“…However, they have disadvantages in the resonator size. For example, S patch ≈ (λ g /2) 2 , S disk ≈ (1.84λ g /π) 2 , S ring ≈ (λ g /π) 2 , where λ g is the guided wavelength of central frequency [4]. A lot of structures have been investigated to reduce the size of the dual-mode resonators, such as cross-slotted patch [5], square ring [4], meandering ring [6], multiarc ring [7], capacitive loaded ring [8,9] and stub-loaded ring [10].…”