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1 Development of an advanced program for the design of direct radiate loudspeaker systems 00

2 Development of an advanced program for the design of direct radiate loudspeaker systems

3 00

4 i List of Figures iii List of Tables vi Nomenclature vii xii

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5 Thiele-mall Thiele-mall Abstract

46 4 ---------------------------------- 46 4 --------------------------------------- 47 5 - -----------------------------------------

6 Figure Figure Figure 3 Figure 4 Figure 5 List of Figures Generalized direct-radiator loudspeaker system Acoustical analogous circuit of generalized direct-radiator loudspeaker system Acoustical analogous circuit of infinite-baffle loudspeaker system Electrical equivalent circuit of moving-coil electro-dynamic driver Driver voice-coil impedance magnitude Figure 6 implified acoustical analogous circuit corresponding to Fig Figure 7 Figure 8 Figure 9 Figure 0 Figure Figure Figure 3 Figure 4 Figure 5 Figure 6 Figure 3 Figure 3 Figure 33 Figure 34 Figure 35 Normalized frequency response of infinite baffle loudspeaker system Normalized displacement of driver mounted on infinite baffle implified electrical equivalent circuit of closed-box loudspeaker system Acoustical analogous circuit of vented-box loudspeaker system (a) Crossover network branch from several order, (b) Crossover network branch from several quality factor implified 4 th order filter Measuring setup (a) Equipment and test speaker picture (b) Block diagram Mounting of loudspeaker and laser displacemeter implified electrical circuit of loudspeaker at low frequencies Magnitude of diaphragm velocity to driver current ratio frequency response Magnitude of diaphragm velocity to input voltage ratio frequency response Figure 36 Inverse of curve shown in Fig 35 multiplied by ( T M )

analogous circuit corresponding to Fig Figure 7 Figure 8 Figure 9 Figure 0 Figure Figure Figure 3 Figure 4 Figure 5 Figure 6 Figure 3 Figure 3 Figure 33 Figure 34 Figure 35 Normalized frequency

7 Bl is given at resonant frequency by Y value of main cursor Figure 37 Calculation of dc resistance of voice-coil E is given at resonant Figure 38 Figure 39 frequency by Y value of main cursor Figure 30 Figure 3 Figure 3 Figure 4 Figure 4 Figure 43 Figure 44 Figure 45 Figure 46 Magnitude of element frequency response (a) mh coil (b) 475µF condenser Magnitude of crossover network frequency response (a) nd order low-pass filter (b) nd order high-pass filter Magnitude of crossover network frequency response (a) Inphase summation (b) Out of phase summation

46 Magnitude of element frequency response (a) mh coil (b) 475µF condenser Magnitude of crossover network frequency response (a) nd order

8 List of Tabels Table Table Table 3 Four basic parameters used by Thiele elationship between impedance and circle element General Method vs Proposed Method (Use Laser-Displacemeter)

9 Nomenclature B AB weber/ m [ 5 C Acoustic compliance of air in enclosure [ m / N 5 C Acoustic compliance of passive radiator suspension [ m / N AP 5 C Acoustic compliance of driver suspension [ m / N 5 C Total acoustic compliance of driver and enclosure [ m / N AT CM Mechanical compliance of driver suspension [ m / N C Electrical capacitance correspond to vent mass M MEP AP C ME Electrical capacitance representing moving mass ( M ) of system c [ m / sec e g Open-circuit output voltage of ource (Thevenin s equivalent generator for amplifier output port) [ F [ F [V f B esonance frequency of vented enclosure [ Hz f C esonance frequency of closed box system [ Hz f CT esonance frequency of driver in closed, unfilled, unlined test enclosure [ Hz f esonance frequency of unenclosed driver [ Hz G(s) k x L CEB esponse function Displacement constant Electrical inductance correspond to enclosure compliance CAB [ H LCE Electrical inductance due to driver compliance [ H l Length of voice-coil conductor in magnetic gap [m M AC M AP 4 [ kg / m Acoustic mass of port or passive radiator including air load 4 [ kg / m

capacitance representing moving mass ( M ) of system c [ m / sec e g Open-circuit output voltage of ource (Thevenin s equivalent generator for amplifier output port) [ F [ F [V f B esonance frequency

10 M M M PA PA Acoustic mass of driver diaphragm assembly including air load Mechanical mass of driver diaphragm assembly including air load Acoustic output power Displacement-limited acoustic power rating 4 [ kg / m [kg PE Nominal electrical input power [W PE Displacement-limited electrical power rating [W P E (max) Thermally-limited maximum input power [W pg [ atio of reactance (series Circuit) or resistance to reactance(parallel circuit) N / m ECT E of driver at E only of driver at E only f CT considering electrical resistance f considering electrical resistance L of driver at f B resulting from the leakage losses MC of system at f C M of driver at resistance only f considering driver non-electrical T TC AB AL Total of driver at f including all system resistances of system at f C Acoustic resistance of enclosure losses caused by internal energy absorption Acoustic resistance of enclosure losses caused by leakage 5 [ N sec/ m 5 [ N sec/ m

Circuit) or resistance to reactance(parallel circuit) N / m ECT E of driver at E only of driver at E only f CT considering electrical resistance f considering electrical resistance L of driver at f B

11 5 Acoustic resistance of port or passive radiator losses [ N sec/ m AP Acoustic resistance of driver suspension losses [ AT N 5 sec/ m 5 Acoustic resistance of total driver-circuit losses [ N sec/ m Total system resistance 5 [ N sec/ m ATC E DC resistance of driver voice-coil [Ω EL E g Electrical resistance correspond to enclosure leakage resistance AL Electrical resistance representing driver suspension losses Output resistance of source (Thevenin s equivalent resistance for amplifier output port) [Ω [Ω [Ω M Mechanical resistance of driver suspension losses [Ω 5 Acoustic radiation resistance [ N sec/ m A D Effective surface area of driver diaphragm [m s Complex frequency variable T Time constant 3 U Volume velocity entering enclosure [ m / sec B 3 U Volume velocity of the driver [ m / sec D 3 U Volume velocity caused by enclosure leak [ m / sec L 3 U Volume velocity of the port [ m / sec P U0 Total volume velocity of the enclosure 3 [ m / sec u Linear velocity [ m / sec u Linear velocity of driver diaphragm [ m / sec D V D Volume of air having same acoustic compliance as driver suspension 3 [ m 3 V Peak displacement volume of driver diaphragm [ m Vin V VT X (s) m 3 [ Displacement function

suspension losses Output resistance of source (Thevenin s equivalent resistance for amplifier output port) [Ω [Ω [Ω M Mechanical resistance of driver suspension losses [Ω 5 Acoustic radiation

12 x Linear displacement [m xmax Peak linear displacement of driver diaphragm [m 5 Z [ N sec/ m A Z AA Z AB Z 5 [ N sec/ m 5 [ N sec/ m N sec/ m 5 [ ZE [Ω (s) Z VC α η 0 Voice-coil impedance function = C / Efficiency ρ Density of air [ 8 m C AB 3 kg / ] [ kg 3 / m σ x(p) tatic displacement sensitivity of unenclosed driver expressed in meters per watt / [ N / W ω adian frequency variable [ π f ] [ Hz

C / Efficiency ρ Density of air [ 8 m C AB 3 kg / ] [ kg 3 / m σ x(p) tatic displacement

13 PC,

16 3

17 , a) (),, U D, UL () UP U D U P U L Fig Generalized direct-radiator loudspeaker system 4

18 U () 0 U = U + U + U 0 D P L () () () P A = U 0 A () () Allison Berkovitz (3) [] A ρ0ω = πc (3) (3),, (4) U0 = U B (4) U B (4) (5) 5

19 6 +L + + = 3 B B B B U U U U (5) (5) (4), (), b) (6) E E g g E e P + = (6) (6) E 80%

20 ()(6) η(7) ( + ) PA g E η = = U0 A (7) PE eg E (7) U0 e g () ( + ) g B l E D M C U D UB UL U P e Bl g ( ) g + E D C AB AB AL M AP C AP U 0 AP Fig Acoustical analogous circuit of generalized direct-radiator loudspeaker system (), () 7

21 AT M C e Bl g ( g + E ) D U 0 Fig 3 Acoustical analogous circuit of infinite-baffle loudspeaker system (3) (3) (8) AT B l = + (8) ( + ) g E D (3) (9) U egbl = G( ) (9) sm 0 s ( g + E ) D ( s) = s C s CM M + sc G (0) AT +, s s = jω, (5) (9)(7) () 8

22 ρ B l η( jω) ω π 0 G( j ) c EDM = () G( jω) (0) G(s) G( jω) () () G( jω) G( jω), (9) () G( jω) G( jω) () (3) (), 9

23 3, a), (Bl ), E D, C M, M M M, () 4 Table Four basic parameters used by Thiele Parameter Description Unit f esonance frequency of unenclosed driver Hz V Volume of air having same acoustic compliance as driver suspension Liter M of driver at resistance only f considering driver non-electrical E of driver at f considering electrical resistance E only b) (4) 0

24 g E e g E CME LCE Fig 4 Electrical equivalent circuit of moving-coil electro-dynamic driver ω = πf T (4) () T = C L = C = ω ME CE M () E ( g = 0 ) () (4) M = ω CMEE = (3) ω C E ω M ω CME E = B l E D = (4) V (5) V ρ 0 c C = (5) c) (4)

25 (6) VC ( s) = E + E s T st / M + st / M + Z (6) ( ) (6) = s (5) Z VC ( ) Fig 5 Driver voice-coil impedance magnitude d) f (5) dc E r 0, E (Appendix ) r 0 (7) (8)

26 M f 0 = (7) f r f = r M E (8) 0 V [4][5][6] f CT ECT V (Appendix ) (9) f CTECT = VT f E V (9) 3

27 4 a) (6) () 4 U D Z UB UA p g Z AB Z AA U 0 Fig 6 implified acoustical analogous circuit corresponding to Fig p p g (0) e Bl g g = (0) ( g + E ) D Z () Z ( s) = AT + sm + () sc ZAB () Z AB ( s) = AB + () sc AB Z AA 4

28 (6) U () U U A (6) (3) L P ( ) G s U 0 = sm pg = Z AB + Z sm + Z AB Z Z AA (3) b) s,, (4) (Appendix ) T ω C = (4) AT T (0) () (4) (5) ( s ) = s T s T + st G (5) T + c), 5

29 ( ) Minimum Phase,,,, (5) (6) ( s ) = s T 0 s T0 + a st G (6) 0 + (6), 0 T = a T = T (6) (5) G( jω) (7) T 6

30 Fig 7 Normalized frequency response of infinite baffle loudspeaker system T T (7) = 0 5, = 07 = T (Butterworth) db, 35dB, 6dB, Butterworth (Half Power Point), 7

31 5 ) P E (max) ( ( ) P E (max), (7) V Dx max D = (7), b) U D u D s ( ) x (8) D D 8

32 x D = P σ (8) E x ( P) kxx ( s) P E (), σx( P ) dc (9) C B l σ x = M ( P ) = (9) E k x X ( s ) 0Hz V πρ0c f ED, X ( s ) P σ (8)(6)(9) E x( P ), sc (30) k x X ( s) = sc Z AB + Z AB Z + Z + Z Z AB AA Z AA (30) ( X s ) (30) kx (3) (3) ( s ) = s T + st X (3) T + ( jω) X (8) 9

33 Fig 8 Normalized displacement of driver mounted on infinite baffle 0

34 6 a) (8) x D x max (3) P xmax = σx jω ( P ) k x X ( ) max E (3) P E X( jω) max, (7) (9)(3) (33) P f V = E D E πρ0c Vkx X (33) ( jω) max b) (33) (34) P 3 4π ρ c 0 k x X f 4 V D ( jω) max A = (34) (34) k x (35),

35 P 4π ρ c A ( IB) = D (35) X f V ( jω) max (33) k x (36) E ( IB) = πρ0c E D (36) P V f X V ( jω) max

36 ( + ) g B l E D M AC C e Bl g ( g + E ) D U 0 C AB AB Fig 9 Acoustical analogous circuit of closed-box loudspeaker system (Impedance analogy) (9) (0) ATC M AC CAT e Bl g ( g + E ) D U 0 Fig 0 implified acoustical analogous circuit of closed-box loudspeaker system (0) )(37) C ( AT C AT C C AB = (37) AB C + C ( ATC )(38) 3

37 ATC B l = + + (38) AB ( + ) g e D (9) Dot Method (39) () Z E B l Z = (39) A D g E e g E CME LCET Fig implified electrical equivalent circuit of closed-box loudspeaker system () (40),(4),(4) C ME M AC B l D = (40) L CET C B l AT = (4) D EC ( + ) AB B l = (4) D 4

38 (),(3),(4) T = C M AC (43) = ω C (44) M ME E = ω C (45) E ME E (46) E B l E D = (46) (47) V ρ 0 c C = (47) (37)(43) Appendix(a3),(a5),(a,7) C C AT =α+ (48) f f C T = = α T C ( +) (49) EC E = ( α+) (50) 5

39 6 ( ) + + = TC C C C st T s T s s G (5) ( ) + + = TC C C st T s s X (5) ( ) = MC C C MC C EC E VC st T s st s Z (53)

40 3 ( + ) g B l E D M C U D U B U L UP e Bl g ( g + E ) D C AB AB AL M AP U 0 AP Fig Acoustical analogous circuit of vented-box loudspeaker system () (3) AT M C U D U B UL U P p g C AB AL M AP U 0 Fig 3 implified acoustical analogous circuit of vented-box loudspeaker system (3)(54),(55) p AT B l = + (54) e ( + ) Bl g ( g + E ) D E D = g g (55) 7

41 (4) g E LCEB EL e g E CME LCE CMEP Fig 4 implified electrical equivalent circuit of vented-box loudspeaker system (56), (57) T = C M = C B = ω B AB AP MEP L CEB (56) L = ωbc ABAL = (57) ω C B MEP EL (3) (4) ω = πf - ω, L B (43), (44), (45), (47) (58) B B 4 s ( ) ( TB T ) = 4 3 T B T TBT TB TT TB T s ( T T ) + s + s ( α+ ) T + + T s + G s B T L + B L + L + T (58) (59) 8

42 X ( s ) s TB + stb L + D s = (59) ( ) D( s) (58) (60) Z VC ( s ) ( s) ( T )( s T + st + ) s M B B L = E + E (60) D' D' D( s) ( s) T M 9

43 ,,,,, 3 3, ( ), (5) (a) Chebychev (=), Butterworth (=0707), Bessel (=0575), Linkwitz-iley (=049), (5) (b) (-6dB/ ), (-db/ ), 3 (-8dB/ ), 4 (-8dB/ ) Gain(dB) -9 Gain (db) st Order nd Order 3rd Order 4th Order -5-8 = (Chebychev) =0707 (Butterworth) =0575 (Bessel) =049 (Linkwitz-iley) Frequency (Hz) Frequency (Hz) (a) (b) Fig 5 (a) Crossover network branch from several order, (b) Crossover network branch from several quality factor 30

44 (-6dB/ ) 4 (-8dB/ ) Chebychev, Butterworth, Bessel, Linkwitz-iley, Legendre, Gaussian, Linear-Phase, -Way (6) 4 Appendix I Z c Vin Z Z Z a b Z ( V ) c V out (6) Fig 6 implified 4 th order filter Vin Za Z Z Z b c = V s (6)(6) I V out I V Z = (6) c s + V out Z c = Vs I Zc = Vs Zc + (6) () 3

45 Impedance Table elationship between impedance and circle element Lowpass Filter Highpass Filter Element Value Element Value Z Coil jωl jωc Z jωc Coil jωl Z Coil jωl 3 jωc Z jωc Coil jωl 4 3

46 3 3 3 Thiele-mall Thiele mall Moreno FFT, Hz 00Hz FFT B&K Pulse (Type 3560), (KEYENCE Laser Displacement Meter LC-30) Pulse,, (B&K Power Amplifier Type 7) 3 Tech ound E-8300, (3) (a) FFT Pulse,, (3) (b) (3) (a) mm MDF 3 ( (33)(b) ), 33

47 Fig 3 Measuring setup (a) Equipment and test speaker picture (b) Block diagram (a) Fig 3 Mounting of loudspeaker and laser displacemeter (b) 34

48 3 f M (33) ( ) Z (3) = φ Z (3) 3 = 3 φ3 g E e g E CME LCE Z Z 3 Fig 33 implified electrical circuit of loudspeaker at low frequencies g = 0 u e Bl g D = (33) 3 (33) e g / 3 u i D Bl = (34 ) D ud i D Bl - ) f M ( ( 35

49 Bl ) (34) f (35) (34), M f f = (35) Magnitude(m/sec/A) Frequency(Hz) Fig 34 Magnitude of diaphragm velocity to driver current ratio frequency response 36

50 33 T T (34) G = / A ( 3 ) ( (35)) (33) (36) (34) u e g GA Bl D = (36 ) Magnitude(m/sec/V) Frequency(Hz) Fig 35 Magnitude of diaphragm velocity to input voltage ratio frequency response 37

51 34 E E Appendix (37) E M T = (37) M T 35 Bl (33) Bl (38) Bl e g = (38 ) 3 u D (39) Z jωω / M ( ω) = + E E ω ω + jωω / M ( 39 ) / (39) 3 (30) 3 Z = E ( ω ) (30) (30)(38) E / Z ωs T, ( ) M (3) Bl ( (36) ) 38

52 ( ω ) ( ) T ω e Bl = g ud M (3) Magnitude(V/m/sec) Frequency(Hz) Fig 36 Inverse of curve shown in Fig 35 multiplied by ( T M ) Bl is given at resonant frequency by Y value of main cursor 39

53 36 E (39) (3) E E ( ) E = Z ω (3) (3) (33)(34) (35) Z ( ) e ( ω ) ( ω ) g ω = (33 ) id ( ω ) ( ) T ω e = g E id M (34) E e = i g D ( ω ) ( ) T ω M (35 ) Magnitude(V/A) Frequency(Hz) Fig 37 Calculation of dc resistance of voice-coil by Y value of main cursor E is given at resonant frequency 40

54 37 M M, M, CM, V, η 0 E, M, T, Bl M, C M, M M M M ( Bl) ω E = (36) E M M ω M = (37) M C M M = (38) M ω V (3) V = ρ c C (39) 0 M D (30) 4π f V 3 η 0 = (30 ) 3 c E 4

55 4 3 (8Ω), (3), ( (38) ) (39) mh, 475µF, 8µF (a) (b)

56 3 3 Thiele-mall (3) Thiele-mall Table 3 General Method vs Proposed Method (Use Laser-Displacemeter) T/ Parameters General Method Proposed Method Unit f Hz E Ω M T E Bl 0 08 M M g M 3 3 kg/s CM m/n V Liter η %, 43

57 3 (30) (a) (b), (a) (b) Fig 30 Magnitude of element frequency response (a) mh coil (b) 475µF condenser (3) (a), (b), (3) (a) (b) (3) (a) (3) (b) 3~4dB 44

58 (a) (b) Fig 3 Magnitude of crossover network frequency response (a) nd order low-pass filter (b) nd order high-pass filter (a) (b) Fig 3 Magnitude of crossover network frequency response (a) Inphase summation (b) Out of phase summation 45

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65 [] LL Beranek, Acoustics, Acoustical ociety of America, 993 Edition [] J Ashley and MD wan, Experimental Determination of Low-Frequency Loudspeaker Parameters, Journal of Audio Engineering ociety, vol7, pp55-53 (969) [3] Jorge N Moreno, Measurement of Loudspeaker Parameters Using a Laser Velocity Transducer and Two-Channel FFT Analyser, Journal of Audio Engineering ociety, vol39, pp43-49 (99) [4] Vance Dickason, The Loudspeaker Design Cookbook, Audio Amateur Press, 6 th Edition [5] Joseph D Appolito, Testing Loudspeakers, Audio Amateur Press, st Edition [6] ay Alden, Advanced peaker Designs for the Hobbyist and Technician, Prompt Publications, st Edition [7],, Enclosure Design Institute, 999 Edition [8] H mall, Direct-adiator Loudspeaker ystem Analysis, Journal of Audio Engineering ociety, vol0, no5, pp (June 97) [9] H mall, Closed-Box Loudspeaker ystems-part I : Analysis, An anthology of articles on loudspeakers from the pages of the Journal of the Audio Engineering ociety, vol-5, pp85-95 ( ), nd Edition [0] H mall, Vented-Box Loudspeaker ystems-part I : mall-ignal Analysis, An anthology of articles on loudspeakers from the pages of the Journal of the Audio Engineering ociety, vol-5, pp36-35 ( ), nd Edition [] H mall, Vented-Box Loudspeaker ystems-part II : Large-ignal Analysis, An anthology of articles on loudspeakers from the pages of the Journal of the Audio Engineering ociety, vol-5, pp36-33 ( ), nd Edition 5

66 [] F Allison and Berkovitz, The ound Field in Home Listening ooms, Presented at the 39 th Convention of the Audio engineering ociety, Oct 970, Preprint

67 Abstract With the use of PC software, the calculation task is eliminated, and it is much easier to accomplish what-if situations And it can quickly perform some very powerful calculations to place drivers in a enclosure of the correct size to meet specific design goals Proposed speaker design program executes many additional sophisticated computations For example, speaker design can calculates frequency response of the closed box system and port box system And also calculates the frequency response of the crossover network type 54

68 APPENDIX A A (3) (4) (a) M = E (a) E E dc (a) ( (5) ) + E E r = = + E M 0 (a) E (a) (a) (a3) = r M E (a3) 0 ( = 0 ) (a4) g + M T E = M E = (a4) M r 0 (a4) (6) (a5) Z r + ( st + / st ) ( st + / st ) 0 M VC( s) = E (a5) + M 55

69 Z VC ( jω) M M ( ω/ ω ω / ω) ( ω/ ω ω / ω) r0 + = E (a6) + ω ω = ω ( ω < ω ) (a6) (a7) ( j ) ( ) = ZVC jω = r E ZVC ω (a7) VC ( jω ) r Z =, E M M [( ω ω / ω )] [( ω ω / ω )] r0 + = E (a8) + M ω = ω r r 0 ω r (a9) r = r 0 (a9)(a0) M f 0 = (a0) f r f f f r = 0, r r 0 E f f 56

70 57 (a) f f f = (a) (a) Hz (a)

71 A V T, C AB (a), C AB = VT / ρ0c (a) M C, (a3) T = / ω = M C ( a3) (a3) (a4) C AB T CT = C C AB / ω CT = M ACT ( a4) CAB + C M ACT ω ω CT M C + C = M ACT AB (a5) (4) ( B ) = M / l (a6) E ω E D ( B ) = M / l (a7) ECT ω CT E ACT D 58

72 59 ECT E CT ACT M M ω ω = (a8) (a5) (a8) E ECT CT AB C C ω ω = + (a9) (5) (a) T AB V V C C = (a0) = E ECT CT T V V ω ω (a) = E ECT CT T f f V V (a) ( f E ) MCT AB C

73 ω (a3) c ω c = T C = C AT M AC = C MEC L CET (a3) MC f C (a4) = ω C (a4) MC C MEC EC EC f C (a5) ) ( E = ω C (a5) EC C MEC E TCO f C (a6) ( = 0 g ) TCO EC MC = (a6) EC + MC α (a7) C C α = (a7) AB 60

74 4 4 (a) Z Z 3 Vin(V ) Z Z 4 Fig a implified 4 th order filter (a) Thevenin (a)(a) Z 3 Z 3 Vin ( A) Z Vin Z Z Z 4 ( A) Z Z Z Z + Z Z4 (a) (b) (a) (b) (a) (a) Circuit of applied the Thevenin s theory Z Z Z + Z (b) Unite the parallel element = Za (a3)(a), Norton 6

75 Z Z a 3 Z a + Z 3 Vin Z a ( V ) Z Z4 Vin Za( V ) Z Z4 (a) (b) (a3) (a) Circuit of applied the Norton s theory (b) Unite the series element (a3) (b) Z + Z 3 = Z, Thevenin a (a4)(a) b Vin Z a ( A) Z Z b Z b Z 4 VinZ a ( A) Z Z b Zb Z 4 Z + Z b 4 (a) (b) (a4) (a) Circuit of applied the Thevenin s theory (b) Unite the parallel element Z Z (a4) (b) b b Z4 + Z 4 = Z c (6) 6

Coriolis.hwp

Coriolis.hwp MCM Series 주요특징 MaxiFlo TM (맥시플로) 코리올리스 (Coriolis) 질량유량계 MCM 시리즈는 최고의 정밀도를 자랑하며 슬러리를 포함한 액체, 혼합 액체등의 질량 유량, 밀도, 온도, 보정된 부피 유량을 측정할 수 있는 질량 유량계 이다. 단일 액체 또는 2가지 혼합액체를 측정할 수 있으며, 강한 노이즈 에도 견디는 면역성, 높은 정밀도,