Reciprocity of linear systems with smart materials utilized for precise measurement techniques

In electromechanical measurement techniques, passive transducers and passive electrical networks often interact. In some applications, continua are considered as part of the system, where fields are formed and waves are propagated. In this article, networks, continua, and electromechanical transducers feature sufficient amplitude linear behavior in their environment (e.g. for operation around a bias) and are reciprocal. In addition, all elements of the system have constant parameters during the measurement. Then, the skillful application of the inherent reciprocity of these systems can lead to surprisingly useful benefits. This is shown by actual examples from metrology. The examples include the precise determination of transduction coefficients. It is also shown how the linearity of a system is checked by utilizing reciprocity relations. Although the facts of the matter are well known, its potential is often overlooked or disregarded in measurement techniques.