Dependence of the induced loss factor on the coupling forms and coupling strengths: energy analysis

In two recent papers, the induced loss factor is determined via the modification to the loss factor in the linear impedance of a master oscillator caused by its coupling to a set of satellite oscillators. A loss factor is basically an energetic quantity and, therefore, one may inquire whether the induced loss factor may be estimated via an energy analysis (EA). An answer to this question is sought. It is shown that the linear impedance analysis and EA yields identical results for the induced loss factor in the appropriate frequency range. This frequency range spans the distribution of resonance frequencies of the satellite oscillators. In this frequency range, the identity of the results is not only in terms of gross features but also in detail. Finally, the relationship of EA to statistical energy analysis (SEA) is explored. The loss factors assigned to the satellite oscillators are cast in terms of modal overlap parameters. It is found necessary for the validation of SEA, in the light of EA, that these parameters exceed a certain threshold. In specific situations of interest the threshold values may exceed unity.