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BOOKSHELF SPEAKER DESIGN PROPOSAL

Charles Young FA 4740 spring 2009

These speakers will be used primarily to monitor CDs and music generated by

music composing programs to accompany musical instrument practice. They will

be located in a spare bedroom used as a music practice room. Space for

speakers is limited in the room and thus the speakers will be small and may be

mounted on a wall. Proposed design size is 8 inches thick with a baffle of 10 by

12 inches, thus fitting my bookshelves, with a volume of .55 cubic ft or 15 liters.

Anticipated loudness or power handling capability is small, less than 30 watts

RMS amplifier capacity. It is expected that the driver design shall consist of a 4

to 6 inch woofer, a tweeter and a crossover. Possible enhancements to the

frequency response should include enhanced bass response with a ported

enclosure and separate attenuation of mid-range and high frequency response,

to accommodate personal taste. Half-wave resonances in this size box are 500,

600 and 750 Hz based on c=1000 ft/sec.

Proposed frequency response should have 3 to 5 dB ripple over the range 60 to

12,000 Hz, with a fall-back narrower range of 200 to 5000 Hz. Some smooth

variation may be included for personal listening taste. It is doubtful that the sound

pressure level will exceed 90 dB at 1 meter. Some low frequency enhancement

is expected since the speakers will be mounted near or close to the wall,

Subjective qualities should include 1) clarity of individual musical instruments and

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clear high frequencies for reproduction of cymbals and high partials on stringed

instruments and 2) clear low frequencies for reproduction of string basses and

bass drum sounds. These qualities should be reflected in a wide, flat frequency

response and a transient response, which is non-oscillating; smooth for the

woofer and single-spiked for the tweeter. An extended low end of the frequency

response is achievable at a cost of enclosure size and increased cost. The

fundamental frequency for the low E string on a string bass is 41 Hz, which is

about the lowest musical note that a listener may encounter, but it is well known

that humans perceive the musical note not by its fundamental frequency but by

its partials (harmonics), and the partials have amplitudes as great or greater than

the fundamental tone. Thus, even if a speaker cannot produce such a low note,

the sensation of the sound from such a musical instrument can still be

convincingly created.

The cost of the speakers should be modest. I can appreciate that some builders

will be very serious audiophiles who want to spend plenty of money to have the

very best. My goal is to learn the design, building and evaluation techniques but I

don’t feel I have to spend top dollar in the process.

ADDITIONAL DESIGN CONSDERATIONS

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It is desirable to avoid the step in frequency response due to transition from

infinite baffle to sealed or ported box as the signal frequency is reduced. (AKA

“baffle step” 1. Solutions to the baffle step effect are:

1: Incorporate a baffle filter in the crossover.

2: Place the speaker near the wall. The combination of the speaker and the wall

approximates an infinite baffle. These speakers will be placed on or near a wall.

Also, I want to roll off the woofer response enough to reduce audibility of cone

breakup and furthermore to provide some attenuation of midrange to

accommodate personal taste. A plot of woofer response shows undulations

about 1500 Hz, followed by a roll off with increasing frequency and a bump at

about 8 kHz. I want to roll off the tweeter response with lower frequencies to

reduce audibility of tweeter resonance at about 800 Hz.

It is desirable to use a Zobel filter to counteract the inductance of the woofer

voice coil 2. The crossover design usually assumes that the woofer is pure

resistance, ignoring the inductive reactance of the voice coil. The inductive

reactance reduces the effectiveness of the crossover at higher frequencies.

1 Rod Elliot, Elliot Sound Products, http://sound.westhost.com/bafflestep.htm)., (Dec 2001), Accessed Feb 13, 2009). 2 John L. Murphy, “Neutralizing L (e) with a Zobel”, True Audio, http://www.trueaudio.com/st_zobel.htm, ND, Accessed Feb 13,2009.l

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DESIGN CHOICES AND ALTERNATIVES

Woofers and all other parts and their data sheets were found at the Parts

Express website 3. The woofers were chosen from others costing approximately

twenty dollars. Shielding of the driver magnets is not important since the

speakers will be about 1 meter away from any CRT display.

Woofer possible choices and specifications are:

Dayton DC-160-8 6 ½ inch classic woofer specifications.

Specifications: * Power handling: 50 watts RMS/75 watts max * Voice coil

diameter: 1-3/8" * Le: 2.34 mH * Impedance: 8 ohms * DC resistance: 6.7

ohms * Frequency response: 30-4,000 Hz * Magnet weight: 15 oz. * Fs: 34

Hz * SPL: 88 dB 1W/1m * Vas: .87 cu. ft. * Qms: 3.47 * Qes: .36 * Qts: .33

Goldwood GW-206/4 Specifications: *Power handling: 90 watts RMS/180 watts max

*Voice coil diameter: 1-1/2" *Le: .4 mH *Re: 3.7 ohms *Frequency range: 60-3,000 Hz

*Fs: 60 Hz *SPL: 91 dB 2.83V/1m *Vas: .42 cu. ft. *Qms: 3.50 *Qes: .73 *Qts: .61

*Xmax: 3.5 mm

Vifa TP16WJ-06-08 6-1/2" Woofer 8 Ohm (frequency response plot not

available)

Specifications: *Power handling: 70 watts RMS/100 watts max *VCdia: 1-1/4"

*Le: 1.0 mH *Impedance: 8 ohms *Re: 5.6 ohms *Frequency response: 38-5,000

Hz *Fs: 38 Hz *SPL: 87 dB 1W/1m *Vas: 1.05 cu. ft. *Qms: 2.48 *Qes: 0.52 *Qts:

0.43 *Xmax: 4.0 mm

3---------------, http://www.parts-express.com/home Accessed Feb 13, 2009.

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The frequency response plots are given below. Parts Express did not have

frequency response plots for many of the drivers in this price range.

Figure 1. Dayton DC-160-8 frequency response.

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Figure 2. Frequency response for Goldwood GW-206/4

The source for all response plots is data sheets from Parts Express website.

Of these drivers, I reject the Vifa because no plot is available, and I find the

Dayton DC-160-8 preferable because its Fs is lower, and because of the lower

magnitude of the cone breakup effects at about 5000 Hz, and because it has less

drop in frequency response at about 1200 Hz.

Tweeter. The tweeters were chosen from Parts Express website from among

many others costing approximately twenty dollars.

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Dayton DC28F-8 silk dome tweeter, resonance at about 600 Hz (shown in

impedance plot on spec sheet), undulations in frequency response between 3000

and 15,000 similar to cone breakup in a woofer. The response plot is given

below. Specifications: * Power handling: 50 watts RMS/75 watts max * Voice

coil diameter: 1-1/8" * Impedance: 8 ohms * Re: 5.5 ohms * Frequency

response (± 2 dB): 1,300-20,000 Hz * Fs: 637 Hz * SPL: 89 dB 1W/1m *

Magnet weight: 6 oz.

Figure 3. Frequency Response of Dayton DC28F-8 Silk dome tweeter.

Tang Band 25-11666SJ 1 inch Neodymimum Tweeter. Specifications:

*Power Handling: 50 watts RMS/80 watts max *Voice coil diameter: 1"

*Impedance: 4 ohms *Re: 3.0 ohms *Frequency range: 2,000-22,000 Hz

*Fs: 900 Hz *SPL: 93 dB 2.83V/1m

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Figure 4. Tang Band 25-11666SJ 1 inch Neodymimum Tweeter.

HiVi X1 1" Textile Dome Tweeter Specifications: *Power handling: 15

watts RMS/30 watts max *Impedance: 4 ohms: *Frequency range: 2,000-

20,000 Hz *Fs: 1,300 Hz *SPL: 92 dB 2.83V/1m *Dimensions: A: 4-9/16",

B: 3-1/2", C: 1-1/8". No frequency plot available.

The technical specifications for the Tang Band tweeter exceeds the Dayton:

The bandwidth is greater, but the power handling capability is smaller, which is

acceptable in a bookshelf speaker intended for low SPL. The high frequency

response may not be important in this application, since the listener is a senior

citizen with poor high frequency hearing. I will choose the Dayton tweeter

because it has a price and convenience-in-ordering advantage because it is part

of the BR-1 parts kit.

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CROSSOVER DESIGN

The proposed crossover design is shown below. The woofer crossover provides

a second order low pass filter (L2 and C2) with a 3 dB down point at about 2300

Hz, and a Zobel impedance equalizer (R1 and C3) with a 3dB down point at

about 2200 Hz. The tweeter crossover provides a high pass filter (the 6.2 mfd

capacitor and 0.4 mH inductor) with a 3 dB down point of about 1000 Hz and an

~3dB attenuator (the 4 and 6.2 ohm resistors) to equalize the slightly higher

tweeter sensitivity. The above computations were carried out with a quick

analysis of RLC filters4. The response of the completed crossover will be

measured with spectrum analysis software.

Figure 5. Proposed crossover design. 5

FINAL CONSIDERATION OF PARTS CHOICE:

4-------------, “Okawa Electric Design, RLC Filter Design Tool, ” http://sim.okawa-denshi.jp/en/RLCtool.php Accessed February 13, 2009. 5-----------------, BR-1 2-Way Reference Monitor System, Dayton Audio, Dayton Loudspeaker Co., PO Box 52, Springboro, Ohio 45066-1158 http://www.parts-express.com/pdf/300-640.pdf, page 5, Accessed February 13. 2009.

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The parts are available as a single order item from Parts Express as a BR-1 2

Way Reference Monitor kit at a cost of $139 representing about a $25 savings

compared to purchasing the parts separately. I have compared the drivers to

others in the same price range, and justified their choice. The cabinets from the

BR-1 kits will be fitted with old towels and used as cat apartments.

ENCLOSURE DETAILS

The enclosure dimensions were determined by personal taste and anticipated

space available.

Sealed box computations:

The box resonance computation6 uses the data for the DC-160-8:

Qts=.33, Vas=.87, Fs=34 Hz.

Box volume 0.25 ft3

Assumed Qtc=1 computed f3=81

Assumed Qtc=0.7 computed f3=73 Hz

Assumed Qtc=1.0 computed f3=91 Hz

Vented box computations7. I find a vented .25 ft3 box (with a port diameter of

2 inches and length of 5.43 inches) should give an f3 of 34 Hz, which is more

6 ----------------, “Sealed Speaker Enclosure Design Calculator”, (ND) http://www.carstereo.com/help/Articles.cfm?id=26, Accessed February 13, 2009. 7 -------------------, Subwoofer Box Enclosure Design Calculator - Sealed Ported Bandpass

Closed Vented, AJ Design Software, http://www.ajdesigner.com/fl_subwoofer/subwoofer.php,

(ND), accessed February 13, 2009.

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than adequate to cover the low range of a string bass. These dimensions and

frequencies seem realistic for my planned enclosure.

The port needs to be in the baffle because the speaker may be mounted on a

wall. The external finish will be flat black paint and simple grill cloth for now, or

maybe I will paint it with day-glo orange tiger stripes to shock my audience. I will

leave the edges “sharp” so I can add hardwood veneer and an eye-catching grill

cloth at my leisure. I have provided a draft “three view” diagram of the enclosure

and a cutting diagram for the MDF sheet. These were drawn without

consideration of panel thicknesses, edge-fitting rabbets or saw kerfs. These will

be added prior to cutting.

Parts will be ordered from Parts Express, MDF will be purchased and panels cut

at McGann’s Lumber in Hancock, dados and circles cut in MTU theater shop.

Estimated cost is $182.94 plus glue.

BIBLIOGRAPHY

(NON-WWW) Thiele and Small papers may be downloaded from

http://diyaudioprojects.com/Technical/

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Small, R. H., “Vented-Box Loudspeaker Systems Part I: Small-Signal Analysis”, J

of the Audio Engineering Society, 21 (1973) 316-325

Small, R. H., “Vented-Box Loudspeaker Systems Part II: Large-Signal Analysis”,

J of the Audio Engineering Society, 21, (1973) 326-313.

Small, R. H., “Vented-Box Loudspeaker Systems Part III: Synthesis”, J of the

Audio Engineering Society, 21, (1973) 333-339.

Small, R. H., “Vented-Box Loudspeaker Systems Part IV: Appendices”, J of the

Audio Engineering Society, 21, (1973) 339-344.

Thiele, A. N., “Loudspeakers in Vented Boxes, Part I”,

Journal of the Audio Engineering Society, 19, (1971), 382-392.

Thiele, A. N., “Loudspeakers in Vented Boxes, Part II”,

Proceedings of the IRE Australia, 22, (1971), 487-508.

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APPENDIX I: PARTS LIST, COST ESTIMATE, BOX DETAIL, AND

CUTTING DIAGRAM.

Source: Parts Express price each total

295-305 2 woofers 18.61 37.22

275-070 2 tweeters 18.5 37

999-200 2 crossover boards 8 16

027-352 2 47mfd 100v caps 0.88 1.76

027-452 2 .1mfd 400v caps 0.9 1.8

004-B 2 8 ohm resistor 0.24 0.48

027-418 2 4 mfd 250 poly cap 1.79 3.58

266-832 2 1.l5 mh inductor 10.1 20.2

027-427 2 6.2 mfd poly cap 2.53 5.06

015-4 2 4 ohm 5w resistor 0.24 0.48

015-6.2 2 6.2 ohm 5w resistor 0.19 0.38

260-721 2 .4 mh inductor 3.6 7.2

999-201 2 terminal cups 4 8

100-140 1 6 ft 16 gua wire 2 2

095-282 24 .205 in disconnectors 2 2

260-316B 2 acoustic foam 6.89 13.78

156.94

Cabinet:

1/2 sheet 3/4 in MDF 18

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cutting charge at McGann's 5

100 #6 1 in screws 1 3

glue is on hand

parts total 182.94

Need grill cloth too.

APPENDIX II

1. Three-views of speaker enclosure (draft).

2. Cutting diagram for MDF (draft).

3. Winspeakers response plots