Presented at the 32 nd AES Conference, 2007 September 21-23, 2007, Hillerod, Denmark Application of Linear-Phase Digital Crossover Filters to Pair-Wise Symmetric y Multi-Way Loudspeakers Part 2: Control of Beamwidth and Polar Shape D. B. (DON) KEELE, JR. Harman/Becker Automotive Systems, Martinsville, Indiana, USA ULRICH HORBACH Harman Consumer Group, Northridge, California, USA Sept. 22, 2007 Sept. 22, 2007 Application of Linear Application of Linear- -Phase Digital Crossover Filters: Part 2 Phase Digital Crossover Filters: Part 2 Slide Slide 1 1

Presented at the 32 nd AES Conference, 2007 September 21-23, 2007, Hillerod, Denmark Introduction In part 2, we simplify the design process and emphasize beamwidth and polar shape of the array. shape of the array. We do this by restricting the level of the forced-to-be-flat off-axis angle to -6 dB. f d t b fl t ff i l t 6 dB This forces the beamwidth of the array to This forces the beamwidth of the array to be flat and with appropriate selection of driver spacing, makes the polar patterns fairly uniform as well. fairly uniform as well Sept. 22, 2007 Sept. 22, 2007 Application of Linear Application of Linear- -Phase Digital Crossover Filters: Part 2 Phase Digital Crossover Filters: Part 2 Slide Slide 2 2

Presented at the 32 nd AES Conference, 2007 September 21-23, 2007, Hillerod, Denmark Outline • Polar Pattern of Two Separated Point Sources – Beamwidth – Side-lobe level • Li Linear Combination of Patterns of Two Pairs of Separated C bi ti f P tt f T P i f S t d Point Sources – Summing ratios – Consistency of off-axis response • Calculation of Crossover Frequency Responses – Four sources: Two pairs of sources – Three sources: A single pair of sources with a single central source • Five-way Design Example Five way Design Example – Front panel design – Crossover responses – Beamwidth and directivity • • Summary Summary Sept. 22, 2007 Sept. 22, 2007 Application of Linear Application of Linear- -Phase Digital Crossover Filters: Part 2 Phase Digital Crossover Filters: Part 2 Slide Slide 3 3

Presented at the 32 nd AES Conference, 2007 September 21-23, 2007, Hillerod, Denmark Frontal Polar Pattern of Two Separated Point Sources Versus Wavelength Spacing D/ λ = 0.1 D/ λ = 0.47, D/ λ = 0.5, Beamwidth = 180º Beamwidth = 90º Beamwidth = 83.6º D/ λ = 0.53, D/ λ = 0.6, D/ λ = 1, Beamwidth = 77.5º Beamwidth = 67.1º, Beamwidth = 38.7º Sept. 22, 2007 Sept. 22, 2007 Application of Linear Application of Linear- -Phase Digital Crossover Filters: Part 2 Phase Digital Crossover Filters: Part 2 Slide Slide 4 4

Presented at the 32 nd AES Conference, 2007 September 21-23, 2007, Hillerod, Denmark Frontal Polar Pattern of Two Separated Point Sources Versus Wavelength Spacing D/ λ = 0.1 D/ λ = 0.47, D/ λ = 0.5, Beamwidth = 180º Beamwidth = 90º Beamwidth = 83.6º Note narrowing of pattern and increasing side- lobe levels at higher frequencies. D/ λ = 0.53, D/ λ = 0.6, D/ λ = 1, Beamwidth = 77.5º Beamwidth = 67.1º, Beamwidth = 38.7º Sept. 22, 2007 Sept. 22, 2007 Application of Linear Application of Linear- -Phase Digital Crossover Filters: Part 2 Phase Digital Crossover Filters: Part 2 Slide Slide 5 5

Presented at the 32 nd AES Conference, 2007 September 21-23, 2007, Hillerod, Denmark Vertical Beamwidth (-6 dB) vs. V ti l B idth ( 6 dB) Separation Distance p Sept. 22, 2007 Sept. 22, 2007 Application of Linear Application of Linear- -Phase Digital Crossover Filters: Part 2 Phase Digital Crossover Filters: Part 2 Slide Slide 6 6

Presented at the 32 nd AES Conference, 2007 September 21-23, 2007, Hillerod, Denmark V Vertical Beamwidth (-6 dB) vs. ti l B idth ( 6 dB) Separation Distance p The “Effective Operating Range” is the range of source wavelength separations that provide usable polar shapes with side lobes down 10 dB or more with beamwidths in the range of 67 to 113 degrees. This is the source separation at the array’s critical frequencies. Sept. 22, 2007 Sept. 22, 2007 Application of Linear Application of Linear- -Phase Digital Crossover Filters: Part 2 Phase Digital Crossover Filters: Part 2 Slide Slide 7 7

Presented at the 32 nd AES Conference, 2007 September 21-23, 2007, Hillerod, Denmark Side Lobe Level (at ±90º) vs. Sid L b L l ( t 90º) Separation Distance p Sept. 22, 2007 Sept. 22, 2007 Application of Linear Application of Linear- -Phase Digital Crossover Filters: Part 2 Phase Digital Crossover Filters: Part 2 Slide Slide 8 8

Presented at the 32 nd AES Conference, 2007 September 21-23, 2007, Hillerod, Denmark Linear Combination of the Linear Combination of the Patterns of Two Pairs of Separated Point Sources Separated Point Sources • Part 1 shows that a linear combination of the acoustic outputs of adjacent pairs f th ti t t f dj t i of drivers can maintain essentially flat off-axis frequency response over a +1.5 +X2 = +1.0 S1 significant range of off-axis vertical f f ff +X1 = +0.5 S2 angles. Drive1 0.0 Drive2 • Part 2 will show that this linear S3 -X1 = -0.5 combination of outputs can also -X2 = -1.0 S4 -1.5 maintain beamwidth and vertical polar shape in the same range of frequencies. p g q Sept. 22, 2007 Sept. 22, 2007 Application of Linear Application of Linear- -Phase Digital Crossover Filters: Part 2 Phase Digital Crossover Filters: Part 2 Slide 9 Slide 9

Presented at the 32 nd AES Conference, 2007 September 21-23, 2007, Hillerod, Denmark Polar Pattern Summing for Two P l P tt S i f T Pairs of Separated Point Sources p • The following series of graphs illustrate that it is possible to approximate a desired polar pattern by linearly summing the patterns of two pairs of sources over a tt f t i f range of frequencies, although the patterns of the individual pairs of sources patterns of the individual pairs of sources may be incorrect! Sept. 22, 2007 Sept. 22, 2007 Application of Linear Application of Linear- -Phase Digital Crossover Filters: Part 2 Phase Digital Crossover Filters: Part 2 Slide Slide 10 10

Presented at the 32 nd AES Conference, 2007 September 21-23, 2007, Hillerod, Denmark Constant Beamwidth Frequency and Constant Beamwidth Frequency and Summing Ratios for Two Pairs of Sources Sources Frequency Normalized Drive1 Drive2 Identifier Identifier Frequency Frequency (Outermost Sources (Outermost Sources (Innermost Sources (Innermost Sources S 1 and S 4 ) S 2 and S 3 ) 1) Lower critical 0.285 0.00 (Off) 1.00 (Full on) +1.5 frequency +X2 = +1 0 +X2 = +1.0 S1 S1 2) Intermediate 0.3185 0.25 0.75 +X1 = +0.5 S2 frequency Drive1 0.0 Drive2 3) Intermediate 0.367 0.50 0.50 S3 -X1 = -0.5 frequency q y (crossover) -X2 = -1.0 S4 -1.5 4) Intermediate 0.443 0.75 0.25 frequency 5) Upper critical 5) Upper critical 0 570 0.570 1 00 (Full on) 1.00 (Full on) 0 00 (Off) 0.00 (Off) frequency Sept. 22, 2007 Sept. 22, 2007 Application of Linear Application of Linear- -Phase Digital Crossover Filters: Part 2 Phase Digital Crossover Filters: Part 2 Slide Slide 11 11

b) Presented at the 32 nd AES Conference, 2007 September 21-23, 2007, Hillerod, Denmark Polar Pattern Summing Over Polar Pattern Summing Over +1.5 +X2 = +1.0 S1 +X1 = +0.5 S2 a Range of Frequencies Drive1 0.0 Drive2 S3 -X1 = -0.5 -X2 = -1.0 S4 -1.5 Sept. 22, 2007 Sept. 22, 2007 Application of Linear Application of Linear- -Phase Digital Crossover Filters: Part 2 Phase Digital Crossover Filters: Part 2 Slide Slide 12 12

b) Presented at the 32 nd AES Conference, 2007 September 21-23, 2007, Hillerod, Denmark Polar Pattern Summing Over Polar Pattern Summing Over +1.5 +X2 = +1.0 S1 +X1 = +0.5 S2 a Range of Frequencies Drive1 0.0 Drive2 S3 -X1 = -0.5 -X2 = -1.0 S4 -1.5 Note that the resultant summed polar patterns are roughly the same even though the individual patterns are different! This over an octave range! This over an octave range! Sept. 22, 2007 Sept. 22, 2007 Application of Linear Application of Linear- -Phase Digital Crossover Filters: Part 2 Phase Digital Crossover Filters: Part 2 Slide Slide 13 13

Presented at the 32 nd AES Conference, 2007 September 21-23, 2007, Hillerod, Denmark Polar Pattern Overlays for a Double Pair of Sources Separated by Different Spacing Ratios for a Critical Design Wavelength of 0.5 λ Ratio = 2:1 Ratio = 2.5:1 Ratio = 3:1 Ratio = 4:1 To generate each polar overlay, the frequency was varied in 10 steps between the two critical frequencies so as to maintain a constant beamwidth of 83.6º. b idth f 83 6º Sept. 22, 2007 Sept. 22, 2007 Application of Linear Application of Linear- -Phase Digital Crossover Filters: Part 2 Phase Digital Crossover Filters: Part 2 Slide Slide 14 14

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