{"title":"晶体振荡器“昏睡病”的随机模型","authors":"Y. Shmaliy, R. Brendel","doi":"10.1109/FREQ.2006.275451","DOIUrl":null,"url":null,"abstract":"A stochastic model of a crystal oscillator is discussed at low drive levels, where a crystal resonator exhibits the effect termed \"sleeping sickness\". In the model, resonator losses are supposed to be nonlinear, R<sub>1</sub>(I<sub>r</sub>) = R<sub>10</sub>(1 + gamma<sub>R</sub>/I<sub>r</sub> <sup>n</sup>), where I<sub>r</sub> is a peak amplitude of the piezoelectric current, gamma<sub>R</sub> is a drive level dependence (DLD) coefficient, and n is a degree of nonlinearity. We show that a nonlinear crystal resonator with sleeping sickness does not fall to an \"absolute sleep\" in the oscillator, when a feedback becomes insufficient after a long storage. It rather generates the noise-induced oscillations at the noise level","PeriodicalId":445945,"journal":{"name":"2006 IEEE International Frequency Control Symposium and Exposition","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Stochastic Model of \\\"Sleeping Sickness\\\" of Crystal Oscillators\",\"authors\":\"Y. Shmaliy, R. Brendel\",\"doi\":\"10.1109/FREQ.2006.275451\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A stochastic model of a crystal oscillator is discussed at low drive levels, where a crystal resonator exhibits the effect termed \\\"sleeping sickness\\\". In the model, resonator losses are supposed to be nonlinear, R<sub>1</sub>(I<sub>r</sub>) = R<sub>10</sub>(1 + gamma<sub>R</sub>/I<sub>r</sub> <sup>n</sup>), where I<sub>r</sub> is a peak amplitude of the piezoelectric current, gamma<sub>R</sub> is a drive level dependence (DLD) coefficient, and n is a degree of nonlinearity. We show that a nonlinear crystal resonator with sleeping sickness does not fall to an \\\"absolute sleep\\\" in the oscillator, when a feedback becomes insufficient after a long storage. It rather generates the noise-induced oscillations at the noise level\",\"PeriodicalId\":445945,\"journal\":{\"name\":\"2006 IEEE International Frequency Control Symposium and Exposition\",\"volume\":\"25 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-06-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2006 IEEE International Frequency Control Symposium and Exposition\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/FREQ.2006.275451\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2006 IEEE International Frequency Control Symposium and Exposition","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/FREQ.2006.275451","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Stochastic Model of "Sleeping Sickness" of Crystal Oscillators
A stochastic model of a crystal oscillator is discussed at low drive levels, where a crystal resonator exhibits the effect termed "sleeping sickness". In the model, resonator losses are supposed to be nonlinear, R1(Ir) = R10(1 + gammaR/Irn), where Ir is a peak amplitude of the piezoelectric current, gammaR is a drive level dependence (DLD) coefficient, and n is a degree of nonlinearity. We show that a nonlinear crystal resonator with sleeping sickness does not fall to an "absolute sleep" in the oscillator, when a feedback becomes insufficient after a long storage. It rather generates the noise-induced oscillations at the noise level