Master Thesis Study on a second-order bandpass Σ -modulator for flexible AD-conversion Hanna Svensson LiTH - ISY - EX -- 08/4064 -- SE
Study on a second-order bandpass Σ -modulator for flexible AD-conversion Electronics systems, Linköpings Universitet Hanna Svensson LiTH - ISY - EX -- 08/4064 -- SE Supervisor: Per Löwenborg, Electronics systems, Linköpings Universitet Examiner: Per Löwenborg, Electronics systems, Linköpings Universitet Linköping: February 2008
Avdelning, Institution Division, Department Institutionen för systemteknik 5 83 LINKÖPING SWEDEN Datum Date February 2008 Språk Language x Svenska/Swedish Engelska/English Rapporttyp Report category x Licentiatavhandling Examensarbete C-uppsats D-uppsats Övrig rapport ISBN ISRN LiTH - ISY - EX -- 08/4064 -- SE ISSN 0348-2960 Serietitel och serienummer Title of series, numbering URL för elektronisk version http://www.ep.liu.se Titel Title Study on a second-order bandpass Σ -modulator for flexible ADconversion Författare Author Hanna Svensson Sammanfattning Abstract An important component in many communication system is the digital to analog converter. The component is needed in order to convert real world analog quantities to digital quantities which are easier to process. As the market for hand held devices with wireless communication with the outer world has increased new approaches for sharing the frequency spectrum are needed. Therefore it would be interesting to look at the possibility to design an analog to digital converter that, in runtime, can change the frequency band converted, and hence the used standard. This thesis study one of the possibilities to design such an ADC, as a Σ modulator, and more precise the structure called Cascade of resonators with distributed feedback and input (CRFB). The order of the modulator in this study is two. Nyckelord Keyword Sigma-Delta, Delta-Sigma, bandpass modulators, flexible ADC.
Abstract An important component in many communication system is the digital to analog converter. The component is needed in order to convert real world analog quantities to digital quantities which are easier to process. As the market for hand held devices with wireless communication with the outer world has increased new approaches for sharing the frequency spectrum are needed. Therefore it would be interesting to look at the possibility to design an analog to digital converter that, in runtime, can change the frequency band converted, and hence the used standard. This thesis study one of the possibilities to design such an ADC, as a Σ modulator, and more precise the structure called Cascade of resonators with distributed feedback and input (CRFB). The order of the modulator in this study is two. Keywords: Sigma-Delta, Delta-Sigma, bandpass modulators, flexible ADC. Svensson, 2008. vii
viii
119 PC Coeff. disturbed one by one. no: 10 : 4 PC Coeff. disturbed one by one. no: 47 : 4 PC Coeff. disturbed one by one. no: 95 : 4 PC Coeff. disturbed one by one. no: 150 : 4 Figure D.6: when perturbing every coefficient one at a time. For power complementary structure 4.
120 Appendix D. Sensitivity SC Coeff. disturbed one by one. no: 10 : 4 SC Coeff. disturbed one by one. no: 47 : 4 SC Coeff. disturbed one by one. no: 95 : 4 SC Coeff. disturbed one by one. no: 150 : 4 Figure D.7: when perturbing every coefficient one at a time. For strict complementary structure 4.
121 AP Coeff. disturbed one by one. no: 10 : 4 AP Coeff. disturbed one by one. no: 47 : 4 AP Coeff. disturbed one by one. no: 95 : 4 AP Coeff. disturbed one by one. no: 150 : 4 Figure D.8: when perturbing every coefficient one at a time. For allpass structure 4.
122 Appendix D. Sensitivity All coeff. all AP structures, eps: 1000 no: 10 All coeff. all AP structures, eps: 1000 no: 47 All coeff. all AP structures, eps: 1000 no: 100 All coeff. all AP structures, eps: 1000 no: 150 Figure D.9: Sensitvity
123 All coeff. for all PC structures, eps: 1000 no: 10 All coeff. for all PC structures, eps: 1000 no: 47 All coeff. for all PC structures, eps: 1000 no: 100 All coeff. for all PC structures, eps: 1000 no: 150 Figure D.10: Sensitvity
124 Appendix D. Sensitivity All coeff. all SC structures, eps: 1000 no: 10 All coeff. all SC structures, eps: 1000 no: 47 All coeff. all SC structures, eps: 1000 no: 100 All coeff. all SC structures, eps: 1000 no: 150 Figure D.11: Sensitvity
LINKÖPING UNIVERSITY ELECTRONIC PRESS Copyright The publishers will keep this document online on the Internet - or its possible replacement - for a period of 25 years from the date of publication barring exceptional circumstances. The online availability of the document implies a permanent permission for anyone to read, to download, to print out single copies for your own use and to use it unchanged for any non-commercial research and educational purpose. Subsequent transfers of copyright cannot revoke this permission. All other uses of the document are conditional on the consent of the copyright owner. The publisher has taken technical and administrative measures to assure authenticity, security and accessibility. According to intellectual property law the author has the right to be mentioned when his/her work is accessed as described above and to be protected against infringement. For additional information about the Linköping University Electronic Press and its procedures for publication and for assurance of document integrity, please refer to its WWW home page: http://www.ep.liu.se/ Upphovsrätt Detta dokument hålls tillgängligt på Internet - eller dess framtida ersättare - under 25 år från publiceringsdatum under förutsättning att inga extraordinära omständigheter uppstår. Tillgång till dokumentet innebär tillstånd för var och en att läsa, ladda ner, skriva ut enstaka kopior för enskilt bruk och att använda det oförändrat för ickekommersiell forskning och för undervisning. Överföring av upphovsrätten vid en senare tidpunkt kan inte upphäva detta tillstånd. All annan användning av dokumentet kräver upphovsmannens medgivande. För att garantera äktheten, säkerheten och tillgängligheten finns det lösningar av teknisk och administrativ art. Upphovsmannens ideella rätt innefattar rätt att bli nämnd som upphovsman i den omfattning som god sed kräver vid användning av dokumentet på ovan beskrivna sätt samt skydd mot att dokumentet ändras eller presenteras i sådan form eller i sådant sammanhang som är kränkande för upphovsmannens litterära eller konstnärliga anseende eller egenart. För ytterligare information om Linköping University Electronic Press se förlagets hemsida http://www.ep.liu.se/ c 2008, Hanna Svensson Svensson, 2008. 125