Analysis of Injection-Lock in Oscillators versus Phase Variation of Injected Signal

In this paper, behavior of an oscillator under injection of another signal has been investigated. Also, variation of output signal amplitude versus injected signal phase variation, the effect of varying the amplitude of injected signal and quality factor of the oscillator has been investigated. The results show that the locking time depends on phase and the best locking time happens at 180-degrees phase. Also, the effect of injected lock has been discussed. Simulations show that the locking time decreases with signal injection to bulk. Locking time has been investigated versus various phase differences. The effect of phase and amplitude changes on locking time of a typical LC oscillator in 180 nm technology has been investigated.

Authors:

• M. Yousefi
• N. Nasirzadeh

Keywords:

• Injection-lock oscillator
• oscillator
• analysis
• phase modulation.

References:

[1] R. Adler, “A study of locking phenomena in oscillators,” Proc. IRE,vol. 34, no. 6, 1946, pp. 351–357.
[2] A. Hajimiri and T. Lee, “A general theory of phase noise in electrical oscillators,” IEEE J. Solid-State Circuits, vol. 33, no. 2, 1998, pp. 179–194,Feb.
[3] L. Paciorek, “Injection locking of oscillators,” Proc. IEEE, vol. 53, no.11, pp. 1723–1727, Nov. 1965.
[4] F. Ramírez, E. d. Cos, and A. Suárez, “Nonlinear analysis tools for the optimized design of harmonic-injection frequency dividers,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 6, 2003, pp. 1752–1762.
[5] B. Razavi, “A study of injection locking and pulling in oscillators,” IEEE J. Solid-State Circuits, vol. 39, no. 9, pp. 1415–1424, Sep. 2004.
[6] J. Bae, L. Yan, H-J. Yoo, “A low energy injection-locked FSK transceiver with frequency-to-amplitude conversion for body sensor applications,” Solid-State Circuits, IEEE Journal of, 2011, vol. 46, no 4, p. 928-937.
[7] S. Verma, H. R. Rategh, and T. H. Lee, “A unified model for injection locked frequency dividers,” IEEE J. Solid-State Circuits, vol. 38, no.6, 2003, pp. 1015–1027.
[8] M. Tiebout, “A CMOS direct injection-locked oscillator topology as high-frequency low power frequency divider,” IEEE J. Solid-State Circuits, vol. 39, no. 7, 2004, pp. 1170–1174.
[9] S. D. Toso, A. Bevilacqua, M. Tiebout, N. Da Dalt, A. Gerosa, and A. Neviani, “An integrated divide-by-two direct injection-locking frequency divider for bands s through Ku,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 7, 2010, pp. 1686–1695.
[10] K. Yamamoto and M. Fujishima, “A 44- W 4.3-GHz injection-locked frequency divider with 2.3-GHz locking range,” IEEE J. Solid-State Circuits, vol. 40, no. 3, 2005, pp. 671–677.
[11] J.-C. Chien and L.-H. Lu, “Analysis and design of wideband injection locked ring oscillators with multiple-input injection,” IEEE J. Solid-State Circuits, vol. 42, no. 9, 2007, pp. 1906–1915,.