Tech Design.....
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Crossover transitions between sources with different radiation
patterns.
Presented below are examples of the radiation patterns between combinations of different sources;
dipole, monopole and cardioid, when using either a 4th order Linkwitz/Riley or 3rd order Butterworth
crossover. This important topic is seldom discussed. As is evident, the transition of the radiation pattern
is dependent on the type of crossover. This is because Linkwitz/Riley crossovers sum flat on axis when
there is zero interdriver phase difference. The Butterworth crossovers sum flat in phase quadrature, 90
degrees interdriver phase difference. This difference in phase effects how the sources sum off axis.
Higher or lower order crossovers of the same type would yield similar results but the transition regions
would occur over a narrower or wider frequency range. The plots below span about one to two octaves
to either side of the crossover point. Crossovers between similar sources are omitted for the obvious
rerason.
Radiation patterns between various combinations of dipole, monopole and cardioid sources through
the crossover region when using a 4th order Linkwitz/Riley crossover
Dipole to Cardioid: The dipole
nulls at 90 degrees gradually
swing to the rear and converge to
the single cardioid null at 180
degrees.
Dipole to Monopole: The
dipole response morphs into a
cardioid at the crossover
frequency which then expands
into a typical monopole response.
(green and yellow are transposed)  
Monopole to Cardioid: There is
a smooth reduction in rearward
radiation ending in the cardioid
response.
Radiation patterns between various combinations of dipole, monopole and cardioid sources through
the crossover region when using a 3rd order Butterworth crossover
Dipole to Cardioid: The dipole
null disappear because the
phase angle between the dipole
and cardioid response is always
+/-90 degrees and nulls in the
summed response can not occur
unless the amplitude of one
component goes to zero.
Dipole to Monopole: The
transition from dipole to monopole
is fairly fast without the
intermediate cardioid pattern at
the crossover point. Again, this is
due to the +/-90 degree phase
difference between the sources.
(green and yellow are transposed)  
Monopole to Cardioid: The
monopole to cardioid transition
looks qualitatively similar to the
LR4 result. However there are
small quantitative differences.