A large-diameter coaxial relativistic backward-wave oscillator is presented. The linearized Lorentz force equation, continuity equation, and Maxwell equations are used to calculate the system dispersion relations for a backward-wave oscillator with a dual-plate rippled-wall waveguide. The system also includes an infinitely thin relativistic electron beam propagating between the opposing plates. Using this theory, the influences of various system parameters on the beam-wave interaction, especially on the exponential growth rate of the wave, are discussed in detail. This theory is also used to design a large-diameter coaxial relativistic backward-wave oscillator in 3cm waveband.