Optimization problem formulation for semi-digital FIR digital-to-analog converter considering coefficients precision and analog metrics
Optimization problem formulation for semi-digital FIR digital-to-analog converter (SDFIR DAC) is investigated in this work. Magnitude and energy metrics with variable coefficient precision are defined for cascaded digital Σ Δ modulators, semi-digital FIR filter, and Sinc roll-off frequency response...
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| Published in | Analog integrated circuits and signal processing Vol. 99; no. 2; pp. 287 - 298 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
15.05.2019
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0925-1030 1573-1979 1573-1979 |
| DOI | 10.1007/s10470-018-1370-7 |
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| Abstract | Optimization problem formulation for semi-digital FIR digital-to-analog converter (SDFIR DAC) is investigated in this work. Magnitude and energy metrics with variable coefficient precision are defined for cascaded digital
Σ
Δ
modulators, semi-digital FIR filter, and
Sinc
roll-off frequency response of the DAC. A set of analog metrics as hardware cost is also defined to be included in SDFIR DAC optimization problem formulation. It is shown in this work, that hardware cost of the SDFIR DAC, can be significantly reduced by introducing flexible coefficient precision while the SDFIR DAC is not over designed either. Different use-cases are selected to demonstrate the optimization problem formulations. A combination of magnitude metric, energy metric, coefficient precision and analog metrics are used in different use cases of optimization problem formulation and solved to find out the optimum set of analog FIR taps. A new method with introducing the variable coefficient precision in optimization procedure was proposed to avoid non-convex optimization problems. It was shown that up to 22% in the total number of unit elements of the SDFIR filter can be saved when targeting the analog metric as the optimization objective subject to magnitude constraint in pass-band and stop-band. |
|---|---|
| AbstractList | Optimization problem formulation for semi-digital FIR digital-to-analog converter (SDFIR DAC) is investigated in this work. Magnitude and energy metrics with variable coefficient precision are defined for cascaded digital
Σ
Δ
modulators, semi-digital FIR filter, and
Sinc
roll-off frequency response of the DAC. A set of analog metrics as hardware cost is also defined to be included in SDFIR DAC optimization problem formulation. It is shown in this work, that hardware cost of the SDFIR DAC, can be significantly reduced by introducing flexible coefficient precision while the SDFIR DAC is not over designed either. Different use-cases are selected to demonstrate the optimization problem formulations. A combination of magnitude metric, energy metric, coefficient precision and analog metrics are used in different use cases of optimization problem formulation and solved to find out the optimum set of analog FIR taps. A new method with introducing the variable coefficient precision in optimization procedure was proposed to avoid non-convex optimization problems. It was shown that up to 22% in the total number of unit elements of the SDFIR filter can be saved when targeting the analog metric as the optimization objective subject to magnitude constraint in pass-band and stop-band. Optimization problem formulation for semi-digital FIR digital-to-analog converter (SDFIR DAC) is investigated in this work. Magnitude and energy metrics with variable coefficient precision are defined for cascaded digital sigma modulators, semi-digital FIR filter, and Sinc roll-off frequency response of the DAC. A set of analog metrics as hardware cost is also defined to be included in SDFIR DAC optimization problem formulation. It is shown in this work, that hardware cost of the SDFIR DAC, can be significantly reduced by introducing flexible coefficient precision while the SDFIR DAC is not over designed either. Different use-cases are selected to demonstrate the optimization problem formulations. A combination of magnitude metric, energy metric, coefficient precision and analog metrics are used in different use cases of optimization problem formulation and solved to find out the optimum set of analog FIR taps. A new method with introducing the variable coefficient precision in optimization procedure was proposed to avoid non-convex optimization problems. It was shown that up to 22% in the total number of unit elements of the SDFIR filter can be saved when targeting the analog metric as the optimization objective subject to magnitude constraint in pass-band and stop-band. Optimization problem formulation for semi-digital FIR digital-to-analog converter (SDFIR DAC) is investigated in this work. Magnitude and energy metrics with variable coefficient precision are defined for cascaded digital ΣΔ modulators, semi-digital FIR filter, and Sinc roll-off frequency response of the DAC. A set of analog metrics as hardware cost is also defined to be included in SDFIR DAC optimization problem formulation. It is shown in this work, that hardware cost of the SDFIR DAC, can be significantly reduced by introducing flexible coefficient precision while the SDFIR DAC is not over designed either. Different use-cases are selected to demonstrate the optimization problem formulations. A combination of magnitude metric, energy metric, coefficient precision and analog metrics are used in different use cases of optimization problem formulation and solved to find out the optimum set of analog FIR taps. A new method with introducing the variable coefficient precision in optimization procedure was proposed to avoid non-convex optimization problems. It was shown that up to 22% in the total number of unit elements of the SDFIR filter can be saved when targeting the analog metric as the optimization objective subject to magnitude constraint in pass-band and stop-band. |
| Author | Wikner, J. Jacob Gustafsson, Oscar Sadeghifar, M. Reza |
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| Keywords | Optimization of SDFIR DAC Semi-digital FIR filter Digital Sigma-delta modulator Analog FIR |
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| References | WebbJLHMunsonDCChebyshev optimization of sparse FIR filters using linear programming with an application to beamformingIEEE Transactions on Signal Processing19964481912192210.1109/78.533712 OzgunMTTorlakMEffects of random delay errors in continuous-time semi-digital transversal filtersIEEE Transactions on Circuits and Systems I: Regular Papers201461118319010.1109/TCSI.2013.2264692 PetragliaAFundamental frequency response bounds of direct-form recursive switched-capacitor filters with capacitance mismatchIEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing200148434035010.1109/82.933792 LinACYSuDKHesterRKWooleyBAA CMOS oversampled DAC with multi-bit semi-digital filtering and boosted subcarrier SNR for ADSL central office modemsIEEE Journal of Solid-State Circuits200641486887510.1109/JSSC.2006.870919 NorsworthySRSchreierRTemesGCDelta-sigma data converters: Theory, design, and simulation1996New YorkIEEE Press10.1109/9780470544358 Gebreyohannes, F. T., Frappé, A., & Kaiser, A. (2015). Semi-digital FIR DAC for low power single carrier IEEE 802.11ad 60 GHz transmitter. In Proceedings of IEEE 13th International New Circuits and Systems Conference (NEWCAS) (pp. 1–4). https://doi.org/10.1109/NEWCAS.2015.7182016. Doorn, T. S., Tuijl, E., Schinkel, D., Annema, A. J., Berkhout, M., & Nauta, B. (2005). An audio FIR-DAC in a BCD process for high power class-D amplifiers. In Proceedings of the 31st European Solid-State Circuits Conference ESSCIRC. https://doi.org/10.1109/ESSCIR.2005.1541659. 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Employing incremental sigma delta DACs for high resolution SAR ADC. In Proceedings of 21st IEEE International Conference on Electronics, Circuits and Systems (ICECS) (pp. 132–135). https://doi.org/10.1109/ICECS.2014.7049939. Su, D., & Wooley, B. (1993). A CMOS oversampling D/A converter with a current-mode semi-digital reconstruction filter. In 40th IEEE International Solid-State Circuits Conference (ISSCC)—Digest of Technical Papers (pp. 230–231). https://doi.org/10.1109/ISSCC.1993.280036. Sadeghifar, M. R., Wikner, J. J., & Gustafsson, O. (2014). Linear programming design of semi-digital FIR filter and ΣΔ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Sigma \Delta$$\end{document} modulator for VDSL2 transmitter. 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J. (2001). Studies on CMOS digital-to-analog converters. Ph.D. thesis, Linköping University, Sweden. Dissertation No: 667. 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| References_xml | – reference: BarkinDLinASuDWooleyBA CMOS oversampling bandpass cascaded D/A converter with digital FIR and current-mode semi-digital filteringIEEE Journal of Solid-State Circuits200439458559310.1109/JSSC.2004.825245 – reference: LinACYSuDKHesterRKWooleyBAA CMOS oversampled DAC with multi-bit semi-digital filtering and boosted subcarrier SNR for ADSL central office modemsIEEE Journal of Solid-State Circuits200641486887510.1109/JSSC.2006.870919 – reference: ParksTMcClellanJChebyshev approximation for nonrecursive digital filters with linear phaseIEEE Transactions on Circuit Theory197219218919410.1109/TCT.1972.1083419 – reference: YuXSunYRheeWWangZAn FIR-embedded noise filtering method for ΔΣ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \Sigma $$\end{document} fractional-N PLL clock generatorsIEEE Journal of Solid-State Circuits20094492426243610.1109/JSSC.2009.2021086 – reference: GebreyohannesFTFrappéAKaiserAA configurable transmitter architecture for IEEE 802.11ac and 802.11ad standardsIEEE Transactions on Circuits and Systems II: Express Briefs201663191310.1109/TCSII.2015.2468920 – reference: WebbJLHMunsonDCChebyshev optimization of sparse FIR filters using linear programming with an application to beamformingIEEE Transactions on Signal Processing19964481912192210.1109/78.533712 – reference: Gebreyohannes, F. T., Frappé, A., & Kaiser, A. (2015). Semi-digital FIR DAC for low power single carrier IEEE 802.11ad 60 GHz transmitter. 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| SubjectTerms | Circuits and Systems Coefficients Convexity Digital to analog conversion Digital to analog converters Electrical Engineering Engineering FIR filters Formulations Frequency response Hardware Modulators Optimization Signal,Image and Speech Processing |
| Title | Optimization problem formulation for semi-digital FIR digital-to-analog converter considering coefficients precision and analog metrics |
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