AN ANALYTICAL INVESTIGATION OF THE DIRECT MEASUREMENT METHOD OF ESTIMATING THE ACOUSTIC IMPEDANCE OF A TIME-VARYING SOURCE

This paper presents an analytical investigation of the direct method of measurement of the source impedance of a linear time-variant source. The direct method yields a frequency-dependent effective source impedance which is routinely used in a time-invariant analysis to determine the insertion loss of two different acoustic loads applied to the same source. In such an analysis the strength of the source is assumed to be invariant with load. It is shown here that there is generally no precise correspondence between the effective source impedance as given by the direct method and the characteristics of the actual source. Furthermore, it is shown that the effective source impedance values given by the direct method are functions of the acoustic load and the location of the injected signal as used in the measurement. However, the effective source resistance is always found to be positive, in accordance with experimental measurements. In this regard the direct method is an improvement on the indirect method, where physically implausible negative resistance values are often found. Finally, it is shown that the effective impedance values as given by the direct method when used with a time-invariant analysis give rise to very accurate predictions of insertion loss, even when the strength of the actual time-variant source is allowed to vary with the acoustic load.