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Linear Programming Design of Semi-Digital FIR Filter and Sigma Delta Modulator for VDSL2 Transmitter
Linköping University, Department of Electrical Engineering, Electronics System. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Electronics System. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Computer Engineering. Linköping University, The Institute of Technology.ORCID iD: 0000-0003-3470-3911
2014 (English)In: 2014 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS (ISCAS), IEEE , 2014, 2465-2468 p.Conference paper (Refereed)
Abstract [en]

An oversampled digital-to-analog converter including digital Sigma Delta modulator and semi-digital FIR filter can be employed in the transmitter of the VDSL2 technology. To select the optimum set of coefficients for the semi-digital FIR filter, an integer optimization problem is formulated in this work, where the model includes the FIR filter magnitude metrics as well as Sigma Delta modulator noise transfer function. The semi-digital FIR filter is optimized with respect to magnitude constraints according to the International Telecommunication Union Power Spectral Density mask for VDSL2 technology and minimizing analog cost as the objective function. Utilizing the semi-digital FIR filter with one bit DACs, high linearity required in high-bandwidth profiles of VDSL2, can be achieved. The resolution of the conventional DACs are limited by the mismatch between DAC unit elements. By utilizing one-bit DACs in semi-digital FIR filter, there will be less degradation caused by mismatch between unit elements. The optimization problem is solved in two conditions; fixed passband gain and variable passband gain. It is shown in this paper that 38% saving in total number of unit elements can be achieved by employing variable passband gain in the optimization problem.

Place, publisher, year, edition, pages
IEEE , 2014. 2465-2468 p.
Keyword [en]
Digital-to-analog converter; DAC; oversampled DAC; semi-digital FIR filter; SDFIR filter; digital Sigma Delta modulator; integer optimization
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
URN: urn:nbn:se:liu:diva-113793DOI: 10.1109/ISCAS.2014.6865672ISI: 000346488600616ScopusID: 2-s2.0-84907381691ISBN: 978-1-4799-3432-4OAI: diva2:785064
IEEE International Symposium on Circuits and Systems (ISCAS), 1-5 June, Melbourne, Australia.
Available from: 2015-02-02 Created: 2015-01-30 Last updated: 2015-03-26Bibliographically approved
In thesis
1. On High-Speed Digital-to-Analog Converters and Semi-Digital FIR Filters
Open this publication in new window or tab >>On High-Speed Digital-to-Analog Converters and Semi-Digital FIR Filters
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

High-speed and high-resolution digital-to-analog converters (DACs) are vital components in all telecommunication systems. Radio-frequency digital-to-analog converter (RFDAC) provides high-speed and high-resolution conversion from digital domain to an analog signal. RFDACs can be employed in direct-conversion radio transmitter architectures. The idea of RFDAC is to utilize an oscillatory pulse-amplitude modulation instead of the conventional zero-order hold pulse amplitude modulation, which results in DAC output spectrum to have high energy high-frequency lobe, other than the Nyquist main lobe. The frequency of the oscillatory pulse can be chosen, with respect to the sample frequency, such that the aliasing images of the signal at integer multiples of the sample frequency are landed in the high-energy high-frequency lobes of the DAC frequency response. Therefore the high-frequency images of the signal can be used as the output of the DAC, i.e., no need to the mixing stage for frequency up-conversion after the DAC in the radio transmitter. The mixing stage however is not eliminated but it is rather moved into the DAC elements and therefore the local oscillator (LO) signal with high frequency should be delivered to each individual DAC element.

In direct-conversion architecture of IQ modulators which utilize the RFDAC technique, however, there is a problem of finite image rejection. The origin of this problem is the different polarity of the spectral response of the oscillatory pulse-amplitude modulation in I and Q branches. The conditions where this problem can be alleviated in IQ modulator employing RFDACs is also discussed in this work.

ΣΔ modulators are used preceding the DAC in the transmitter chain to reduce the digital signal’s number of bits, still maintain the same resolution. By utilizing the ΣΔ modulator now the total number of DAC elements has decreased and therefore the delivery of the high-frequency LO signal to each DAC element is practical. One of the costs of employing ΣΔ modulator, however, is a higher quantization noise power at the output of the DAC. The quantization noise is ideally spectrally shaped to out-of-band frequencies by the ΣΔ modulator. The shaped noise which usually has comparatively high power must be filtered out to fulfill the radio transmission spectral mask requirement.

Semi-digital FIR filter can be used in the context of digital-to-analog conversion, cascaded with ΣΔ modulator to filter the out-of-band noise by the modulator. In the same time it converts the signal from digital domain to an analog quantity. In general case, we can have a multi-bit, semi-digital FIR filter where each tap of the filter is realized with a sub-DAC of M bits. The delay elements are also realized with M-bit shift registers. If the output of the modulator is given by a single bit, the semi-digital FIR filter taps are simply controlled by a single switch assuming a current-steering architecture DAC. One of the major advantages is that the static linearity of the DAC is optimum. Since there are only two output levels available in the DAC, the static transfer function, regardless of the mismatch errors, is always given by a straight line.

In this work, the design of SDFIR filter is done through an optimization procedure where the ΣΔ noise transfer function is also taken into account. Different constraints are defined for different applications in formulation of the SDFIR optimization problem. For a given radio transmitter application the objective function can be defined as, e.g., the hardware cost for SDFIR implementation while the constraint can be set to fulfill the radio transmitter spectral emission mask.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2014. 52 p.
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1708
DAC, RFDAC, SDFIR, FIR, semi-digital FIR filter, digital-to-analog converter, D/A converter, data converter, mixed-signal integrated circuits, mixer DAC, IQ modulator, transmitter
National Category
Signal Processing
urn:nbn:se:liu:diva-114274 (URN)10.3384/lic.diva-114274 (DOI)978-91-7519-122-5 (print) (ISBN)
2015-02-13, Visionen, Building B, Campus Valla, Linköping University, Linköping, 10:15 (English)
Available from: 2015-02-19 Created: 2015-02-16 Last updated: 2015-02-19Bibliographically approved

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