Measurement of the scattering-matrix of acoustical two-ports

Abstract

In this paper a method for measuring the scattering-matrix of an acoustical two-port is presented and tested. All earlier works on experimental characterisation of acoustical two-ports have focused on the measurement of the transfer-matrix. Since the scattering-matrix has not been tested before, it represents a new approach to the problem. It can be argued that this is the best approach since a scattering-matrix gives the most basic description of a wave interaction problem. However, when one type of matrix description of a two-port is known, all other types can be obtained from linear transformations. From this point of view the choice of description is not so important. A more important difference between this paper and earlier works is; the formulation of the measurement method. Here the basis for the method is a direct estimation of the state vectors. In the author's opinion this represents the most straight-forward formulation since it is based directly on the definition of a two-port matrix. One advantage with this formulation is that it can easily be extended to the general case of an N-port. Another difference between this paper and earlier works on the problem is the method to suppress disturbing noise. Here a reference signal, perfectly correlated with the acoustic field, is used. To suppress noise the transfer function between the reference signal and each state vector component is measured.