Interpreting S-parameter spectra in coupled resonant systems: the role of probing configurations

The S-parameter <i>S</i>₂₁ is widely used to characterize the resonant properties of various systems. However, we demonstrate that the reliability of <i>S</i>₂₁ as a true indicator of system resonances depends heavily on the specific probing setup employed. While point-probe or weak probes preserve the integrity of the <i>S</i>₂₁ spectrum and accurately reflect system resonances, multi-point and strong probes can introduce significant discrepancies. These discrepancies can manifest as misleading features such as repulsive level anti-crossing or attractive level crossing, even in fundamentally uncoupled systems. This highlights the critical importance of selecting appropriate probing techniques to ensure a precise evaluation of system resonances.