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Coherent power-combining by using several magnetrons is essential because the output power of one single magnetron cannot meet the need of large-scale industrial applications. In order to obtain phase coherence condition of the power-combining of normal magnetrons, injection-locking technology should be adopted to make sure the stability of the operating frequency and phase difference. Under impedance matching conditions, equivalent circuit of injection-locked magnetron is analyzed with the conditions of the magnetron stable frequency. The small injection-ratio and large injection-ratio situations of the injection-locked magnetrons are both derived. Furthermore, large injection-ratio situation indicates a greater frequency-locked bandwidth than small injection-ratio situation. Theoretical results are analyzed by MATLAB and injection-locked theory is verified by three-dimensional particle-in-cell simulation. The frequency-locked bandwidth and phase differential equation are given and curves of the phase difference are drawn for different initial phases. Output power and frequency of A6 magnetron are obtained by simulation under both free and injection-locked oscillation conditions. Simulation results show that magnetron can be locked and working stably in frequency-locked bandwidth predicted by both situations. Moreover, in the large injection ratio status the large injection-ratio situation is more accurate than the small injection-ratio situation.
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Keywords:
- magnetron /
- inject-locking /
- injection-ratio /
- phase-difference
[1] Adler R 1946 Proc. Ire. 34 6
[2] Slater J C 1950 Microwave Electronics (New York: Van Nostrand) pp205-210
[3] David E E 1952 Proc. Ire. 40 6
[4] David E E 1961 Crossed Field Microwave Devices (Vol. 2) (New York and London: Academic Press) P375
[5] Behzad Razavi 2004 IEEE J. Solid-State Circuits 39 9
[6] Woo W, Benford J, Fittinghoff D, Harteneck B, Price D, Smith R, Sze H 1988 J. Appl. Phys. 65 2
[7] Benford J, Sze H, Woo W, Smith R R, Harteneck B 1989 Phys. Rev. Lett. 62 8
[8] Henry S, Smith R R, Benford J N, Harteneck B D 1992 IEEE Trans. Electromagn. Compat. 34 3
[9] Treado T A, Brown P D, HansenT A, Aiguier D J 1994 IEEE Trans. Plasma Sci. 22 5
[10] Zhu X Y, Jen L, Liu Q X, Du X S 1996 Rev. Sci. Instrum. 67 5
[11] Zhang Z T 1981 Principles of Microwave Tubes (Beijing: National Defence Industry Press) p105 (in Chinese) [张兆镗 1981 微波电子管原理 (北京: 国防工业出版社) 第105页]
[12] Deng X l, Liu Y G, Li W 2010 Journal of Microwaves 26 Supplement (in Chinese) [邓小龙, 刘永贵, 李伟 2010 微波学报 26 增刊]
[13] Chen X, Esterson M, Lindsay P A 1996 SPIE 2843 47
[14] Kim J I, Won J H, Ha H J, Shon J C, Park G S 2004 IEEE Trans.Plasma Sci. 32 5
[15] Bruce G, Larry L, David S, Gary W 1995 Computer Physics Communications 87 1
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[1] Adler R 1946 Proc. Ire. 34 6
[2] Slater J C 1950 Microwave Electronics (New York: Van Nostrand) pp205-210
[3] David E E 1952 Proc. Ire. 40 6
[4] David E E 1961 Crossed Field Microwave Devices (Vol. 2) (New York and London: Academic Press) P375
[5] Behzad Razavi 2004 IEEE J. Solid-State Circuits 39 9
[6] Woo W, Benford J, Fittinghoff D, Harteneck B, Price D, Smith R, Sze H 1988 J. Appl. Phys. 65 2
[7] Benford J, Sze H, Woo W, Smith R R, Harteneck B 1989 Phys. Rev. Lett. 62 8
[8] Henry S, Smith R R, Benford J N, Harteneck B D 1992 IEEE Trans. Electromagn. Compat. 34 3
[9] Treado T A, Brown P D, HansenT A, Aiguier D J 1994 IEEE Trans. Plasma Sci. 22 5
[10] Zhu X Y, Jen L, Liu Q X, Du X S 1996 Rev. Sci. Instrum. 67 5
[11] Zhang Z T 1981 Principles of Microwave Tubes (Beijing: National Defence Industry Press) p105 (in Chinese) [张兆镗 1981 微波电子管原理 (北京: 国防工业出版社) 第105页]
[12] Deng X l, Liu Y G, Li W 2010 Journal of Microwaves 26 Supplement (in Chinese) [邓小龙, 刘永贵, 李伟 2010 微波学报 26 增刊]
[13] Chen X, Esterson M, Lindsay P A 1996 SPIE 2843 47
[14] Kim J I, Won J H, Ha H J, Shon J C, Park G S 2004 IEEE Trans.Plasma Sci. 32 5
[15] Bruce G, Larry L, David S, Gary W 1995 Computer Physics Communications 87 1
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