Tech Design.....
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Modeling Rectangular Dipole Baffles and the Equivalence of
Circular and Rectangular Dipole Baffles at low frequency.
Figure 1. Rectangular
baffle with offset driver
mounting.
Figure 2. Defining the relationship between angular position and
distance from the driver center to baffle edge.
Baffle modeling results:

To the left you will find a series of
figures for the dipole response on
rectangular baffles with different driver
position and baffle size. These
simulations were performed with
Music
and Design's
 proprietary dipole baffle
simulation tool. The plots present the
predicted on axis response for a
directional driver in blue, the response
at 20 degrees off axis (to one side not
both) in the green/yellow dotted line,
the approximate response at 90
degrees, accounting for asymmetry
between the front and rear driver
response, and the response of an
omnidirectional source centered on a
circular baffle of the equivalent radius
as determined from the analysis
presented above. In all cases note the
agreement between the low frequency
driver on axis response and the
equivalent circular baffle results at low
frequency. The slight differences at
very low frequency are a result of
differences between the driver model
and the omnidirectional source. An
omnidirectional source positioned at
the same point as the driver on the
rectangular baffle would match the
equivalent circular baffle result exactly
at low frequency.

The result of Figure 3 is for a 100 cm
H by 40 cm wide baffle with the driver
centered. Figure 4  shows the effect of
moving the driver off center vertically
to 20 cm from the top. Figure 5 then
additionally moves the driver 5 cm to
the side.

Figure 6 shows the result for a 100 cm
by 100 cm baffle with the driver
positioned 30 cm from the top and 20
cm from one side. Note that with this
significant offset the 20 degree off axis
response is predicted to be higher
then the on axis response between 20
and 500 Hz. In this case, the off axis
angle is towards the wider side making
the baffle appear more symmetrical.
This type of behavior can make wide
baffles with offset driver mounting
undesirable for dipole speakers. at it
tends to rotate the dipole axis with
increasing frequency.

Clearly such a design tool is of
significant value in the preliminary
evaluation of baffles for dipole speaker
systems.
Figure 3. Comparison of dipole response of driver on a 100cm H x 40 cm W baffle with driver centered at
50cm, 20 cm. Blue = directional driver model, Green = 20 degrees off axis, yellow = omnidirectional source
on equivalent circular baffle. maroon = driver model at 90 degrees.
Figure 4. Comparison of dipole response of driver on a 100cm H x 40 cm W baffle with driver offset vertically
at 20cm, 20 cm. Blue = directional driver model, Green = 20 degrees off axis, yellow = omnidirectional
source on equivalent circular baffle. maroon = driver model at 90 degrees.
Figure 5. Comparison of dipole response of driver on a 100cm H x 40 cm W baffle with driver offset vertically
and horizontally at 20cm, 15cm. Blue = directional driver model, Green = 20 degrees off axis, yellow =
omnidirectional source on equivalent circular baffle. maroon = driver model at 90 degrees.