Theoretical investigation of frequency characteristics of free oscillation and injection-locked magnetrons

The frequency characteristics of free oscillation magnetron（FOM） and injection-locked magnetron（ILM） are theoretically investigated.By using the equal power voltage obtained from the experiment data,expressions of the frequency and radio frequency（RF） voltage of FOM and ILM,as well as the locking bandwidth,on the anode voltage and magnetic field are derived.With the increase of the anode voltage and the decrease of the magnetic field,the power and its growth rate increase,while the frequency increases and its growth rate decreases.The theoretical frequency and power of FOM agree with the particle-in-cell（PIC） simulation results.Besides,the theoretical trends of the power and frequency with the anode voltage and magnetic field are consistent with the experimental results,which verifies the accuracy of the theory.The theory provides a novel calculation method of frequency characteristics.It can approximately analyze the power and frequency of both FOM and ILM,which promotes the industrial applications of magnetron and microwave energy.