Driver in a U Frame Transmission Line - Acoustic and Electrical Response 5/03/11. Copyright 2011 by Martin J. King. All Rights Reserved.

Transcription

1 Driver in a U Frame Transmission Line - Acoustic and Electrical Response 5/3/11 Software : by Martin J. King MJKing57@aol.com Copyright 211 by Martin J. King. All Rights Reserved. Line Configuration : Near End Open -> Driver in the Line -> 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) Woofer Series Resistance R add := Ω Input Power Power := 1 watt (Input Power) Applied Voltage Reference ---> R ref := 8 Ω Extended Range Driver Thiele / Small Parameters : Jordan JX92S f d := Hz V ad := liter R e := 5.3 Ω Q ed :=.76 L vc :=.125 mh Q md := 2.29 Bl newton 1 1 := Q td := + amp Q ed Q md π S d := ( 1 mm 4 )2 Q td =.524 Bass Driver Thiele / Small Parameters : Goldwood GW " Woofer f d := 3 Hz V ad := liter Adjustments R e := 5.5 Ω Q ed := 1.15 R e := R e + R add ( ) L vc :=.976 mh Q md := Q ed := Q ed R e R e R add Bl 1.8 newton 1 1 := Q td := + amp Q ed Q md π S d := ( 43.2 mm 4 )2 Q td =.95

2 U Frame Enclosure Geometry Definition : Model of Internal Air Volume L := 7.5 in (Total Length of the U Frame) S := 2 in 2 in (Area of the Driver End) S L := 2 in 2 in (Area of the Open End) 3 Density := lb ft (Stuffing Density : lb/ft 3 < D < 1 lb/ft 3 ) Crossover Definition For Even Order Crossovers : Type 1 = Linkwitz-Riley Type 2 = Bessel Type 3 = BEC Type 4 = Butterworth Low Pass Filter High Pass Filter f LP := 1 Hz f HP := 5 Hz (Filter Frequency) LP order := 2 HP order := 2 (Filter Order :, 1, 2, 3, or 4) LP type := 1 HP type := 2 (Filter Type : 1, 2, 3, or 4 for even order only, for odd order this entry is ignored) Crossover Phase Connection LP phase := 1 HP phase := 1 (Phase : 1 = in phase, -1 = out of phase) Low Frequency Boost LP boost :=. db Sub High Pass Filter (Use to Limit Low Frequency Woofer Displacement) f sub := 2 Hz (Filter Frequency) SHP order := (Filter Order :, 1, 2, 3, or 4) SHP type := 4 (Filter Type : 1, 2, 3, or 4 for even order only, for odd order this entry is ignored) End of Abbreviated User Input

3 Resulting Acoustic Impedance for the U Frame Impedance Magnitude Z alr ρ c Impedance Phase () arg( Z alr ) rdω Hz rdω Hz Frequency (Hz) Velocity at the Terminus of the U Frame for a 1 m/sec Excitation at the Driver 1 Epsilon Magnitude ε r rdω Hz Epsilon Phase () arg( ε r ) rdω Hz Frequency (Hz)

4 U Frame and Extended Range Driver Impedance Solid Red is the U Frame Impedance Solid Blue is the Extended Range Driver Impedance Dashed Red is the Woofer Infinite Baffle Impedance 9 Phase () arg( z Lr ) ( ) arg z Hr ( ) arg z or r Impedance (ohms) z Lr z Hr z or r Frequency (Hz)

5 Driver RMS Displacements Solid Red is the U Frame Woofer Response Solid Blue is the OB Driver Response 5 RMS Deflection (mm) x Wr mm x Hr mm rdω Hz Frequency (Hz)

6 Part 2 : Detailed SPL Response Calculation Calculation Includes : Position of the Driver and the Terminus on the Baffle. Baffle Step of the Driver and the Terminus. Room Reflections for the Driver and the Rear Terminus. Geometry Coordinate System : Origin is the lower left corner of the U Frame y = horizontal direction z = vertical direction The variables num_r, n_drv, and n_mth control the number of simple sources used in the calculations. Increasing each will improve accuracy at the expense of longer calculation times. Increase each variable until final plotted SPL stops changing at which point the solution has converged. Enclosure Geometry Input X := 3ft (Front Baffle Distance from Rear Wall > Depth of Enclosure) Y := 2ft (Front Baffle Distance from Side Wall) θ := 3 (Rotation Towards Room Center) Z := 8ft (Floor to Ceiling Distance) stand := m (Height from Floor to Bottom Edge of Front Baffle) num_r := 2 (Number of Points per Unit Length of Baffle Edge) U Frame Geometry Input U width := 21.5 in (U Frame External Width) U height := 21.5 in (U Hrame External Height) depth := L +.75 in (U Frame External Depth) y c := 1.75 in (Terminus Center y Coordinate) z c := 1.75 in (Terminus Center z Coordinate) w mth := 2 in (Terminus Width) n_mth := 1 (Number of Points Across the Width) Extended Range Driver OB Geometry Input OB width := 2 in (OB panel width) OB height := 2 in (OB panel height) y dc := 13 in (Driver Center y Coordinate w.r.t. lower left corner of OB) z dc := 12 in (Driver Center z Coordinate w.r.t. lower left corner of OB) ξ ob :=.5 (Fraction of the Total Depth of the H Frame :.1 < ξ <.999) n_high := 4 (Number of Points Across Diameter)

7 Listening Position n_listen = radius := θ := z p := 33 in 1 m (Listening Position Relative to Speaker) (Calculation Radius Along Axis of the Extended Range Driver) ( is along the Driver's Axis, -8 < θ < 8 ) (Default Height is Equal to Seated Height) n_listen = 1 X p := 1ft Y p := Z p := 7ft 33 in n_listen := (Listening Position Relative to the Room Corner) (Default Height is Equal to Seated Height) (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 Inc_rear := Inc_side := Inc_ceiling := (Floor, Z = ) (Rear Wall, X = ) (Left Side Wall, Y = ) (Ceiling)

8 U Frame and Extended Range Driver Simple Source Pattern with Baffle Edge Outline Front View 1.5 z W 1 z d z rm z o y W, y d, y rm, y o Side View 1.5 z W 1 z rm z d z o x W, x rm, x d, x o Blue sources represent extended range driver. Red sources represent U frame driver. Red sources represent the rear terminus. Black outline represents the baffle edge. Origin is at the bottom front left corner of the enclosure.

9 Three Dimensional View Axis Length (m) axis := 2 <---- Change value of "axis" to rescale plots Room Corner is the Origin 2 Side view z front z outline 1.5 z rear z driver 1 Side View - looking out from side wall z ob z mic x front, x outline, x rear, x driver, x ob, x mic

10 2 Front View z front z outline 1.5 z rear z driver 1 Front View - looking towards rear wall z ob z mic y front, y outline, y rear, y driver, y ob, y mic 2 Top View y front y outline 1.5 y rear y driver 1 Top View - looking down from ceiling y ob y mic x front, x outline, x rear, x driver, x ob, x mic

11 Plotted Response for the Extended Range Driver Phase (rees) Phase r SPL (db) rdω Hz SPL Hr rdω Hz Frequency (Hz)

12 Plotted Baffle Step and Reflection SPL Response for the U Frame Driver Phase (rees) Phase r rdω Hz SPL (db) SPL r rdω Hz Frequency (Hz)

13 Plotted Baffle Step and Reflection SPL Response for the Rear Terminus Phase (rees) Phase r rdω Hz SPL (db) SPL r rdω Hz Frequency (Hz)

14 Plotted SPL Response for the U Frame Phase (rees) Phase Lr rdω Hz SPL (db) SPL Lr rdω Hz

15 Plotted SPL Response for the System Phase (rees) Phase r rdω Hz SPL (db) SPL r 95 SPL 9 Hr 85 8 SPL Lr rdω Hz Frequency (Hz)

16 System Time Response for an Impulse Input 4 U Frame Sound Pressure in Time Domain 2 p framer Pa rdt 2 System Sound Pressure in Time Domain 125 p summedr Pa rdt Time (sec)