High-accuracy measurements on biperiodical circuits

Coupled resonators in an assembled structure lose their individuality and in co-operation contribute to the generation of structure modes (resonant frequencies). The resonant frequencies of these modes are the only measurable quantities. In order to predict structural behaviour in a variety of cases, the problem that arises is the extraction of all the parameters characterizing the structure from the measurements mentioned here. If all the modes are confined in a bandwidth that is small with respect to the central frequency, the total coupled resonator system is well represented by a circuit of unknown lumped constants.

The structure modes are the solutions of the equation obtained by equating to zero the determinant relevant to the lumped circuit representation. The equation is a polynomial of the squared frequency variable, the degree of which is equal to the number M of circuits.

The analysis method described in this paper consists in varying, by an unknown amount, the frequency of a single resonator in the chain. This variation will produce a change in the frequencies of all structure modes. It is possible to find certain invariants linearly dependent on all the unchanged parameters of the circuit. These invariants have an algebraic representation that allows the extraction of the structure parameter values with extremely high accuracy. The proposed method is quite general and, in the present work, we give an example applying the method to the characterization of a side-coupled linac (SCL).