Ground-Plane Constant Beamwidth Plane Constant

Transcription

Ground--Plane Constant Beamwidth
Ground
Transducer (CBT) Loudspeaker
Ci
Circular
Circularl -Arc
A Li
Line A
Arrays
D. B. (Don) Keele, Jr.
Douglas J. Button
Principle Consultant
DBK Associates and Labs
Bloomington, IN, USA
www.DBKeele.com
(AES Paper Presented Oct. 2005)
JBL Professional
Northridge, California, USA
[email protected]
Overview

Introduction
A Brief CBT History and Overview
Steps to Create a Ground
Ground--Plane Array from a
Free--Standing Array
Free
Sound--Field Simulations
Sound
Measurements: Frequency Response Over the
Ground Plane
Conclusions: Advantages of CBT GroundGround-Plane
Array
Keele, Oct. 7, 2005
GroundGround-Plane CBT Line Arrays
Overview of Constant Beamwidth
T
Transducer
d
Theory
Th

First formulated in JASA papers published in 1978 and 1983
describing underwater transducers based on shaded
spherical caps (U.S. Naval Research Labs)

P. H. Rogers, and A. L. Van Buren, “New Approach to a Constant
Beamwidth Transducer,” J. Acous. Soc. Am., vol. 64, no. 1, pp. 3838-43 (1978
July).
A. L. Van Buren, L. D. Luker, M. D. Jevnager, and A. C. Tims, “Experimental
Constant Beamwidth Transducer,” J. Acous. Soc. Am., vol. 73, no. 6, pp.
2200--2209 (1983 June).
2200
Applied to loudspeaker arrays in four AES papers by Keele
in 2000, 2002, and 2003

[1] “The Application of Broadband Constant Beamwidth Transducer (CBT)
Theory to Loudspeaker Arrays,” presented at the 109th convention of the
Audio Engineering Society, Preprint 5216 (Sept. 2000).
[2] “Implementation of StraightStraight-Line and Flat
Flat--Panel Constant Beamwidth
Transducer (CBT) Loudspeaker Arrays Using Signal Delays,” 113th Convention of
the Audio Engineering Society, Preprint 5653 (Oct. 2002).
[3] “The FullFull-Sphere Sound Field of Constant Beamwidth Transducer (CBT)
Loudspeaker Line Arrays,” J. Aud. Eng. Soc., vol. 51, no. 7/8., pp. 611611-624
(July/August 2003).
2003)
[4] “Practical Implementation of Constant Beamwidth Transducer (CBT)
Loudspeaker CircularCircular-Arc Line Arrays,” presented at the 115th Convention of
the Audio Engineering Society, New York (Oct. 2003).
Keele, Oct. 7, 2005
Rogers & Van Buren 1978
(Lots of heavyheavy-duty math!)
Keele, Oct. 7, 2005
Highlighted Text

“With such a ‘constant beamwidth
transducer’
t
d
’ (CBT) th
the spectral
t l
content of the acoustic signal would
b iindependent
be
d
d t off bearing.”
b
i
”
Keele, Oct. 7, 2005
Spherical--Cap CBT Transducers
Spherical
Overview
100° Circular
Ci l Spherical
S h i l Cap
C
Oblique View
Keele, Oct. 7, 2005
Side View
Spherical--Cap CBT Transducers
Spherical
Overview Cont.:
Legendre Shading of Surface Pressure
No Shading
⎧1 for θ ≤ θ 0
p (θ ) = ⎨
⎩0 for θ > θ 0
Keele, Oct. 7, 2005
With Shading
⎧ P ( cos θ ) for θ ≤ θ 0
p (θ ) = ⎨ v
0 for θ > θ 0
⎩
Spherical-Cap CBT Transducers
SphericalO
Overview
i
C
Cont.: Ob
Observations
i

Provides extremely uniform polars above a certain
frequency which are independent of distance

Beamwidth = 0.64 x Cap Angle

Surface
S f
pressure distribution,
di t ib ti
nearfield
fi ld pressure pattern,
tt
and farfield pressure pattern are all essentially the same!
No nearfield!
Don’t need the rest of the sphere!
Keele, Oct. 7, 2005
-12 dB
Applied to CircularCircular-Arc
Line Arrays
-9 dB
-6 dB
-3 dB
CBT Curved Line Source
(Circular Wedge)
Truncated and Stepped Legendre Shading
(Power Loss = 2.3 dB)
0 dB
-3 dB
-6 dB
-9 dB
-12 dB
Keele, Oct. 7, 2005
First CBT
Line-Line
Array
Array
Prototype
yp
of 2003
1 m (40”)
(Passive Shading)
• 18 Ea 57mm (2.25”)
drivers
• 50 Ea 19mm (0.75”)
drivers.
Keele, Oct. 7, 2005
Ground--Plane RF Antennas
Ground
Common Whip Antennas
One half of a half-wave dipole mounted
over an electromagnetic ground plane that
supplies the missing half.
Keele, Oct. 7, 2005
Ground-Plane Techniques Have
GroundNever Been Applied to
Loudspeakers Before!
Keele, Oct. 7, 2005
Personalized Amplification
S
System™
™
Photos courtesy Bose Corp.
(www.bose.com/musicians)
Keele, Oct. 7, 2005
Steps to Create a GroundGround-Plane Array
from a FreeFree-Standing CBT Array
1. Free-standing
array
2. Free-standing array
over ground plane
3. Free-standing array
over ground plane with
reflection
4. Chop off bottom
half of array
7. Array is now effectively
7
double the size of the original
6. Now double its size
5. Lower to ground plane
Keele, Oct. 7, 2005
Vertical-Plane SoundVerticalSound-Field
Si l i
Simulations
and
dM
Movies
i

Four Configurations Were Analyzed Over a
Ground Plane (all point
point--source arrays):
• Single point source
• Typical three
three--way system with 2nd2nd-order LinqwitzLinqwitz-Riley
crossovers at 200 Hz and 2 kHz
• Straight
Straight--line source, no shading
• Circular
Circular--arc curvedcurved-line source with Legendre
g
shading
g

Additional Configurations Analyzed in Paper but
not Shown Here
• StraightStraight-line source, with Hann shading
• Circular
Circular--arc curvedcurved-line source, no shading
• Delay
Delay--curved straight
straight--line source with/without Legendre
shading
Keele, Oct. 7, 2005
Single--Point Source Over a Ground
Single
Plane:
(Non--Reflective
(Non
vs.
Reflective)
Sound-Field Movie
False-Color Scale
Constant-Pressure
C
P
Contours (Isobar)
Every 3 dB
Keele, Oct. 7, 2005
Three-Way Floor
ThreeFloor--Standing System
Over a Ground Plane (point sources):
(Non--Reflective
(Non
vs.
Reflective)
Linqwitz-Riley
crossovers at
200 Hz and 2 kHz.
Keele, Oct. 7, 2005
Un--Shaded StraightUn
Straight-Line Source
over a Ground Plane:
(Non--Reflective
(Non
vs.
Reflective)
3
Watch for grating lobes!
2
50 Point Source
Straight-Line Array
HEIGHT
m
0 dB
1
0 dB
0 dB
1.25m
0 dB
0
Ground Plane
0 dB
0
1
2
3
4
DISTANCE - m
Keele, Oct. 7, 2005
Legendre-Shaded CircularLegendreCircular-Arc Line
S
Sources
over a Ground
G
d Plane:
Pl
(Both Reflective!!)
Reflective!!)
Keele, Oct. 7, 2005
Measurements: Frequency
R
Response
O
Over the
h G
Ground
d Pl
Plane

Measured three different systems:
• A conventional two
two--way compact powered monitor
• Experimental straight
straight--line array, no shading.
• Experimental ground
ground--plane circular
circular--arc curved line array,
Legendre shading (a CBT array).

Measurement technique:
• All measurements were taken with a “Farina”
Farina log sinesine-sweep
technique covering the frequency range of 100 to 20 kHz.
• The resultant impulse response was windowed with a 50 ms
Hann window centered over the signal’s first arrival.
• The windowed time response was then converted to the
frequency domain and then sampled at 1/100th1/100th-decade
intervals.
• The resultant frequency response was either displayed as is or
1/10th/
-octave fivefive-p
point binomial Gaussian
smoothed with a 1/10th
filter.
Keele, Oct. 7, 2005
R
Response
O
Over the
h G
Ground
d Pl
Plane

Measured frequency response magnitude at 25 grid points in
the vertical plane of a 3 m high by 4 m deep region over a
reflective ground plane.
NEAR-FAR
UP-DOWN
Keele, Oct. 7, 2005
R
Response
O
Over the
h G
Ground
d Pl
Plane

Measured offoff-axis frequency response magnitude at 4 points in
the horizontal plane at two meters over a reflective ground
plane at a height of 0 m and 1 m.
Keele, Oct. 7, 2005
Conventional TwoTwo-Way Compact
Powered
P
dM
Monitor
i
1m
Keele, Oct. 7, 2005
A
JBL model LSR 25
25P
P
mounted on a stand.
stand. The
height of the monitor was
raised so that its axis was 1 m
high (a point midway between
the tweeter and woofer).
woofer).
On--Axis Response (Unsmoothed)
On
Keele, Oct. 7, 2005
Response vs. Height
(at Different Distances)
Color Code
0.1 m
Keele, Oct. 7, 2005
0.5 m
1m
2m
4m
Response vs. Distance
(at Two
T o Different Heights)
1.5 m
High
1m
High
Keele, Oct. 7, 2005
Color Code
Response vs. Angle
(at Two
1m
High
0m
Hi h
High
Keele, Oct. 7, 2005
Color Code
Experimental StraightStraight-Line Array
The array is 1.25 m high and contains 36 miniature 30 mm widewiderange
g drivers.
drivers. All drivers were driven with equal
q
in-phase
p
levels.
1.25 m
Keele, Oct. 7, 2005
On
(Normalized to
0 dB at 1 kHz)
Keele, Oct. 7, 2005
Response vs. Height
Color Code
EQ d Flat
EQ’d
Here
0.1 m
Keele, Oct. 7, 2005
0.5 m
1m
2m
4m
(at Two
Color Code
1.5 m
High
EQ’d Flat
Here
1m
High
Keele, Oct. 7, 2005
Response vs. Angle
(at Two
Color Code
1m
High
EQ’d Flat Here
(0 Degs)
0m
Hi h
High
Keele, Oct. 7, 2005
Experimental CircularCircular-Arc Curved
Curved-Li CBT A
Line
Array
The 45º
45º circular
circular--arc array is 1.1 m high and contains 36
miniature
i i t
30 mm widewide
id -range drivers
d i
drivers.
. Legendre
L
d
shading
h di
(frequency independent). Driven by three 12-channel
automotive amplifiers.
11m
1.1
Keele, Oct. 7, 2005
On
Note gentle
HF rolloff.
Keele, Oct. 7, 2005
(Normalized to
0 dB at 1 kHz)
Response vs. Height
Color Code
EQ d Flat
EQ’d
Here
0.1 m
Keele, Oct. 7, 2005
0.5 m
1m
2m
4m
(at Two
Color Code
1.5 m
High
EQ’d Flat
Here
1m
High
Keele, Oct. 7, 2005
Response vs. Angle
(at Two
Color Code
1m
High
EQ’d Flat
Here
0m
Hi h
High
Keele, Oct. 7, 2005
Working Off the Side of the Pattern

At specific heights, the variation of nearnear-far SPL is
minimized because the trajectories approximately
coincide with specific constantconstant-pressure contours.
contours
Main axis of
free-standing
CBT array.
Keele, Oct. 7, 2005
Main axis of groundplane CBT array.
Axis grazes the
ground-plane!
Typical listening axis for a
ground-plane CBT array.
The listener listens o
on an
a
axis that is offset from the
main axis of the array.
Constant--Pressure 3Constant
3-dB Contours
(Ho i ont l lines
(Horizontal
line are
e drawn
d
n where
he e the SPL is
i constant
on t nt within
ithin ±1 dB)
Range: 1.2 to 4 m
Height: 1.7 m Æ
Height: 1.4 m Æ
Range: 0.6
0 6 to 3.3
33m
This works quite well because the polars of the CBT array
are so consistent with frequency!
Keele, Oct. 7, 2005
Conclusions: Advantages of CBT
G
Ground
Groundd-Plane
Pl
A
Array

•
Minimizes/eliminates detrimental floor reflections.
reflections
Extremely uniform coverage: upup-down, right
right--left, and near
near--far.
Can be implemented without DSP, passive speakerspeaker-level
shading can be used.
Mi i i
Minimizes
near-far
nearf variation
i ti
off SPL att certain
t i heights.
h i ht
The beneficial effects of the groundground-plane can be taken
advantage of in two ways:
Increase Effective Size:

•
effective
ff
array height.
h h
array sensitivity (+6 dB).
array maximum sound pressure level (SPL) capability (+6 dB).
operating bandwidth down by an octave (or two depending on
beamwidth is defined).
)
Decrease Physical Size:

•
Doubles
bl
Doubles
Doubles
Extends
how the
Can half the physical height of the array but maintain the same
performance as the fullfull-size free
free--standing array when a ground plane is
available.
Or a combination of the two!
Keele, Oct. 7, 2005
Thank Yo
You!!
Keele, Oct. 7, 2005