The resonance properties of circular vertical-cavity surface-emitting lasers (VCSELs) are studied by using a newly developed equivalent network approach. Optical parameters, such as the stop-band or the reflectivity of periodic Bragg mirrors and the resonance wavelength, are explored for the design of these structures. To evaluate the differential quantum efficiency and the threshold current density, a transverse resonance condition of circular modal transmission-line theory is also utilized. This approach dramatically reduces the computational time as well as gives an explicit insight to explore the optical characteristics of circular VCSELs.