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A frequency-agile relativistic magnetron in S-band is studied in the theory and experiment. The effects of zero-order component and frequency separation are analyzed in the different resonated structures. It shows that the zero-order component is a main obstacle in the higher frequency section in contrast to the frequency separation in the lower frequency section. The experimental research is carried out to verify the theoretical results. The 500-MHz bandwidth is attained under the power of about 1 GW in the experiments of frequency-agile relativistic magnetron.