{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T09:41:14Z","timestamp":1698313274471},"reference-count":31,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,12,13]],"date-time":"2006-12-13T00:00:00Z","timestamp":1165968000000},"content-version":"vor","delay-in-days":4609,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Circuit Theory &amp; Apps"],"published-print":{"date-parts":[[1994,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Negative\u2010conductance oscillators are termed adiabatic when their transient operation signal can be represented as a narrowband\u2010modulated Fourier series with a finite number only of dominant components, including the DC one. the method presented here allows one to perform the complete analysis of such oscillators in a rigorous shortened manner. Indeed, it merges the approach of the describing function technique into the classical frame of perturbation theory, so as to replace the oscillator model in the instantaneous variables with a simplified one in the dominant variables, i.e. the complex envelopes of the dominant components. More precisely, the starting model comprises the input impedance and the open\u2010circuit voltage of the Th\u00e9venin equivalent one\u2010port of the linear network in the complex frequency domain and the voltage\/current characteristic of the non\u2010linear resistor in the time domain. the final model instead comprises as many such triads as there are dominant components. Each triad is made up of an input impedance and an open\u2010circuit voltage in the baseband complex frequency domain and a voltage\/current describing characteristic in the slow time domain. Standard circuit analysis tools are then used to obtain the equations of the dominant dynamics, steady state and dynamical stability of the oscillator.<\/jats:p><jats:p>To facilitate reading the paper, as soon as a new formula is proposed or derived, the result of its application to the well\u2010known van der Pol oscillator is also provided. In the end, to highlight the simplicity and efficiency of the method, a much more complex case (an eighth\u2010order oscillator with three dominant components) is analysed in detail.<\/jats:p>","DOI":"10.1002\/cta.4490220303","type":"journal-article","created":{"date-parts":[[2007,7,2]],"date-time":"2007-07-02T10:50:12Z","timestamp":1183373412000},"page":"175-189","source":"Crossref","is-referenced-by-count":0,"title":["The describing function perturbation method for the dominant behaviour analysis of adiabatic negative\u2010conductance oscillators"],"prefix":"10.1002","volume":"22","author":[{"given":"Antonino M.","family":"Sommariva","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,12,13]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Introduction to Non\u2010linear Mechanics","author":"Kryloff N.","year":"1947"},{"key":"e_1_2_1_3_2","volume-title":"Asymptotic Methods in the Theory of Nonlinear Oscillations","author":"Bogoliubov N. 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