References - PDF document

References [l] R.H. SMALL: “Direct Radiator Loudspeaker System Analysis”,IEEE Trans. Audio & Electro-acoustics, Vol. AU-19 (Dec. 1971) J.R. ASHLEY M.D. SWAN: at 37’h Convention of the Audio Engineering Society, New York [3] H. HERLUFSEN: “Dual Channel FFT Analysis (Part I)“, Brüel &Kjær Technical Review, No.1 Technical Review, No.1 L.L. BERANEK: “, McGraw-Hill, New York, 1954 R.H. SMALL: Loud- speaker System Analysis, Part 1:Analysis “, J. Audio Engineering Society, Vol. 10 (Dec. 1972) nique can be increased by using aand perform the calculations. Input 1 &. V, Diameter Perform r-l 1 ZI Measurement {Free- Find Fs, IZI,.,, F,, Fz Standin 9) I I I + . Place Driver InTest Box J Perform IZI Measurement Find Fc, IZI,. F,, F2 1 .Calculate 0,s. 0,s Qrs. v*s C,,. M,sz BL. no 1 Plot I&l (f) 8 I&l (f) Fig. 4. Flow chart for control/calculationprogram. 1 5. Diagram of FFT-based measurement system for measuring Thiele-Small parameters Dual Channel SignalAnalyzer Type 2032134Channel A

Channel E “Direct Input” “Direct Input” A0 0261 EC/IEEE nterface BUS THIELE - SMALL PARAtlETERS RS 40-124OD Fs- 153.5 Hz FC- 208 Hz Fls- 129 Hz F2s=179 Hz Flc- 186 Hz F2c=230 Hz Re- 6.5 ohms Zmars- 24.20 ohms Zmaxc- 25.40 ohms Qms- 5.86 Wmc- 9.34 Pcs- 2.15 Pec- 3.21 c!ts= 1.58 4tc- 2.39 Vas- 3.07 liters Ca?#= 2.1744E-08 m”5/N Mas- 4.9442E+Ol kg/m”4 Ra?,= S.l304E*03 Ns/m”5 Bl = 2.861 W/m no = 494 % (21 @ :OO Hz = 7.9 ohms Driver Diameter 9.0 centimeters Uolums of Test Box- 3 liters test driver The resonant frequency, F,, of the driver is found where the impedance is (Z,,,). If RE is the DC resistance of the driver, then according Small,131 the ratio of the maximum voice-coil impedance to the DC resis-tance is defined as r0 = Zmaxl& (2) Two frequencies, F,, F, and F2s � Fs, can be found on the imped- ance plot where IZI =fi& (3) thenQ Fs 6 MS= F,s-F,s (41 andQES_ &MS r. - 1 (5) The measurement procedure is thenrepeated with the driver mounted in aadd a known compliance

to the sys-tem. An upward shift in the resonantfrequency is observed as shown inFig. 3. The new resonant frequency is Fcr, and the corresponding frequencies FICT and FzCT are obtained using the same procedure describedabove. Then,QMCT = FCT ti F F (6) XT- IC? andQECT_ QMCT To 1 (7) CalculationsThe remaining parameters can becalculated from the previously mea-sured data. From Small[ll: QQMS QESTS = + (8) andVAS= VT FCT QECT _ 1 Fs QES 1 (9) where VT is the internal volume of thetest box. VT and VAS are generally ex- pressed in liters. From this, the acous-tic compliance of the driver can bedeterminedCVASAS= 1ooop,c* where p0 is the density of air and c is the velocity of sound, the factor of1000 converts VAS from liters to cubic meters. So (11) The units are meters5/Newton. The acoustic mass of the driver can be re-lated to the compliance with the reso-nant frequencyL41 = 1 4*‘Fs2CAS (121 Here, the units are kilograms/meter4. The BL product can also be calculated from these parameters. First, we cal-culate the a

coustic mass of the driverin the test box,MACT = MAS -$[I (13) Then, let So be the effective surfacearea of the driver. This is calculated cl, of the driver from the middle of the surroundto the middle of the surround. Then SD d2 CT- 4and BL =JY measured in Webers/meter. Theacoustic resistance of the driver sus- (14) (15) RAS = B2L2Q~s QMS RE SD* (16) The units are Newton-seconds/meter5. The acoustic reference efficiency is 472 70 Fs3 V,s z-x- cs Q ESFor VAS in liters (171 70 = 9,6 x lo-10 9 (18) ESThis number is usually multiplied by100 and expressed in percent.ApplicationA tuned closed or ported box systemcan be designed using these parame-be predicted by varying the volume ofthe box to be designed to obtain thedesired alignment. The reference ef- ficiency is used to match drivers ofsimilar efficiency in a multi-way sys-tem. CAS, and RAS can be used for equivalent circuit modelling. The BLproduct is used in the design and qual-ity control of drivers.Computer Implementa-tionEven with a hand calculator, thecalculations

involved in this analysismentation is attractive for several rea-sons. The calculations can be per-1000 Q resistor is used in the measure- and The scaling factor of 1000 is easily a V to I converter(transconductance amplifier) could beused. For most drivers, however, theThe output resistance of the genera-tor can also affect the impedance mea-with the 1 kR resistor and the voice coil resistance. If the output voltage ofthe generator does not drop under loadimpedance measurement.[‘l. Input SourceTraditionally, swept-sine measure-ments have been used to determinethe response versus frequency of a lin-ear system. This method, while accu-these measurements has the option ofwhite noise, or pseudo-random noise.One advantage of using a random sig-tered to suit the particular frequencydynamic range of the measurement.l”] When using white noise as an inputexcitation, a Hanning weighting func-the analysis. The pseudo-random sig-yields discrete frequency componentscoincident with the frequency lines inthe analyzer. An advantage of usi

ngfact that fewer averages are requiredwhite-noise excitation, while some-what slower, should be used for non-linear systems, as it provides the opti-sponse function.131 In addition to the speed advantagegained in using an FFT analyzer, theresult appears in a format that can beinterpreted immediately by the user.The analyzer can be scaled to read out4 Type 2032 sign. : Christopher Mess. Object:RS 40-124OD 4 inch driverComments:Fig. 2. Impedance plot for free-standing driver. Plot made with Graphics Plotter Type 2319Type 2032 Sign. : ChristopherJ. Struck Mess. m,ect: RS 40-l 240 D4 inch drivercomments:Fig. 3. Impedance plot for driver mounted in test box. Plot made with Graphics Plotter Type2319directly in ohms and Hertz, linearly orwith a digital plotter via the IEEE 488MeasurementThe first measurement is taken withthe driver free-standing. The imped-ance plots obtained will have the char-vents in the rear of the magnet struc-ture, if the driver is so equipped. Dur-ing the measurement, the driver maytest table, provided this structur