Offset Driver in an Open Ended Transmission Line - Acoustic and Electrical Response 7/03/09. Copyright 2009 by Martin J. King. All Rights Reserved.

Transcription

1 Offset Driver in an Open Ended Transmission Line - Acoustic and Electrical Response 7/3/9 Software : by Martin J. King MJKing57@aol.com Copyright 29 by Martin J. King. All Rights Reserved. Line Configuration : Near End Closed -> Offset Driver -> Far End Open. Unit and Constant Definition cycle := 2 π rad Hz := cycle sec Air Density : ρ := 1.25 kg m 3 Speed of Sound : c := 344 m sec Part 1 : Thiele-Small Consistent Calculation Detailed 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-167E in a BIB Enclosure f d := 51.5 Hz V ad := liter Adjustments R e := 7.1 Ω Q ed :=.33 R e := R e + R add ( ) L vc := mh Q md := 4.63 Q ed := Q ed R e R e R add Bl 6.92 newton 1 1 := Q td := + amp Q ed Q md S d := π ( 65 mm) 2 Q td =.38 Enclosure Geometry Definition L := 136 in (Length) Driver Distance ξ :=.2 (Driver Position Ratio :.1 < ξ <.999) ξ L S :=.1 in 2 (Area of the Closed End) S L := in 2 (Area of the Open End) 3 Density :=.25 lb ft (Stuffing density : lb/ft 3 < D < 1 lb/ft 3 ) = 27.2 in Power := 1 watt (Input Power) Applied Voltage Reference ---> R ref := 8 Ω End of Abbreviated User Input

2 Pre Formated Geometry and Stuffing Location Input (Only Edit Details Below to Change Defaults) Transmission Line Definition ( lb/ft 3 < D < 1 lb/ft 3 ) n_closed := 4 (n_closed > 1) n_open := 4 (n_open > 1) Geometry Definition ( ) L 1 TR := S L S TR =.16 m Closed End of Transmission Line (Driver ---> Closed End) Section Length Initial Area Final Area Stuffing Density L c L c1 L c2 L c3 L c4 := L ξ ( n_closed + 1) S c := S, + TR ξ L S c1 := S c TR L c D c := Density := L ξ ( n_closed + 1) S c1 := S c1 S c11 := S c1 TR L c1 D c1 := Density := L ξ ( n_closed + 1) S c2 := S c11 S c21 := S c2 TR L c2 D c2 := Density := L ξ ( n_closed + 1) S c3 := S c21 S c31 := S c3 TR L c3 D c3 := Density := L ξ ( n_closed + 1) S c4 := S c31 S c41 := S, D c4 := Density Open End of Transmission Line (Driver ---> Open End) Section Length Initial Area Final Area Stuffing Density ( ) L o := L 1 ξ ( n_open + 1) S o := S c S o1 := S o + TR L o D o := Density L o1 L ( 1 ξ) := ( n_open + 1) S o1 := S o1 S o11 := S o1 + TR L o1 D o1 := Density L o2 L ( 1 ξ) := ( n_open + 1) S o2 := S o11 S o21 := S o2 + TR L o2 D o2 := Density L o3 L ( 1 ξ) := ( n_open + 1) S o3 := S o21 S o31 := S o3 + TR L o3 D o3 := Density L o4 L ( 1 ξ) := ( n_open + 1) S o4 := S o31 S o41 := S, L D o4 := Density

3 Total Length of the Transmission Line n_closed n_open L ci + L oi = 136. in i = i = Total Amount of Stuffing n_closed S cr + S cr1 n_open S or + S or1 L cr D cr + L or D or =.234 lb 2 2 r = r = 4 Transmission Line Profile Area / Sd Area r 2S d Area r 2S d Length r in Length (in) End of Detailed Input End of Part 1 Input

4 Resulting Acoustic Impedance for the Transmission Line Impedance Magnitude Impedance Phase () Z alr ρ c arg( Z alr ) rdω Hz rdω Hz Velocity at the Terminus of the Transmission Line for a 1 m/sec Excitation at the Driver 1 Epsilon Magnitude ε r rdω Hz 18 Epsilon Phase () arg( ε r ) rdω Hz

5 Far Field Transmission Line 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

6 Transmission Line System and Infinite Baffle Impedance Phase () arg( Z or ) arg( Z r ) rdω Hz Impedance (ohms) Z or Z r rdω Hz

7 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 15 p summedn 1 Pa ndt Time (sec)

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

9 Part 2 : Detailed SPL Response Calculation Calculation Includes : Position of Driver and Terminus on the Baffle. Baffle Step Defraction for the Driver and the Terminus. Room Reflections for the Driver and the Terminus. 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 := (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 := in (Bottom Right Corner) := in z o1 := 68 in (Top Right Corner) := in z o2 := 68 in (Top Left Corner) := in (Bottom Left Corner) depth := in (Depth of Enclosure)

10 Driver Geometry Input y dc := in (Driver Center x Coordinate) z dc := 4.5 in (Driver Center z Coordinate) n_dvr := 5 (Number of Points Across Diameter) Terminus Geometry Input x mc := in (Terminus Center x Coordinate) y mc := in (Terminus Center y Coordinate) w mth := in (Terminus Width) n_mth := 5 (Number of Points Across the Width) Locate := 1 ( = Bottom Baffle Terminus, 1 = Top Baffle Terminus) 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 + stand (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 := 1 (Rear Wall, X = ) Inc_side := 1 (Left Side Wall, Y = ) Inc_ceiling := 1 (Ceiling)

11 Circular Driver and TL Terminus Simple Source Pattern with Baffle Edge Outline Front View Side View z d 1.25 z d 1.25 z m 1 z m 1 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 terminus. Black outline represents the baffle edge. Origin is at the bottom front left corner of the enclosure.

12 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

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

14 Plotted Baffle Step and Reflection SPL Response for the TL Terminus Phase (rees) Phase r rdω Hz SPL (db) SPL r rdω Hz

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

16 Part 3 : Baffle Step Correction Circuit Design Input Center Frequency of the Baffle Step and the desired db of Attenuation. f center := 4 Hz <--- Input Center Frequency db := 1 <--- Input db of Attenuation Calculated Component Values db 2 R e 1 =.866 Ω Parallel Resistor User Assigned Component Values Based on Calculated Values at Left Input Value ---> R parallel := 1 Ω R parallel f center =.398 mh BSC Inductor Input Value ---> L BSC :=.4 mh Plotted Corrected SPL Response for the System Phase (rees) Phase r rdω Hz SPL (db) SPL r rdω Hz

17 Transmission Line Corrected System and Infinite Baffle Impedance 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)