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Tech Design.....
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Design of woofer with varying directionality.
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Design of woofer with varying directionality.
© 2006 John Kreskovsky
In the discussion of power matching of midranges to woofers it was shown that for a speaker with dipole or
cardioid midrange operating in a 4 Pi environment and a woofer system operating in a 2 Pi environment, the
directivity factor of the woofer, DF, must be one half that of the midrange on the speakers axis if flat on axis
response is to be achieved while at the same time radiating constant total power vs frequency. A novel solution was
presented for matching dipole mids and woofers in which the woofer was rotated by 45 degrees relative to the
system axis. However, it was also shown that if the radiation pattern for the woofer is to be aligned with that of the
system, then the woofer system can not have a dipole radiation pattern, but must have a radiation pattern with DF
equal to 1.5 along the axis of maximum intensity. It was suggested that such a woofer system could be developed
by combining a dipole woofer with a monopole. The chart below shows how the radiation pattern of such a
combined woofer behaves as a function of the relative strength of the on axis radiation of the dipole and the
monopole. From left to right the chart shown the variation in radiated power (left vertical axis) and on axis DF (right
vertical axis). The relative on axis strength of the monopole source varies form 60 dB greater than the dipole
source at the extreme left to 120dB below the dipole at the extreme right. The total radiated power of the combined
sources is shown in pink and the on axis DF in blue. As we move from left to right, at the point where the monopole
and dipole are of equal strength the radiation pattern, shown at the far right, is a cardioid with DF = 3 and total
radiated power -4.77 dB relative to a pure monopole source with same on axis intensity. Moving further to the right
we find a maximum DF of 4 and a minimum in radiated power of -6dB at the point where the monopole component
of the combined source has an on axis SPL is -9.54 dB (0.33333x) that of the dipole component. Note the shape of
the radiation pattern. As the dipole strength continues to increase DF comes down and asymptotes to 3, the same
values as for a cardioid, and the radiated power is -4.77 dB. Examining the curve for DF we see that a DF of 1.5
occurs at the point where the monopole on axis SPL is approximately 12.56dB (4.25x) greater than the dipole. The
radiation pattern is shown second from the bottom. While difficult to see in the plot, the sound pressure level at 180
degrees is just over 4 dB below the on axis SPL for this case. A woofer with this radiation pattern, operating in 2 Pi
space (close to a floor), would produce the same total radiated power, when the on axis SPL was matched, as a
dipole operating in 4 Pi space. Such a woofer could be constructed using a single monopole woofer and a an H
frame dipole with the same on axis response. The dipole woofer could likely be smaller then the monopole woofer
due to the significantly lower SPL levels required. Such a woofer would likely require two channels of amplification
since the monopole and dipole woofer must have the same on axis response and would probably require
application of different response shaping networks in addition the required dipole equalization of the H-frame.
Potentially, a low power amplifier could be used to drive the H-frame due to the low level of the required output.
However, it is questionable that the benefits of match the radiated power out weigh the complexity of using a single
monopole woofer would result in only a 1.76 dB mismatch between woofer and midrange.
cardioid midrange operating in a 4 Pi environment and a woofer system operating in a 2 Pi environment, the
directivity factor of the woofer, DF, must be one half that of the midrange on the speakers axis if flat on axis
response is to be achieved while at the same time radiating constant total power vs frequency. A novel solution was
presented for matching dipole mids and woofers in which the woofer was rotated by 45 degrees relative to the
system axis. However, it was also shown that if the radiation pattern for the woofer is to be aligned with that of the
system, then the woofer system can not have a dipole radiation pattern, but must have a radiation pattern with DF
equal to 1.5 along the axis of maximum intensity. It was suggested that such a woofer system could be developed
by combining a dipole woofer with a monopole. The chart below shows how the radiation pattern of such a
combined woofer behaves as a function of the relative strength of the on axis radiation of the dipole and the
monopole. From left to right the chart shown the variation in radiated power (left vertical axis) and on axis DF (right
vertical axis). The relative on axis strength of the monopole source varies form 60 dB greater than the dipole
source at the extreme left to 120dB below the dipole at the extreme right. The total radiated power of the combined
sources is shown in pink and the on axis DF in blue. As we move from left to right, at the point where the monopole
and dipole are of equal strength the radiation pattern, shown at the far right, is a cardioid with DF = 3 and total
radiated power -4.77 dB relative to a pure monopole source with same on axis intensity. Moving further to the right
we find a maximum DF of 4 and a minimum in radiated power of -6dB at the point where the monopole component
of the combined source has an on axis SPL is -9.54 dB (0.33333x) that of the dipole component. Note the shape of
the radiation pattern. As the dipole strength continues to increase DF comes down and asymptotes to 3, the same
values as for a cardioid, and the radiated power is -4.77 dB. Examining the curve for DF we see that a DF of 1.5
occurs at the point where the monopole on axis SPL is approximately 12.56dB (4.25x) greater than the dipole. The
radiation pattern is shown second from the bottom. While difficult to see in the plot, the sound pressure level at 180
degrees is just over 4 dB below the on axis SPL for this case. A woofer with this radiation pattern, operating in 2 Pi
space (close to a floor), would produce the same total radiated power, when the on axis SPL was matched, as a
dipole operating in 4 Pi space. Such a woofer could be constructed using a single monopole woofer and a an H
frame dipole with the same on axis response. The dipole woofer could likely be smaller then the monopole woofer
due to the significantly lower SPL levels required. Such a woofer would likely require two channels of amplification
since the monopole and dipole woofer must have the same on axis response and would probably require
application of different response shaping networks in addition the required dipole equalization of the H-frame.
Potentially, a low power amplifier could be used to drive the H-frame due to the low level of the required output.
However, it is questionable that the benefits of match the radiated power out weigh the complexity of using a single
monopole woofer would result in only a 1.76 dB mismatch between woofer and midrange.
