Omnidirectional point-source driver array calculator
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This Excel spreadsheet will display polar and frequency
response graphs for an array of omnidirectional point-source radiators
(for example, subwoofer loudspeakers) in a specified arrangement.
The main fields for user entry are shown with yellow backgrounds.
The table below with a grey background defines the positions and characteristics
of the sources (radiators).
Each source is defined in terms of its position in three
axes relative to the origin. The X axis extends to the right, the
Y axis extends to the front (towards the bottom of the polar chart), and
the Z axis extends upwards. The ground is assumed to be at Z=0.
Each source also has a gain value in decibels, a delay in milliseconds,
and a polarity control. The sources may be switched on and off using
the "Use" column. The number of sources to be used is
defined in the "Number of sources" box (cell B17, set to two
in the example above). Any sources beyond the number defined that
appear within the table are ignored. The small graph to the left
of the table of sources gives a pictorial indication of the positions
(in X and Y axes only) for all sources within the table. Each "tick"
mark represents 1m (i.e. there's 5m in each axis in each direction).
The ear height of the listener (i.e. height in the Z
axis) should be specified in cell B4. The value given here affects
both the polar and frequency response plots.
The calculations can optionally include the effects
of "ground bounce", i.e. reflections from the plane of the ground
at Z=0. This can be switched on or off using the "Include ground
bounce" box (cell B5). If ground bounce is switched off here,
there's no longer anything special about the plane of Z=0 and other ground
bounce options within the spreadsheet are ignored.
polar pattern display resolution is 5dB per annular division, and will
show a minimum value of –40dB. The heavy black line indicates
unity (0dB). The direction of the positive X axis extends towards
the right of the graph and the direction of the positive Y axis extends
towards the bottom of the graph. The chart is drawn with 1 degree
The frequency for the polar chart is selected in cell
B7 and may be swept up and down using Ctrl-A and Ctrl-S.
The radius distance for the polar (i.e. the distance
from the origin to the listener) is selected in cell B8 and may be swept
up and down using Ctrl-Q and Ctrl-W.
The reference level for the polar chart is a single
driver at unity gain positioned at the origin. However, the reference
level may optionally include the "ground bounce" (i.e. reflection
from the plane of Z=0, increasing the reference level by 6dB), and this
is controlled using cell B9.
After making changes, the polar chart should be updated
by clicking the "Recalc Polar" button or by pressing Ctrl-R.
"Polar levels" box shows numeric levels at particular points
on the polar chart. "On axis" is towards the bottom of
the chart; "behind" is towards the top, and "90 degrees"
is towards the right.
The "Polar average" level is the RMS average
around the entire polar. Note that this average is calculated using
the values at the 1 degree resolution employed for the display.
As a result, if the polar contains very sharp nulls, the average value
shown may not be identical to the theoretical calculated value.
Frequency response graph
frequency response graph shows frequency from 10Hz to 1kHz using a logarithmic
scale, and SPL in decibels relative to the reference value.
The X and Y positions for the listener (i.e. the position
at which the frequency response is calculated) must be specified in cells
B11 and B12. The X position (i.e. to the left or right) may be swept
up and down using Ctrl-K and Ctrl-L. The Y position (i.e. to the
front or back) may be swept up and down using Ctrl-I and Ctrl-O.
The Z position of the listener is the ear height specified in cell B4.
The reference level for the frequency response graph
may be either a single driver at unity gain positioned at the origin,
or the first source within the list of sources (including its specified
gain). The reference level may optionally include the "ground
bounce" (the reflection from the plane of Z=0). The reference
level to be used for the frequency response chart is specified in cell
The frequency response graph may optionally include
a phase trace which is shown in blue. This is enabled using cell
B14. The phase values are shown in blue on the right-hand end of
the graph. The phase display may be removed from the graph using
the "Clear phase trace" button. The "time of flight"
between the origin and the listener may optionally be subtracted out,
and this is controlled using cell B15. An additional time of flight
may be subtracted out (whether or not "Subtract time of flight"
is enabled) by specifying the required value in milliseconds in cell E15.
This value may be swept up and down in tenths of a millisecond by using
Ctrl-D and Ctrl-F.
After making changes, the frequency response graph should
be updated by clicking the "Recalc Freq Response" button or
by pressing Ctrl-R.
"Construct array" box provides a quick way to construct a rectangular
array of sources. Select the number of sources to be created both
horizontally and vertically, the spacing between their centres both horizontally
and vertically, and click the "Construct array" button.
The sources are always placed at Y=0 and centred at
X=0. The array sits on the ground (above Z=0), and the vertical
position of the bottom row of sources is one half of the vertical spacing
The gain, delay, and polarity values within the list
of sources are not changed by the "Construct array" function.
Naturally, the positions generated can be tweaked at will.
The example graphs above show two sources spaced apart
by 10m (for example, subwoofers on either side of a stage). The
polar shows the response at 50Hz at 20m radius, and the frequency response
shows the response for a listener 10m in front of the sources at 2m off
to the right.
|As another example, consider a 4x2 array of drivers
as defined by the "Construct array" box shown above.
The polar at 20m at 100Hz is shown at the right. Note some narrowing
of the dispersion pattern to the sides.
|Now consider two drivers in a "cardioid sub"
arrangement with one driver spaced behind the other by 1.43m, delayed
by 4.17ms, and with its polarity inverted. The polar shown is
for 60Hz at 20m radius.
|Lastly, consider a single driver 2m above the ground
and a listener 5m away (ear height 1.8m). This is the frequency
response caused by inclusion of the "ground bounce" (i.e.
the reflection from the ground).
© 2014, 100dB sound