Active multi driver cardioid speaker?

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Running from a Hypex FA123, would it be possible to get cardioid pattern with this setup? Similar drivers on front and back, one on the back in reverse phase. Is it smarter to run the drivers on the back crossed only to reproduce bass frequencies? Hypex would allow adjusting negative woofer level for more or less cardioid effect?
 
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Thanks, so playing around with this setup can work. Takes alot of testing and tuning, but is possible. My thought was to drive one woofer at front to crossover point other woofers would cross off at baffle step frequency. Just trying to get cardioid in bass territory to make it suitable for close to wall positioning.
 
Rule of thumb is: quarter wavelength distance between front and rear drivers, quarter wavelength delay + polarity flip on rear drivers. You can use a lower lowpass on the rear drivers, but keep in mind the relative phase response has to be controlled.