from the port. The vented port enclosure acts as a high-pass crossover filter allowing the high frequencies to pass4.
2 way enclosures work well for compact home stereo and the simplicity of the crossover handles the power for P. A. systems, monitors, and keyboard speakers.
For the optimum high fidelity performance the 3 way enclosure has been used for decades. This system contains a high frequency tweeter, mid-range driver, low frequency "woofer" driver, and a 3 way crossover circuit . Large sound systems will use an amplifier for each driver with the cross over circuit dividing the frequency before the amplifiers. Another approach to high fidelity is to have enclosures for the left and right side (stereo) and a sub woofer (mono) for low frequencies.
All-pass crossovers will produce a symmetrical acoustical radiation pattern which has a lobe of maximum sound pressure on a central axis perpendicular to the speaker5. The symmetrical positioning of dual driver system with a tweeter in a with the Butterworth 3rd order 2 way crossover will produce a quasi- spherical vertical response pattern6. This reduces the "lobbing" effect greatly.
There are several shapes of the enclosures for various reasons such as size, portability, or propose. However, for cancellation of resonating frequencies a rectangular enclosure a ratio of 1 : 1.618 : 0.618 provides the best result. This ratio is used in calculating the dimensions of the enclosure.
The formulas used in the calculations were derived from the works of the gurus listed below:
1D. B. Keele, Jr. unpublished letters to engineers and colleges.
2Ray Alden "Advance Speaker Systems," Master Publishing, Inc., 1995
3Youngmark, J. A. "Loudspeaker baffles and cabinets" Jour. Brit. I.R.E. 13.2 (February 1953)
4A. N. Thiele, "Loudspeakers in Vented Boxes," Journal of Acoustical Engineering Society (JAES), May-June 1971.
5R. Small, "Vented-Box Loudspeaker Systems," JAES, June-October 1973
6Siegfried Linkwitz, "Passive Crossover Networks for Noncoincident Drivers," JAES, March 1978.
7Dr. Joseph D'Appolito 1983, "A Geometric Approach to Eliminating Lobbing Errors in Multiway Loudspeakers," concluded while reading Linkwitz a symmetrical positioning of 3 drivers in a 2-way design, used with a 3rd-order crossover, would produce the quasi-spherical vertical response pattern. The distance between the centers of the adjacent drivers should be one wavelength of the crossover's frequency.
And special mention:
F. Langford-Smith "Radiotron Designer's Handbook," Fourth Edition, Electron Tube Division Radio Corporation of America, 1953.