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We study the dispersion characteristics of a rectangular waveguide grating for microwave amplifier applications. The Floquet theorem and an appropriate standing waves expansion is employed to express the fields in the vacuum region and inside the grooves, respectively. The application of the boundary conditions leads to an infinite system of equations, which is solved numerically by truncation. The main advantage of the procedure employed is that it gives directly and with a few spatial harmonics the dispersion relation. Furthermore, an adequate procedure (simulation tool) has been introduced in order to distinguish the real roots from spurious solutions and it has been found to work effectively for all cases presented in this work. Numerical results are presented for both shallow and deep grooves and comparison with previously published works is made.