In this paper, a class of triple-band bandpass filters with two transmission poles in each passband is proposed using three pairs of degenerate modes in a ring resonator. In order to provide a physical insight into the resonance movements, the equivalent lumped circuits are firstly developed, where two transmission poles in the first and third passbands can be distinctly tracked as a function of port separation angle. Under the choice of 135 and 45 port separations along a ring, four open-circuited stubs are attached symmetrically along the ring and they are treated as perturbation elements to split the two second-order degenerate modes, resulting in a two-pole second passband. To verify the proposed design concept, two filter prototypes on a single microstrip ring resonator are finally designed, fabricated, and measured. The three pairs of transmission poles are achieved in all three passbands, as demonstrated and verified in simulated and measured results.