radioelectronicsИзвестия высших учебных заведений России. РадиоэлектроникаJournal of the Russian Universities. Radioelectronics1993-89852658-4794Saint Petersburg Electrotechnical University10.32603/1993-8985-2020-23-2-19-25radioelectronics-414Research ArticleРАДИОТЕХНИЧЕСКИЕ СРЕДСТВА ПЕРЕДАЧИ, ПРИЕМА И ОБРАБОТКИ СИГНАЛОВRADIO ELECTRONIC FACILITIES FOR SIGNAL TRANSMISSION, RECEPTION AND PROCESSINGNoise Properties of Two Mutually Coupled Spin-Transfer Nanooscillators in the Phase Locking RegimeNoise Properties of Two Mutually Coupled Spin-Transfer Nanooscillators in the Phase Locking Regimehttps://orcid.org/0000-0001-7447-9841MitrofanovA. A.MitrofanovA. A.

Alexander A. Mitrofanov, PhD in Technical Sciences in the specialty of "Radioengineering Including Systems and Television Devices" (2018), Researcher (PostDoc) 

The author of more than 10 scientific publications. Area expertise: radiophysics; the theory of oscillations and waves; spintronics; physics of magnetic phenomena. 

Alexander A. Mitrofanov, PhD in Technical Sciences in the specialty of "Radioengineering Including Systems and Television Devices" (2018), Researcher (PostDoc)

The author of more than 10 scientific publications. Area expertise: radiophysics; the theory of oscillations and waves; spintronics; physics of magnetic phenomena.

mitrofanov_alexander@mail.ruhttps://orcid.org/0000-0001-6507-6573SafinA. R.SafinA. R.

Ansar R. Safin, Cand. Sci. (Eng.) in "Radio Engineering Including Television Systems and Devices" (2014), Head of the Department of Radio Signal Generation and Processing

Senior Researcher at the Institute of Radio Technologies and Electronics

The author of more than 50 scientific publications. Area of expertise: radiophysics and electronics; physics of magnetic phenomena; spintronics. 

Ansar R. Safin, Cand. Sci. (Eng.) in "Radio Engineering Including Television Systems and Devices" (2014), Head of the Department of Radio Signal Generation and Processing 

Senior Researcher at the Institute of Radio Technologies and Electronics

The author of more than 50 scientific publications. Area of expertise: radiophysics and electronics; physics of magnetic phenomena; spintronics.

arsafin@gmail.comTorinaE. M.TorinaE. M.

Elena M. Torina, Cand. Sci. (Eng.) in "Radio Engineering Including Television Systems and Devices" (2017), Senior Lecturer of the Department of Radio Signal Generation and Processing

The author of more than 20 scientific publications. Area of expertise: design and study of nonlinear radio engineering devices for generating radio signals.

Elena M. Torina, Cand. Sci. (Eng.) in "Radio Engineering Including Television Systems and Devices" (2017), Senior Lecturer of the Department of Radio Signal Generation and Processing

The author of more than 20 scientific publications. Area of expertise: design and study of nonlinear radio engineering devices for generating radio signals.

dro.em@yandex.ruUdalovN. N.UdalovN. N.

Nikolai N. Udalov, Dr. Sci. (Eng.) in "Theoretical Foundations of Radio Engineering" (1995), Professor of the Department of Radio Signal Generation and Processing

The author of more than 100 scientific publications. Area of expertise: statistical radio engineering; phase synchronization systems and frequency synthesis; theoretical radio engineering. 

Nikolai N. Udalov, Dr. Sci. (Eng.) in "Theoretical Foundations of Radio Engineering" (1995), Professor of the Department of Radio Signal Generation and Processing 

The author of more than 100 scientific publications. Area of expertise: statistical radio engineering; phase synchronization systems and frequency synthesis; theoretical radio engineering.

arnellemorte@gmail.comEmory UniversityСоединённые Штаты АмерикиEmory UniversityUnited StatesNational Research University "MPEI", Kotel’nikov Institute of Radioengineering and Electronics of Russian Academy of SciencesРоссияNational Research University "MPEI"; Kotel’nikov Institute of Radioengineering and Electronics of Russian Academy of SciencesRussian FederationNational Research University "MPEI"РоссияNational Research University "MPEI"Russian Federation2020280420202321925Copyright © Mitrofanov A.A., Safin A.R., Torina E.M., Udalov N.N., 20202020Mitrofanov A.A., Safin A.R., Torina E.M., Udalov N.N.Mitrofanov A.A., Safin A.R., Torina E.M., Udalov N.N.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://re.eltech.ru/jour/article/view/414Introduction

Introduction. Today, many research endeavors are devoted to the miniaturization of microwave sources. One of the promising approaches is the use of magnetic nanostructures (spintronics elements), providing a wide range of frequency tuning and low power consumption. The main disadvantage of spintronics generators (spintransfer nanoscillators ‒ STNO) is a low output power of generated oscillations (tens of nanowatts and less). A possible solution is to sum up the power of many STNOs in a mutual synchronization mode.

Aim

Aim. The investigation of noise properties of two connected STNOs with identical and non-identical parameters in a phase synchronization mode.

Materials and methods

Materials and methods. A model was developed of two STNOs interconnected by spin waves taking into account thermal noises. Spectral power densities of the amplitude and phase noise were obtained by the method of effective linearization.

Results

Results. Dependencies were obtained in a general form for attenuation coefficients of the amplitude and phase fluctuations of noise sources for each STNO. Three cases of synchronization were considered: completely identical STNOs, two identical STNOs but with different oscillation frequencies, and two non-identical STNOs, differing in an allowance of self-excitation by frequencies and amplitudes of the oscillations. It was possible to obtain a gain in the amplitude and phase noise for two identical STNOs. In this case, an increase in the allowance of self-excitation led to a decrease in the level of phase and amplitude noise.

Conclusion

Conclusion. This analysis of the attenuation coefficients for non-identical STNOs demonstrates the possibility of improving the noise properties of each of the generators. In this case, the best noise value is obtained for an STNO with greater stability in a stand-alone mode.

Introduction

Introduction. Today, many research endeavors are devoted to the miniaturization of microwave sources. One of the promising approaches is the use of magnetic nanostructures (spintronics elements), providing a wide range of frequency tuning and low power consumption. The main disadvantage of spintronics generators (spintransfer nanoscillators ‒ STNO) is a low output power of generated oscillations (tens of nanowatts and less). A possible solution is to sum up the power of many STNOs in a mutual synchronization mode.

Aim

Aim. The investigation of noise properties of two connected STNOs with identical and non-identical parameters in a phase synchronization mode.

Materials and methods

Materials and methods. A model was developed of two STNOs interconnected by spin waves taking into account thermal noises. Spectral power densities of the amplitude and phase noise were obtained by the method of effective linearization.

Results

Results. Dependencies were obtained in a general form for attenuation coefficients of the amplitude and phase fluctuations of noise sources for each STNO. Three cases of synchronization were considered: completely identical STNOs, two identical STNOs but with different oscillation frequencies, and two non-identical STNOs, differing in an allowance of self-excitation by frequencies and amplitudes of the oscillations. It was possible to obtain a gain in the amplitude and phase noise for two identical STNOs. In this case, an increase in the allowance of self-excitation led to a decrease in the level of phase and amplitude noise.

Conclusion

Conclusion. This analysis of the attenuation coefficients for non-identical STNOs demonstrates the possibility of improving the noise properties of each of the generators. In this case, the best noise value is obtained for an STNO with greater stability in a stand-alone mode.

spin-transfer nanooscillatormutual phase lockingnoise propertiesspectral power densityspin-transfer nanooscillatormutual phase lockingnoise propertiesspectral power densityRussian President Grant for young scientists № MK-283.2019.8, RFBR grant № 19-29-03015Russian President Grant for young scientists № MK-283.2019.8, RFBR grant № 19-29-03015ReferencesRohde U., Poddar A., Böck G. The Design of Modern Microwave Oscillators for Wireless Applications: Theory and Optimization. New Jersey, John Wiley & Sons, 2005, 560 p.Rohde U., Poddar A., Böck G. The Design of Modern Microwave Oscillators for Wireless Applications: Theory and Optimization. New Jersey, John Wiley & Sons, 2005, 560 p.Slavin A., Tiberkevich V. Nonlinear Auto-Oscillator Theory of Microwave Generation by Spin-Polarized Current. IEEE Trans. on Magnetics. 2009, vol. 45, no. 4, pp. 1875‒1918. doi: 10.1109/TMAG.2008.2009935Slavin A., Tiberkevich V. 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The authors declare that there are no conflicts of interest present.