Single Pass Measurement of Thiele and Small Parameters using a
Contents
1. AN 003 E APPLICATION NOTE SINGLE PASS MEASUREMENT OF THIELE AND SMALL PARAMETERS USING A LASER TRANSDUCER by Daniele Ponteggia do audiomatica com INTRODUCTION CLIO 10 has introduced the support for laser displacement transducers and stereo si nusoidal measurements These two new features together with the I Sense impedance measurement mode allows to measure in a single sinusoidal sweep the impedance and the displacement as function of frequency of the loudspeaker under test Consequently this allows to obtain the Thiele amp Small driver parameters in a sin gle pass instead of the two measurements plus post processing required by the added mass or known volume approaches The loudspeaker can be modeled as a lumped electrical mechanical acoustical circuit the Thiele amp Small theory deals with the parameters of this equivalent circuit i R Z u Mys Ois Rus electrical mechanical acoustical Figure 1 Equivalent Circuit AN 003 1209 1 11 SINGLE PASS MEASUREMENT OF T amp S PARAMETERS USING LASER TRANSDUCER A complete treatment of the subject is outside the scope of this application note a good reference on the subject are the D Appolito 1 and Leach 2 books From its earliest versions the CLIO system allowed to measure the complex imped ance seen from the electrical loudspeaker port with a single sinusoidal sweep The knowledge of the loudspeaker impedance in free air it is not sufficient to the com2. MEASURING DISPLACEMENT AND IMPEDANCE We suppose here that the reader is familiar with impedance measurements using CLIO and the QCBox I Sense mode The CLIO FW O1 input B is already connected to the QCBox I Sense output To proceed with displacement and impedance simultaneous measurement open the Sinusoidal menu Select CH A amp B as inputs and dBmeter as Y scale unit then into the Sinusoidal set tings check the Ohm Right Scale and QCBox Select options see figure 9 rc KS CLIO 10 ELECTRICAL amp ACOUSTICAL TESTS Sinusoidal dow Help j a w Eaa p x AN we Ts YE le Ro BM Op b EAN en g ITHD CHA dBV I v oidal Sweep Gating Impedance Stepped Gated vV Ohm Right Scale speed Delay ms C Internal Normal v 0 000 f QC Box Select Resolution 1 24 Oct Distortion tie M Auto Delay M R amp B Enabled Freq Max Hz THD Enabled 22388 Freq Min Hz Auto Del Freq Hz 10 m 10000 Rise dB 30 000 o L i _ e n Tie 0 20 50 100 200 500 1k Hz 2k 5k 10k 20k Filename CHA dBV 1 6 Octave Unsmoothed 48kHz Delay ms 0 000 Distortion Rise dB 30 00 SweepTime ms 0 00 ae sit ee 0dBY Y a vw co aca l 0 dBV AB A e g Out 1000V v a G Fh 1P ao amp 48kHz Figure 9 Sinusoidal Settings for Displacement and Impedance Measurement Check the output output level this will affect the voltage at which the measurement is performed Please be aware of the fac
3. plete identification of the parameters of the previous equivalent circuit The impedance measurement allow only the identification of the parameters of the electrical equivalent circuit jw Re 40w E Figure 2 Equivalent Circuit of Electrical Impedance where the Z j is the voice coil inductance There are some different models to represent this element CLIO uses internally the Leach equivalent circuit which represent the voice coil lossy inductance as Z jw jw Le Without loss of generality the loudspeaker electrical impedance as a function of fre quency can be wrote as E jw I joo JL oes Z jw R_ Z jw Loes 1 Res foo LoesCuestj w The parameters that can be calculated from the impedance curve and with a previous measurement of the Res coil direct current resistance are basically the resonance fre quency f the quality factors Qys Qes and Qs or the motional impedance equivalent parameters Cumes Lees and Res The CLIO Thiele amp Small menu renders available two algorithms to calculate these pa rameters by points using a widely accepted procedure described by Thiele in one of its seminal papers 3 or using a Least Square Error fitting algorithm The parameters calculated using the electrical equivalent impedance circuit are linked to the parameters of the complete electrical mechanical acoustical equivalent circuit by means of two conversion factors the force factor BI coupl
4. since there are outside the band of the sensor and at low level these effects can be neglected A short note on the y axis units is needed the reading in dBmeter is the RMS dis placement captured by the sensor expressed in decibels units referred to 1 meter To convert to and from dBmeters and meters _ x m x dBmeter aBmeter 20log imt xlm 10 6 11 www audiomatica com SINGLE PASS MEASUREMENT OF T amp S PARAMETERS USING LASER TRANSDUCER If we generate a low frequency sinewave while running the FFT analysis we should get a situation similar to one depicted in figure 8 FFT dBmeter HHH 1 29 2010 3 29 23 PM 60 0 100 0 n Ph vot Min ELT NANA w LUTE AE W WA 10 100 1k Hz 2k 10k 20k CHA dBmeter 48kHz 16384 2 93Hz Rectangular Unsmoothed i id ia U File noise_floor fft Figure 7 Laser Displacement Sensor Noise Floor 1 29 2010 3 32 11 PM 40 0 dBmeter 60 0 Q O O E es a es fe Sl 100 200 500 1k Hz 2k 10k 20k CHA dBmeter 48kHz 16384 2 93Hz Rectangular Unsmoothed iy en el NAL wed iii a File 100Hz_ 15dBu fft Figure 8 100 Hz Sinewave Displacement It is also possible to check the displacement readings using the Multimeter Menu here selecting Displacement is it possible to see the results in terms of RMS peak and peak to peak values 7 11 www audiomatica com SINGLE PASS MEASUREMENT OF T amp S PARAMETERS USING LASER TRANSDUCER
5. CLIO output connected to CLIO FW O1 input A QCBox I sense output connected to CLIO FW O1 input B CLIO FW 01 output A connected to QCBox from CLIO input Laser sensor output connected to QCBox input 4 the laser need also to be con nected to a power supply in order to operate Loudspeaker terminals connected to the QCBox D U T power output Once the connections are in place it is necessary to instruct CLIO to route the QCBox model V input 4 to the CLIO FW 0O1 input A This can be done using the QCBox amp LPT control panel as in the following figure QCBox amp LPT Controls Ea NONE WCB ox Amplifier amp Switch Box Controls Input 1 t Input 2 E m m C mpl Sense Sense A Ohm Model 5 0 100 Figure 5 QCBox Input Channel Selection The routing is now completed the laser sensor must be placed in front of the loud speaker diaphragm at the sensor focal distance which in our case is between 30 and 5 11 www audiomatica com SINGLE PASS MEASUREMENT OF T amp S PARAMETERS USING LASER TRANSDUCER 70 mm A proper loudspeaker mounting must be provided and the laser sensor must be perfectly orthogonal to the cone plane The laser should be pointed at the center of the dome if available otherwise should be pointed towards a loudspeaker part which is rigidly moving with the coil a white dot can be drawn with a white pencil to help the laser reading Please be careful when handling the l
6. aser distance sensor since even relatively small amounts of laser light can lead to permanent eye injuries QCBox amp LPT Controls NONE QCBox Model 5 Controls o ooy J l a in ac o00v IN 4 DC 495V g 2 0 A Out Current 0 01 4 i ees a i i oe r F biai Figure 6 QCBox V DC reading panel In order to help to place the laser sensor at the center of its operating range it is pos sible to use the DC reading capability of the QCBox model V input 4 To activate the DC reading use the QCBox amp LPT controls tab specific to the QCBox model V Since no signal conditioning is provided with this laser we will use only half of its op erating range from 30 to 50 mm to match with the QCBox model V DC reading range Moving the laser closer to the cone will lower the DC reading moving it away will in crease the DC reading It is possible to use the IN 4 DC reading to place the laser sensor at about one fourth of its range 40 mm distance this corresponds to a IN 4 DC reading of 2 50 V DISPLACEMENT MEASUREMENTS We are now ready to collect a first displacement measurement to get in touch with the new CLIO features Open the FFT menu select channel A and dBmeter as y axis scale then run the FFT Adjust the input sensitivity to 40dBV We should see the noise floor captured by the laser displacement sensor see figure 7 Note that above 1kHz there are strong artifacts due to the sensor DAC output but
7. es the electrical and me chanical parts the piston area Sp couples the mechanical and acoustical parts The estimate of the other mechanical and acoustical parameters requires the knowl edge of these two conversion factors or at least of other parameters that allow to calculate them Prior the introduction of simultaneous displacement and impedance measurements 2 11 www audiomatica com SINGLE PASS MEASUREMENT OF T amp S PARAMETERS USING LASER TRANSDUCER CLIO used two approaches Single free air driver impedance measurement and knowledge of the piston area Sp and one parameter between Mms Mmo Cys and BI Two impedance measurements with the second carried out with a known mass attached to the cone added mass or with the driver mounted in a known vol ume enclosure known volume Knowledge of the piston area Sp is required to calculate the parameters of the acoustical part Usually a prior knowledge of the key mechanical parameters is not available thus it is necessary to rely on the latter approach and perform a second impedance measure ment The resonant frequency of the system changes from the free air case measuring the shift lead to the estimate of the moving mass in the added mass case and the compliance in the known volume case Both techniques have their pros and cons but both require the manual intervention of the operator to put the mass into the cone or to mount the speaker on a box With the introduction i
8. ete amp AN A N la YR Tg YE le a oR Y lO gt amp FileData Manufacturer Sica Modelsample 5 inch 79 5920 Hz Vas 5 6674L Re 5 9100 Q 1 5518 Qes 0 3656 Qrs 0 2960 7 5800 T m dBse_ 91 1159 So 0 0087 m 0 5623 mm N Mus 7 1107 g Rus 2 2915 Om 4 22E 0008 m5 N Mas 94 84 kg m Ras 30562 On 123 7596 uF Lees 32 3089 mH Res 2507390 160223 On Rear 12 0133 On Mmo 6 6547 g T 3136 Q fuax 30 9839 0O fave 149970 0 0 7791 Likuz 0 4869 mH Lioknz 0 2534 mH Filename InputA dBfs i 20dBV a w inputB dBfs A 30dBY a w 48 amp Gf Out 15 0dBu a ao S 48kHz a Figure 12 T amp S Parameters Calculated CONCLUSIONS A single pass measurement of the full set of Thiele and Small parameters using the CLIO system has been introduced This has been possible thanks to the usage of a laser displacement sensor and simultaneous acquisition of the two A amp B channels in Si nusoidal mode 10 11 www audiomatica com SINGLE PASS MEASUREMENT OF T amp S PARAMETERS USING LASER TRANSDUCER The parameters calculations is based on a direct estimate of the B product this can Cause small deviations from the other methods as the added mass or known volume REFERENCES 1 J D Appolito Testing Loudspeakers Audio Amateur Press 1988 2 M J Leach Jr Introduction to Electroacoustics and Audio Amplifier Design Third Edition Kendall Hunt 2001 3 N Thiele Loudspeakers in Vented Boxes Part 2 JAES V
9. kHz is adequate In our tests we used a Baumer OADM 2016441 S14F this sensor can be supplied by Audiomatica with a cabling set suitable for R amp D usage with CLIO the sensor has a measuring range from 30 70 mm with a voltage output swinging 0 10 V The displacement sensor sensitivity in V m can be calculated as sensitivity 250 V m Y 0 040 This data must be entered into the CLIO options under the Units Conversion tab as showed in figure 3 CLIO Options aul General Units Conversion Graphics Hardware OC Operators amp Passwords l Fressure Microphone Sensitivity mPa CHA 30 00 CHB 30 00 Frequency Correction HA CHE Displacement Laser Sensitivity vm CHA 250 00 CHE 250 00 Velocity Laser Sensitivity vV imis CHA 10 00 CHB 10 00 Acceleration Sensitivity mmis CHA i 0 00 CHB i 0 00 Current Q Box Sense vi 0 100 Figure 3 CLIO Options Units Conversion Window The laser sensor should be connected to the QCBox input 4 which is capable of mea suring also DC voltages in the range O 5 V this will help to put the laser sensor in place into its operating range 4 11 www audiomatica com SINGLE PASS MEASUREMENT OF T amp S PARAMETERS USING LASER TRANSDUCER LASER CO SO Figure 4 Measurement Setup The connection between CLIO FW 01 the QCBox model V the loudspeaker under test and the laser sensor should be see figure 4 QCBox to
10. n CLIO 10 of the stereo sinusoidal measurement and the sup port of the laser displacement sensor it is possible in a single pass to collect the loudspeaker impedance and displacement The displacement as function of frequency can be calculated putting into a system the equations of the electrical and mechanical acoustical loudspeaker equivalent circuit parts wL i E jw Re Z jo I jw jw L cesC mes tJ w a 1 ES E jw Re Z jw jw Bl jwX jw then the current can be eliminated from the system and the displacement X jw can be expressed as a function of the Thiele amp Small parameters and the driving voltage El jw J OL oes L JO Les Cues J e 1 R e Z ju i fi PRE Jw Lees Cues j on 1 ES The force factor BI can be directly estimated fitting the model to the displacement curve The method has the great benefit that can be performed in a single measurement sweep and doesn t need to modify the loudspeaker free air mounting 3 11 www audiomatica com SINGLE PASS MEASUREMENT OF T amp S PARAMETERS USING LASER TRANSDUCER MEASUREMENT SETUP In order to perform the measurements described in this document the following mate rial is needed Audiomatica CLIO FW 01 box Audiomatica QCBox model V CLIO 10 software Displacement laser sensor with analog voltage output a sensor with a mea surement range of 20 mm and a resolution of at least 0 02 mm and a bandpass around 1
11. olume 19 Issue 6 pp 471 483 June 1971 4 Audiomatica CLIO 10 user s manual www audiomatica com 2010 5 J Moreno Measurement of Loudspeaker Parameters Using a Laser Velocity Trans ducer and Two Channel FFT Analysis JAES Volume 39 Issue 4 pp 243 249 April 1991 6 U Seidel W Klippel Fast and Accurate Measurement of the Linear Transducer Pa rameters presented at the 110 AES Convention Amsterdam May 2001 11 11 www audiomatica com
12. ser_imp sin CHA amp B dBmeter 1 24 Octave Unsmoothed 48kHz Delay ms 0 000 Distortion Rise dB 30 00 SweepTime ms 0 00 apua 20dBV a w ae ae 30dBV a w ASB A ct amp Out 0 140V v a i v to 1p aa amp 48kHz Figure 10 Displacement and Impedance Stereo Measurement THIELE AND SMALL PARAMETERS The Thiele and Small parameters are calculated using the Thiele amp Small menu In or der to calculate the entire set of parameters few additional data is needed the DC resistance of the voice coil and the diaphragm diameter Open the Thiele amp Small menu and select the data origin between File and SinData in this example we will use the data just measured in the sinusoidal menu then press the go button The Parameters Input will pop up see figure 11 Here is it possible to enter the Manufacturer Model and the two important figures Re in ohm and diameter d in millimeters Pressing OK will give immediately the full T amp S parameters results see figure 12 9 11 www audiomatica com SINGLE PASS MEASUREMENT OF T amp S PARAMETERS USING LASER TRANSDUCER T amp S Parameters Input Known f None f Mms f Mmd f Cms sample 5 inch M pl Manufacturer Sicd Diameter rm 105 Re Ohm 5 91 Area fom 2 86 59 cnet Figure 11 T amp S Parameters Input Window WE CLIO 10 ELECTRICAL amp ACOUSTICAL TESTS Thiele amp Small Parameters eml File Analysis Controls Window Help Shab
13. t that the output level is a tradeoff between two opposed demands Measurement SNR asks for high levels while Thiele amp Small small signal model theory require low levels in order not to push the loudspeaker into its non linear range Common CLIO FW output levels balanced that can be adopted us ing the previously described laser displacement sensor and the QCBox model V amplifier are ranging between 0 05 V and 0 25 V Check also the input gain levels for both channels A displacement and B current a proper setting is very important in order to get reliable results In our example here we used a non stepped sinusoidal sweep with 1 24 octave reso lution and frequency range from 22388 Hz to 10 Hz 8 11 www audiomatica com SINGLE PASS MEASUREMENT OF T amp S PARAMETERS USING LASER TRANSDUCER We are now ready to start our measurement If everything was done correctly we must end up with something which is similar to figure 10 where the blue curve is the displacement in dBmeter and the orange curve is the impedance in ohm Save the measurement as sin file E XO CLIO 10 ELECTRICAL amp ACOUSTICAL TESTS Sinusoidal ollel z an File Analysis Controls Window Help TL Lr a bai la 2 Wi Nk Ts YF le we W O gt EN 7 A K O THD CH A amp B v dBmeter v Unsmoothed 0 Anc a0 a0 ag ig ag ag a c e Ot S T S A EERE i 20 0 10 0 FERT H 10 20 100 200 500 10k 20k Filename sica_la
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