Figure 1

An example of the effect of perturbation on a square dual-mode planar resonator. The center frequency (f_c = f₀) before perturbation (a) is shifted up due to the 45°-cut at the corner of the resonator (b). This illustrates how the two initially-degenerate modes split into two observable separate modes (rotated by 45 degrees with respect to the original modes) that are not equally shifted around the original center frequency (f₀). The new frequencies after perturbation are f′₁ and f′₂, and the new center frequency is . The shown curves are qualitative, to indicate the characteristic behaviour under discussion. Scattering parameters (S_ij) are generally used to describe energy reflection (S₁₁, S₂₂) and transmission (S₁₂, S₂₁) between the ports.