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Many musicians and sound/recording/mixing engineers prefer building their own speaker systems, to tailor the acoustic characteristics of their listening environment. The design is not that difficult using the Thiele/Small parameters which are provided by most of the speaker driver manufactures, and the drivers can be purchased over the Internet at many different on-line suppliers, like Parts-Express. There are many good sites on the Internet dedicated to designing subwoofers, (for example, AJ Design Software and The Subwoofer Design Page, which provided many of the design parameters used below.) To design a subwoofer means balancing many parameters to arrive at a cost effective, small, high performance design-which can easily get out of hand. A reasonable methodology is to get the Thiele/Small parameters for a large number of subwoofer drivers, and then automate the design process, such that the desirable attributes of a speaker can be manipulated, creating many optimal designs-and then selecting the best design, and modifying it for the desired qualities. Parts-Express offers the Thiele/Small parameters to the speaker drivers they sell on their web site, and a database can be made by cut-and-stick from a browser, and a short Calc(1) script used to optimize the speaker configuration. The scripts used, below, are:
The database is the same for all optimization scripts, and is appended to the end of each file. Each file can be modified for a specific design, (using initial assumptions, eliminating inappropriate candidates,) and the frequency response command, (its at the bottom of each file, and should be un-commented, and placed below each likely candidate in the file,) and then the parameters fine tuned to provide a desirable design. In the design alternatives, below, a reasonable, cost effective, amplifier will be selected, and the different speaker configurations analyzed and optimized for room size, speaker size, low frequency cutoff, and cost. The Dayton SA240 240W Subwoofer Amplifier is rated at 240 W into 4 Ohms, and has a stock frequency response down to -3 dB @ 13 Hz., and a price of $129.88, (which seems to be the highest Watt/unit cost). For a room with a maximum dimension of 17'6", (2 meters = 6.5', i.e., about third or half the room would be above +85 dB SPL, half lower-85 dB SPL is from OSHA 1910.95, and the beginning of Fletcher-Munson Equal Loudness Contours "flat" loudness curves, and a typical speaker SPL / Watt @ 1 meter of 91 dB SPL; all typical values, as a first order assumption, in an acoustically inert environment; the crossover is assumed to be about 70 Hz.):
Sealed Enclosure Candidate Design Alternatives:Choosing those speakers which have a Qtc >= 0.39, AND, an F3 less than 40, AND, a cubic box edge size of approximately 1 foot, (Vb = 1^3 feet, or less,) below, there are two candidates. (Note: the Dayton SWC-1CO, 1.0 ft^3 Subwoofer Cabinet w/Cutouts at $119.88 is a "bolt together" construction alternative for this application.) For the RSS265HF-4, (Qtc = 1 / sqrt (2), configuration,) the bass is down 15 dB at just below 20 Hz., meaning 2 poles at 20 Hz. of bass boost/compensation, and two zeros at 40 Hz. would be flat down to 20 Hz., which would be down 6 dB. Note that this is a Butterworth, (Qtc = 1 / sqrt (2),) implementation, which is the lowest frequency sealed implementation possible. (The poles could be moved lower, since the program level at 14 Hz. is about -10 dB below the midrange level, and the output power of the Dayton SA240 240W Subwoofer Amplifier is the limiting factor-possibly as low as 14 Hz., which is the low frequency cutoff for the SA240-requiring an 18.25 dB, power, gain at 14 Hz., which is a factor of 8.175 in input voltage to the SA240; an adequate solution from a cost consideration-the two poles, plus the input pole in the SA240, would be down about 3 dB at 20 Hz., 9 dB at 14 Hz.)
Qtc = 1 / sqrt (2);
Dayton TIT320C-4 12" Titanic Mk III Subwoofer, 4 Ohm, $159.66:
Vb = 46.69703223215296274508 = net box volume, liters
= 22.940 X 14.178 X 8.762 = golden ratio inside box size, inches
Fb = 35.67675123259398873118 = box resonant frequency, Hz.
F3 = 35.67675123259398873118 = box -3 dB frequency, Hz.
Q = 0.70710678118654752440 = box quality factor
@ 0 = maximum peak or dip in speaker system response, db
L = 15.83664376603384815908 = minimum longest room dimension, feet
Dayton RSS265HF-4 10" Reference HF Subwoofer, 4 Ohm, $115.00:
Vb = 26.24477339637711223395 = net box volume, liters
= 18.931 X 11.700 X 7.231 = golden ratio inside box size, inches
Fb = 39.88807483616421932522 = box resonant frequency, Hz.
F3 = 39.88807483616421932522 = box -3 dB frequency, Hz.
Q = 0.70710678118654752440 = box quality factor
@ 0 = maximum peak or dip in speaker system response, db
L = 14.16463447585961336378 = minimum longest room dimension, feet
The sealed enclosure is a desirable candidate because it handles frequencies below its resonant frequency, 39.9 Hz., well, with a minimum of distortion products, (i.e., bass boost/compensation strategies are applicable,) and probably explains why it is a favorite of musicians and sound/recording engineers. Additional notes on sealed enclosures:
Using the Dayton RSS265HF-4 10" Reference HF Subwoofer as a critically damped speaker:
Qtc = 1 / 2;
Dayton RSS265HF-4 10" Reference HF Subwoofer, 4 Ohm, $115.00:
Vb = 93.26411301940344582454 = net box volume, liters
= 28.889 X 17.854 X 11.035 = golden ratio inside box size, inches
Fb = 28.20512820512820512821 = box resonant frequency, Hz.
F3 = 43.824394139308744566 = box -3 dB frequency, Hz.
Q = 0.5 = box quality factor
@ 0 = maximum peak or dip in speaker system response, db
L = 12.89236305706773921462 = minimum longest room dimension, feet
If Qtc is at least twice Qts, the sealed speaker is an acoustic suspension speaker, and at frequencies less than Fb, the compressive effects of the air in the enclosure provide the "springiness" locating the speaker cone, (as opposed to the speaker's surround.) Since a Chebyshev is not a desirable alternative, (except for small size compromised designs,) this means that Qts <= 1 / (2 * sqrt (2)). Using the Dayton RSS265HF-4 10" Reference HF Subwoofer as an acoustic suspension speaker, (slight Chebyshev characteristics):
Qtc = 2 * 0.39;
Dayton RSS265HF-4 10" Reference HF Subwoofer, 4 Ohm, $115.00:
Vb = 20.00998611571246405046 = net box volume, liters
= 17.294 X 10.689 X 6.606 = golden ratio inside box size, inches
Fb = 44 = box resonant frequency, Hz.
F3 = 40.26844833757789313468 = box -3 dB frequency, Hz.
Q = 0.78 = box quality factor
@ 0.14010409771834019229 = maximum peak or dip in speaker system response, db
L = 14.03083613412416338778 = minimum longest room dimension, feet
The enclosure dimensions should follow the golden ratio, phi = (1 + sqrt (5)) / 2 = 1.618. This is important for midrange speakers for better control of internal standing waves. The longest internal dimension should be the middle internal dimension multiplied by phi; the smallest internal dimension should be middle internal dimension divided by phi. (If this is impractical, no side should be an integer multiple of the other two sides.) This is less important for woofers where the internal dimensions are much less than the wavelength of the highest frequency of sound produced. The back of the speaker driver should not be less than one half its diameter from the back of the speaker cabinet. Acoustic Suspension Enclosure Candidate Design Alternatives:Choosing those speakers which have an F3 less than 41, AND, a cubic box edge size of approximately 1 foot, (Vb = 1^3 feet, or less,) AND, a passband ripple less than 0.6 dB, below, there are two candidates.
Dayton TIT320C-4 12" Titanic Mk III Subwoofer, 4 Ohm, $159.66:
Vb = 24.63493573679694866589 = net box volume, liters
= 18.536 X 11.456 X 7.080 = golden ratio inside box size, inches
Fb = 44.4 = box resonant frequency, Hz.
F3 = 37.32198093236940515102 = box -3 dB frequency, Hz.
Q = 0.88 = box quality factor
@ 0.58268005582627837440 = maximum peak or dip in speaker system response, db
L = 15.13853192904813706169 = minimum longest room dimension, feet
Dayton RSS265HF-4 10" Reference HF Subwoofer, 4 Ohm, $115.00:
Vb = 20.00998611571246405046 = net box volume, liters
= 17.294 X 10.689 X 6.606 = golden ratio inside box size, inches
Fb = 44 = box resonant frequency, Hz.
F3 = 40.26844833757789313468 = box -3 dB frequency, Hz.
Q = 0.78 = box quality factor
@ 0.14010409771834019229 = maximum peak or dip in speaker system response, db
L = 14.03083613412416338778 = minimum longest room dimension, feet
Acoustic suspension speakers are known for their ability to handle power below their cutoff frequency, F3, i.e., frequency contouring for bass boost/compensation is a very practical alternative. Note that the Dayton RSS265HF-4 10" Reference HF Subwoofer is also very close to being maximally flat, too, (i.e., this design is quite similar to its sealed box configuration.) Ported/Vented Enclosure Candidate Design Alternatives:Choosing those speakers which have a 0.3 <= Qtc <= 0.4, AND, an F3 less than 24, AND, a cubic box edge size of approximately 1.5', (Vb = 1.5^3 feet, or less,) below, there are two candidates. For the RSS265HF-4, the bass is down 3 dB at just above 23 Hz. Unfortunately, it is inappropriate to use bass boost/compensation below Fb for ported/vented configurations because of distortion considerations, (when the speaker decouples from the enclosure.) Note that the sealed enclosure is a superior alternative because of its flexibility, unless, a lower frequency of 20 Hz., without bass boost/compensation is adequate, (i.e., the programming is mostly CDs, with a few DVDs-the alternative is included for completeness.)
Dayton RSS390HO-4 15" Reference HO Subwoofer, 4 Ohm, $159.80:
Vb = 97.92322269446991942281 = net box volume, liters
= 29.362 X 18.147 X 11.215 = golden ratio inside box size, inches
Fb = 22.94191320354384403386 = box resonant frequency, Hz.
F3 = 23.80878281048788610796 = box -3 dB frequency, Hz.
@ 0.06626054427026401982 = maximum peak or dip in system response, dB
L = 23.73073854708417588069 = minimum longest room dimension, feet
Dayton RSS265HF-4 10" Reference HF Subwoofer, 4 Ohm, $115.00:
Vb = 53.69220514634528767659 = net box volume, liters
= 24.032 X 14.853 X 9.180 = golden ratio inside box size, inches
Fb = 22.77426077388994222482 = box resonant frequency, Hz.
F3 = 23.10700579853260126994 = box -3 dB frequency, Hz.
@ 0.07083312086216486123 = maximum peak or dip in system response, dB
L = 24.45145878813429127082 = minimum longest room dimension, feet
Note that the passband ripple is 0.07 dB. Allowing a passband ripple of about 1 dB, (by increasing Vb by 50% to 80.53830771951793151488 liters,) for the RSS265HF-4 10" Reference HF Subwoofer.
Vb = 80.53830771951793151488;
Dayton RSS265HF-4 10" Reference HF Subwoofer, 4 Ohm, $115.00:
Vb = 80.53830771951793151488 = net box volume, liters
= 27.510 X 17.002 X 10.508 = golden ratio inside box size, inches
Fb = 20.08426758384232658538 = box resonant frequency, Hz.
F3 = 19.33140944191145008144 = box -3 dB frequency, Hz.
@ -0.98571443347192259122 = maximum peak or dip in system response, dB
L = 29.22704636191979387568 = minimum longest room dimension, feet
lowering F3 from 23 Hz. to 19 Hz., (about a 20% decrease,) with 1 dB, (i.e., +/- 0.5 dB,) of passband ripple, and increasing the cubic box edge size from 1.24' to 1.42', (about a 20% increase.) As mentioned, above, bass boost/compensation below 19 Hz. is to be avoided on ported/vented configurations. There are frequencies down to about 5 Hz. on CDs and DVDs, (they are down about -10 dB below the average program level,) and will create substantial distortion products if not adequately high pass filtered prior to the speaker. Because of this, this configuration is probably not a likely candidate. Note that the ported/vented enclosure candidates have, roughly, about twice the volume of the sealed candidates, and an F3 that is about half the sealed enclosure. 4'th Order Candidate Design Alternatives:Choosing those speakers which have solutions for an F3 of 10 Hz., AND, less than 1 dB "ripple" in the passband, (i.e., S = 0.6, b = 0.9560, to minimize enclosure size,) AND, a cubic box edge size of approximately 2 feet, (Vb = 2^3 feet, or less,) AND, a Pa of -15 dB or less, (allowing a 3 dB headroom margin of error in the inefficiency of the speakers,) below, there are two candidates. Note that this is not an optimal design-its only to select design alternatives-passband ripple can be used to, (i.e., hidden behind room acoustic characteristics,) to enhance the listening area, (allowing a smaller enclosure size if ripple can be hidden/tolerated via integrated into the room environment.) There is the possibility of hiding the speaker cabinet behind a wall, and reversing the tuned port out of the speaker cabinet, venting into the listening room, (the sound from the driver/cabinet is totally from the port in this configuration.) Also, not that the Dayton RSS265HF-4 10" Reference HF Subwoofer is the only driver that is common to all configurations, (i.e., sealed, ported/vented, 4'th order, enclosures,) with a low frequency cutoff from about 10 to 20 Hz., in a cubic enclosure from 1 to 2 feet on an edge, and an efficiency that is, (at least,) can be electronically enhanced with less than 18 dB of gain, (or hidden in listening room characteristics.) This does not imply that there are superior alternatives for a specific application.
S = 0.6;
b = 0.9560;
Fl = 10;
Dayton RSS265HF-4 10" Reference HF Subwoofer, 4 Ohm, $115.00:
Vb = 200.25591007796222702122 = net box volume, liters
= 7.07217764354029062081 = net box volume, cubic feet
Vf = 13.14800159702342017856 = net volume of vented chamber, liters
= 15.035 X 9.292 X 5.743 = golden ratio inside box size, inches
Vr = 187.10790848093880684266 = net volume of sealed chamber, liters
= 36.435 X 22.518 X 13.917 = golden ratio inside box size, inches
Ff = 25.28402759217864961497 = box resonant frequency of vented chamber, Hz.
Fb = 25.28402759217864961497 = box resonant frequency of sealed chamber, Hz.
F3 = 10 = box -3 dB frequency, Hz.
Pa = -10.77322288605405222329 = gain, db
Fh = 63.92820512820512820513 = upper -3 db cutoff frequency, Hz.
L = 56.5 = minimum longest room dimension, feet
Dayton RSS265HO-4 10" Reference HO Subwoofer, 4 Ohm, $115.00:
Vb = 94.58733667944141709569 = net box volume, liters
= 3.34041800597014925373 = net box volume, cubic feet
Vf = 5.32848563103662110619 = net volume of vented chamber, liters
= 11.127 X 6.877 X 4.250 = golden ratio inside box size, inches
Vr = 89.25885104840479598950 = net volume of sealed chamber, liters
= 28.469 X 17.595 X 10.874 = golden ratio inside box size, inches
Ff = 28.20058026482304978473 = box resonant frequency of vented chamber, Hz.
Fb = 28.20058026482304978473 = box resonant frequency of sealed chamber, Hz.
F3 = 10 = box -3 dB frequency, Hz.
Pa = -13.29032044729626047180 = gain, db
Fh = 79.52727272727272727273 = upper -3 db cutoff frequency, Hz.
L = 56.5 = minimum longest room dimension, feet
Infinite Baffle Candidate Design Alternative(s):Choosing those speaker(s) which are billed as being able to be mounted between two rooms, (or between a wall and garage, attic, floor, etc.,) approximating an enclosure of infinite size, below, there is one candidate. Note that this would be a simple 20 Hz. low frequency cutoff design, with superior efficiency, acoustic environment permitting. (Note that for 23 Hz., low frequency cutoff, the cubic box size is 4' on an edge; a larger "enclosure room" may have different characteristics, generally a higher F3, and slower low frequency roll off.)
Qtc = 1 / sqrt (2);
Dayton IB385-8 15" IB Subwoofer, 8 Ohm, $121.01:
Vb = 1715.02814201159002020309 = net box volume, liters
= 76.252 X 47.126 X 29.125 = golden ratio inside box size, inches
Fb = 22.62741699796952078085 = box resonant frequency, Hz.
F3 = 22.62741699796952078085 = box -3 dB frequency, Hz.
Q = 0.70710678118654752440 = box quality factor
@ 0 = maximum peak or dip in speaker system response, db
L = 24.96970821064995945538 = minimum longest room dimension, feet
Note, also, that sound leakage, (for example, a listening room, with the speaker driver mounted in the wall between the listening room and garage,) is quite high-the back side SPL is the same as the front side SPL-perhaps an annoyance to others. Because of this, this configuration is probably not a likely candidate. 4'th Order Limit Solutions For The Dayton RSS265HF-4 10" Reference HF Subwoofer:The lowest F3 is attainable when:
S = 0.5;
b = 1.2712;
Fl = 7;
which has 1.25 dB of passband ripple, (i.e., +/- 0.625 dB,) and a Pa of -15 dB, which is very inefficient, but within the design criteria of -18 dB. Note that the F3 of 7 Hz., is very close to the 5 Hz. low frequency cutoff for DVDs specified by the SMPTE RP 155, (although most casual listening environments would be incapable of supporting such low frequencies, and the Dayton SA240 240W Subwoofer Amplifier wound not, either.) The Fh of 79 Hz. is probably adequate for a subwoofer that is used to supplement the audio system/speakers supplied with LCD television sets, etc., (although the THX specification for DVD playback says +10 dB below 123 Hz.) The enclosure size, (cubic box size of 2.5' on an edge,) is too large for most listening environments, but could be mounted externally, (in a garage, attic, etc.,) and the sound passed through a wall via the port, (the port tube would be mounted externally on the enclosure, rather than internally.)
Dayton RSS265HF-4 10" Reference HF Subwoofer, 4 Ohm, $115.00:
Vb = 443.03221157314395316447 = net box volume, liters
= 15.64599267425367990677 = net box volume, cubic feet
Vf = 9.13055666459959734622 = net volume of vented chamber, liters
= 13.314 X 8.229 X 5.086 = golden ratio inside box size, inches
Vr = 433.90165490854435581824 = net volume of sealed chamber, liters
= 48.227 X 29.806 X 18.421 = golden ratio inside box size, inches
Ff = 23.47255899217266087092 = box resonant frequency of vented chamber, Hz.
Fb = 23.47255899217266087092 = box resonant frequency of sealed chamber, Hz.
F3 = 7 = box -3 dB frequency, Hz.
Pa = -15.23190538305753647109 = gain, db
Fh = 78.70871794871794871795 = upper -3 db cutoff frequency, Hz.
L = 80.71428571428571428571 = minimum longest room dimension, feet
The Dayton SA240 240W Subwoofer Amplifier has a stock low frequency response of -3 dB @ 13 Hz., and matching this with the speaker's F3 gives the smallest enclosure size:
S = 0.5;
b = 1.2712;
Fl = 13;
which has 1.25 dB of passband ripple, (i.e., +/- 0.625 dB,) and a Pa of -9 dB, and a (cubic box size of 1.25' on an edge,) which is probably realizable in most casual listening environments, (although it does have 1.25 dB peaks and floor that might aggravate standing waves in most casual listening environments.) The Fh of 85 Hz. is probably adequate for a subwoofer that is used to supplement the audio system/speakers supplied with LCD television sets, etc., and the SA240's crossover frequency would be used for precise matching.
Dayton RSS265HF-4 10" Reference HF Subwoofer, 4 Ohm, $115.00:
Vb = 56.20423163383956483730 = net box volume, liters
= 1.98489178311118791992 = net box volume, cubic feet
Vf = 9.13055666459959734622 = net volume of vented chamber, liters
= 13.314 X 8.229 X 5.086 = golden ratio inside box size, inches
Vr = 47.07367496923996749108 = net volume of sealed chamber, liters
= 23.001 X 14.216 X 8.786 = golden ratio inside box size, inches
Ff = 33.18453455050007678687 = box resonant frequency of vented chamber, Hz.
Fb = 33.18453455050007678687 = box resonant frequency of sealed chamber, Hz.
F3 = 13 = box -3 dB frequency, Hz.
Pa = -9.21689372925793013983 = gain, db
Fh = 84.70871794871794871795 = upper -3 db cutoff frequency, Hz.
L = 43.46153846153846153846 = minimum longest room dimension, feet
Most music distributed on CD ROMs has a 20 Hz., lower frequency limit, which if the speaker is designed for CD's, MP3's, etc., would permit a smaller enclosure size, (with 0 dB ripple in the passband,) although the 61 Hz., Fh may be problematical, but is commensurate in enclosure size with the ported/vented and sealed designs, above:
S = 1 / sqrt (2);
b = 0.7206;
Fl = 20;
Dayton RSS265HF-4 10" Reference HF Subwoofer, 4 Ohm, $115.00:
Vb = 58.11723542950609907072 = net box volume, liters
= 2.05245085125780854295 = net box volume, cubic feet
Vf = 18.26111332919919469249 = net volume of vented chamber, liters
= 16.775 X 10.368 X 6.408 = golden ratio inside box size, inches
Vr = 39.85612210030690437823 = net volume of sealed chamber, liters
= 21.760 X 13.448 X 8.312 = golden ratio inside box size, inches
Ff = 34.82792866916744138267 = box resonant frequency of vented chamber, Hz.
Fb = 34.82792866916744138267 = box resonant frequency of sealed chamber, Hz.
F3 = 20 = box -3 dB frequency, Hz.
Pa = -2.35661718603070008226 = gain, db
Fh = 60.64923076923076923077 = upper -3 db cutoff frequency, Hz.
L = 28.25 = minimum longest room dimension, feet
Or, with 1.25 dB, (i.e., +/- 0.625 dB,) of passband ripple, giving a one cubic foot enclosure, and an Fh of 92 Hz., which would be quite adaquate for CDs, MP3's, television, etc., since all except DVDs use 20 Hz. as the low frequency cutoff:
S = 0.5;
b = 1.2712;
Fl = 20;
Dayton RSS265HF-4 10" Reference HF Subwoofer, 4 Ohm, $115.00:
Vb = 30.64962910653616421443 = net box volume, liters
= 1.08241310663769921455 = net box volume, cubic feet
Vf = 9.13055666459959734622 = net volume of vented chamber, liters
= 13.314 X 8.229 X 5.086 = golden ratio inside box size, inches
Vr = 21.51907244193656686820 = net volume of sealed chamber, liters
= 17.719 X 10.951 X 6.768 = golden ratio inside box size, inches
Ff = 42.82726186641353533754 = box resonant frequency of vented chamber, Hz.
Fb = 42.82726186641353533754 = box resonant frequency of sealed chamber, Hz.
F3 = 20 = box -3 dB frequency, Hz.
Pa = -4.78551059405607858393 = gain, db
Fh = 91.70871794871794871795 = upper -3 db cutoff frequency, Hz.
L = 28.25 = minimum longest room dimension, feet
But notice that the minimum longest room dimension is 28', otherwise, frequencies lower than 20 Hz. will not be accurately reproduced by the speaker. In principle, the passband ripple of the speaker should be chosen such that it does not to aggravate standing waves in the listening environment, where possible. Note that the ported and sealed, (with modest bass boost/compensation,) and the 4'th order design, (with modest inefficiency,) all come very close to meeting the 20 Hz. specification, (within reason,) with approximately a one cubic foot enclosure. The typical casual listening environment has a minimum longest room dimension of 16-18', giving a minimum frequency, (due to the lowest frequency standing wave,) of about 565 / 17 = 33 Hz., creating a increase in the apparent loudness at about 35 Hz. in most rooms. Note that the 40 Hz. low frequency cutoff of the sealed design tends to cancel the increase in loudness, and probably accounts for the popularity of using a sealed "bookshelf" enclosures of approximately one cubic foot volume in such environments. The other typical room dimensions are 13' and a ceiling height of 8', creating standing waves at 44 Hz., and 71 Hz., respectively, (these standing wave create the "booming'ness" of bass frequencies heard in these environments.) A low frequency roll off at about 38 Hz. can be beneficial if the environment is "live," (i.e., the walls, ceiling, and floor, do not have sound damping to absorb the reflected sound waves created by the speaker,) meaning that bass boost/compensation of the sealed design may not be necessary, (and may be, even, detrimental.) As a concluding example:
S = 0.5;
b = 1.2712;
Fl = 17.8;
Dayton RSS265HF-4 10" Reference HF Subwoofer, 4 Ohm, $115.00:
Vb = 35.32335736303465291914 = net box volume, liters
= 1.24746909162572289210 = net box volume, cubic feet
Vf = 9.13055666459959734622 = net volume of vented chamber, liters
= 13.314 X 8.229 X 5.086 = golden ratio inside box size, inches
Vr = 26.19280069843505557291 = net volume of sealed chamber, liters
= 18.918 X 11.692 X 7.226 = golden ratio inside box size, inches
Ff = 39.91560070307322190897 = box resonant frequency of vented chamber, Hz.
Fb = 39.91560070307322190897 = box resonant frequency of sealed chamber, Hz.
F3 = 17.8 = box -3 dB frequency, Hz.
Pa = -6.00861617192788814919 = gain, db
Fh = 89.50871794871794871795 = upper -3 db cutoff frequency, Hz.
L = 31.74157303370786516854 = minimum longest room dimension, feet
and note that the rear sealed chamber volume, 26.2 liters, and resonance, 39.3 Hz., is identical to the sealed design, above, (i.e., this design is the sealed box, above, driving a ported/vented enclosure in front.) The efficiency at 18 Hz. is significantly better at -6 dB, (where the sealed enclosure is about -14.5 dB at 18 Hz.) As mentioned, above, in the ported/vented enclosure candidate design, bass boost/compensation below 18 Hz. is to be avoided. There are frequencies down to about 5 Hz. on CDs and DVDs, (they are down about -10 dB below the average program level,) and will create substantial distortion products if not adequately high pass filtered prior to the speaker-usually creating port and de-coupling distortion products. Of course, extending F3 down to 5 Hz. is a viable alternative. Using Vb = Vf = 9.13055666459959734622 in the design equations for a ported/vented enclosure:
Vb = 9.13055666459959734622;
Dayton RSS265HF-4 10" Reference HF Subwoofer, 4 Ohm, $115.00:
Vb = 9.13055666459959734622 = net box volume, liters
= 13.314 X 8.229 X 5.086 = golden ratio inside box size, inches
Fb = 39.4423356403321409769 = box resonant frequency, Hz.
F3 = 50.38320918272507914752 = box -3 dB frequency, Hz.
@ 4.68731702965274584347 = maximum peak or dip in system response, dB
L = 11.21405343496304887074 = minimum longest room dimension, feet
and the resonant frequency is the same as the sealed enclosure at 39.44 Hz. (a 4th order design can be seen to be a sealed enclosure and ported/vented enclosure, with the same resonant frequency, that are tightly acoustically coupled by using a common driver.) Purpose Designed Alternative:Note that the RSS265HF-4 10" Reference HF Subwoofer speaker driver was chosen for its flexibility and versatility-it performed well in sealed, ported, and 4th order enclosures, allowing many design options. As an example of a speaker driver that is purpose designed, (for example, optimized for 4th order enclosure,) the Peerless 830500 XLS 12" Subwoofer exhibits poor performance in a sealed enclosure:
Qtc = 1 / sqrt (2);
Peerless 830500 XLS 12" Subwoofer, 8 Ohm, $178.65:
Vb = 12.11433121689565091813 = net box volume, liters
= 14.630 X 9.042 X 5.588 = golden ratio inside box size, inches
Fb = 63.99316369738255095835 = box resonant frequency, Hz.
F3 = 63.99316369738255095835 = box -3 dB frequency, Hz.
Q = 0.70710678118654752440 = box quality factor
@ 0 = maximum peak or dip in speaker system response, db
L = 8.82906809658341107814 = minimum longest room dimension, feet
with an F3 of 64 Hz. Likewise, in a ported/vented enclosure:
Peerless 830500 XLS 12" Subwoofer, 8 Ohm, $178.65:
Vb = 13.75391275645652176386 = net box volume, liters
= 15.263 X 9.433 X 5.830 = golden ratio inside box size, inches
Fb = 37.10270647978230075209 = box resonant frequency, Hz.
F3 = 50.13370752565382968153 = box -3 dB frequency, Hz.
@ 0.01282619858966126054 = maximum peak or dip in system response, dB
L = 11.26986269090281946519 = minimum longest room dimension, feet
with an F3 of 50 Hz. But the 4th order enclosure is impressive:
S = 0.5;
b = 1.2712;
Fl = 5;
Peerless 830500 XLS 12" Subwoofer, 8 Ohm, $178.65:
Vb = 172.99586891300087849957 = net box volume, liters
= 6.10947020777086512483 = net box volume, cubic feet
Vf = 5.57259235977199942235 = net volume of vented chamber, liters
= 11.294 X 6.980 X 4.314 = golden ratio inside box size, inches
Vr = 167.42327655322887907722 = net volume of sealed chamber, liters
= 35.110 X 21.699 X 13.411 = golden ratio inside box size, inches
Ff = 24.49934693007142180399 = box resonant frequency of vented chamber, Hz.
Fb = 24.49934693007142180399 = box resonant frequency of sealed chamber, Hz.
F3 = 5 = box -3 dB frequency, Hz.
Pa = -22.69976286047823509780 = gain, db
Fh = 120.0436 = upper -3 db cutoff frequency, Hz.
L = 113 = minimum longest room dimension, feet
which has an F3 of 5 Hz., and an Fh of 120 Hz., (exactly the Dolby/THX specification for a theater subwoofer.) However, an acoustically adequate room, (i.e., no parallel walls/ceiling/floor to minimize standing wave phenomena, sound absorption techniques to minimize reflected sound waves-and very large, in excess of 2500/3500 cubic feet,) would have to be used for the listening area, (note that the enclosure cubic box size is less than 2' on an edge, too.) Not to mention the inefficiency, (-23 dB,) requiring copious amounts of power, (that the 830500 may not be able to handle, except in modest sized rooms,) down to 5 Hz., (a non-trivial electronic design exercise.) As a conclusion, for high quality, low distortion, low frequency, sound reproduction, there are two applicable speaker alternatives: a sealed enclosure with electronic frequency contouring that provides bass boost/compensation to correct the low frequency roll off of the design; or, a 4th order enclosure with a sufficiently low frequency passband that handles only frequencies between F3 and Fh-all other frequencies should be filtered prior to the speaker.
Figure I. Various Dayton RSS265HF-4 10" Reference HF Subwoofer ConfigurationsFigure I is a plot of the frequency responses of various configurations of the Dayton RSS265HF-4 10" Reference HF Subwoofer:
Figure II. Frequency Response of Dayton RSS265HF-4 for Various Values of Qtc in a Sealed EnclosureFigure II is a plot of the frequency responses the Dayton RSS265HF-4 10" Reference HF Subwoofer for various values of Qtc in a sealed enclosure, with the -3 dB low frequency cutoff and internal enclosure dimensions for each Qtc:
LicenseA license is hereby granted to reproduce this design for personal, non-commercial use. THIS DESIGN IS PROVIDED "AS IS". THE AUTHOR PROVIDES NO WARRANTIES WHATSOEVER, EXPRESSED OR IMPLIED, INCLUDING WARRANTIES OF MERCHANTABILITY, TITLE, OR FITNESS FOR ANY PARTICULAR PURPOSE. THE AUTHOR DOES NOT WARRANT THAT USE OF THIS DESIGN DOES NOT INFRINGE THE INTELLECTUAL PROPERTY RIGHTS OF ANY THIRD PARTY IN ANY COUNTRY. So there. Copyright © 1992-2008, John Conover, All Rights Reserved. Comments and/or problem reports should be addressed to:
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