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A method of quickly and accurately getting the dispersion curves for both symmetric and asymmetric modes in arbitrary slow-wave structures is investigated analytically. A universal dispersion equation is derived by utilizing the field theory and expressing the slow-wave structure's profile in a finite Fourier series. In principle, this method can be applied to arbitrary axisymmetric profiles. As examples, numerical results for three typical slow-wave structures (namely, rippled-wall, disk-loaded, and modified disk-loaded structures) are presented.