S.A. Vinokurov1, D. A. Frolov2, A. R. Safin3

1-3 National Research University "MPEI" (Moscow, Russia)

1,3 V.A. Kotelnikov Institute of Radio Engineering and Electronics of the Russian Academy of Sciences (Moscow, Russia)

1 sergey.vinokurow@yandex.ru; 2 frolovdan12@gmail.com; 3 arsafin@gmail.com

Problem statement. The ability to synchronize with other auto generators and the width of the generation line are among the important characteristics of AG. The synchronization property is important for calculating the behavior of autogenerators connected to an ensemble. There are many examples of using arrays of autogenerators in physics and microwave electronics (for example, generating Josephson junctions or torque nanogenerators), for which the synchronization property is extremely important, since individual ags have relatively low output power, and for practical use of these devices, the action of a synchronized matrix is necessary. Delayed feedback autogenerators (AG) have a number of advantages that distinguish them from similar generators with concentrated parameters: a wide range of frequency tuning, low level of phase noise, high sensitivity to external influences, etc. Despite this, they continue to be actively developed and improved.

The purpose of the work. Investigation of the effect of delay on the stationary mode of AG and on the amplitude and phase noise of AG.

Results. The delay line has an effect on the phase and frequency of the AG signal, so the delay time value has a strong effect on phase noise.  The delay does not affect the amplitude value, because of this, changing the delay time has little effect on the amplitude noise. Using the delay line, it is possible to change the phase of the AG signal, as well as the oscillation frequency.

Practical significance. The article presents studies of the effect of the delay value on amplitude and phase noise, on the stationary mode of AG, as well as the observation of the non-isochronous property. The data obtained can provide significant assistance in modeling and calculating hypertension with delayed feedback.

The work was supported by the Russian Federation state assignment at the V.A. Kotelnikov Institute of Radio Engineering and Electronics, RAS.

Vinokurov S.A., Frolov D.A., Safin A.R. The effect of the delay line on the stationary mode and the noise of the generator. Radiotekhnika. 2025. V. 89. №1. P. 99−109. DOI: https://doi.org/10.18127/j00338486-202501-09 (In Russian)

1. Chernikov A., Schmidt G. Conditions for synchronization in Josephson-junction arrays. Phys. Rev. E. 1995. V. 52. № 4. P. 3415–3419.
2. Slavin A.N., Tiberkevich V.S. Nonlinear auto-oscillator theory of microwave generation by spin-polarized current. IEEE Transaction on Magnetics. 2009. V. 45. № 4. P. 1875–1910.
3. Ruotolo A. et al. Phase-locking of magnetic vortices mediated by antivortices. Nature Nanotechnology. 2009. V. 4. P. 528–532.
4. Leeson D.B. A simple model of feedback oscillator noise spectrum. Proc. IEEE. 1966. V. 54. № 2. P. 329.
5. Razavi B. Analysis, modeling, and simulation of phase noise in monolithic voltage controlled oscillators. In Monolithic Phase-Locked Loops and Clock Recovery Circuits: Theory and Design. IEEE. 1996. P. 195-198, DOI:10.1109/CICC.1995.518195.
6. Robins W.P. Phase Noise in Signal Sources. The Institution of Engineering and Technology. 2007. P. 338.
7. Lee T.H., Hajimiri A. Oscillator phase noise: a tutorial. IEEE J. Solid-State Circuits. 2000. V. 35. № 3. P. 326–336.
8. Hajimiri A., Lee T.H. A general theory of phase noise in electrical oscillators. IEEE J. Solid-State Circuits. 1998. V. 33. № 2. P. 179.
9. Demir A., Mehrotra A., Roychowdhury J. Phase noise in oscillators: a unifying theory and numerical methods for characterization. IEEE Transactions on Circuits and Systems: Fundamental Theory and Applications. 2000. V. 47. № 5. P. 655–674.
10. Keller M.W., Pufall M.R., Rippard W.H., Silva T.J. Nonwhite frequency noise in spin torque oscillators and its effect on spectral linewidth. Phys. Rev. B 82. 2010. Р. 054416.
11. Pykovsky A., Rosenblum M., Kurths J. Synchronization: a universal concept in nonlinear science. Cambridge University Press. 2003. P. 432.
12. Kaka S. et al. Mutual phase-locking of microwave spin torque nano-oscillators. Nature. 2005. № 437. P. 389–39.
13. Hoppensteadt F.C., Izhikevich E.M. Synchronization of laser oscillators, associative memory, and optical neurocomputing. Phys. Rev. E. 2000. V. 62. № 3. P. 4010–4013.
14. Rezavi B. A study of injection locking and pulling in oscillators. IEEE J. Solid-State Circuits. 2004. № 39. P. 1415–1424.
15. Strogatz S.H. Sync: The Emerging Science of Spontaneous Order. Hyperion Press. 2003. 360 р.
16. Rubiola E. Phase Noise and Frequency Stability in Oscillators. Cambridge University Press. 2009. 228 р.
17. Schuster H.G., Wagner P. Mutual entrainment of two limit cycle oscillators with time delayed coupling. Prog. Theor. Phys. 1989. № 81. P. 939–945.
18. Yeung M.K.S., Strogatz S.H. Time delay in the Kuramoto model of coupled oscillators. Phys. Rev. Lett. 1999. № 82. P. 648–651.
19. D’Huys O., Vicente R., Erneux T., Danckaert J., Fischer I. Synchronization properties of network motifs: Influence of coupling delay and symmetry. Chaos. 2008. V. 18. Р. 037116.
20. Popovych O.V., Krachkovskyi V., Tass P.A. Phase-locking swallows in coupled oscillators with delayed feedback. Phys. Rev. E. 2010.
    № 82. Р. 046203.
21. Tiberkevich V.S., Khymyn R.S., Tang H.X., Slavin A.N. Sensitivity to external signals and synchronization properties of a non-isochronous auto-oscillator with delayed feedback. Sci. Rep. 2014. V. 4. Р. 3873. DOI: 10.1038/srep03873.