ESTIMATING THE SPECTRAL DENSITY OF FLICKER NOISE OF LOW-NOISE OSCILLATORS AT INFRA-LOW FREQUENCIES
Subject and Purpose. Designers of the research radars intended for detecting manifestations of biological activity of living organisms may be interested in the noise characteristics shown by their oscillators at offsets about 10-2 Hz or even 10-3 Hz from the carrier frequency. Unfortunately, the pro...
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Konovalov, V. M. Lukin, K. O. ESTIMATING THE SPECTRAL DENSITY OF FLICKER NOISE OF LOW-NOISE OSCILLATORS AT INFRA-LOW FREQUENCIES |
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Article |
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Konovalov, V. M. Lukin, K. O. |
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Konovalov, V. M. Lukin, K. O. |
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Konovalov, V. M. |
| title |
ESTIMATING THE SPECTRAL DENSITY OF FLICKER NOISE OF LOW-NOISE OSCILLATORS AT INFRA-LOW FREQUENCIES |
| title_short |
ESTIMATING THE SPECTRAL DENSITY OF FLICKER NOISE OF LOW-NOISE OSCILLATORS AT INFRA-LOW FREQUENCIES |
| title_full |
ESTIMATING THE SPECTRAL DENSITY OF FLICKER NOISE OF LOW-NOISE OSCILLATORS AT INFRA-LOW FREQUENCIES |
| title_fullStr |
ESTIMATING THE SPECTRAL DENSITY OF FLICKER NOISE OF LOW-NOISE OSCILLATORS AT INFRA-LOW FREQUENCIES |
| title_full_unstemmed |
ESTIMATING THE SPECTRAL DENSITY OF FLICKER NOISE OF LOW-NOISE OSCILLATORS AT INFRA-LOW FREQUENCIES |
| title_sort |
estimating the spectral density of flicker noise of low-noise oscillators at infra-low frequencies |
| title_alt |
ОЦІНКА СПЕКТРАЛЬНОЇ ЩІЛЬНОСТІ ФЛІКЕР-ШУМУ МАЛОШУМІВНИХ ГЕНЕРАТОРІВ НА ІНФРАНИЗЬКИХ ЧАСТОТАХ |
| description |
Subject and Purpose. Designers of the research radars intended for detecting manifestations of biological activity of living organisms may be interested in the noise characteristics shown by their oscillators at offsets about 10-2 Hz or even 10-3 Hz from the carrier frequency. Unfortunately, the producing companies do not practice regular information on noise performance of their products at frequencies below 1 Hz. The present authors have set the goal of deriving an analytical expression for the spectral density of flicker noise which should allow radar engineers estimating the probable noise performance of low-noise oscillators over any frequency range.Methods and Methodology. A great number of writers considering spectral properties of flicker noise tend to support the assertion that its spectral density increases continuously with a decrease in frequency, following the power law 1/fγ. Meanwhile, the present authors assume availability of a certain frequency fm below which the spectral density should most likely remain unchanged, even to as low as zero frequency. Also, there is a range of frequencies above which the spectral density of flicker noise remains constant and the total spectral density is determined solely by thermal noise.Results. The spectral density of noise follows the power law 1/fγ throughout the range from fm and up to the point where thermal noise starts to overbalance the flicker noise. The authors have proposed an approximating function to describe the behavior of the averaged spectral density of noise from the oscillator within the entire frequency range.Conclusions. The results obtained shall allow radio system designers to make estimates of the probable noise performance of low-noise oscillators in any frequency range, using only known reference data provided by the manufacturer.Keywords: flicker noise, 1/fγ noise, color noise, low-noise oscillators, bioactivity, bio-radarManuscript submitted 03.04.2022Radio phys. radio astron. 2022, 27(3): 229-239REFERENCES1. Oven Controlled Crystal Oscillator (OCXO). [viewed: 23.08.2022]. Available from: http://www.nelfc.com/ocxo/index.html#thumb2. Johnson, J.B., 1925. The Schottky Effect in Low Frequency Circuits. Phys. Rev., 26(1), pp. 71–85. DOI:https://doi.org/10.1103/PhysRev.26.713. Voss, R.F., 1979. 1/f (Flicker) Noise: A Brief Review. In: 33rd Annual Symposium on Frequency Control. Atlantic City, NJ, USA. 30 May – 1 June 1979. DOI:https://doi.org/10.1109/FREQ.1979.2002974. Van der Ziel, A.,1979. Flicker noise in electron devices. Adv. Electron. Electron Phys., 49, pp. 225–297. DOI:https://doi.org/10.1016/S0065-2539(08)60768-45. Van der Ziel, A. 1980. History of Noise Research. Adv. Electron. Electron Phys., 50, pp. 351–409. DOI:https://doi.org/10.1016/S0065-2539(08)61066-56. Keshner, M.S, 1982. 1/ƒ noise. Proc. IEEE. 70(3), pp. 212–218. DOI:https://doi.org/10.1109/PROC.1982.122827. Bochkov, G.N., Kuzovlev, Yu.E., 1983. New in 1/f-noise research. Phys.-Usp., 141(1) (in Russian). DOI: https://doi.org/10.3367/UFNr.0141.198309d.01518. Zhvirblis, V.E.,1983. The mystery of flicker noise. Znanie - sila, 9, pp. 36-39 (in Russian).9. Kogan, Sh.M., 1985. Low-frequency current noise with spectrum type 1/f in solids. Phys.-Usp., 145(2) (in Russian). DOI: https://doi.org/10.3367/UFNr.0145.198502d.028510. Handel, P.H.; Chung, A.L., 1993. Noise in Physical Systems and 1/f Fluctuations. New York: American Institute of Physics Publ.11. Josephson, B.D., 1995. A Trans-human source for music? In: Pylkkänen, P. and Pylkkö P. eds., 1995. New Directions in Cognitive Science. Finnish Artificial Intelligence Society. Saariselkä 4-9 Aug. 1995. Helsinki, pp. 280-285.12. Ciofi, C., Diligenti, A., and Neri, B., 1995.Electromigration noise in submicrometric lines. In: Proc. 13th Int. Conf.Noise in Physical Systems and 1/f Fluctuations (ICNF '95).Palanga, Lithuania, 29 May-3 June 1995. Singapore: World Scientific, pp. 618-621.13. Zhigalsky, G.P., 1997.1/f noise and nonlinear effects in thin metal covers. Phys.-Usp., 167(6), pp. 623-648(in Russian). DOI: https://doi.org/10.1070/PU1997v040n06ABEH00024614. Hajimiri, A. and Lee, T.H., 1998. General Theory of Phase Noise in Electrical Oscillators. IEEE J. Solid-State Circuits, 33(2), pp.179-194. DOI: https://doi.org/10.1109/4.65861915. Hajimiri A., Limotyrakis, S. and Lee, T.H., Jitter and Phase Noise in Ring Oscillators. IEEE J. Solid-State Circuits, 34(6), pp.790-804. DOI: https://doi.org/10.1109/4.76681316. Handel, P.H. 2000. The General Nature of Fundamental 1/f Noise in Oscillators and in the High Technology Domain. In: Lecture notes in physics, 550, pp. 232-264. DOI: https://doi.org/10.1007/3-540-45463-2_1217. Milotti, E., 2002. 1/f noise: a pedagogical review. [viewed: 23.08.2022]. Available from: arXiv:physics/0204033. https://www.researchgate.net/publication/2167452_1f_Noise_A_pedagogical_review18. Norton, M.P., Karczub, D.G., 2003. Fundamentals of noise and vibration analysis for engineers. 2nd ed. Cambridge, UK: Cambridge University ress. DOI: https://doi.org/10.1017/CBO978113916392719. Mukherjee, Ja., Roblin, P., Akhtar, S., 2007. An Analytic Circuit-Based Model for White and Flicker Phase Noise in LC Oscillators. IEEE Trans. Circuits Syst. I Regul. Pap., 54(7), pp. 1584-1598. DOI: https://doi.org/10.1109/TCSI.2007.89867320. Ward, L.M. and Greenwood, P.E., 2007. 1/f noise. Scholarpedia, 2(12), pp. 1537.DOI: https://doi.org/10.4249/scholarpedia.153721. Cao, T., Wisland, D., Lande, T., Moradi, F., 2009. A bulk-controlled ring-VCO with 1/f-noise reduction for frequency ΔΣ modulator.In: 2009MIXDES: 16th Int. Conf. Mixed Design of Integrated Circuits & Systems (MIXDES '09): proc. Lodz, Poland, 25-27 June 2009.22. Chen Sh.-M., Fang Y.-K., JuangF.-R.,Chen C.-C., Liu S.; Kuo C.-W., Chao C.-P.;Tseng H.-C., 2011. A Low-Flicker Noise Gate-Controlled Lateral-Vertical Bipolar Junction Transistor Array With 55-nm CMOS Technology. IEEE Trans. Electron Devices, 58(10), pp. 3276-3282. DOI: https://doi.org/10.1109/TED.2011.216131223. Kendal, W.S., Jørgensen, B.R., 2011. Tweedie convergence: a mathematical basis for Taylor's power law, 1/f noise and multifractality. Phys. Rev. E, 84(6),p. 066120. DOI: https://doi.org/10.1103/PhysRevE.84.06612024. Pepe, F., Bonfanti, A., Levantino, S., Lacaita, A.L., 2014.Impact of non-quasi-static effects on 1/f3 phase noise in a 1.9-to-2.6 GHz oscillator. In: Proc. 2014 IEEE Radio Frequency Integrated Circuits Symposium. Tampa, FL, USA, 1-3 June 2014, pp. 425-428. DOI: https://doi.org/10.1109/RFIC.2014.685175825. Ioannidis, E.G., Theodorou, C.G., Karatsori, T.A., Haendler, S., Dimitriadis, C.A., and Ghibaudo, G., 2015. Drain-Current Flicker Noise Modeling in nMOSFETs From a 14-nm FDSOI Technology. IEEE Trans. Electron Devices, 62(5), pp. 1574-1579. DOI: https://doi.org/10.1109/TED.2015.241167826. Kuzovlev, Yu.E., 2015. Why nature needs 1/f noise. Phys. Usp., 58(7), pp. 719-729. DOI: https://doi.org/10.3367/UFNe.0185.201507d.077327. Hu, S., Wang, F., Wang, H., 2016. A transformer-based inverted complementary cross-coupled VCO with a 193.3 dBc/Hz FoM and 13 kHz 1/f3 noise corner. In: Proc. 2016 IEEE Radio Frequency Integrated Circuits Symposium (RFIC). San Francisco, CA, USA, 22-24 May 2016. DOI: https://doi.org/10.1109/RFIC.2016.750824228. Yadav, A.C., Ramaswamy, R. and Dhar, D., 2017. General mechanism for the 1/f noise. Phys. Rev. E, 96(2), p. 022215. DOI: https://doi.org/10.1103/PhysRevE.96.02221529. Coen, Ch.T., Ildefonso, A., Fleetwood, Z.E., Cressler, J.D., 2017.A 19-34 GHz SiGe HBT square-law detector with ultra-low 1/f noise for atmospheric radiometers.In: Proc. 12th European Microwave Integrated Circuits Conference (EuMIC). Nuremberg, Germany, 8-10 Oct. 2017. DOI: https://doi.org/10.23919/EuMIC.2017.823068530. Jara, M., Alessandri, C., Abusleme, A., 2018. Time-Domain 1/f Noise Analysis of a Charge-Redistribution Track-and-Hold Circuit. IEEE Trans. Circuits Syst. II Express Briefs, 65(2), pp. 161-165. DOI: https://doi.org/10.1109/TCSII.2017.268412331. Krapf, D., Marinari, E., Metzler, R., Oshanin, G., Xu, X., Squarcini, A., 2018.Power spectral density of a single Brownian trajectory: what one can and cannot learn from it. New J. Phys., 20(2), p. 023029. DOI: https://doi.org/10.1088/1367-2630/aaa67c32. Muhea, W.E., Gneiting, Th., Iñiguez, B., 2019. UMEM based 1/f noise model for amorphous ESL IGZO TFTs. In: Proc.2019 Latin American Electron Devices Conf. (LAEDC 2019). Armenia, Colombia, 24-27 Feb. 2019. DOI: https://doi.org/10.1109/LAED.2019.871474433. Hu, Y., Siriburanon, T., Staszewski, R.B., 2021.Oscillator Flicker Phase Noise: A Tutorial. IEEE Trans. Circuits Syst. II Express Briefs, 68(2), pp. 538-544. DOI: https://doi.org/10.1109/TCSII.2020.304316534. Tchaikovsky, W., 2015. Flicker noise puzzle solved. [viewed: 23.08.2022]. Available from: https://habr.com/ru/post/262015/ (in Russian).35. Gertsenshtein, M. A little more about noises. Commentary on the article by V. Zhvirblis "The Puzzle of Flicker Noise". [viewed: 23.08.2022]. Available from: http://www.integro.ru/system/eretics/flicker/flicker2.htm (in Russian).36. Prokhorov, A.M. ed., 1998. Physical encyclopedia. Vol. 5. Moscow: Great Russian Encyclopedia Publ.(in Russian).37. Kogan, Sh.M., 1985. Low-frequency current noise with 1/f type spectrum in solids. Sov. Phys.-Usp., 145(2), p. 285 (in Russian). DOI: https://doi.org/10.3367/UFNr.0145.198502d.028538. Prussov, P.D. The nature of flicker noise. [viewed: 04.12.2020]. Available from: http://bourabai.kz/prussov/flikker.htm (in Russian).39. Melnyk, S.S., Usatenko, O.V., Yampol'skii, V.A., and Golick, V.A, 2005. Competition between two kinds of correlations in literary texts. Phys. Rev. E., 72(2), p. 026140. DOI: https://doi.org/10.1103/PhysRevE.72.02614040. Bak, P., 1996. How Nature Works: The Science of Self-Organized Criticality. New York: Copernicus Publ. DOI: https://doi.org/10.1007/978-1-4757-5426-1 |
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Видавничий дім «Академперіодика» |
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oai:ri.kharkov.ua:article-13972023-06-20T14:17:41Z ESTIMATING THE SPECTRAL DENSITY OF FLICKER NOISE OF LOW-NOISE OSCILLATORS AT INFRA-LOW FREQUENCIES ОЦІНКА СПЕКТРАЛЬНОЇ ЩІЛЬНОСТІ ФЛІКЕР-ШУМУ МАЛОШУМІВНИХ ГЕНЕРАТОРІВ НА ІНФРАНИЗЬКИХ ЧАСТОТАХ Konovalov, V. M. Lukin, K. O. Subject and Purpose. Designers of the research radars intended for detecting manifestations of biological activity of living organisms may be interested in the noise characteristics shown by their oscillators at offsets about 10-2 Hz or even 10-3 Hz from the carrier frequency. Unfortunately, the producing companies do not practice regular information on noise performance of their products at frequencies below 1 Hz. The present authors have set the goal of deriving an analytical expression for the spectral density of flicker noise which should allow radar engineers estimating the probable noise performance of low-noise oscillators over any frequency range.Methods and Methodology. A great number of writers considering spectral properties of flicker noise tend to support the assertion that its spectral density increases continuously with a decrease in frequency, following the power law 1/fγ. Meanwhile, the present authors assume availability of a certain frequency fm below which the spectral density should most likely remain unchanged, even to as low as zero frequency. Also, there is a range of frequencies above which the spectral density of flicker noise remains constant and the total spectral density is determined solely by thermal noise.Results. The spectral density of noise follows the power law 1/fγ throughout the range from fm and up to the point where thermal noise starts to overbalance the flicker noise. The authors have proposed an approximating function to describe the behavior of the averaged spectral density of noise from the oscillator within the entire frequency range.Conclusions. The results obtained shall allow radio system designers to make estimates of the probable noise performance of low-noise oscillators in any frequency range, using only known reference data provided by the manufacturer.Keywords: flicker noise, 1/fγ noise, color noise, low-noise oscillators, bioactivity, bio-radarManuscript submitted 03.04.2022Radio phys. radio astron. 2022, 27(3): 229-239REFERENCES1. Oven Controlled Crystal Oscillator (OCXO). [viewed: 23.08.2022]. Available from: http://www.nelfc.com/ocxo/index.html#thumb2. Johnson, J.B., 1925. The Schottky Effect in Low Frequency Circuits. Phys. Rev., 26(1), pp. 71–85. DOI:https://doi.org/10.1103/PhysRev.26.713. Voss, R.F., 1979. 1/f (Flicker) Noise: A Brief Review. In: 33rd Annual Symposium on Frequency Control. Atlantic City, NJ, USA. 30 May – 1 June 1979. DOI:https://doi.org/10.1109/FREQ.1979.2002974. Van der Ziel, A.,1979. Flicker noise in electron devices. Adv. Electron. Electron Phys., 49, pp. 225–297. DOI:https://doi.org/10.1016/S0065-2539(08)60768-45. Van der Ziel, A. 1980. History of Noise Research. Adv. Electron. Electron Phys., 50, pp. 351–409. DOI:https://doi.org/10.1016/S0065-2539(08)61066-56. Keshner, M.S, 1982. 1/ƒ noise. Proc. IEEE. 70(3), pp. 212–218. DOI:https://doi.org/10.1109/PROC.1982.122827. Bochkov, G.N., Kuzovlev, Yu.E., 1983. New in 1/f-noise research. Phys.-Usp., 141(1) (in Russian). DOI: https://doi.org/10.3367/UFNr.0141.198309d.01518. Zhvirblis, V.E.,1983. The mystery of flicker noise. Znanie - sila, 9, pp. 36-39 (in Russian).9. Kogan, Sh.M., 1985. Low-frequency current noise with spectrum type 1/f in solids. Phys.-Usp., 145(2) (in Russian). DOI: https://doi.org/10.3367/UFNr.0145.198502d.028510. Handel, P.H.; Chung, A.L., 1993. Noise in Physical Systems and 1/f Fluctuations. New York: American Institute of Physics Publ.11. Josephson, B.D., 1995. A Trans-human source for music? In: Pylkkänen, P. and Pylkkö P. eds., 1995. New Directions in Cognitive Science. Finnish Artificial Intelligence Society. Saariselkä 4-9 Aug. 1995. Helsinki, pp. 280-285.12. Ciofi, C., Diligenti, A., and Neri, B., 1995.Electromigration noise in submicrometric lines. In: Proc. 13th Int. Conf.Noise in Physical Systems and 1/f Fluctuations (ICNF '95).Palanga, Lithuania, 29 May-3 June 1995. Singapore: World Scientific, pp. 618-621.13. Zhigalsky, G.P., 1997.1/f noise and nonlinear effects in thin metal covers. Phys.-Usp., 167(6), pp. 623-648(in Russian). DOI: https://doi.org/10.1070/PU1997v040n06ABEH00024614. Hajimiri, A. and Lee, T.H., 1998. General Theory of Phase Noise in Electrical Oscillators. IEEE J. Solid-State Circuits, 33(2), pp.179-194. DOI: https://doi.org/10.1109/4.65861915. Hajimiri A., Limotyrakis, S. and Lee, T.H., Jitter and Phase Noise in Ring Oscillators. IEEE J. Solid-State Circuits, 34(6), pp.790-804. DOI: https://doi.org/10.1109/4.76681316. Handel, P.H. 2000. The General Nature of Fundamental 1/f Noise in Oscillators and in the High Technology Domain. In: Lecture notes in physics, 550, pp. 232-264. DOI: https://doi.org/10.1007/3-540-45463-2_1217. Milotti, E., 2002. 1/f noise: a pedagogical review. [viewed: 23.08.2022]. Available from: arXiv:physics/0204033. https://www.researchgate.net/publication/2167452_1f_Noise_A_pedagogical_review18. Norton, M.P., Karczub, D.G., 2003. Fundamentals of noise and vibration analysis for engineers. 2nd ed. Cambridge, UK: Cambridge University ress. DOI: https://doi.org/10.1017/CBO978113916392719. Mukherjee, Ja., Roblin, P., Akhtar, S., 2007. An Analytic Circuit-Based Model for White and Flicker Phase Noise in LC Oscillators. IEEE Trans. Circuits Syst. I Regul. Pap., 54(7), pp. 1584-1598. DOI: https://doi.org/10.1109/TCSI.2007.89867320. Ward, L.M. and Greenwood, P.E., 2007. 1/f noise. Scholarpedia, 2(12), pp. 1537.DOI: https://doi.org/10.4249/scholarpedia.153721. Cao, T., Wisland, D., Lande, T., Moradi, F., 2009. A bulk-controlled ring-VCO with 1/f-noise reduction for frequency ΔΣ modulator.In: 2009MIXDES: 16th Int. Conf. Mixed Design of Integrated Circuits & Systems (MIXDES '09): proc. Lodz, Poland, 25-27 June 2009.22. Chen Sh.-M., Fang Y.-K., JuangF.-R.,Chen C.-C., Liu S.; Kuo C.-W., Chao C.-P.;Tseng H.-C., 2011. A Low-Flicker Noise Gate-Controlled Lateral-Vertical Bipolar Junction Transistor Array With 55-nm CMOS Technology. IEEE Trans. Electron Devices, 58(10), pp. 3276-3282. DOI: https://doi.org/10.1109/TED.2011.216131223. Kendal, W.S., Jørgensen, B.R., 2011. Tweedie convergence: a mathematical basis for Taylor's power law, 1/f noise and multifractality. Phys. Rev. E, 84(6),p. 066120. DOI: https://doi.org/10.1103/PhysRevE.84.06612024. Pepe, F., Bonfanti, A., Levantino, S., Lacaita, A.L., 2014.Impact of non-quasi-static effects on 1/f3 phase noise in a 1.9-to-2.6 GHz oscillator. In: Proc. 2014 IEEE Radio Frequency Integrated Circuits Symposium. Tampa, FL, USA, 1-3 June 2014, pp. 425-428. DOI: https://doi.org/10.1109/RFIC.2014.685175825. Ioannidis, E.G., Theodorou, C.G., Karatsori, T.A., Haendler, S., Dimitriadis, C.A., and Ghibaudo, G., 2015. Drain-Current Flicker Noise Modeling in nMOSFETs From a 14-nm FDSOI Technology. IEEE Trans. Electron Devices, 62(5), pp. 1574-1579. DOI: https://doi.org/10.1109/TED.2015.241167826. Kuzovlev, Yu.E., 2015. Why nature needs 1/f noise. Phys. Usp., 58(7), pp. 719-729. DOI: https://doi.org/10.3367/UFNe.0185.201507d.077327. Hu, S., Wang, F., Wang, H., 2016. A transformer-based inverted complementary cross-coupled VCO with a 193.3 dBc/Hz FoM and 13 kHz 1/f3 noise corner. In: Proc. 2016 IEEE Radio Frequency Integrated Circuits Symposium (RFIC). San Francisco, CA, USA, 22-24 May 2016. DOI: https://doi.org/10.1109/RFIC.2016.750824228. Yadav, A.C., Ramaswamy, R. and Dhar, D., 2017. General mechanism for the 1/f noise. Phys. Rev. E, 96(2), p. 022215. DOI: https://doi.org/10.1103/PhysRevE.96.02221529. Coen, Ch.T., Ildefonso, A., Fleetwood, Z.E., Cressler, J.D., 2017.A 19-34 GHz SiGe HBT square-law detector with ultra-low 1/f noise for atmospheric radiometers.In: Proc. 12th European Microwave Integrated Circuits Conference (EuMIC). Nuremberg, Germany, 8-10 Oct. 2017. DOI: https://doi.org/10.23919/EuMIC.2017.823068530. Jara, M., Alessandri, C., Abusleme, A., 2018. Time-Domain 1/f Noise Analysis of a Charge-Redistribution Track-and-Hold Circuit. IEEE Trans. Circuits Syst. II Express Briefs, 65(2), pp. 161-165. DOI: https://doi.org/10.1109/TCSII.2017.268412331. Krapf, D., Marinari, E., Metzler, R., Oshanin, G., Xu, X., Squarcini, A., 2018.Power spectral density of a single Brownian trajectory: what one can and cannot learn from it. New J. Phys., 20(2), p. 023029. DOI: https://doi.org/10.1088/1367-2630/aaa67c32. Muhea, W.E., Gneiting, Th., Iñiguez, B., 2019. UMEM based 1/f noise model for amorphous ESL IGZO TFTs. In: Proc.2019 Latin American Electron Devices Conf. (LAEDC 2019). Armenia, Colombia, 24-27 Feb. 2019. DOI: https://doi.org/10.1109/LAED.2019.871474433. Hu, Y., Siriburanon, T., Staszewski, R.B., 2021.Oscillator Flicker Phase Noise: A Tutorial. IEEE Trans. Circuits Syst. II Express Briefs, 68(2), pp. 538-544. DOI: https://doi.org/10.1109/TCSII.2020.304316534. Tchaikovsky, W., 2015. Flicker noise puzzle solved. [viewed: 23.08.2022]. Available from: https://habr.com/ru/post/262015/ (in Russian).35. Gertsenshtein, M. A little more about noises. Commentary on the article by V. Zhvirblis "The Puzzle of Flicker Noise". [viewed: 23.08.2022]. Available from: http://www.integro.ru/system/eretics/flicker/flicker2.htm (in Russian).36. Prokhorov, A.M. ed., 1998. Physical encyclopedia. Vol. 5. Moscow: Great Russian Encyclopedia Publ.(in Russian).37. Kogan, Sh.M., 1985. Low-frequency current noise with 1/f type spectrum in solids. Sov. Phys.-Usp., 145(2), p. 285 (in Russian). DOI: https://doi.org/10.3367/UFNr.0145.198502d.028538. Prussov, P.D. The nature of flicker noise. [viewed: 04.12.2020]. Available from: http://bourabai.kz/prussov/flikker.htm (in Russian).39. Melnyk, S.S., Usatenko, O.V., Yampol'skii, V.A., and Golick, V.A, 2005. Competition between two kinds of correlations in literary texts. Phys. Rev. E., 72(2), p. 026140. DOI: https://doi.org/10.1103/PhysRevE.72.02614040. Bak, P., 1996. How Nature Works: The Science of Self-Organized Criticality. New York: Copernicus Publ. DOI: https://doi.org/10.1007/978-1-4757-5426-1 Предмет і мета роботи. Розробників дослідницьких радарів, що призначені для спостереження проявів біологічної активності живих організмів, можуть цікавити шумові характеристики генераторів при значеннях розстроювання від несучоїчастоти в декілька сотих, або навіть тисячних часток герца. На жаль, фірми-виробники генераторів далеко не завжди наводять дані про шуми своїх виробів на частотах нижче 1 Гц. Автори даної роботи поставили за мету вивести такий аналітичний вираз для спектральної щільності флікер-шуму, який дозволить розробникам радіосистем робити оцінки ймовірних характеристик малошумівних генераторів у будь-якій частотній області.Методи і методологія. В літературі з дослідження властивостей флікер-шуму стверджується про безперервне зростання його спектральної щільності зі зниженням частоти за ступеневим законом 1/fγ. Автори даної роботи припускають існування певної частоти fm , нижче якої спектральна щільність шумів, швидше за все, залишається незмінною аж до нульових частот. Також, існує область частот, вище яких спектральна щільність флікер-шуму залишається постійною, а сумарна спектральна щільність визначається тепловими шумами.Результати. У діапазоні від fm і до частот, при яких над флікер-шумами починають переважати теплові шуми, поведінка спектральної щільності визначається степеневим законом. Для всього частотного діапазону запропоновано апроксимуючу функцію, що описує поведінку усередненої спектральної щільності шумів генераторів.Висновки. Результати, що отримано, дозволяють розробникам радіосистем робити оцінки ймовірних характеристик малошумівних генераторів у будь-якій частотній області, використовуючи при цьому лише відомі довідкові дані, що наводяться виробниками апаратури.Ключові слова: флікер-шум, шум 1/fγ кольоровий шум, малошумівні генератори, біоактивність, біолокаторСтаття надійшла до редакції 03.04.2022Radio phys. radio astron. 2022, 27(3): 229-239БІБЛІОГРАФІЧНИЙ СПИСОК1. Oven Controlled Crystal Oscillator (OCXO). URL: http://www.nelfc.com/ocxo/index.html#thumb2. Johnson J.B. The Schottky Effect in Low Frequency Circuits. Phys. Rev. 1925. Vol. 26, Iss. 1. P. 71—85. DOI: 10.1103/PhysRev.26.71.3. Voss R.F. 1/f (Flicker) Noise: A Brief Review. 33rd Annual Symposium on Frequency Control. Atlantic City, NJ, USA. 30 May — 1 June 1979.4. Van der Ziel A. 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Melnyk S.S., Usatenko O.V., Yampol’skii V.A., and Golick V.A. Competition between two kinds of correlations in literary texts. Phys. Rev. E. 2005. Vol. 72, Iss. 2. P. 026140.40. Bak P. How Nature Works: The Science of Self-Organized Criticality. New York: Copernicus, 1996. Видавничий дім «Академперіодика» 2023-06-15 Article Article application/pdf http://rpra-journal.org.ua/index.php/ra/article/view/1397 10.15407/rpra27.03.229 РАДИОФИЗИКА И РАДИОАСТРОНОМИЯ; Vol 27, No 3 (2022); 229 RADIO PHYSICS AND RADIO ASTRONOMY; Vol 27, No 3 (2022); 229 РАДІОФІЗИКА І РАДІОАСТРОНОМІЯ; Vol 27, No 3 (2022); 229 2415-7007 1027-9636 10.15407/rpra27.03 uk http://rpra-journal.org.ua/index.php/ra/article/view/1397/pdf Copyright (c) 2022 RADIO PHYSICS AND RADIO ASTRONOMY |