{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,1]],"date-time":"2024-02-01T23:57:46Z","timestamp":1706831866849},"reference-count":12,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,12,13]],"date-time":"2006-12-13T00:00:00Z","timestamp":1165968000000},"content-version":"vor","delay-in-days":5094,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Circuit Theory & Apps"],"published-print":{"date-parts":[[1993,1]]},"abstract":"Abstract<\/jats:title>Oversampled sigma\u2010delta analogue\u2010to\u2010digital conversion has been the focus of much research attention in recent years. Converters based on this principle have been found to be particularly suited to integrated circuit implementation owing to their simple structure and robustness to circuit imperfection. the analysis of the sigma\u2010delta system is complicated by the presence of a discontinuous non\u2010linear element, with the result that until very recently few rigorous studies of such converters had appeared in the literature.<\/jats:p>In this paper we study the operation of the single\u2010loop sigma\u2010delta modulator, consisting of a quantizer and a discrete\u2010time integrator in a feedback loop, with constant input. Our analysis uses the tools of non\u2010linear dynamics to derive rigorous descriptions of system behaviour. In particular we focus on the effects of the discontinuous nonlinear element\u2010the quantizer. In the most basic case the quantizer has two levels. We study the effect of quantizer offsets in conjunction with leaky integration on the behaviour of this system. We then study the effect on system operation of increasing the number of quantization levels and explain in quantitative terms the structure of the resultant input versus average output characteristic.<\/jats:p>","DOI":"10.1002\/cta.4490210105","type":"journal-article","created":{"date-parts":[[2007,7,2]],"date-time":"2007-07-02T06:16:26Z","timestamp":1183356986000},"page":"61-83","source":"Crossref","is-referenced-by-count":5,"title":["Multilevel and non\u2010ideal quantization in \u2211 \u03b4 modulation"],"prefix":"10.1002","volume":"21","author":[{"given":"Orla","family":"Feely","sequence":"first","affiliation":[]},{"given":"Leon O.","family":"Chua","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,12,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCOM.1974.1092194"},{"key":"e_1_2_1_3_2","first-page":"174","article-title":"Digital\u2010to\u2010analog conversion in playing a compact disc","volume":"40","author":"Goedhart D.","year":"1982","journal-title":"Philips Tech. Rev."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/26.3777"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCOM.1987.1096814"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/26.31143"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1049\/el:19880715"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/31.99158"},{"key":"e_1_2_1_9_2","volume-title":"Elementary Symbolic Dynamics","author":"Hao B.\u2010L.","year":"1989"},{"key":"e_1_2_1_10_2","volume-title":"An Introduction to Chaotic Dynamical Systems","author":"Devaney R.","year":"1989"},{"key":"e_1_2_1_11_2","unstructured":"B.Boser Design and implementation of oversampled analog\u2010to\u2010digital converters' Ph.D. Thesis Stanford University October1988."},{"key":"e_1_2_1_12_2","first-page":"942","article-title":"Map of the line onto itself","volume":"2","author":"Leonov N. N.","year":"1959","journal-title":"Radiofisica"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1142\/S021812749200032X"}],"container-title":["International Journal of Circuit Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fcta.4490210105","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cta.4490210105","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T06:06:52Z","timestamp":1698214012000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/cta.4490210105"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,1]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1993,1]]}},"alternative-id":["10.1002\/cta.4490210105"],"URL":"https:\/\/doi.org\/10.1002\/cta.4490210105","archive":["Portico"],"relation":{},"ISSN":["0098-9886","1097-007X"],"issn-type":[{"value":"0098-9886","type":"print"},{"value":"1097-007X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,1]]}}}