پیوندهای مفید
آمار
| تعداد نشریات | 8 |
| تعداد شمارهها | 440 |
| تعداد مقالات | 5,679 |
| تعداد مشاهده مقاله | 7,814,296 |
| تعداد دریافت فایل اصل مقاله | 6,388,485 |
The Transient Behavior of LC and Ring Oscillators under External Frequency Injection | ||
| AUT Journal of Electrical Engineering | ||
| مقاله 5، دوره 46، شماره 2، بهمن 2014، صفحه 35-45 اصل مقاله (807.98 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22060/eej.2015.512 | ||
| نویسندگان | ||
| A. Tofangdarzade* 1؛ A. Jalali2 | ||
| 1PhD Student, Electrical Department of Shahid Beheshti University, Tehran, Iran | ||
| 2Assistant professor, Electrical Department of Shahid Beheshti University, Tehran, Iran | ||
| چکیده | ||
| In this work, time domain analysis is used to solve Adler’s equation in order to obtain the required time, for an oscillator under external injection, reaching the steady-state condition. Mathematical approach has been applied to fully describe the transient of frequency acquisition in injection-locked LC and Ring oscillators considering their time-varying nature. Then, the analysis is verified by simulations of a ring as well as a typical RF-LC oscillator. Likewise, the effect of initial phase difference of injection signal on locking time and phase noise is theoretically studied. For Ring oscillators, a delay-based time–domain and perturbation analysis are used to reveal the dependency of circuit parameters to the locking time. Finally, the design insights are deduced which enable the designers to evaluate and minimize the timing budget required to achieve injection locking in designing a fast locking oscillator. The mathematical consequences in this work explain why there is no transient behavior while ring oscillator signal propagates from a stage to another, or why the initial phase shift of injection signal has no effect on the phase noise of oscillator. | ||
| کلیدواژهها | ||
| Adler’s equation؛ Time-domain analysis؛ Injection locking؛ Oscillator | ||
| عنوان مقاله [English] | ||
| The Transient Behavior of LC and Ring Oscillators under External Frequency Injection | ||
| نویسندگان [English] | ||
| A. Tofangdarzade1؛ A. Jalali2 | ||
| 1PhD Student, Electrical Department of Shahid Beheshti University, Tehran, Iran | ||
| 2Assistant professor, Electrical Department of Shahid Beheshti University, Tehran, Iran | ||
| چکیده [English] | ||
| In this work, time domain analysis is used to solve Adler’s equation in order to obtain the required time, for an oscillator under external injection, reaching the steady-state condition. Mathematical approach has been applied to fully describe the transient of frequency acquisition in injection-locked LC and Ring oscillators considering their time-varying nature. Then, the analysis is verified by simulations of a ring as well as a typical RF-LC oscillator. Likewise, the effect of initial phase difference of injection signal on locking time and phase noise is theoretically studied. For Ring oscillators, a delay-based time–domain and perturbation analysis are used to reveal the dependency of circuit parameters to the locking time. Finally, the design insights are deduced which enable the designers to evaluate and minimize the timing budget required to achieve injection locking in designing a fast locking oscillator. The mathematical consequences in this work explain why there is no transient behavior while ring oscillator signal propagates from a stage to another, or why the initial phase shift of injection signal has no effect on the phase noise of oscillator. | ||
| کلیدواژهها [English] | ||
| Adler’s equation, Time-domain analysis, Injection locking, Oscillator | ||
| مراجع | ||
|
[1] Adler, R., “A study of locking phenomena in oscillators”, Proc. IEEE, 61, 1380–1385, 1973. [2] Kurokawa, K., “Injection locking of microwave solid-state oscillators”, Proc. IEEE, 61, 1336-1410, 1973. [3] Paciorek, L. j., “Injection locking of oscillators”, Proc. IEEE, 53, 1723-1727, 1965. [4] Razavi, B., “A study of injection locking and pulling in oscillators”, IEEE J. Solid-state circuits, 39, 1415-1424, 2004. [5] Maffezzoni, P., “Analysis of Oscillator Injection Locking Through Phase-Domain Impulse-Response”, IEEE Trans. Circuits Syst. I, Reg. Papers, 55, 1297-1305, 2008. [6] Tong, H., Cheng, S., Karsilayn, A. I., and Martinez, J. S., “An injection-Locked Frequency Divider With Multiple Highly Nonlinear Injection Stages and Large Division Ratios”, IEEE Trans. Circuits Syst. II, Exp. Briefs, 54, 313-317, 2007 [7] Rategh, H. R., and Lee, T. H., “Super Harmonic Injection-Locked Frequency Dividers”, IEEE J. Solid-state circuits. 34, 813-821, 1999. 51, 1989-1993, 2003. [8] Verma, S., Rategh, H. R., and Lee, T. H., “ A unified model for injection-locked frequency dividers”, IEEE J. Solid-state circuits, 38, 1015-1027, 2003. [9] Kamogawa, K., Tokumitsu, T., and Aikawa, A., “Injection-locked oscillator chain: A possible solution to millimeter-wave MMIC synthesizers”, IEEE Trans. Microwave Theory Tech., 45, 1578-1584, 1997. [10] Lyles, U., Copani, T., Bakkaloglu, B., and Kiaei, S., “An Injection- Locked Frequency-Tracking ΣΔ Direct Digital Frequency Synthesizer”, IEEE Trans. Circuits Syst. II, Exp. Briefs, 54, 402-406, 2007. [11] Chang, H., “Stability Analysis of Self-Injection-Locked oscillators”, IEEE Trans. Microwave Theory Tech., [12] Chang, H., “Phase Noise in Self-Injection-Locked Oscillators, Theory and Experiment”, IEEE Trans. Microwave Theory Tech., 51, 1994-1999, 2003. [13] Chang, H., Cao, X., Mishra, U., and York, R., “Phase noise in coupled oscillators: Theory and experiment”, IEEE Trans. Microwave Theory Tech., vol. 45, pp.604 -615, 1997. [14] Chang, H., Cao, X., Vaughan, M., Mishra, U., and York, R., “Phase noise in externally injection-locked oscillator arrays”, IEEE Trans. Microwave Theory Tech., vol. 45, pp.2035 -2042, 1997. [15] Maffezzoni, P., D'Amore, D., “Phase-Noise Reduction in Oscillators via Small-Signal Injection”, IEEE Transactions on Circuits and Systems I: Regular Papers, Volume: 58, Issue: 10, 2498 - 2507, Oct. 2011. [16] Harjani, R., Lanka, N., and Patnaik, S., “Fast hopping injection locked frequency generation for UWB”, Proc. IEEE Int. Conf. Ultra-WideBand, pp.502 -507, 2007. [17] Lanka, N., Patnaik, S., and Harjani, R., “Sub-10 ns frequency hopping synthesizer based on injection-locking”, Proc. 38th European Microwave Conf., pp.1581 -1584, 2008. [18] Lanka, N., Patnaik, S., and Harjani, R., “Frequency-hopped quadrature frequency synthesizer in 0.13 μm technology”, IEEE J. Solid-State Circuits, vol. 46, no. 5, pp.2021 -2032, 2011. [19] Lanka, N., Patnaik, S., and Harjani, R., “Understanding the transient behavior of injection locked LC oscillators”, Proc. IEEE 2007 Custom Integrated Circuits Conf. (CICC), pp.TP-291 -TP-294, 2007. [20] Mirzaei, A., Heidari, M., and Abidi, A., “Analysis of oscillators locked by large injection signals: Generalized Adler's equation and geometrical interpretation”, Proc. IEEE Custom Integrated Circuits Conf. (CICC), pp.737 -740, 2006. [21] Mirzaei, A., Heidari, M., Bagheri, R., Chehrazi, S., and Abidi, A., “The quadrature LC oscillator: A complete portrait based on injection locking”, IEEE Journal of Solid-State Circuits, vol. 42, pp. 1916-1932, 2007. [22] Mirzaei, A., Heidari, M., Bagheri, R., Chehrazi, S., and Abidi, A., “Multi-phase injection widens lock range of ring-oscillator-based frequency dividers”, IEEE J. Solid-State Circuits, vol. 43, no. 3, pp.656 -671, 2008. [23] Saniei, N., Tofangdarzade, A., and Ng, W. T., “Locking Time of Oscillators under External Frequency Injection”, in Proc. IEEE ICEE, 18th Irainian Conference on Electrical Engineering, pp. 391-396, 2010. [24] Gangasani, G., and Kinget, P., “A time-domain model for predicting the injection locking bandwidth of non-harmonic oscillators”, IEEE Trans. Circuits Syst. II, Exp. Briefs, 53, 1035-1038, 2006. [25] Leeson, D., “A simple model of feedback oscillator noise spectrum”, Proc. IEEE, vol. 54, no. 2, pp.329 -330, 1966. [26] Razavi, B., “A study of phase noise in CMOS oscillators”, IEEE J. Solid-State Circuits, vol. 31, no. 3, pp.331-343,1996. [27] Everard, J., Xu, M., Bale, S., “A Simplified phase noise model for negative-resistance oscillators and a comparison with feedback oscillator models”, IEEE Trans. On Ultrusonics, Ferroelectrics and frequency control. Vo. 59, No. 3, pp. 382-390, 2012. [28] Hajimiri, A., and Lee, T., “A general theory of phase noise in electrical oscillators”, IEEE J. Solid-State Circuits, vol. 33, no. 2, pp.179 -194, 1998. [29] Samori, C., Lacaita, A., Villa, F., and Zappa, F., “Spectrum folding and phase noise in LC tuned oscillators”, IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 45, no. 7, pp.781 -790, 1998. [30] Rael, J. and Abidi, A., “Physical processes of phase noise in differential LC oscillators”, Proc. IEEE Custom Integr. Circuits Conf., pp.569 -572, 2000. [31] Murphy, D., Rael, J., Abidi, A., “Phase noise in LC oscillators: A phasor based analysis of a general result and of loaded Q”, IEEE Transactions on Circuits and Systems I Regular Papers, Volume.57, No. 6, pp. 1187-1203, 2012. [32] Lee, T., and Hajimiri, A., “Oscillator phase noise: A tutorial”, IEEE J. Solid-State Circuits, vol. 35, no. 3, pp.326 -336, 2000. [33] Demir, A., Mehrotra, A., Roychowdhury, J., “Phase Noise in oscillators: A unifying theory and numerical methods for characterization”, IEEE Transactions on Circuits and Systems I Fundam. Theory Appl., Volume.47, No. 5, pp. 655-647, 2000 [34] Kalia, S., Elbadry, M., Sadhu, B., Patnaik, S., Qiu, J., Harjani, R., “A simple, unified phase noise model for injection-locked oscillators”, Radio Frequency Integrated Circuits Symposium (RFIC), IEEE, 1 – 4, 2011. [35] Buonomo, A., Lo Schiavo, A., “Analytical Approach to the Study of Injection-Locked Frequency Dividers”, IEEE Transactions on Circuits and Systems I: Regular Papers, Volume: 60, Issue: 1, 51 – 62, 2013. | ||
|
آمار تعداد مشاهده مقاله: 2,117 تعداد دریافت فایل اصل مقاله: 2,415 |
||