Analysis of the injection-locked magnetron with a mismatched circulator

Based on the scatter matrix of the four-port lossless mismatched circulator, the phase differential equation of the injection-locked magnetron is derived by comparing different effects of the mismatched and perfect circulator on the injection ratio. Besides, the locking range of the injection-locked magnetron with the mismatched circulator is deduced by functional operation. In addition, the phase differential equation and the locked bandwidth of the injection-locked system with a mismatched circulator are compared with those of the small injection-ratio case with a perfect circulator. The influence of the circulator reflection coefficient on the injection-locked magnetron is also analyzed by numerical calculation. Theoretical analysis shows that the decrement of the locked bandwidth is less than 1% and decrement of the stable phase difference is less than 1.2% when the reflection coefficient is less than 0.1.