Abstract: Ridge of a ridge substrate integrated waveguide (RSIW) made of a linear metallic via array is equivalent to a solid metallic ridge. Based on the equivalent width analytical formulas of substrate integrated waveguide (SIW), the calculating formulas of equivalent ridge width are given in the paper. The formulas for calculating the cut-off frequency of TE_m0 modes RSIW are derived by transverse resonant method. The cut-off frequencies of TE₁₀ mode, TE₂₀ mode and TE₃₀ mode are calculated using the formulas given in this paper, respectively, and compared with the simulated results by HFSS and the calculated results given in reference. The comparison results show that the formulas given in this paper have higher precision, and are handy. The relationships of cut-off frequency versus ridge width and ridge gap are studied, and a wide ridge RSIW structure for wide bandwidth application is discussed.