Active noise cancellation: Where does the extra power go?

Active noise cancellation (ANC) is a method of reducing an undesired signal, i.e., noise, by introducing an “antinoise” signals from secondary sources. A fundamental issue for noise cancellation is the destiny of the excess noise power. The noise and the anti-noise sum to create at least twice the power of the original noise, and with the summed power minimized at the site of the cancellation, the excess power must appear elsewhere - often defeating the purpose of the ANC. While ANC is best known for acoustic waves, including vibration control, very similar techniques hold for the signals of electromagnetic waves as used in diversity and MIMO communications antennas, electromagnetic cloaking, and other signal processing such as polarization cancellers, equalizers, multi-user detectors, in communications, sonar and radar. We present here a simple and insightful tour of the cancellation mechanisms of ANC, and the destiny of the excess power generated. For a closed, lossless situation, we demonstrate using a transmission line formulation that both the primary noise and secondary anti-noise are reflected back to their own sources, and dissipated in their source impedances.