Field-matching technique was used to analyse a disc-loaded-coaxial waveguide in the azimuthally symmetric TE modes for its dispersion relation that includes space-harmonics in the disc-free region as well as modal-harmonics in the disc-occupied region of the structure. The phase propagation constant, obtainable from the dispersion relation, was fed back in the small-signal gain-equation of the gyro-TWT and the gain-frequency response of a disc-loaded-coaxial gyro-TWT was plotted. Further, the effect of the radius of coaxial rod insert on gain-frequency response has been studied, and the parameter has been optimised for high gain and wideband of the device.