This article focuses on the consequences of introducing an electronic level offset between sources in a 2-element cardioid configuration in an attempt to maximize cancellation.
Both end-fired and gradient cardioid configurations partially rely on physical displacement of the sources to achieve the desired effect. The displacement, because of the inverse square law, causes a relative level difference between the sources that changes over distance. The difference in level is bigger in the near field than in the far field.
At one meter distance to the first source and e.g. two meters to the second source (1 meter spacing) the difference is 2:1 or 6 dB, assuming both sources where equally loud to begin with. However at 50 meters, using the same spacing, the difference is 51:50 or 0,17 dB. In other words the relative level difference will automatically approach zero over distance both behind and in front of the array.
Most of us however will measure and optimize cardioid configurations in the near field and might feel tempted to compensate the level difference, caused by displacement, electronically, to maximize cancellation behind the array. This absolute offset however is permanent and remains constant over distance preventing you from achieving increasingly more effective cancellation over distance. At the same time you won't achieve full or 6 dB of summation in front of the array.
The gallery to the right demonstrates the effects of offset for 50 Hz, 63 Hz and 80 Hz optimized 2-element cardioid configurations. The top chart shows relative level over distance, the bottom chart maximum summation and cancellation over distance. Notice how in each situation relative level approaches the absolute offset value or 0 dB in case of no offset.
Without offset, far field front-to-back ratios exceed 36 dB. But the introduction of 1 dB offset reduces this to approx. 28 dB. Near field cancellation has improved, with slightly less frontal output over distance. But when offset is increased to as much as 3 dB, far field front-to-back ratios have been reduced to a mere 16 dB, one tenth in comparison to no offset.
The animation (click on the thumbnail to play) at the beginning of this article clearly shows maximum cancellation moving toward the array but at the same time far field cancellation is reduced. Also notice the reduced output in front of the array.
As always the best approach depends on the application but some restraint might be appropriate.
For more information on cardioid subwoofer configurations please refer to the Subwoofer Array Designer manual.