Driver in a Double Bass Reflex Enclosure - Acoustic and Electrical Response 8/14/09. Copyright 2009 by Martin J. King. All Rights Reserved.

Transcription

1 Driver in a Double Bass Reflex Enclosure - Acoustic and Electrical Response 8/14/9 Software : by Martin J. King MJKing57@aol.com Copyright 29 by Martin J. King. All Rights Reserved. Unit and Constant Definition cycle := 2 π rad Air Density : ρ := 1.25 kg m Hz := cycle sec Speed of Sound : c := 344 m sec Part 1 : Thiele-Small Consistent Calculation Abbreviated User Input (Edit This Section and Input the Parameters for the System to be Analyzed) Series Resistance R add :=. Ω Driver Thiele / Small Parameters : Fostex FE-27E Driver Properties f d := 39 Hz V ad := liter Adjustments R e := 6.73 Ω Q ed :=.28 R e := R e + R add ( ) L vc := mh Q md := 3.86 Q ed := Q ed R e R e R add Bl 9.41 newton 1 1 := Q td := + amp Q ed Q md S d := 26.1 cm 2 Q td =.261 Enclosure Geometry Definition (Ref : Fostex Recommended Enclosure for FE-27E) Lengths L := 858 mm (Total Internal Length of Enclosure) L top := 25 mm (Internal Length of Top Chamber) t divider := 21 mm (Thickness of Dividing Panel) L bot := 587 mm (Internal Length of Bottom Chamber) L top z driver + t divider + L bot = 858 mm <---- Must Equal Total Internal Length := 125 mm (Inside Distance from Top to Driver) z := 761 mm (Inside Distance from Top to Port)

2 Areas S := 25 mm 25 mm (Area of the Top End) S L := 25 mm 25 mm (Area of the Bottom End) S divider := 11 mm 11 mm (Area of Divider Internal Port) L divider := 131 mm (Length of Divider Internal Port) S := 11 mm 11 mm (Area of Exit Port) L := 111 mm (Length of Exit Port) Stuffing Definition 3 Density 1 :=.2 lb ft (Stuffing density in top chamber : lb/ft 3 < D 1 < 1 lb/ft 3 ) 3 Density 2 :=.2 lb ft (Stuffing density in bottom chamber : lb/ft 3 < D 2 < 1 lb/ft 3 ) Power Power := 1 watt (Input Power) Applied Voltage Reference ---> R ref := 8 Ω End of Abbreviated User Input Calculated Detailed Input Values (Derived From User Input Data Entered Above) ( ) L 1 TR := S L S TR = m L D := L top z driver (Length from Driver to Near Edge of Divider) ( ) S D := S + TR L top (Area at Near Edge of Plate) L T := L L top t divider (Length from Far Edge of Divider to Bottom) ( ) S T := S + TR L L T (Area at Far Edge of Divider) L P := z L top t divider (Length from Far Edge of Divider to Port Centerline) ( ) S P := S T + TR L P (Area at Port Center Line) S L := L +.6 (Corrected Port Length) π L B := L T L P (Length from Port Centerline to Bottom)

3 Pre Formated Geometry and Stuffing Location Input (Only Edit Details Below to Change Defaults) Ported Box Definition n_top := 4 n_open := 12 n_bottom := 4 n_ := 4 Closed End of Transmission Line ( lb/ft 3 < D < 1 lb/ft 3 ) (n_top > 1) (n_open > 1) (n_bottom > 1) (n_ > 1) (Driver ---> Closed End) Section Length Initial Area Final Area Stuffing Density L c := z driver ( n_top + 1) L c1 := z driver ( n_top + 1) L c2 := z driver ( n_top + 1) L c3 := z driver ( n_top + 1) L c4 := z driver ( n_top + 1) S c := S + TR z driver S c1 := S c1 S c2 := S c11 S c3 := S c21 S c4 := S c31 S c1 := S c S c11 := S c1 S c21 := S c2 S c31 := S c3 S c41 := S TR L c TR L c1 TR L c2 TR L c3 D c := Density 1 D c1 := Density 1 D c2 := Density 1 D c3 := Density 1 D c4 := Density 1 Open End of Transmission Line (Driver ---> Divider) Section Length Initial Area Final Area Stuffing Density L o := L D ( n_open 7) L o1 := L D ( n_open 7) L o2 := L D ( n_open 7) L o3 := L D ( n_open 7) L o4 := L D ( n_open 7) S o := S S o1 := S o1 S o2 := S o11 S o3 := S o21 S o4 := S o31 S o1 := S o S o11 := S o1 S o21 := S o2 S o31 := S o3 S o41 := S o4 + TR L o + TR L o1 + TR L o2 + TR L o3 + TR L o4 D o := Density 1 D o1 := Density 1 D o2 := Density 1 D o3 := Density 1 D o4 := Density 1 Divider Port (Internal Port Driver End ---> Internal Port Terminus End) Section Length Initial Area Final Area Stuffing Density L o5 :=.6 S divider π S o5 := S divider S o51 := S divider D o5 := Density 1 L o6 := L divider S o6 := S divider S o61 := S divider D o6 3 := lb ft L o7 :=.6 S divider π S o7 := S divider S o71 := S divider D o7 := Density 2

4 Open End of Transmission Line (Divider Terminus End ---> External Port Centerline) Section Length Initial Area Final Area Stuffing Density L o8 := L P ( n_open 7) L o9 := L P ( n_open 7) L o1 := L P ( n_open 7) L o11 := L P ( n_open 7) L o12 := L P ( n_open 7) S o8 := S T S o9 := S o81 S o1 := S o91 S o11 := S o1 1 S o12 := S o11 1 S o81 := S o8 S o91 := S o9 S o1 := S o1 1 S o11 := S o11 1 S o12 := S o TR L o8 + TR L o9 + TR L o1 + TR L o11 + TR L o12 D o8 := Density 2 D o9 := Density 2 D o1 := Density 2 D o11 := Density 2 D o12 := Density 2 Bottom Section of Enclosure (External Port Centerline ---> Bottom of Enclosure) Section Length Initial Area Final Area Stuffing Density L b := L B ( n_bottom + 1) L b1 := L B ( n_bottom + 1) L b2 := L B ( n_bottom + 1) L b3 := L B ( n_bottom + 1) L b4 := L B ( n_bottom + 1) S b := S P S b1 := S b1 S b2 := S b11 S b3 := S b21 S b4 := S b31 S b1 := S b S b11 := S b1 S b21 := S b2 S b31 := S b3 S b41 := S L + TR L b + TR L b1 + TR L b2 + TR L b3 D b := Density 2 D b1 := Density 2 D b2 := Density 2 D b3 := Density 2 D b4 := Density 2 Port Section of Enclosure (External Port Inside ---> External Port Outside) Section Length Initial Area Final Area Stuffing Density L p := L ( n_ + 1) L p1 := L ( n_ + 1) L p2 := L ( n_ + 1) L p3 := L ( n_ + 1) L p4 := L ( n_ + 1) S p := S S p1 := S S p2 := S S p3 := S S p4 := S S p1 := S S p11 := S S p21 := S S p31 := S S p41 := S D p D p1 D p2 D p3 D p4 3 := lb ft 3 := lb ft 3 := lb ft 3 := lb ft 3 := lb ft Total Amount of Stuffing ( ) ( ) n_top S cr + S cr1 n_open S or + S or1 L cr D cr + L or D or... =.376 lb 2 2 r = r = n_bottom ( S br + S br1 ) n_ L br D br ( S pr + S pr1 ) + + L pr D pr 2 2 r = r = End of Pre Formatted Default Input End of Part 1 Input

5 Resulting Acoustic Impedance for the Enclosure Impedance Magnitude Impedance Phase () Z alr ρ c arg( Z alr ) rdω Hz rdω Hz Velocity at the Terminus of the Ported Box for a 1 m/sec Excitation at the Driver Position 1 Epsilon Magnitude ε r rdω Hz 18 Epsilon Phase () arg( ε r ) rdω Hz

6 Far Field Ported Box System and Infinite Baffle Sound Pressure Level Responses Phase () arg( p or ) arg( p r ) SPL (db) SPL or SPL r rdω Hz rdω Hz Woofer and Terminus Far Field Sound Pressure Level Responses Phase () arg( p dr ) ( ) arg p Lr SPL (db) SPL dr SPL Lr rdω Hz rdω Hz

7 Ported Box System and Infinite Baffle Impedance 9 Phase () arg( Z or ) arg( Z r ) rdω Hz Impedance (ohms) Z or Z r rdω Hz

8 Woofer RMS Displacement 6 RMS Deflection (mm) x dr mm x r mm rdω Hz System Time Response for an Impulse Input 2 Sound Pressure in Time Domain p summedn 1 Pa ndt Time (sec)

9 System Group Delay Phase () p angleq Phase Angle of System Pressure qdω Hz.5 System Group Delay.4 φ q sec qdω Hz Port Air Velocity (should be < 1 m/sec / 344 m/sec =.3).3 Port Air Velocity / Speed of Sound.25 Velocity Ratio v r.2 c rdω Hz

10 Part 2 : Detailed SPL Response Calculation Calculation Includes : Position of Driver and Port on the Baffle. Baffle Step Defraction for the Driver and the Port. Room Reflections for the Driver and the Port. Geometry Baffle Coordinate System : Origin is the lower left corner of the front baffle y = horizontal direction z = vertical direction The variables num_r n_drv and n_mth control the number of simple sources that are used in the calculations. Increasing each will improve accuracy at the expense of longer calculation times. Increase each variable until plotted SPL stops changing at which point the solution has converged. Enclosure Geometry Input X := 2ft (Front Baffle Distance from Rear Wall > Depth of Enclosure) Y := 2ft (Front Baffle Distance from Side Wall) θ := 45 (Rotation Towards Room Center) Z := 8ft (Floor to Ceiling Distance) stand := m (Height from Floor to Bottom Edge of Front Baffle) num_r := 1 (Number of Points per Unit Length of Baffle Edge) Corner Coordinates Y coordinate Z coordinate y o y o1 y o2 y o3 := 292 mm (Bottom Right Corner) := 292 mm z o1 := 9 mm (Top Right Corner) := in z o2 := 9 mm (Top Left Corner) := in (Bottom Left Corner) depth := 32 mm (Depth of Enclosure)

11 Driver Geometry Input y dc := 146 mm (Driver Center y Coordinate) z dc := 754 mm (Driver Center z Coordinate) n_dvr := 5 (Number of Points Across Diameter) Port Geometry Input y mc z mc := 146 mm (Port Center y Coordinate) := 118 mm (Port Center z Coordinate) n_mth := 4 (Number of Points Across Diameter) Locate := ( = Front Baffle Port 1 = Rear Baffle Port) Listening Position (Default Location is at 1 m Distance Along the Driver's Axis) n_listen = (Listening Position Relative to Speaker) radius := 1 m (Calculation Radius Effective Radius is Greater if y p is Changed from Default) θ := ( is along the Driver's Axis -8 < θ < 8 ) z p := z dc (Default Height is Equal to Driver Height) n_listen = 1 (Listening Position Relative to the Room Corner) X p := 1ft Y p := 7ft Z p := z dc + stand (Default Height is Equal to Driver Height) n_listen := (Method Selection) Floor Condition Reflect := 1 ( = hardwood or concrete 1 = carpeted) Refective Surface Selections (if 1 reflective surface is included if reflective surface is removed) Inc_floor := 1 (Floor Z = ) Inc_rear := (Rear Wall X = ) Inc_side := (Left Side Wall Y = ) Inc_ceiling := (Ceiling)

12 Circular Driver and Circular Mouth Simple Source Pattern with Baffle Edge Outline Front View Side View z d 1 z d 1 z m.8 z m.8 z o z o y d y m y o x d x m x o Red sources represent the driver. Blue sources represent the. Black outline represents the baffle edge. Origin is at the bottom front left corner of the enclosure.

13 Three Dimensional View Axis Length (m) axis := 2 <---- Change value of "axis" to rescale plots Room Corner is the Origin 2 Side view z driver z outline z term 1 Side View - looking out from side wall z mic x driver x outline x term x mic 2 Front View z driver z outline z term 1 Front View - looking towards rear wall z mic y driver y outline y term y mic 2 Top View y driver y outline y term 1 Top View - looking down from ceiling y mic x driver x outline x term x mic

14 Plotted Baffle Step and Reflection SPL Response for the Circular Driver Source Phase (rees) Phase r rdω Hz SPL (db) SPL r rdω Hz

15 Plotted Baffle Step and Reflection SPL Response for the Circular Port Source Phase (rees) Phase r rdω Hz SPL (db) SPL r rdω Hz

16 Plotted SPL Response for the System Phase (rees) Phase r rdω Hz SPL (db) SPL r rdω Hz

17 Part 3 : Baffle Step Correction Circuit Design Input Center Frequency of the Baffle Step and the desired db of Attenuation. f center := 35 Hz <--- Input Center Frequency db := 2 <--- Input db of Attenuation Calculated Component Values db 2 R e 1 = Ω Parallel Resistor User Assigned Component Values Based on Calculated Values at Left Input Value ---> R parallel := 2 Ω R parallel f center =.99 mh BSC Inductor Input Value ---> L BSC := 1mH Plotted Corrected SPL Response for the System Phase (rees) Phase r rdω Hz SPL (db) SPL r rdω Hz

18 Ported Box Corrected System and Infinite Baffle Impedance 9 Phase () arg( Z or ) arg( Z r ) rdω Hz 12 Impedance (ohms) Z or Z r rdω Hz System Time Response for an Impulse Input 2 Sound Pressure in Time Domain p summedr 1 Pa rdt Time (sec)