When we were studying the vacuum switch,we found that the vacuum diode can radiate a broadband microwave.The vacuum diode is comprised of a cathode with a trigger device and planar anode,there is not a metallic bellows waveguide structure in this device,so the radiation mechanism of the vacuum diode is different from the plasma filled microwave device.It is hard to completely imitate the theory of the plasma filled microwave device.This paper analyzes the breakdown process of the vacuum diode,establishes the mathematical model of the radiating microwave from the vacuum diode.Based on the analysis of the dispersion relation in the form of a refractive index,the electromagnetic waves generated in the vacuum diode will resonate.The included angle between the direction of the electromagnetic radiation and the initial motion direction of electron beam is 45 degrees.The paper isolates the electrostatic effect from the beam-plasma interaction when the electromagnetic radiation occurs.According to above analyses,the dispersion relations of radiation are obtained by solving the wave equation.The dispersion curves are also obtained based on the theoretical dispersion relations.The theoretical dispersion curves are consistent with the actual measurement time-frequency maps of the radiation.Theoretical deduction and experiments indicate that the reason for microwave radiating from the vacuum diode can be well explained by the interaction of the electron beam and magnetized plasma. When we were studying the vacuum switch, we found that the vacuum diode can radiate a broadband microwave. The vacuum diode is comprised of a cathode with a trigger device and planar anode, there is not a metallic bellows waveguide structure in this device, so the radiation mechanism of the vacuum diode is different from the plasma filled microwave device. It is hard to completely imitate the theory of the plasma filled microwave device. This paper analyzes the breakdown process of the vacuum diode, established the mathematical model of the radiating microwave from the vacuum diode. Based on the analysis of the dispersion relation in the form of a refractive index, the electromagnetic waves generated in the vacuum diode will resonate. The included angle between the direction of the electromagnetic radiation and the initial motion direction of the electron beam is 45 degrees. The paper isolates the electrostatic effect from the beam-plasma interaction when the electromagnetic radiation occurs. Accordin g to above analyses, the dispersion relations of radiation are obtained by solving the wave equation. the dispersion curves are also obtained based on the theoretical dispersion relations.The theoretical dispersion curves are consistent with the actual measurement time-frequency maps of the radiation.Theoretical deduction and experiments indicate that the reason for microwave radiating from the vacuum diode can be well explained by the interaction of the electron beam and magnetized plasma.