In this paper, a new linear method for optimizing compact low noise oscillators for RF/MW applications will be presented. The first part of this paper makes an overview of Leeson's model. It is pointed out, and it is demonstrates that the phase noise is always the same inside the oscillator loop. It is presented a general phase noise optimization method for reference plane oscillators. The new method uses Transpose Return Relations (RRT ) as true loop gain functions for obtaining the optimum values of the elements of the oscillator, whatever scheme it has. With this method, oscillator topologies that have been designed and optimized using negative resistance, negative conductance or reflection coefficient methods, until now, can be studied like a loop gain method. Subsequently, the main disadvantage of Leeson's model is overcome, and now it is not only valid for loop gain methods, but it is valid for any oscillator topology. The last section of this paper lists the steps to be performed to use this method for proper phase noise optimization during the linear design process and before the final non-linear optimization. The power of the proposed RRT method is shown with its use for optimizing a common oscillator, which is later simulated using Harmonic Balance (HB) and manufactured. Then, the comparison of the linear, HB and measurements of the phase noise are compared.
2. Fernandez Garcia, M., S. Ver Hoeye, C. Vazquez Antuna, G. R. Hotopan, R. Camblor Diaz, and F. Las-Heras, "Design and analysis of a multi-carrier Tx-Rx system based on rationally synchronized oscillators for localization applications ," Progress In Electromagnetics Research, Vol. 120, 1-16, 2011, doi:10.2528/PIER11071504.
3. Shi, Z.-G., S. Qiao, K. S. Chen, W.-Z. Cui, W. Ma, T. Jiang, and L.-X. Ran, "Ambiguity functions of direct chaotic radar employing microwave chaotic Colpitts oscillator," Progress In Electromagnetics Research, Vol. 77, 1-14, 2007, doi:10.2528/PIER07072001.
4. Chen, D. and B. Sun, "Multi-wavelength fiber optical parametric oscillator based on a highly nonlinear fiber and a Sagnac loop filter," Progress In Electromagnetics Research, Vol. 106, 163-176, 2010, doi:10.2528/PIER10061506.
5. Robins, W. P., Phase Noise in Signal Sources (Theory and Applications), IEE Telecommunications Series 9, Peter Peregrinus Ltd., London, UK, 1982, ISBN-13: 978-086341026 .
6. Richardson, A., WCDMA Design Handbook, Cambridge University Press, 2005, ISBN-13: 978-0521187824.
7. Barton, D. K., Radar System Analysis and Modeling, Artech House, Boston, 2005, ISBN-13: 978-1580536813.
8. Kurokawa, K. K., "Some basic characteristics of broadband negative resistance oscillator circuits," Bell Systm. Tech. J., Vol. 48, No. 6, 1937-1955, 1969.
9. Rhea, R. W., Discrete Oscillator Design: Linear, Nonlinear, Transient, and Noise Domains, Artech House Publishers, New York, 2010, ISBN-13: 978-1608070473.
10. Fernandez Garcia, M., S. Ver Hoeye, C. Vazquez Antuna, G. R. Hotopan, R. Camblor Diaz, and F. Las-Heras, "Optimization of the synchronization bandwidth of ratio-nally synchronized oscillators based on bifurcation control," Progress In Electromagnetics Research, Vol. 119, 299-313, 2011, doi:10.2528/PIER11062007.
11. Randall, M. and M. J. Hock, "General oscillator characterization using linear open-loop S-parameters," IEEE Transactions on Microwave Theory and Techniques, Vol. 49, No. 6, 1094-1100, 2001, doi:10.1109/22.925496.
12. Jackson, R. W., "Criteria for the onset of oscillation in microwave circuits," IEEE Transactions on Microwave Theory and Techniques, Vol. 40, No. 3, 566-569, 1992, doi:10.1109/22.121734.
13. Gonzalez-Posadas, V., J. L. Jimenez-Martin, A. Parra-Cerrada, D. Segovia-Vargas, and L. E. Garcia-Munoz, "Oscillator accurate linear analysis and design. Classic linear methods review and comments," Progress In Electromagnetics Research, Vol. 118, 89-116, 2011, doi:10.2528/PIER11041403.
14. Jimenez-Martin, J. L., V. Gonzalez-Posadas, A. Parra-Cerrada, D. Segovia-Vargas, and L. E. Garcia-Munoz, "Provisos for classic linear oscillator design methods. New linear oscillator design based on the NDF/RRT," Progress In Electromagnetics Research, Vol. 1236, 17-48, 2012, jpier:vol126/02.11112308.
15. Bode, H. W., Network Analysis and Feedback Amplifier Design , ASIN: B003UT90Z4, Van Nostrand Co. Inc., New York, 1945.
16. Platzker, A. and W. Struble, "Rigorous determination of the stability of linear N-node circuits from network determinants and the appropriate role of the stability factor K of their reduced two-ports," Int. Integr. Nonlinear Microw. Millimeter wave Circuits Workshop, 93-107, 1994, doi:10.1109/INMMC.1994.512515.
17. Leeson, D. B., "A simple model of feedback oscillator noise spectrum," Proceeding of the IEEE, 329-330, 1966, doi:10.1109/PROC.1966.4682.
18. Hajimiri, A. and T. Lee, "A general theory of phase noise in electrical oscillators," IEEE J. Solid-State Circuits, Vol. 33, No. 2, 179-194, Feb. 1998, doi:10.1109/4.658619.
19. Demir, A., A. Mehrotra, and J. Roychowdhury, "Phase noise in oscillators: A unifying theory and numerical methods for characterization," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., Vol. 47, No. 5, 655-674, May 2000, doi:10.1109/81.847872.
20. Everard, J. K. A. and J. Bitterling, "Low phase noise highly power efficient oscillators," IEEE International Frequency Control Symposium, USA, May 27-30, 1997, doi:10.1109/FREQ.1997.639209.
21. Everard, J., Fundamentals of RF Circuit Design with Low Noise Oscillators, Wiley, Dec. 2000, reprinted Oct. 2002, ISBN-13: 978-0471497936.
22. Everard, J. K. A., "A review of low noise oscillator. Theory and design," Proceedings of the 1997 IEEE International on Frequency Control Symposium, 909-918, 1997, doi:10.1109/FREQ.1997.639208.
23. Asadi, S. and M. C. E. Yagoub, "Efficient time-domain noise modeling approach for millimeter-wave fets," Progress In Electromagnetics Research, Vol. 107, 129-146, 2010, doi:10.2528/PIER10042012.
24. Guo, B. and G. Wen, "Periodic time-varying noise in current-commutating cmos mixers," Progress In Electromagnetics Research, Vol. 117, 283-298, 2011, doi:10.2528/PIER11040706.
25. Wang, R., J. Xu, C. L. Wei, M.-Y. Wang, and X.-C. Zhang, "Improved extraction of coupling matrix and unloaded Q from S-parameters of lossy resonator filters," Progress In Electromagnetics Research, Vol. 120, 67-81, 2011, doi:10.2528/PIER11072804.
26. Rohde, U. L., C. R. Chang, and J. W. Gerber, "Design and optimization of low-noise oscillators using nonlinear CAD tools," IEEE Frequency Control Symp. Proc., 548554, 1994, doi:10.1109/FREQ.1994.398283.
27. Esdale, D. J. and M. J. Howes, "A reflection coefficient approach to the design of one port negative impedance oscillators," IEEE Transactions on Microwave Theory and Techniques, Vol. 29, No. 8, 770-776, 1981, doi:10.1109/TMTT.1981.1130445.