POWER OUTPUT MINIMIZATION AND POWER ABSORPTION IN THE ACTIVE CONTROL OF SOUND

Active minimization of total power output and active absorption of sound power are analyzed, using a general impedance-based approach, for an array of controllable secondary sources and an array of original primary sources. When the total power output of the two arrays is minimized, and the primary source array is all in phase, the power output of each of the secondary sources is found to be exactly zero. When the power absorption of the secondary source array is maximized, the net power output of the primary source array can be either reduced or increased, compared to that in the absence of control, depending on the properties of the transfer impedances. If the primary and secondary sources are well coupled (as is the case when they are spaced less than a quarter wavelength apart in free-space or when they are in an enclosure excited near the natural frequency of a lightly damped mode) minimizing the total power output gives worthwhile reductions in the radiated power of the primary source. Maximizing the power absorption of the secondary source under these conditions, however, can considerably increase the power output of the primary source. If the sources are well separated, compared with the wavelength, in the free-field, or are placed in a diffuse sound field in an enclosure, the coupling between the sources is weak. Under these conditions the secondary source can effect little reduction in the power output of the primary source. Although acoustic power can still be absorbed by the secondary source under such circumstances, the amount of absorbed power will always be small compared with the power output of the primary source.