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

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

Tutorial on designing and simulating a truncation spurs-free direct digital synthesizer (DDS) on a field-programmable gate array (FPGA)

Direct digital synthesis is a technique for using digital data processing blocks as a means to generate a frequency and phase tunable output signal referenced to a fixed-frequency precision clock source. Many telecommunication applications require such a high-speed switching, fine- tuning and superior quality signal source for their components. This thesis will introduce the direct digital synthesizer (DDS) and investigate the signal integrity issues associated with the DDS design. In order to minimize the size of the lookup table to save hardware and lower the power consumption, we normally truncate the phase word output from the phase accumulator in the standard approach of designing DDS. However, this process will generate spurious frequencies (spurs), which degrade the quality of the output signals. It is considered one of the main signal integrity issues in the DDS design. Previous research introduces a novel spurs-free truncation method for compressing the lookup table to avoid using phase truncation without significant hardware change. This thesis aims to implement this DDS with novel truncation spurs-free structure and test it in a practical environment. It does so by providing a tutorial on designing, implementing and simulating the DDS on an Altera DE2-115 FPGA using Altera Quartus II FPGA design software and ModelSim Simulator. The Verilog hardware description language is used as the development language. This thesis will describe entire designs of both DDS with traditional structure and DDS with novel truncation spurs-free structure. By comparing the outputs, it also examines the corresponding simulation results and verifies the improvement of the signal quality

Hybrid DDS-PLL based reconfigurable oscillators with high spectral purity for cognitive radio

Analytical, design and simulation studies on the performance optimization of reconfigurable architecture of a Hybrid DDS – PLL are presented in this thesis. The original contributions of this thesis are aimed towards the DDS, the dithering (spur suppression) scheme and the PLL. A new design of Taylor series-based DDS that reduces the dynamic power and number of multipliers is a significant contribution of this thesis. This thesis compares dynamic power and SFDR achieved in the design of varieties of DDS such as Quartic, Cubic, Linear and LHSC. This thesis proposes two novel schemes namely “Hartley Image Suppression” and “Adaptive Sinusoidal Interference Cancellation” overcoming the low noise floor of traditional dithering schemes. The simulation studies on a Taylor series-based DDS reveal an improvement in SFDR from 74 dB to 114 dB by using Least Mean Squares -Sinusoidal Interference Canceller (LM-SIC) with the noise floor maintained at -200 dB. Analytical formulations have been developed for a second order PLL to relate the phase noise to settling time and Phase Margin (PM) as well as to relate jitter variance and PM. New expressions relating phase noise to PM and lock time to PM are derived. This thesis derives the analytical relationship between the roots of the characteristic equation of a third order PLL and its performance metrics like PM, Gardner’s stability factor, jitter variance, spur gain and ratio of noise power to carrier power. This thesis presents an analysis to relate spur gain and capacitance ratio of a third order PLL. This thesis presents an analytical relationship between the lock time and the roots of its characteristic equation of a third order PLL. Through Vieta’s circle and Vieta’s angle, the performance metrics of a third order PLL are related to the real roots of its characteristic equation

Transceiver architectures and sub-mW fast frequency-hopping synthesizers for ultra-low power WSNs

Wireless sensor networks (WSN) have the potential to become the third wireless revolution after wireless voice networks in the 80s and wireless data networks in the late 90s. This revolution will finally connect together the physical world of the human and the virtual world of the electronic devices. Though in the recent years large progress in power consumption reduction has been made in the wireless arena in order to increase the battery life, this is still not enough to achieve a wide adoption of this technology. Indeed, while nowadays consumers are used to charge batteries in laptops, mobile phones and other high-tech products, this operation becomes infeasible when scaled up to large industrial, enterprise or home networks composed of thousands of wireless nodes. Wireless sensor networks come as a new way to connect electronic equipments reducing, in this way, the costs associated with the installation and maintenance of large wired networks. To accomplish this task, it is necessary to reduce the energy consumption of the wireless node to a point where energy harvesting becomes feasible and the node energy autonomy exceeds the life time of the wireless node itself. This thesis focuses on the radio design, which is the backbone of any wireless node. A common approach to radio design for WSNs is to start from a very simple radio (like an RFID) adding more functionalities up to the point in which the power budget is reached. In this way, the robustness of the wireless link is traded off for power reducing the range of applications that can draw benefit form a WSN. In this thesis, we propose a novel approach to the radio design for WSNs. We started from a proven architecture like Bluetooth, and progressively we removed all the functionalities that are not required for WSNs. The robustness of the wireless link is guaranteed by using a fast frequency hopping spread spectrum technique while the power budget is achieved by optimizing the radio architecture and the frequency hopping synthesizer Two different radio architectures and a novel fast frequency hopping synthesizer are proposed that cover the large space of applications for WSNs. The two architectures make use of the peculiarities of each scenario and, together with a novel fast frequency hopping synthesizer, proved that spread spectrum techniques can be used also in severely power constrained scenarios like WSNs. This solution opens a new window toward a radio design, which ultimately trades off flexibility, rather than robustness, for power consumption. In this way, we broadened the range of applications for WSNs to areas in which security and reliability of the communication link are mandatory

Techniques for high-performance digital frequency synthesis and phase control

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 183-190).This thesis presents a 3.6-GHz, 500-kHz bandwidth digital [delta][sigma] frequency synthesizer architecture that leverages a recently invented noise-shaping time-to-digital converter (TDC) and an all-digital quantization noise cancellation technique to achieve excellent in-band and out-of-band phase noise, respectively. In addition, a passive digital-to-analog converter (DAC) structure is proposed as an efficient interface between the digital loop filter and a conventional hybrid voltage-controlled oscillator (VCO) to create a digitally-controlled oscillator (DCO). An asynchronous divider structure is presented which lowers the required TDC range and avoids the divide-value-dependent delay variation. The prototype is implemented in a 0.13-am CMOS process and its active area occupies 0.95 mm². Operating under 1.5 V, the core parts, excluding the VCO output buffer, dissipate 26 mA. Measured phase noise at 3.67 GHz achieves -108 dBc/Hz and -150 dBc/Hz at 400 kHz and 20 MHz, respectively. Integrated phase noise at this carrier frequency yields 204 fs of jitter (measured from 1 kHz to 40 MHz). In addition, a 3.2-Gb/s delay-locked loop (DLL) in a 0.18-[mu]m CMOS for chip-tochip communications is presented. By leveraging the fractional-N synthesizer technique, this architecture provides a digitally-controlled delay adjustment with a fine resolution and infinite range. The provided delay resolution is less sensitive to the process, voltage, and temperature variations than conventional techniques. A new [delta][sigma] modulator enables a compact and low-power implementation of this architecture. A simple bang-bang detector is used for phase detection. The prototype operates at a 1.8-V supply voltage with a current consumption of 55 mA. The phase resolution and differential rms clock jitter are 1.4 degrees and 3.6 ps, respectively.by Chun-Ming Hsu.Ph.D

Digital enhancement techniques for fractional-N frequency synthesizers

Meeting the demand for unprecedented connectivity in the era of internet-of-things (IoT) requires extremely energy efficient operation of IoT nodes to extend battery life. Managing the data traffic generated by trillions of such nodes also puts severe energy constraints on the data centers. Clock generators that are essential elements in these systems consume significant power and therefore must be optimized for low power and high performance. The focus of this thesis is on improving the energy efficiency of frequency synthesizers and clocking modules by exploring design techniques at both the architectural and circuit levels. In the first part of this work, a digital fractional-N phase locked loop (FNPLL) that employs a high resolution time-to-digital converter (TDC) and a truly ΔΣ fractional divider to achieve low in-band noise with a wide bandwidth is presented. The fractional divider employs a digital-to-time converter (DTC) to cancel out ΔΣ quantization noise in time domain, thus alleviating TDC dynamic range requirements. The proposed digital architecture adopts a narrow range low-power time-amplifier based TDC (TA-TDC) to achieve sub 1ps resolution. Fabricated in 65nm CMOS process, the prototype PLL achieves better than -106dBc/Hz in-band noise and 3MHz PLL bandwidth at 4.5GHz output frequency using 50MHz reference. The PLL achieves excellent jitter performance of 490fsrms, while consumes only 3.7mW. This translates to the best reported jitter-power figure-of-merit (FoM) of -240.5dB among previously reported FNPLLs. Phase noise performance of ring oscillator based digital FNPLLs is severely compromised by conflicting bandwidth requirements to simultaneously suppress oscillator phase and quantization noise introduced by the TDC, ΔΣ fractional divider, and digital-to-analog converter (DAC). As a consequence, their FoM that quantifies the power-jitter tradeoff is at least 25dB worse than their LC-oscillator based FNPLL counterparts. In the second part of this thesis, we seek to close this performance gap by extending PLL bandwidth using quantization noise cancellation techniques and by employing a dual-path digital loop filter to suppress the detrimental impact of DAC quantization noise. A prototype was implemented in a 65nm CMOS process operating over a wide frequency range of 2.0GHz-5.5GHz using a modified extended range multi-modulus divider with seamless switching. The proposed digital FNPLL achieves 1.9psrms integrated jitter while consuming only 4mW at 5GHz output. The measured in-band phase noise is better than -96 dBc/Hz at 1MHz offset. The proposed FNPLL achieves wide bandwidth up to 6MHz using a 50 MHz reference and its FoM is -228.5dB, which is at about 20dB better than previously reported ring-based digital FNPLLs. In the third part, we propose a new multi-output clock generator architecture using open loop fractional dividers for system-on-chip (SoC) platforms. Modern multi-core processors use per core clocking, where each core runs at its own speed. The core frequency can be changed dynamically to optimize for performance or power dissipation using a dynamic frequency scaling (DFS) technique. Fast frequency switching is highly desirable as long as it does not interrupt code execution; therefore it requires smooth frequency transitions with no undershoots. The second main requirement in processor clocking is the capability of spread spectrum frequency modulation. By spreading the clock energy across a wide bandwidth, the electromagnetic interference (EMI) is dramatically reduced. A conventional PLL clock generation approach suffers from a slow frequency settling and limited spread spectrum modulation capabilities. The proposed open loop fractional divider architecture overcomes the bandwidth limitation in fractional-N PLLs. The fractional divider switches the output frequency instantaneously and provides an excellent spread spectrum performance, where precise and programmable modulation depth and frequency can be applied to satisfy different EMI requirements. The fractional divider has unlimited modulation bandwidth resulting in spread spectrum modulation with no filtering, unlike fractional-N PLL; consequently it achieves higher EMI reduction. A prototype fractional divider was implemented in a 65nm CMOS process, where the measured peak-to-peak jitter is less than 27ps over a wide frequency range from 20MHz to 1GHz. The total power consumption is about 3.2mW for 1GHz output frequency. The all-digital implementation of the divider occupies the smallest area of 0.017mm2 compared to state-of-the-art designs. As the data rate of serial links goes higher, the jitter requirements of the clock generator become more stringent. Improving the jitter performance of conventional PLLs to less than (200fsrms) always comes with a large power penalty (tens of mWs). This is due to the PLL coupled noise bandwidth trade-off, which imposes stringent noise requirements on the oscillator and/or loop components. Alternatively, an injection-locked clock multiplier (ILCM) provides many advantages in terms of phase noise, power, and area compared to classical PLLs, but they suffer from a narrow lock-in range and a high sensitivity to PVT variations especially at a large multiplication factor (N). In the fourth part of this thesis, a low-jitter, low-power LC-based ILCM with a digital frequency-tracking loop (FTL) is presented. The proposed FTL relies on a new pulse gating technique to continuously tune the oscillator's free-running frequency. The FTL ensures robust operation across PVT variations and resolves the race condition existing in injection locked PLLs by decoupling frequency tuning from the injection path. As a result, the phase locking condition is only determined by the injection path. This work also introduces an accurate theoretical large-signal analysis for phase domain response (PDR) of injection locked oscillators (ILOs). The proposed PDR analysis captures the asymmetric nature of ILO's lock-in range, and the impact of frequency error on injection strength and phase noise performance. The proposed architecture and analysis are demonstrated by a prototype fabricated in 65 nm CMOS process with active area of 0.25mm2. The prototype ILCM multiplies the reference frequency by 64 to generate an output clock in the range of 6.75GHz-8.25GHz. A superior jitter performance of 190fsrms is achieved, while consuming only 2.25mW power. This translates to a best FoM of -251dB. Unlike conventional PLLs, ILCMs have been fundamentally limited to only integer-N operation and cannot synthesize fractional-N frequencies. In the last part of this thesis, we extend the merits of ILCMs to fractional-N and overcome this fundamental limitation. We employ DTC-based QNC techniques in order to align injected pulses to the oscillator's zero crossings, which enables it to pull the oscillator toward phase lock, thus realizing a fractional-N ILCM. Fabricated in 65nm CMOS process, a prototype 20-bit fractional-N ILCM with an output range of 6.75GHz-8.25GHz consumes only 3.25mW. It achieves excellent jitter performance of 110fsrms and 175fsrms in integer- and fractional-N modes respectively, which translates to the best-reported FoM in both integer- (-255dB) and fractional-N (-252dB) modes. The proposed fractional-N ILCM also features the first-reported rapid on/off capability, where the transient absolute jitter performance at wake-up is bounded below 4ps after less than 4ns. This demonstrates almost instantaneous phase settling. This unique capability enables tremendous energy saving by turning on the clock multiplier only when needed. This energy proportional operation leverages idle times to save power at the system-level of wireline and wireless transceivers

A low-power quadrature digital modulator in 0.18um CMOS

Quadrature digital modulation techniques are widely used in modern communication systems because of their high performance and flexibility. However, these advantages come at the cost of high power consumption. As a result, power consumption has to be taken into account as a main design factor of the modulator.In this thesis, a low-power quadrature digital modulator in 0.18um CMOS is presented with the target system clock speed of 150 MHz. The quadrature digital modulator consists of several key blocks: quadrature direct digital synthesizer (QDDS), pulse shaping filter, interpolation filter and inverse sinc filter. The design strategy is to investigate different implementations for each block and compare the power consumption of these implementations. Based on the comparison results, the implementation that consumes the lowest power will be chosen for each block. First of all, a novel low-power QDDS is proposed in the thesis. Power consumption estimation shows that it can save up to 60% of the power consumption at 150 MHz system clock frequency compared with one conventional design. Power consumption estimation results also show that using two pulse shaping blocks to process I/Q data, cascaded integrator comb (CIC) interpolation structure, and inverse sinc filter with modified canonic signed digit (MCSD) multiplication consume less power than alternative design choices. These low-power blocks are integrated together to achieve a low-power modulator. The power consumption estimation after layout shows that it only consumes about 95 mW at 150 MHz system clock rate, which is much lower than similar commercial products. The designed modulator can provide a low-power solution for various quadrature modulators. It also has an output bandwidth from 0 to 75 MHz, configurable pulse shaping filters and interpolation filters, and an internal sin(x)/x correction filter

Design and Implementation of a Re-Configurable Arbitrary Signal Generator and Radio Frequency Spectrum Analyser

This research is focused on the design, simulation and implementation of a reconfigurable arbitrary signal generator and the design, simulation and implementation of a radio frequency spectrum analyser based on digital signal processing. Until recently, Application Specific Integrated Circuits (ASICs) were used to produce high performance re-configurable function and arbitrary waveform generators with comprehensive modulation capabilities. However, that situation is now changing with the availability of advanced but low cost Field Programmable Gate Arrays (FPGAs), which could be used as an alternative to ASICs in these applications. The availability of high performance FPGA families opens up the opportunity to compete with ASIC solutions at a fraction of the development cost of an ASIC solution. A fast digital signal processing algorithm for digital waveform generation, using primarily but not limited to Direct Digital Synthesis (DDS) technologies, developed and implemented in a field-configurable logic, with control provided by an embedded microprocessor replacing a high cost ASIC design appeared to be a very attractive concept. This research demonstrates that such a concept is feasible in its entirety. A fully functional, low-complexity, low cost, pulse, Gaussian white noise and DDS based function and arbitrary waveform generator, capable of being amplitude, frequency and phase modulated by an internally generated or external modulating signal was implemented in a low-cost FPGA. The FPGA also included the capabilities to perform pulse width modulation and pulse delay modulation on pulse waveforms. Algorithms to up-convert the sampling rate of the external modulating signal using Cascaded Integrator Comb (CIC) filters and using interpolation method were analysed. Both solutions were implemented to compare their hardware complexities. Analysis of generating noise with user-defined distribution is presented. The ability of triggering the generator by an internally generated or an external event to generate a burst of waveforms where the time between the trigger signal and waveform output is fixed was also implemented in the FPGA. Finally, design of interface to a microprocessor to provide control of the versatile waveform generator was also included in the FPGA. This thesis summarises the literature, design considerations, simulation and implementation of the generator design. The second part of the research is focused on radio frequency spectrum analysis based on digital signal processing. Most existing spectrum analysers are analogue in nature and their complexity increases with frequency. Therefore, the possibility of using digital techniques for spectrum analysis was considered. The aim was to come up with digital system architecture for spectrum analysis and to develop and implement the new approach on a suitable digital platform. This thesis analyses the current literature on shifting algorithms to remove spurious responses and highlights its drawbacks. This thesis also analyses existing literature on quadrature receivers and presents novel adaptation of the existing architectures for application in spectrum analysis. A wide band spectrum analyser receiver with compensation for gain and phase imbalances in the Radio Frequency (RF) input range, as well as compensation for gain and phase imbalances within the Intermediate Frequency (IF) pass band complete with Resolution Band Width (RBW) filtering, Video Band Width (VBW) filtering and amplitude detection was implemented in a low cost FPGA. The ability to extract the modulating signal from a frequency or amplitude modulated RF signal was also implemented. The same family of FPGA used in the generator design was chosen to be the digital platform for this design. This research makes arguments for the new architecture and then summarises the literature, design considerations, simulation and implementation of the new digital algorithm for the radio frequency spectrum analyser