Master Thesis. Study on a second-order bandpass Σ -modulator for flexible AD-conversion Hanna Svensson. LiTH - ISY - EX -- 08/ SE

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1 Master Thesis Study on a second-order bandpass Σ -modulator for flexible AD-conversion Hanna Svensson LiTH - ISY - EX -- 08/ SE

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3 Study on a second-order bandpass Σ -modulator for flexible AD-conversion Electronics systems, Linköpings Universitet Hanna Svensson LiTH - ISY - EX -- 08/ SE Supervisor: Per Löwenborg, Electronics systems, Linköpings Universitet Examiner: Per Löwenborg, Electronics systems, Linköpings Universitet Linköping: February 2008

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5 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/ SE ISSN Serietitel och serienummer Title of series, numbering URL för elektronisk version 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.

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7 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, vii

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9 119 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.

10 120 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.

11 121 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.

12 122 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

13 123 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

14 124 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

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