Resonance frequencies and Q-factors of multi-resonance complex electromagnetic systems

We present the calculation results for a lossless TTF cavity-coupler unit, for combination cavity-coupler units and for an 8-cavity accelerating module, at the frequency band corresponding to third dipole band of the 9-cell TTF cavity. Experimental investigations of the copper TESLA Test Facility cavity, equipped with two higher order mode couplers, are also presented, for the original and the modified (“mirrored”) downstream higher order mode couplers.Here we developed the procedure for the determination of resonant frequencies and Q-factors using the dependence of the complex transmission coefficient S$_{m,n}$(f) or the complex reflection coefficient S$_{m,m}$(f) on frequency in the frequency band under investigation. These dependencies were obtained from the numerical calculation of S- parameters of lossless TESLA Test Facility (TTF) modules in the third dipole mode frequency band and from the experimental investigation of the copper TESLA Test Facility cavity equipped with two higher order mode couplers in the first, second and third dipole mode frequency bands, second quadrupole and second monopole mode frequency band. The procedure permits us to determine resonant frequencies and Q- factors (Q$_o$, Q$_{Load}$ and Q$_{ext}$) using a large enough frequency step (∆f) with only few frequency points located on the resonance curve corresponding to the high Q-factor resonance