Reciprocity method with complex nonlinear fitting for primary vibration standards

Abstract

The historical development of two basic types of absolute calibration methods for primary vibration standards, i.e., the reciprocity method and laser interferometry, are briefly reviewed. This paper presents a new reciprocity method with complex nonlinear least-squares fitting, which can be used to determine all basic parameters characterizing the behavior of an electromechanical transducer. For this purpose, the reciprocity calibration theory of electromechanical or electroacoustic transducers is generalized, and a universal calibration formula is derived from a three-parameter model established in this paper. Then the paper describes an application of the theory to improve the piezoelectric reciprocity method (PRM) suited to the high- and ultra-high-frequency vibration calibration, and meanwhile develops a corresponding complex nonlinear fitting program for data process. It is verified that the new method is a distinct improvement on the conventional PRM with three-pair data.