Progress In Electromagnetics Research B
ISSN: 1937-6472
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 59 > pp. 71-87


By Y.-T. Lo and J.-F. Kiang

Full Article PDF (1,286 KB)

A modified Y-parameters approach is proposed to model the behavior of coupled oscillator arrays (COA's). A coupling network with tunable coupling strength is proposed, which has a near-constant input conductance, to ensure the oscillation condition under different attenuation levels. The parameters of oscillators and the coupling network are derived on the TSMC 0.18 μm technology, and their Y parameters are extracted around 10 GHz for illustration. After being verified with full-circuit simulations and other behavior models, including the Adler's equation and the conventional Y-parameters approach, this method is applied to estimate the maximum allowable number of oscillators that can be coupled together. The inter-element phase shift of a COA is controlled by tuning the free-running frequencies of oscillators at both ends. Injection signals with proper phases are proposed to synchronize multiple COA's into a bigger COA.

Y.-T. Lo and J.-F. Kiang, "Analysis on Strongly Coupled Oscillator Arrays Using Modified Y-Parameters Approach," Progress In Electromagnetics Research B, Vol. 59, 71-87, 2014.

1. York, R. A., "Nonlinear analysis of phase relationships in quasi-optical oscillator arrays," IEEE Trans. Microwave Theory Tech., Vol. 41, No. 10, 1799-1809, Oct. 1993.

2. Neff, J. D., B. K. Meadows, E. A. Brown, S. P. DeWeerth, and P. Hasler, "A CMOS coupled nonlinear oscillator array," IEEE Int. Symp. Circ. Syst., Vol. 4, IV-301-IV-304, 2002.

3. Tousi, Y. M., O. Momeni, and E. Afshari, "A novel CMOS high-power terahertz VCO based on coupled oscillators: Theory and implementation," IEEE J. Solid-State Circuits, Vol. 47, No. 12, 3032-3042, Dec. 2012.

4. Stephan, K. D. and W. A. Morgan, "Analysis of inter-injection-locked oscillators for integrated phased arrays," IEEE Trans. Antennas Propagat., Vol. 35, No. 7, 771-781, Jul. 1987.

5. Lynch, J. J. and R. A. York, "Stability of mode locked states of coupled oscillator arrays," IEEE Trans. Circuits Syst. I, Vol. 42, No. 8, 413-418, Aug. 1995.

6. Nogi, S., J. Lin, and T. Itoh, "Mode analysis and stabilization of a spatial power combining array with strongly coupled oscillators," IEEE Trans. Microwave Theory Tech., Vol. 41, No. 10, 1827-1837, Oct. 1993.

7. Georgiadis, A., A. Collado, and A. Suarez, "New techniques for the analysis and design of coupled-oscillator systems," IEEE Trans. Microwave Theory Tech., Vol. 54, No. 11, 3864-3877, Nov. 2006.

9. York, , R. A., P. Liao, and J. J. Lynch, "Oscillator array dynamics with broadband N-port coupling networks," IEEE Trans. Microwave Theory Tech., Vol. 42, No. 11, 2040-2045, Nov. 1994.

9. Pogorzelski, R. J., "On the design of coupling networks for coupled oscillator arrays," IEEE Trans. Antennas Propagat., Vol. 51, No. 4, 794-801, Apr. 2003.

10. Martinez-Lopez, J. I., R. Moussounda, and R. G. Rojas, "Non-reciprocal coupling network for beam-steering coupled oscillator arrays," IET Microwave Antennas Propagat., Vol. 5, No. 8, 940-947, 2011.

11. Lynch, J. J. and R. A. York, "Synchronization of oscillators coupled through narrow-band networks," IEEE Trans. Microwave Theory Tech., Vol. 49, No. 2, 237-249, Feb. 2001.

12. Kurokawa, R., "Injection locking of microwave solid-state oscillators," Proc. IEEE, Vol. 61, No. 10, 1386-1410, Oct. 1973.

13. Seetharam, V. and L. W. Pearson, "Analysis of strong coupling in coupled oscillator arrays," IEEE Trans. Antennas Propagat., Vol. 58, No. 4, 1067-1075, Apr. 2010.

14. Jiang, H. and R. Penno, "Effects of amplitude dynamics on beam steering and shaping in coupled oscillator array," IEEE Antennas Wireless Propagat. Lett., Vol. 9, 474-477, 2010.

15. Herran, L. F., S. V. Hoeye, M. Fernandez, C. Vazquez, and F. L. Heras, "Analysis of phase distribution errors in mutually coupled harmonic self-oscillating mixers," IEEE Trans. Microwave Theory Tech., Vol. 57, No. 12, 2853-2861, Dec. 2009.

16. Pogorzelski, R. J., "Generalization of the linearized discrete model of coupled oscillator arrays to account for coupling delay," Radio Sci., Vol. 43, RS4070, 2008.

17. Maffezzoni, P., "Synchronization analysis of two weakly coupled oscillators through a PPV macromodel," IEEE Trans. Circuits Syst. I, Vol. 57, No. 3, 654-663, Mar. 2010.

18. Ionita, M., D. Cordeau, J. M. Paillot, S. Bachir, and M. Iordache, "A CAD tool for an array of differential oscillators coupled through a broadband network," Int. J. RF Microwave Computer-Aided Eng., Vol. 23, No. 2, 178-187, 2013.

19. Strogatz, S. H. and R. E. Mirollo, "Phase-locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies," Physiza D, Vol. 33, 143-168, 1988.

20. Shen, J. and L. W. Pearson, "The phase error and beam-pointing error in coupled oscillator beam-steering arrays," IEEE Trans. Antennas Propagat., Vol. 53, No. 1, 386-393, Jan. 2005.

21. Vendelin, G. D., A. M. Pavio, and U. L. Rohde, "Microwave Circuit Design Using Linear and Nonlinear Techniques,", 384-391, Wiley-Interscience, 1990.

22. Adler, R., "A study of locking phenomena in oscillators," Proc. IRE, Waves Electrons, Vol. 34, 351-357, Jun. 1946.

23. Ellinger, F., Radio Frequency Integrated Circuits and Technologies, 385-387, Springer, 2007.

24. Martineau, B., O. Richard, N. Rolland, A. Cathelin, and A. Kaiser, "A 20-23 GHz coupled oscillators array in 65nm CMOS for HDR 60 GHz beamforming applications," Euro. Solid State Circuit Conf., 463-466, Helsinki, Finland, Sep. 2011.

25. Lopez, J., D. Y. C. Lie, B. K. Meadow, and J. Cothern, "Fully-integrated 1-dimensional RF coupled-oscillator network for phase-shifterless phased array systems," IEEE Bipolar/BiCMOS Circuit Tech. Meeting, 17-20, Portland, Oregon, USA, Oct. 2010.

26. Van der Pol, B., "The nonlinear theory of electric oscillation," Proc. IRE, Vol. 22, 1051-1085, Sep. 1934.

27. Humphrey, D. E. J., V. F. Fusco, and S. Drew, "Active antenna array behavior," IEEE Trans. Microwave Theory Tech., Vol. 43, No. 8, 1819-1825, Aug. 1995.

28. Cordeau, D., M. Ionita, J. M. Paillot, and M. Iordache, "New formulation of the equations describing the locked states of two Van der Pol oscillators coupled through a broadband network --- Application to the design of two di®erential coupled VCOs," Freq. J. RF --- Eng. Telecommun., Vol. 67, No. 7-8, 237-247, 2013.

29. Jordan, D. W. and P. Smith, Nonlinear Ordinary Differential Equations, 4th Ed., Chapter 8, Oxford University Press, 2007.

30. Pogorzelski, R. J. and A. Georgiadis, Coupled-oscillator Based Active-array Antennas, Chapter 8, John Wiley, 2012.

31. Collado, A. and A. Georgiadis, "Performance of coupled-oscillator arrays with angle-modulated injection signals," IEEE Trans. Circuits Syst. I, Vol. 7, No. 9, 2343-2352, Sep. 2010.

32. Yan, S. H. and T. H. Chu, "A beam-steering antenna array using injection locked coupled oscillators with self-tuning of oscillator free-running frequencies," IEEE Trans. Antennas Propagat., Vol. 56, No. 9, 2920-2928, Sep. 2008.

33. Suarez, A., F. Ramirez, and S. Sancho, "Stability and noise analysis of coupled-oscillator systems," IEEE Trans. Microwave Theory Tech., Vol. 59, No. 4, 1032-1046, Apr. 2011.

34. Zhang, X., I. Mukhopadhyay, R. Dokania, and A. B. Apsel, "A 46-μW self-calibrated gigahertz VCO for low-power radios," IEEE Trans. Circuit Syst. II, Vol. 58, No. 12, 847-851, Dec. 2011.

35., "Boosting PLL design e±ciency, from free-running VCO characterizations to closed-loop PLL evaluations,", Appl. Note, http://cp.literature.agilent.com/litweb/pdf/5989-9848EN.pdf.

36. York, R. A. and T. Itoh, "Injection and phase-locking techniques for beam control," IEEE Trans. Microwave Theory Tech., Vol. 46, No. 11, 1920-1929, Nov. 1998.

37. Collin, R. E., Foundations for Microwave Engineering, 2nd Ed., 327, McGraw-Hill, Inc., 1992.

© Copyright 2010 EMW Publishing. All Rights Reserved