From:
[email protected] (Bill McFadden) Newsgroups: comp.sources.hp48 Subject: v03i035: spkr_3.2 - Speaker Design Equations v3.2, Part01/02 Date: 17 Feb 92 14:44:43 GMT Followup-To: comp.sys.hp48 Organization: Univ. of North Carolina @ Wilmington Checksum: 418176713 (verify with brik -cv) Submitted-by: Bill McFadden
Posting-number: Volume 3, Issue 35 Archive-name: spkr_3.2/part01 BEGIN_DOC spkr.doc [Last modified 7-Feb-92] [This version differs from 3.0 in that I have included the design equations I used.] -------SPEAKER DESIGN EQUATIONS 3.2 written by Bill McFadden 1992 All Rights Reserved 1. Introduction This is a library of equations for designing ported and closed-box speaker enclosures. The equations were taken from speaker design books and technical papers by Richard Small and Neville Thiele (see references below). They are designed for unstuffed enclosures. Refer to the references for more information on stuffing. The equations are intended to be used with the HP48SX multiple equation solver in the equation library ROM card, but can also be run with the built-in HP solver. The binaries are provided in uuencoded and ->ASC form. An RPL version is also provided, but does not include the binary variable Mpar needed by the multiple equation solver. The default speaker parameters when you first download the file are for the Eminence 18029 18" driver. I welcome any comments or refinements. 2. Variables The main directory is called SPKR and consists of two subdirectories: CB PORTED
Closed Box Design Ported Box Design
Running the multiple equation solver from either subdirectory will produce a menu of variables: Vas
Volume of air having same acoustic complaince as driver suspension
Qts Fs PEmax SPL Dia xmax Vb Fb F3dB Fmax dBpeak Par Per \Gno PeakSPL Sd Vd K1 K2
Total driver Q at Fs Resonant frequency of driver Thermally-limited maximum RMS input power Efficiency of driver in dB SPL at 1W/1m Diameter of driver Peak displacement limit of driver diaphragm (1/2 of "throw") Inside volume of enclosure Resonance frequency of enclosure Half-power (-3 dB) frequency of loudspeaker system response Upper frequency limit of driver's piston range Maximum peak or dip of loudspeaker system response Estimated displacement-limited acoustic power rating Estimated displacement-limited electrical power rating Percent driver efficiency (\Gn is greek character eta) Thermally-limited RMS sound pressure level in passband Estimated effective projected surface area of driver diaphragm Peak displacement volume of driver diaphragm Power rating constant SPL rating constant
The following additional variables are defined for the closed box case: Qb Amax Vr Qr
Total Q of system at Fb Maximum amplitude of loudspeaker frequency response Ratio of Vas to Vb Ratio of Qb to Qts and Fb to Fs
The following additional variables are defined for the ported box case: Dmin Dv Lv
Minimum diameter of tubular vent to prevent excessive vent noise Diameter of tubular vent Length of tubular vent
For the ported box case, the following apply: 1. Fb is the tuning frequency for the vent. 2. To use a square vent, enter the vent width times 1.13 or [2/SQRT(pi)] for Dv. 3. Design When designing a loudspeaker, two approaches may be followed. The easiest is to select a driver and design an enclosure for it. The other is to design the enclosure first, then select or build a driver that matches it. The choice between a closed box and ported box depends on several factors. Closed-box systems are the easiest to design and build and have the advantages of smaller box size, good low-frequency power handling, and superior transient response. Ported-box systems are more difficult to design because they require precise duct tuning. However, ported boxes have the advantages of superior bass response, good efficiency, and superior peak power handling in the passband. 3.1 Closed-Box Systems
Closed-box systems are designed around one variable, box volume. Box volume is a function of the driver parameters and the system Q, Qb. To design a system with minimum peak or droop in the passband, Qb must be 0.707. The designer has the choice of setting Qb and solving for the box volume, or setting the box volume and solving for Qb. There is also the choice of assigning values to both of these variables and solving for one of the driver parameters. To design a closed-box system, enter the CB subdirectory and run the multiple equation solver. Alternatively, run the HP solver and select DESIGN.EQ as the current equation. Choose one of the following variables to solve for and assign values to the rest: Vas, Qts, Fs, SPL, Dia, xmax, Qb, and Vb. If you don't have all of the parameters available, purge the ones you don't know, so they'll be undefined and the solver won't attempt to use them. At a minimum, you will need to supply all but one of Vas, Qts, Fs, Qb, and Vb. Next, press <- ALL in the multiple equation solver for solve for all the unknowns. If using the HP solver, you will need to solve for each unknown individually, using NXEQ to sequence through the equations. 3.2 Ported-Box Systems Ported-box systems are a little more difficult than closed box systems because there is an additional variable, tuning frequency. The optimum tuning frequency depends on the driver parameters and box volume. To design a ported-box system, enter the PORTED subdirectory. Run the equation solver of your choice as described above and enter the driver parameters. Notice there is no Qb variable. At this point solving for the unknowns will automatically create a system with optimum passband response. Alternatively, you can specify values for Vb and/or Fb to see what effect they have on the system response. To find the minimum recommended diameter of a tubular vent for the enclosure, solve for Dmin. This is smallest diameter permissible to keep the air velocity below 5% of the speed of sound. Higher velocities can produce audible noise. To calculate the vent dimensions, enter either of Dv and Lv and solve for the other, keeping in mind the minimum recommended value of Dv. 3.3 Cabinet Design In the CST menu of the CB and PORTED subdirectories is a key labeled BCALC. Pressing this key runs the box calculator program. Don't run it directly from the SPKR subdirectory, or it will not work properly. The program is rather crude, and does not handle dual woofers, but is adequate for most designs. It works as illustrated by modeling the driver as a segment of a solid cone:
_____ /| ^ / | | / | | / | | _____ / | | ^ | | | | | | | Rdia | | Dia | | | | __v__ | | | \ | | | \ | | | \ | | | \ | | | \| __v__ | | | |<-Depth->| | | To use, enter the driver's depth (distance from front of driver to back of magnet) and press DEPTH. Enter the rear (magnet) diameter of the driver and press RDIA. If you want the program to account for any extra volume taken up by bracing and other drivers, enter this volume and press XVOL. The program uses the driver's diameter as entered previously in the equation solver. The dimensions default to English units. The program will only accept real numbers as input; unit objects will cause an error. (I said it was crude.) To change units, store a value containing the new unit by typing 'name' STO, where name is one of Depth, Rdia, or Xvol. The units of the results should make sense based on the units of the data, but I won't guarantee it. You can also change the ratio of Height:Width:Depth used in the box calculation by pressing GOLD, 1.25:1, or CUST. GOLD selects the golden mean, 1.62:1:0.62 ((sqrt(5)+1)/2), which is the most common ratio. 1.25:1 selects another common ratio, 1.25:1:0.8. If you wish to use a custom ratio, enter it and press CUST. Each time you change a parameter using a menu key, the results will be recalculated and redisplayed. The display shows, from top to bottom, the driver's front diameter, the driver's rear diameter, the driver's depth, the extra volume taken up by other objects inside the cabinet, the total internal volume of the cabinet (including driver and extra volume), the ratio used to calculate the box dimensions, and the inside height, width, and depth of the cabinet. FIX 2 is the best display format to use with the default units. 3.4 Equalization of Closed-Box Systems There is a subdirectory in CB called EQUALIZER that will find the component values for an active equalizer that can extend
F3dB of any closed box system to any desired lower limit (at the expense of efficiency and power handling--watch out!) See [9] for theory and circuit details. First, use the equation solver in the CB subdirectory to solve for the system as shown above. Next, enter the EQUALIZER subdirectory. Store the new desired cutoff frequency into F3dB, and press CIRCUIT. The component values will appear in the display. The values of R, C, N are chosen by the user to make the remaining component values realistic (see [9]). 4. Analysis 4.1 Frequency Response The equation solver generates three values related to frequency response, F3dB, Fmax, and dBpeak. F3dB is speaker drop 12 for the
the frequency at which the acoustic output power of the drops by half. Below this frequency, the response will dB per octave for the closed box and 24 dB per octave ported box.
Fmax is the upper limit of the driver's piston range. Piston range is defined as the range of frequencies for which the wavelength of sound is greater than the circumference of the driver's diaphragm. In this range, the driver's output is non-directional. Since this package models the driver as a piston, it is important to note that the equations are only accurate up to Fmax. In addition, because it is difficult to predict the driver's high-frequency behavior, it is a good idea to cross over to a smaller driver at or below Fmax. dBpeak is the magnitude of the frequency response peak or dip. For an optimal design, this value will be zero. To examine the frequency response in detail, enter the CB or PORTED subdirectory and run the plotter or HP solver. Select FREQresp from the equations catalog. F is the frequency variable, and dBmag is the response at that frequency. Using the solver you can solve for one in terms of the other. 4.2 Power Handling The equation solver generates power ratings called Par and Per. Par is the displacement-limited acoustic power rating. For the closed box, Par is the worst-case value for wide-band signals (all the way down to DC). For the ported box, it is an estimate based on the characteristics of musical signals. Per is the displacement-limited electrical RMS power rating based on Par. Because displacement-limited power handling is actually a function of frequency, the values of Par and Per only give
small part of the picture. To examine power handling in detail, enter the CB or PORTED subdirectory and run the plotter or HP solver. Select POWresp from the equations catalog. F is the frequency variable, and Pmax is the maximum electrical input power at that frequency. Pmax is plotted first, followed by PEmax, the manufacturer's thermal RMS power rating. At some frequencies, Pmax will exceed PEmax. As frequency increases, Pmax can reach thousands of watts. Exceeding PEmax is permissible for short durations, but under no circumstances should you exceed Pmax even briefly or the driver may be physically damaged. Because Pmax is calculated with sine waves in mind, the peak power rating at a given frequency will be 2*Pmax. Using the ISECT function of the plotter, it is possible to determine the frequency range(s) over which it is safe to apply the full rated thermal power, PEmax, without damage from excessive displacement. Just place the cursor near the intersection of the curves and press ISECT in the FCN submenu. In the same manner, you can also use ISECT to find frequencies where the curves approach one another but don't touch. 4.3 Sound Pressure Level The equation solver generates a value for maximum SPL called PeakSPL. This is the maximum RMS output level of the system in the passband when driven by the thermally-limited maximum input power, PEmax. Like power handling, displacement-limited SPL is a function of frequency. To examine displacement-limited SPL in detail, enter the CB or PORTED subdirectory and run the plotter or HP solver. Select SPLresp from the equations catalog. F is the frequency variable and SPLmax is the displacement-limited SPL at that frequency. SPLmax is plotted first, followed by the thermally-limited RMS sound pressure level. As before, for frequencies where SPLmax exceeds the thermally-limited SPL, the maximum SPL may be limited to a value in between, depending on the peak-to-average power ratio of the input signal. Again, ISECT can be used to find the frequency or frequencies at which the displacement- and thermally-limited SPL ratings are equal. 4.4 Analysis of Equalized Closed-Box System Using an equalizer to extend the bass response of a closed-box system does not come without costs. For each octave of bass extension, a 12 dB boost is necessary (and requires 16 times as much power). To evaluate these costs, two equations are provided in the EQUALIZER subdirectory: FREQresp and POWresp. These function like their counterparts in the CB and PORTED subdirectories, but take into account the effects of the equalizer.
Because I took the equations right out of the article [9] without any optimization for speed, these equations run very slowly. However, I left out the units wherever possible so the equations would run faster. FREQresp calculates the response of the equalizer, rather than the system, to give you an idea of the amount of boost required to equalize the system. The greatest boost occurs at the new F3dB. POWresp calculates the equivalent power handling of the system. At each frequency, Pmax is reduced by the amount of boost the equalizer provides. This is useful to see what the power handling of an equivalent, unequalized system would be. There is no equation for maximum SPL vs. frequency because it is the same as the unequalized system. 5. Design Equations Here are the equations used by the speaker design library. All values have SI (mks) units. ^ denotes exponentiation. LOG() is base 10. 5.1 Contants pi = 3.14159265359 c = speed of sound in air (345 m/s) Ro = density of air (1.18 kg/m^3) 5.2 Closed-Box Systems Vb = Vas/Vr Fb = Qr/Qts F3dB = Qr*Fs*((1/Qb^2-2+((1/Qb^2-2)^2+4)^0.5)/2)^0.5 Fmax = c/(pi*0.83*Dia) dBpeak = 20*LOG(Amax) Par = K1/Amax^2 Per = Par/(\Gno) \Gno = 10^((SPL-112)/10) PeakSPL = SPL+10*LOG(PEmax) Sd = pi*(Dia*0.83)^2/4 Vd = Sd*xmax Amax = Qb^2/(Qb^2-0.25)^0.5 for Qb >1/2^0.5, 1 otherwise K1 = (4*pi^3*Ro/c)*Fb^4*Vd^2 K2 = 112+10*LOG(K1) Vr = Qr^2-1 Qr = (1/Qts)/(1/Qb-0.1) Frequency-dependant equations: Fr = (F/Fb)^2 dBmag = 10*LOG(Fr^2/((Fr-1)^2+Fr/Qb^2)) Pmax = K1*((Fr-1)^2+Fr/Qb^2))/(\Gno) SPLmax = K2+40*LOG(F/Fb) Thermally-limited RMS SPL = PeakSPL+dBmag 5.3 Ported Box Systems Vb = 20*Qts^3.3*Vas
Fb = (Vas/Vb)^0.31*Fs F3dB = (Vas/Vb)^0.44*Fs Fmax = c/(pi*0.83*Dia) dBpeak = 20*LOG(Qts*(Vas/Vb)^0.3/0.4) Par = 3*F3dB^4*Vd^2 Per = Par/(\Gno) \Gno = 10^((SPL-112)/10) PeakSPL = SPL+10*LOG(PEmax) Dmin = (Fb*Vd)^0.5 Lv = 2362*Dv^2/(Fb^2*Vb)-0.73*Dv Sd = pi*(Dia*0.83)^2/4 Vd = Sd*xmax K1 = (4*pi^3*Ro/c)*Fs^4*Vd^2 K2 = 112+10*LOG(K1) Frequency-dependent equations: Fn2 = (F/Fs)^2 Fn4 = Fn2^2 A = (Fb/Fs)^2 B = A/Qts+Fb/(7*Fs) C = 1+A+(Vas/Vb)+Fb/(7*Fs*Qts) D = 1/Qts+Fb/(7*Fs) E = (97/49)*A dBmag = 10*LOG(Fn4^2/((Fn4-C*Fn2+A)^2+Fn2*(D*Fn2-B)^2)) Pmax = (K1/\Gno)*((Fn4-C*Fn2+A)^2+Fn2*(D*Fn2-B)^2)/(Fn4-E*Fn2+A^2) SPLmax = K2+10*LOG(Fn4^2/(Fn4-E*Fn2+A^2)) Thermally-limited RMS SPL = PeakSPL+dBmag END_DOC BEGIN_MISC spkr.txt [Last modified 21-Aug-91] LOUDSPEAKERS TUTORIAL by William K. McFadden For the purposes of this discussion, an optimum enclosure is defined as one that has no peak or droop in the passband response. 1. Power Ratings The power rating of a driver is usually (but not always) specified in watts RMS by the manufacturer. This is the continuous thermal power rating of the driver. Exceeding this rating for more than a moment will cause voice coil overheating, which can result in warping or burn-out. Speaker systems also have a displacement-limited power rating (Per). This is the amount of power the system can take without exceeding the absolute maximum voice coil displacement. Per is a function of frequency and depends on the design of the enclosure. Thus, it is meaningless for manufacturers to specify peak power handling without also specifying the enclosure and the frequency range. At some frequencies, Per will exceed the thermal RMS power rating. For continuous tones, the smaller of the two ratings applies. For signals with large crest factors or low duty cycles, Per applies, providing the average power does not exceed the
thermal rating. Per is calculated for sine waves, which have a 3 dB crest factor. The peak power rating at a given frequency is therefore 2*Per. 2. Efficiency & Loudness The efficiency of a driver is given in decibels of sound pressure level (SPL). 0 dB SPL is defined as 2.0E-10 bar (2.0E-5 N/m^2), which is the lowest level of 1 kHz tone the average person can detect. A 10 dB increase in SPL results in an apparent doubling of the loudness and requires 10 times as much power. Accordingly, a 10 dB decrease halves the loudness and reduces the power requirement by a factor of 10. Most driver manufacturers specify the SPL of the driver with a one watt input measured at a distance of one meter. To calculate the SPL at other power levels, add the following number to the SPL rating: 10*log(POWER), where POWER is in watts, and the log is base 10. This equation is derived from the fact that a doubling of electrical power produces an doubling of acoustic power. To calculate the SPL at other distances, subtract the following number from the SPL rating: 20*log(DISTANCE), where DISTANCE is in meters. This equation is derived from the inverse square law of wave propagation. One watt of acoustic power is equal to 112 dB SPL at one meter. To calculate the efficiency of the speaker in percent, use the following: %EFFICIENCY = 100*(10^((SPL - 112)/10)), where SPL is the driver's SPL rating in dB, at one watt, measured at one meter. For example, a driver with a 92 dB SPL rating @ 1W/1m is 1% efficient. 3. Sealed Box Enclosures For the sealed box enclosure, the optimum volume can be determined. Many designers like to use a 0.62:1:1.62 ratio for the cabinet dimensions. This is known as the golden ratio. A box designed to this ratio will have smaller resonant peaks than one whose dimensions are equal. Another ratio sometimes used is 0.8:1:1.25. You can determine the middle dimension by taking the cube root of the enclosure volume. (Keep in mind this is the inside volume and doesn't take into account the volume taken up by bracing materials and the drivers.) The box will have a resonant frequency and a Q. For an optimum sealed box, the resonant frequency is equal to the -3 dB point, and the Q is 0.707. The -3 dB frequency is also known as the half-power point, because it is the frequency at which the acoustic output power drops by half. Below this frequency, the response will have a second order roll off, e.g., the output decreases 12 dB for every halving of the frequency below the -3 dB point. 4. Ported Box Enclosures The ported enclosure is a little more complicated. As with the sealed box, the ported enclosure has an optimum volume and -3 dB
point. The enclosure also has an optimum tuning frequency, Fb, which is the resonant frequency of the enclosure's duct. The tuning frequency is determined by the cross sectional area and length of the duct. For a tubular duct, the following equation applies, LENGTH = 2118*DIAMETER^2/(Fb^2*Vb) - 0.73*DIAMETER, where LENGTH is the length of the duct in inches, DIAMETER is the inside diameter of the duct in inches, Fb is the tuning frequency in Hz, and Vb is the box volume in cubic feet. Ported enclosures have a steeper roll off than sealed boxes. The roll off is fourth order, or 24dB for every halving of the frequency below the -3dB point. Below Fb, the displacement-limited power rating will be very low because the driver is essentially operating free air. It is therefore wise to roll off the signal below the -3dB frequency to avoid damage. This constraint does not usually apply to sealed boxes, which damp cone movement at all frequencies. REFERENCES: [1] Hobbyist speaker building books, such as the one sold by Radio Shack. [2] L.L. Beranek, Acoustics (McGraw-Hill, New York, 1954). [3] J.F. Novak, "Performance of Enclosures for Low-Resonance High-Compliance Loudspeakers," J. Audio Eng. Soc., vol. 7, p 29 (Jan. 1959). [4] A.N. Thiele, "Loudspeakers in Vented Boxes, Parts I and II," J. Audio Eng. Soc., vol. 19, pp. 382-392 (1971 May); pp. 471-483 (1971 June). [5] R.H. Small, "Direct-Radiator Loudspeaker System Analysis," J. Audio Eng. Soc., vol. 20, pp. 383-395 (1972 June). [6] R.H. Small, "Closed-Box Loudspeaker Systems," J. Audio Eng. Soc., vol. 20, pp. 798-808 (1972 Dec.); vol. 21, pp. 11-18 (1973 Jan./Feb.). [7] R.H. Small, "Vented-Box Loudspeaker Systems," J. Audio Eng. Soc., vol. 21, pp. 363-372 (1973 June); pp. 438-444 (1973 July/Aug.); pp. 549-554 (1973 Sept.); pp. 635-639 (1973 Oct.). [8] G. Margolis and R. H. Small, "Personal Calculator Programs for Approximate Vented-Box and Closed-Box Loudspeaker System Design," J. Audio Eng. Soc., vol. 29, pp. 421-441 (1981 June); pp. 824 (1981 Nov.). [9] W.M. Leach, Jr., "A Generalized Active Equalizer for Closed-Box Loudspeaker Systems," J. Audio Eng. Soc., Vol. 38, pp. 142-145 (March 1990). [1] is useful as an introduction and has a lot of construction tips. [2] is a the industry bible on acoustics. [3] is historically significant, and is the foundation for [4]. [4] and [6] are the landmark works on loudspeaker systems (you can't consider yourself knowledgeable without having read them). [5] is background for [6],
and [7]. [7] updates the original work of [4]. [8] presents versions of the equations of [4] through [7] suitable for programmable calculators as well as example programs using them. [9] is a recent paper that shows how to equalize closed-box systems to any desired low-frequency cutoff. [3], [4], [5], [6], and [7] are reprinted in the AES two-part "Loudspeakers" anthology. END_MISC BEGIN_RDME spkr.rdm [Last modified: 6-Feb-92] Speaker Design 3.2 files: README:
This file
spkr.doc:
Instructions for use
spkr.txt:
Loudspeakers tutorial
spkr.rpl:
RPL Source code BYTES #70F0h 8515
spkr.asc:
->ASC encoded binary (requires memory card to download) BYTES #DFFDh 11522
spkr.uu:
Uuencoded binary BYTES #DFFDh 11522
END_RDME BEGIN_RPL spkr.rpl %%HP: T(3)A(R)F(.); DIR CB DIR FREQresp ' dBmag=Fresp' POWresp.EQ { 'Pmax=Presp' PEmax } SPLresp.EQ { 'SPLmax=K2+40*LOG(F /Fb)' 'PeakSPL+ Fresp' } DESIGN.EQ { ' Vb=Vas/Vr' 'Fb=Qr* Fs' 'F3dB=Qr*Fs*\v/(( 1/Qb^2-2+\v/((1/Qb^22)^2+4))/2)' ' dBpeak=20*LOG(Amax) ' 'Fmax=(345_m/s)/( \pi*.83*Dia)' 'Amax= IFTE(Qb>INV(\v/2),SQ( Qb)/\v/(SQ(Qb)-.25),1 )' 'Vr=Qr^2-1' 'Qr= 1/Qts/(1/Qb-.1)' ' K1=(4*\pi^3*1.18_kg/m
^3)*Fb^4*Vd^2/345_m /s' 'Par=K1/Amax^2' 'K2=112_dB+10*LOG( UVAL(UBASE(K1)))' ' PeakSPL=SPL+10*LOG( UVAL(UBASE(PEmax))) ' 'Per=Par/\Gno' '\Gno= 10^((SPL-112_dB)/10 )' 'Vd=Sd*xmax' 'Sd =\pi*(Dia*.83)^2/4' } Fresp \<< F Fb / SQ \-> Fr \<< Fr DUP SQ SWAP 1 - SQ Fr Qb INV SQ * + / LOG 10 * \>> \>> Presp \<< F Fb / SQ \-> Fr \<< Fr 1 SQ Fr Qb INV SQ * + K1 * \Gno / UBASE \>> \>> Vas '10.7_ft^ 3' Qts .33 Fs '30_Hz' PEmax '200_W' SPL '95_dB' Dia '18_in' xmax '.216_in ' Vb ' 2.47875886772_ft^3' Qb .707106781188 Fb ' 69.1737579888_Hz' F3dB ' 69.1737579886_Hz' Fmax ' 289.390925206_Hz' dBpeak '0_dB' Par ' 3.73964138179_W' Per ' 187.42605189_W' \Gno ' 1.99526231497_ Percent' PeakSPL ' 118.010299957_dB' Sd ' 175.303697504_in^2' Vd ' 37.8655986609_in^3'
Amax 1 K1 ' 3.73964138179_W' K2 ' 117.728299569_dB' Vr 4.3166764381 Qr 2.30579193296 F '102.5_Hz' dBmag ' -21.586698043_dB' Pmax ' 188.735789983_W' SPLmax ' 96.1718445896_dB' Depth '7.75_ in' Rdia '8.375_ in' Xvol '.15_ft^ 3' Ratio 1.61803398875 EQ FREQresp PPAR { (0,-12) (200,6) F 0 (0,0) FUNCTION Y } EQUALIZER DIR CIRCUIT \<< RCLF CLLCD 2 ENG "R1=" ' 1.0824/(C1*\Gw1)' \->NUM \->STR + " R8 =" + '(1-k)/k *R10' \->NUM \->STR + 1 DISP "R2=" '.9239/( C1*\Gw1)' \->NUM \->STR + " R9 =" + '(1-k)/ ABS(m)*R10' \->NUM \->STR + 2 DISP "R3=" '2.613/(C2*\Gw1)' \->NUM \->STR + " R10 =" + R10 \->STR + 3 DISP "R4=" ' .3827/(C2*\Gw1)' \->NUM \->STR + " R11 \>=" + ' 2*n/(\Gw1*C3)' \->NUM \->STR + 4 DISP "R5=" 'ABS(m)*R6' \->NUM \->STR + " C1-3=" + 1 ENG C \->STR + 5 DISP 2 ENG "R6=" R6 \->STR + " C4 \>=" + '2*n* C3' \->NUM \->STR + 6 DISP "R7=" '1/(\Gw1* C3)' \->NUM \->STR + 1 ENG " m= " + m \->NUM \->STR + 7 DISP
3 FREEZE STOF \>> F3dB 16 R 33000 C .000001 n 25 FREQresp 'dBmag=20*LOG(ABS(A (s)))' POWresp ' Pmax=Presp/SQ(ABS(A (s)))' Presp \<< F Fb UBASE UVAL / SQ \-> Fr \<< Fr 1 - SQ Fr Qb INV SQ * + K1 * \Gno / UBASE \>> \>> A \<< \-> s ' 1/(1-k)*(1-k*H1(s)+ m*(\Gw1/s)*H1(s))*H2( s)' \>> H1 \<< \-> s ' (s/\Gw1)^2/((s/\Gw1)^2+ .7654*s/\Gw1+1)' \>> H2 \<< \-> s ' (s/\Gw1)^2/((s/\Gw1)^2+ 1.8478*s/\Gw1+1)' \>> \Gw '2*\pi*F' s 'i*\Gw' \Gw1 '2*\pi* F3dB' \Gwc '2*\pi* Fb/1_Hz' k '1-(\Gw1/ \Gwc)^2' m '\Gw1/(Qb *\Gwc)-.7654' C1 C C2 C C3 C R6 R R10 R F 16 dBmag 22.434400121 Pmax ' 1.07307789402_W' EQ FREQresp PPAR {
(0,-6) (100,24) F 0 (0,0) FUNCTION dBmag } CST { CIRCUIT F3dB R C n } END CST { BCALC EQUALIZER } END PORTED DIR FREQresp ' dBmag=Fresp' POWresp.EQ { 'Pmax=Presp' PEmax } SPLresp.EQ { 'SPLmax=Sresp' ' PeakSPL+Fresp' } DESIGN.EQ { ' Vb=20*Qts^3.3*Vas' 'Fb=(Vas/Vb)^.31*Fs ' 'F3dB=(Vas/Vb)^ .44*Fs' 'dBpeak=20* LOG(Qts*(Vas/Vb)^.3 /.4)' 'Fmax=(345_m/ s)/(\pi*.83*Dia)' '\Gno =10^((SPL-112)/10)' 'Sd=\pi*(Dia*.83)^2/4 ' 'Vd=Sd*xmax' 'K1= (4*\pi^3*1.18_kg/m^3) *Fs^4*Vd^2/345_m/s' 'Par=(3_kg*s/m^4)* F3dB^4*Vd^2' 'K2= 112_dB+10*LOG(UVAL( UBASE(K1)))' ' PeakSPL=SPL+10*LOG( UVAL(UBASE(PEmax))) ' 'Per=Par/\Gno' 'Lv= (2362_m^2/s^2)*Dv^2 /(Fb^2*Vb)-.73*Dv' 'Dmin=\v/(Fb*Vd*1_s/m )' } Fresp \<< F Fs / SQ Fb Fs / SQ \-> Fn2 A \<< A Qts / Fb 7 / Fs / + 1 A + Vas Vb / + Fb 7 / Fs / Qts / + Qts INV Fb 7 / Fs / + \-> B C D \<< Fn2 SQ DUP SQ SWAP C Fn2 * - A + SQ D Fn2 * B - SQ Fn2 * + / LOG 10 * \>> \>>
\>> Presp \<< F Fs / SQ DUP SQ Fb Fs / SQ DUP 97 * 49 / \-> Fn2 Fn4 A E \<< A Qts / Fb 7 / Fs / + 1 A + Vas Vb / + Fb 7 / Fs / Qts / + Qts INV Fb 7 / Fs / + \-> B C D \<< K1 \Gno / Fn4 E Fn2 * - A SQ + / Fn4 C Fn2 * - A + SQ D Fn2 * B - SQ Fn2 * + * UBASE \>> \>> \>> Sresp \<< F Fs / SQ Fb Fs / SQ DUP 97 * 49 / \-> Fn2 A E \<< Fn2 DUP SQ DUP SQ SWAP ROT E * - A SQ + / LOG 10 * K2 + \>> \>> Vas '10.7_ft^ 3' Qts .33 Fs '30_Hz' PEmax '200_W' SPL '95_dB' Dia '18_in' xmax '.216_in ' Vb ' 5.51454614187_ft^3' Fb ' 36.8436116154_Hz' F3dB ' 40.1592705693_Hz' Fmax ' 289.390925206_Hz' dBpeak ' 5.63229874882E-2_dB ' Par ' 3.00439114363_W' Per ' 150.576248601_W' \Gno ' 1.99526231497_ Percent' PeakSPL ' 118.010299957_dB'
Dmin ' 5.95278736648_in' Dv '6_in' Lv ' 5.80912890373_in' Sd ' 175.303697504_in^2' Vd ' 37.8655986609_in^3' K1 ' .132296847403_W' K2 ' 103.215494952_dB' F '50_Hz' dBmag ' -21.2138986833_dB' Pmax ' 29.8704846312_W' SPLmax ' 88.5385240051_dB' Depth '7.75_ in' Rdia '8.375_ in' Xvol '.2_ft^3 ' Ratio 1.61803398875 EQ FREQresp PPAR { (0,-12) (200,6) F 0 (0,0) FUNCTION Y } CST { BCALC } END BCALC \<< BDISP { { "DEPTH" \<< Depth OBJ\-> SWAP DROP \->UNIT 'Depth' STO BDISP \>> } { "RDIA" \<< Rdia OBJ\-> SWAP DROP \->UNIT 'Rdia' STO BDISP \>> } { "XVOL" \<< Xvol OBJ\-> SWAP DROP \->UNIT 'Xvol' STO BDISP \>> } { "GOLD" \<< '(\v/5+1)/2' EVAL 'Ratio' STO BDISP \>> } { "1.25:1" \<< 1.25 'Ratio' STO BDISP \>> } { "CUST" \<< 'Ratio' STO BDISP \>> } } TMENU
\>> BDISP \<< .9 Dia * 2 / Rdia 2 / \-> r1 r2 \<< Depth r1 * r1 r2 - / \-> h1 \<< h1 Depth - \-> h2 \<< 'VOL(r1 ,h1)-VOL(r2,h2)' EVAL \-> dvol \<< "Dia:" Dia \->STR DUP SIZE 1 - 2 SWAP SUB + " RDia:" + Rdia \->STR DUP SIZE 1 - 2 SWAP SUB + 1 DISP "Driver depth:" Depth \->STR + 2 DISP "Extra vol:" Xvol \->STR + 3 DISP "Vt:" Vb dvol + Xvol + \->STR + " R:" + Ratio \->STR + 4 DISP Vb Xvol + dvol + 3 XROOT \-> w \<< "Inside H:" w Ratio * \->STR + 5 DISP "Dimen- W:" w \->STR + 6 DISP "sions D:" w Ratio / \->STR + 7 DISP 3 FREEZE \>> \>> \>> \>> \>> \>> VOL \<< \-> r h '\pi/3*r^ 2*h' \>> Percent .01 CST { CB PORTED } END END_RPL From: [email protected] (Bill McFadden) Newsgroups: comp.sources.hp48 Subject: v03i036: spkr_3.2 - Speaker Design Equations v3.2, Part02/02 Date: 17 Feb 92 14:45:52 GMT Followup-To: comp.sys.hp48 Organization: Univ. of North Carolina @ Wilmington Checksum: 4234289547 (verify with brik -cv) Submitted-by: Bill McFadden Posting-number: Volume 3, Issue 36 Archive-name: spkr_3.2/part02