An analytical, one-dimensional standing wave model of a linear active noise control system in a duct

Abstract

Assuming plane waves, and making use of the transfer matrices and electroacoustic analogies, a standing wave analysis of the active noise control system in a duct is presented incorporating the characteristics of the primary source as well as the auxiliary source. Analytical expressions have thus been derived for the ratio of the two source pressures and certain other ratios or relations of interest for complete or partial cancellation of noise downstream of the auxiliary source. The resulting closed-form expression for the filter transfer function H₀ reveals the real role of the auxiliary source both when it is on and off, and the importance of the distance between the input microphone and the auxiliary source (generally, a loudspeaker). Finally, the analysis is extended to incorporate the convective and dissipative effects of the meanflow and viscothermal damping.