{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:02:32Z","timestamp":1740135752178,"version":"3.37.3"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T00:00:00Z","timestamp":1578614400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T00:00:00Z","timestamp":1578614400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"crossref","award":["E2018502121"],"award-info":[{"award-number":["E2018502121"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004826","name":"Natural Science Foundation of Beijing","doi-asserted-by":"crossref","award":["3192039"],"award-info":[{"award-number":["3192039"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2020,7]]},"DOI":"10.1007\/s00034-019-01340-6","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T03:02:38Z","timestamp":1578625358000},"page":"3350-3371","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Small-Signal Fractional-Order Model of PN Junction Long-Base Diode"],"prefix":"10.1007","volume":"39","author":[{"given":"Guishu","family":"Liang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1685-0013","authenticated-orcid":false,"given":"Hao","family":"Shen","sequence":"additional","affiliation":[]},{"given":"Xin","family":"Liu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,1,10]]},"reference":[{"issue":"5","key":"1340_CR1","doi-asserted-by":"publisher","first-page":"3729","DOI":"10.1109\/20.312751","volume":"30","author":"A Ahmad","year":"1994","unstructured":"A. Ahmad, Ph Auriol, C. Kieny, Shell-form power transformer modeling at high frequencies. IEEE Trans. Magn. 30(5), 3729\u20133732 (1994)","journal-title":"IEEE Trans. Magn."},{"key":"1340_CR2","doi-asserted-by":"crossref","unstructured":"F. Boulgamh, M. Remram, A. Djouambi, Small-signal fractional-order modeling of PN junction diode, in Recent Advances in Electrical Engineering and Control Applications (Springer, Berlin, 2017), pp. 247\u2013255","DOI":"10.1007\/978-3-319-48929-2_19"},{"key":"1340_CR3","doi-asserted-by":"publisher","unstructured":"F. Boulgamh, M. Remram, A. Djouambi, Fractional behaviour of PN junction diode under AC-small-signal conditions, in ICEERE 2018, LNEE, ed. by Hajji et al., vol. 519 (2019), pp. 283\u2013289. https:\/\/doi.org\/10.1007\/978-981-13-1405-6_34","DOI":"10.1007\/978-981-13-1405-6_34"},{"issue":"11","key":"1340_CR4","doi-asserted-by":"publisher","first-page":"1014","DOI":"10.1109\/TCS.1980.1084742","volume":"27","author":"LO Chua","year":"1980","unstructured":"L.O. Chua, Device modeling via nonlinear circuit elements. IEEE Trans. Circuits Syst. 27(11), 1014\u20131044 (1980)","journal-title":"IEEE Trans. Circuits Syst."},{"issue":"2","key":"1340_CR5","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1002\/cta.4490160205","volume":"16","author":"LO Chua","year":"1988","unstructured":"L.O. Chua, C.C. Chen, High-speed non-linear circuit models for p\u2013n junction diodes. Int. J. Circuit Theory Appl. 16(2), 157\u2013190 (1988)","journal-title":"Int. J. Circuit Theory Appl."},{"key":"1340_CR6","volume-title":"Computer-Aided Analysis of Electronic Circuits, Algorithms and Computational Techniques","author":"LO Chua","year":"1975","unstructured":"L.O. Chua, P.M. Lin, Computer-Aided Analysis of Electronic Circuits, Algorithms and Computational Techniques (Computer-Aided Analysis of Electronic Circuits, California, 1975)"},{"key":"1340_CR7","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1002\/cta.4490130204","volume":"13","author":"A Dervisoglu","year":"1985","unstructured":"A. Dervisoglu, L.O. Chua, Modelling non-linear devices exhibiting frequency-dependent capacitances and inductances. Int. J. Circuits Theor. Appl. 13, 133\u2013148 (1985)","journal-title":"Int. J. Circuits Theor. Appl."},{"key":"1340_CR8","unstructured":"L. Dor\u010d\u00e1k, J. Terp\u00e1k, I. Petr\u00e1\u0161, et al., Comparison of the electronic realization of the fractional-order system and its model, in Proceedings of IEEE International Conference on the 13th International Carpathian Control Conference, High Tatras, Slovakia (2012), pp. 119\u2013124"},{"key":"1340_CR9","unstructured":"A. Dzielinski, G. Sarwas, D. Sierociuk, et al., Frequency response based identification of fractional-order dynamical systems, in Proceeding of IEEE International Conference on Carpathian Control, 2011 12th, Velke Karlovice, Czech Republic (2011), pp. 98\u2013102"},{"issue":"1","key":"1340_CR10","first-page":"136","volume":"13","author":"A Dzielinski","year":"2008","unstructured":"A. Dzielinski, D. Sierociuk, Ultracapacitor modelling and control using discrete fractional-order state-space model. Acta Montan. Slovaca 13(1), 136\u2013145 (2008)","journal-title":"Acta Montan. Slovaca"},{"issue":"4","key":"1340_CR11","first-page":"583","volume":"58","author":"A Dzielinski","year":"2010","unstructured":"A. Dzielinski, D. Sierociuk, G. Sarwas, Some applications of fractional-order calculus. Bull. Polish Acad. Sci. Tech. Sci. 58(4), 583\u2013592 (2010)","journal-title":"Bull. Polish Acad. Sci. Tech. Sci."},{"issue":"4","key":"1340_CR12","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1109\/MCAS.2010.938637","volume":"10","author":"A Elwakil","year":"2010","unstructured":"A. Elwakil, Fractional-order circuits and systems: an emerging interdisciplinary research area. IEEE Circuits Syst. Mag. 10(4), 40\u201350 (2010)","journal-title":"IEEE Circuits Syst. Mag."},{"issue":"3","key":"1340_CR13","doi-asserted-by":"publisher","first-page":"1587","DOI":"10.1109\/TPWRD.2005.860281","volume":"21","author":"B Gustavsen","year":"2006","unstructured":"B. Gustavsen, Improving the pole relocating properties of vector fitting. IEEE Trans. Power Delivery 21(3), 1587\u20131592 (2006)","journal-title":"IEEE Trans. Power Delivery"},{"key":"1340_CR14","doi-asserted-by":"publisher","first-page":"1052","DOI":"10.1109\/61.772353","volume":"14","author":"B Gustavsen","year":"1999","unstructured":"B. Gustavsen, A. Semlyen, Rational approximation of frequency domain responses by vector fitting. IEEE Trans. Power Deliv. 14, 1052\u20131061 (1999)","journal-title":"IEEE Trans. Power Deliv."},{"issue":"4","key":"1340_CR15","first-page":"801","volume":"8","author":"A Jalloul","year":"2011","unstructured":"A. Jalloul, J.C. Trigeassou, K. Jelassi et al., Fractional-order modeling of rotor skin effect in induction machines. Int. J. Comput. Sci. Issues 8(4), 801\u2013813 (2011)","journal-title":"Int. J. Comput. Sci. Issues"},{"key":"1340_CR16","unstructured":"A.K. Kamath, J.R. Gandhi, A.S. Bohra, A.V. Goel, D.U. Patil, O.V. Kulkarni, J.O. Chandle. Modeling of transformer characteristics using fractional-order transfer functions, in Proceedings of IEEE International Conference on Control and Automation, ICCA, Christchurch, New Zealand (2009), pp. 2123\u20132128"},{"issue":"7","key":"1340_CR17","doi-asserted-by":"publisher","first-page":"1665","DOI":"10.1109\/JRPROC.1962.288155","volume":"50","author":"SM Krakauer","year":"1962","unstructured":"S.M. Krakauer, Harmonic generation, rectification, and lifetime evaluation with the step recovery diode. Proc. IRE 50(7), 1665\u20131676 (1962)","journal-title":"Proc. IRE"},{"issue":"1","key":"1340_CR18","first-page":"76","volume":"24","author":"BJ Li","year":"2002","unstructured":"B.J. Li, H.Y. Liu, A solving method of overdetermined system. J. Sheng yang Univ. Technol. 24(1), 76\u201377 (2002)","journal-title":"J. Sheng yang Univ. Technol."},{"key":"1340_CR19","unstructured":"J.G. Linvill, Lumped models of transistors and diodes, in Proceedings of IEEE International Conference on Proceedings of the IRE (1958), pp. 1141\u20131152"},{"key":"1340_CR20","unstructured":"X. Liu, G.S. Liang, An algorithm for fractional-order system identification, in Processing of IEEE International Conference on Computational Science and Engineering, Chengdu, China (2015), pp. 66\u201371"},{"issue":"1\u20132","key":"1340_CR21","first-page":"107","volume":"68","author":"JAT Machado","year":"2010","unstructured":"J.A.T. Machado, A.M.S.F. Galhano, Fractional-order inductive phenomena based on the skin effect. Nonlinear Dyn. 68(1\u20132), 107\u2013115 (2010)","journal-title":"Nonlinear Dyn."},{"issue":"2","key":"1340_CR22","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1016\/j.amc.2008.05.146","volume":"206","author":"R Mansouri","year":"2008","unstructured":"R. Mansouri, M. Bettayeb, T. Djamah, S. Djennoune, Vector fitting fractional system identification using particle swarm optimization. Appl. Math. Comput. 206(2), 510\u2013520 (2008)","journal-title":"Appl. Math. Comput."},{"issue":"2","key":"1340_CR23","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1137\/0111030","volume":"11","author":"DW Marquardt","year":"1963","unstructured":"D.W. Marquardt, An algorithm for least squares estimation of non-linear parameters. J. Soc. Ind. Appl. Math. 11(2), 431\u2013441 (1963)","journal-title":"J. Soc. Ind. Appl. Math."},{"key":"1340_CR24","volume-title":"Device Electronics for Integrated Circuits","author":"RS Muller","year":"1977","unstructured":"R.S. Muller, T.L. Kamins, Device Electronics for Integrated Circuits (Wiley, New York, 1977)"},{"key":"1340_CR25","unstructured":"Nano Dot Tek\u2122, What is fractance and why is it useful?. Nano Dot Tek\u2122. Report NDT. 24 (2007), pp. 11\u201337. http:\/\/www.nanodottek.com"},{"key":"1340_CR26","volume-title":"Semiconductor Device Fundamentals","author":"RF Pierret","year":"1996","unstructured":"R.F. Pierret, P. Hall, Semiconductor Device Fundamentals (United States Edition, USA, 1996)"},{"key":"1340_CR27","volume-title":"Research on the Application of Fractional Calculus in Modern Signal Analysis and Processing","author":"Y Pu","year":"2006","unstructured":"Y. Pu, Research on the Application of Fractional Calculus in Modern Signal Analysis and Processing (Sichuan University, Chengdu, 2006)"},{"key":"1340_CR28","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511840685","volume-title":"Understanding Modern Transistors and Diodes","author":"LD Pulfrey","year":"2010","unstructured":"L.D. Pulfrey, Understanding Modern Transistors and Diodes (Cambridge University Press, Cambridge, 2010)"},{"key":"1340_CR29","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1016\/j.sigpro.2010.08.003","volume":"91","author":"M Richard","year":"2011","unstructured":"M. Richard, D.M. Ortigueira, P. Igor, T. Juan, On the fractional signals and systems. Signal Process. 91, 350\u2013371 (2011)","journal-title":"Signal Process."},{"key":"1340_CR30","volume-title":"Physics of Semiconductor Devices","author":"SM Sze","year":"1981","unstructured":"S.M. Sze, K.K. Ng, Physics of Semiconductor Devices, 2nd edn. (Wiley, New York, 1981)","edition":"2"},{"key":"1340_CR31","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1016\/j.cnsns.2018.11.008","volume":"70","author":"JA Tenreiro Machado","year":"2019","unstructured":"J.A. Tenreiro Machado, A.M. Lopes, Fractional-order modeling of a diode. Commun. Nonlinear Sci. Number Simul. 70, 343\u2013353 (2019)","journal-title":"Commun. Nonlinear Sci. Number Simul."},{"key":"1340_CR32","unstructured":"P.P. Wang, F.H. Branin, Jr., Multi-section network modeling of junction diodes, in Proceedings of 4th Annual Pittsburg Conference on Modeling and Simulation, Pittsburg, Penn (1973)"},{"issue":"5","key":"1340_CR33","doi-asserted-by":"publisher","first-page":"826","DOI":"10.1109\/94.326654","volume":"1","author":"S Westerlund","year":"1994","unstructured":"S. Westerlund, L. Ekstam, Capacitor theory. IEEE Trans. Dielectr. Electr. Insul. 1(5), 826\u2013839 (1994)","journal-title":"IEEE Trans. Dielectr. Electr. Insul."}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-019-01340-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00034-019-01340-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-019-01340-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,16]],"date-time":"2021-02-16T17:48:42Z","timestamp":1613497722000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00034-019-01340-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,10]]},"references-count":33,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2020,7]]}},"alternative-id":["1340"],"URL":"https:\/\/doi.org\/10.1007\/s00034-019-01340-6","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"type":"print","value":"0278-081X"},{"type":"electronic","value":"1531-5878"}],"subject":[],"published":{"date-parts":[[2020,1,10]]},"assertion":[{"value":"21 May 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 December 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 December 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 January 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}