Graduate Thesis Or Dissertation
 

Modeling and analysis of spur structure of digital-to-time conversion based frequency synthesizers

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  • Frequency synthesizers are critical components of all communication systems. This thesis considers the issue of undesirable frequency spurs of a relatively recent type of frequency synthesis architecture called digital-to-time conversion (DTC). The DTC-based frequency synthesis architecture has important performance benefits over older frequency synthesizers, such as fast frequency switching, large frequency range and fine frequency resolution. A DTC-based frequency synthesizer requires less power than a traditional direct synthesis based synthesizer with comparable frequency range, resolution and switching time. The DTC architecture is also easily scalable to newer low-cost digital complementary metal-oxide-semiconductor (CMOS) integrated circuit (IC) fabrication technologies. However, the DTC architecture suffers from an important undesirable characteristic: sub-harmonic spurious tones, hereafter, referred to as spurs. Spurs have undesirable effects in both the transmitter and the receiver. In a transmitter, spurs create an out-of-band emission of power that may breach the spectral emission mask set by regulatory agencies to enable co-existence of multiple transmitters in a crowded frequency spectrum. In a receiver, an inopportune-located spur in the local oscillator (LO) signal can mix an out-of-band strong interfering signal into the baseband on top of a mixed-down weak desirable signal. Unlike harmonic spurs that are known to be at multiples of the carrier frequency, sub-harmonic spurs are especially problematic as they have been difficult to predict as part of the design process. In fact, the spur patterns for most pairs of closely placed desired output frequencies for a DTC-based frequency synthesizer are seemingly unrelated. While one output frequency setting might have an output spectrum with only a few spurs, many other close-by output frequency settings might have output spectra with many weaker spurs. The primary contribution of this thesis is the development of spur creation models and analysis tools that can predict spur spectrum and spur power levels for a DTC-based frequency synthesizer. This is an important contribution for assuring achievable performance of frequency synthesizer during the design process. The modeling approach has been successful in accounting of more than 99% of spur spectral locations. Predicted power levels for more than 95% are within 10 dB of actual fabricated DTC-based frequency synthesizer ICs. The results developed in this thesis allow for an understanding of the relationship between spur patterns for different selected output frequencies. In the research reported in this thesis, the spur spectrum for a selected output frequency is shown to be due to periodic occurrences of errors in the locations of rising and falling edges of the output signal. Error sequences for different selected output frequencies are shown to be related in a way that can be exploited by application of the axis-scaling property of the Discrete Fourier Transform (DFT). The axis-scaling property of the DFT relates the transforms of two sets of sequences that are predictably permutated versions of each other. Their respective transforms are also (differently) permutated versions of each other. One key insight made in this thesis is the discovery that the time-domain errors for all output frequencies can be classified into a very small number of error sequence classes. All error sequences within a class are shown to be predictable permutations of each other. This insight along with the DFT axis-scaling property permits the respective spur spectra to be classified into error spectra classes. All error spectra within a spur spectra class are predictable permutations of each other. There are two sources of edge errors: quantization error and buffer delay errors. This classification of spur spectra to a few classes is shown to be possible for both sources of errors. In this thesis, the case of quantization-only error is considered first. The analysis is then extended to the case when both sources of error are present. As a result of the modeling and analytical techniques developed for spur spectra classification described in this thesis, design tools have been created to predict the spur spectra of DTC-based synthesizer designs for all possible selected output frequencies.
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