Post Conversion Correction of Non-Linear Mismatches for Time Interleaved Analog-to-Digital Converters

Time Interleaved Analog-to-Digital Converters (TI-ADCs) utilize an architecture which enables conversion rates well beyond the capabilities of a single converter while preserving most or all of the other performance characteristics of the converters on which said architecture is based. Most of the approaches discussed here are independent of architecture; some solutions take advantage of specific architectures. Chapter 1 provides the problem formulation and reviews the errors found in ADCs as well as a brief literature review of available TI-ADC error correction solutions. Chapter 2 presents the methods and materials used in implementation as well as extend the state of the art for post conversion correction. Chapter 3 presents the simulation results of this work and Chapter 4 concludes the work. The contribution of this research is three fold: A new behavioral model was developed in SimulinkTM and MATLABTM to model and test linear and nonlinear mismatch errors emulating the performance data of actual converters. The details of this model are presented as well as the results of cumulant statistical calculations of the mismatch errors which is followed by the detailed explanation and performance evaluation of the extension developed in this research effort. Leading post conversion correction methods are presented and an extension with derivations is presented. It is shown that the data converter subsystem architecture developed is capable of realizing better performance of those currently reported in the literature while having a more efficient implementation

Time-Interleaved Analog-to-Digital-Converters: Modeling, Blind Identification and Digital Correction of Frequency Response Mismatches

Analog-to-digital-conversion enables utilization of digital signal processing (DSP) in many applications today such as wireless communication, radar and electronic warfare. DSP is the favored choice for processing information over analog signal processing (ASP) because it can typically offer more flexibility, computational power, reproducibility, speed and accuracy when processing and extracting information. Software defined radio (SDR) receiver is one clear example of this, where radio frequency waveforms are converted into digital form as close to the antenna as possible and all the processing of the information contained in the received signal is extracted in a configurable manner using DSP. In order to achieve such goals, the information collected from the real world signals, which are commonly analog in their nature, must be converted into digital form before it can be processed using DSP in the respective systems. The common trend in these systems is to not only process ever larger bandwidths of data but also to process data in digital format at ever higher processing speeds with sufficient conversion accuracy. So the analog-to-digital-converter (ADC), which converts real world analog waveforms into digital form, is one of the most important cornerstones in these systems.The ADC must perform data conversion at higher and higher rates and digitize ever-increasing bandwidths of data. In accordance with the Nyquist-Shannon theorem, the conversion rate of the ADC must be suffcient to accomodate the BW of the signal to be digitized, in order to avoid aliasing. The conversion rate of the ADC can in general be increased by using parallel ADCs with each ADC performing the sampling at mutually different points in time. Interleaving the outputs of each of the individual ADCs provides then a higher digitization output rate. Such ADCs are referred to as TI-ADC. However, the mismatches between the ADCs cause unwanted spurious artifacts in the TI-ADC’s spectrum, ultimately leading to a loss in accuracy in the TI-ADC compared to the individual ADCs. Therefore, the removal or correction of these unwanted spurious artifacts is essential in having a high performance TI-ADC system.In order to remove the unwanted interleaving artifacts, a model that describes the behavior of the spurious distortion products is of the utmost importance as it can then facilitate the development of efficient digital post-processing schemes. One major contribution of this thesis consists of the novel and comprehensive modeling of the spurious interleaving mismatches in different TI-ADC scenarios. This novel and comprehensive modeling is then utilized in developing digital estimation and correction methods to remove the mismatch induced spurious artifacts in the TI-ADC’s spectrum and recovering its lost accuracy. Novel and first of its kind digital estimation and correction methods are developed and tested to suppress the frequency dependent mismatch spurs found in the TI-ADCs. The developed methods, in terms of the estimation of the unknown mismatches, build on statistical I/Q signal processing principles, applicable without specifically tailored calibration signals or waveforms. Techniques to increase the analog BW of the ADC are also analyzed and novel solutions are presented. The interesting combination of utilizing I/Q downconversion in conjunction with TI-ADC is examined, which not only extends the TI-ADC’s analog BW but also provides flexibility in accessing the radio spectrum. Unwanted spurious components created during the ADC’s bandwidth extension process are also analyzed and digital correction methods are developed to remove these spurs from the spectrum. The developed correction techniques for the removal of the undesired interleaving mismatch artifacts are validated and tested using various HW platforms, with up to 1 GHz instantaneous bandwidth. Comprehensive test scenarios are created using measurement data obtained from HW platforms, which are used to test and evaluate the performance of the developed interleaving mismatch estimation and correction schemes, evidencing excellent performance in all studied scenarios. The findings and results presented in this thesis contribute towards increasing the analog BW and conversion rate of ADC systems without losing conversion accuracy. Overall, these developments pave the way towards fulfilling the ever growing demands on the ADCs in terms of higher conversion BW, accuracy and speed

Nonlinear models and algorithms for RF systems digital calibration

Focusing on the receiving side of a communication system, the current trend in pushing the digital domain ever more closer to the antenna sets heavy constraints on the accuracy and linearity of the analog front-end and the conversion devices. Moreover, mixed-signal implementations of Systems-on-Chip using nanoscale CMOS processes result in an overall poorer analog performance and a reduced yield. To cope with the impairments of the low performance analog section in this "dirty RF" scenario, two solutions exist: designing more complex analog processing architectures or to identify the errors and correct them in the digital domain using DSP algorithms. In the latter, constraints in the analog circuits' precision can be offloaded to a digital signal processor. This thesis aims at the development of a methodology for the analysis, the modeling and the compensation of the analog impairments arising in different stages of a receiving chain using digital calibration techniques. Both single and multiple channel architectures are addressed exploiting the capability of the calibration algorithm to homogenize all the channels' responses of a multi-channel system in addition to the compensation of nonlinearities in each response. The systems targeted for the application of digital post compensation are a pipeline ADC, a digital-IF sub-sampling receiver and a 4-channel TI-ADC. The research focuses on post distortion methods using nonlinear dynamic models to approximate the post-inverse of the nonlinear system and to correct the distortions arising from static and dynamic errors. Volterra model is used due to its general approximation capabilities for the compensation of nonlinear systems with memory. Digital calibration is applied to a Sample and Hold and to a pipeline ADC simulated in the 45nm process, demonstrating high linearity improvement even with incomplete settling errors enabling the use of faster clock speeds. An extended model based on the baseband Volterra series is proposed and applied to the compensation of a digital-IF sub-sampling receiver. This architecture envisages frequency selectivity carried out at IF by an active band-pass CMOS filter causing in-band and out-of-band nonlinear distortions. The improved performance of the proposed model is demonstrated with circuital simulations of a 10th-order band pass filter, realized using a five-stage Gm-C Biquad cascade, and validated using out-of-sample sinusoidal and QAM signals. The same technique is extended to an array receiver with mismatched channels' responses showing that digital calibration can compensate the loss of directivity and enhance the overall system SFDR. An iterative backward pruning is applied to the Volterra models showing that complexity can be reduced without impacting linearity, obtaining state-of-the-art accuracy/complexity performance. Calibration of Time-Interleaved ADCs, widely used in RF-to-digital wideband receivers, is carried out developing ad hoc models because the steep discontinuities generated by the imperfect canceling of aliasing would require a huge number of terms in a polynomial approximation. A closed-form solution is derived for a 4-channel TI-ADC affected by gain errors and timing skews solving the perfect reconstruction equations. A background calibration technique is presented based on cyclo-stationary filter banks architecture. Convergence speed and accuracy of the recursive algorithm are discussed and complexity reduction techniques are applied

Analysis and design of low-power data converters

In a large number of applications the signal processing is done exploiting both analog and digital signal processing techniques. In the past digital and analog circuits were made on separate chip in order to limit the interference and other side effects, but the actual trend is to realize the whole elaboration chain on a single System on Chip (SoC). This choice is driven by different reasons such as the reduction of power consumption, less silicon area occupation on the chip and also reliability and repeatability. Commonly a large area in a SoC is occupied by digital circuits, then, usually a CMOS short-channel technological processes optimized to realize digital circuits is chosen to maximize the performance of the Digital Signal Proccessor (DSP). Opposite, the short-channel technology nodes do not represent the best choice for analog circuits. But in a large number of applications, the signals which are treated have analog nature (microphone, speaker, antenna, accelerometers, biopotential, etc.), then the input and output interfaces of the processing chip are analog/mixed-signal conversion circuits. Therefore in a single integrated circuit (IC) both digital and analog circuits can be found. This gives advantages in term of total size, cost and power consumption of the SoC. The specific characteristics of CMOS short-channel processes such as: • Low breakdown voltage (BV) gives a power supply limit (about 1.2 V). • High threshold voltage VTH (compared with the available voltage supply) fixed in order to limit the leakage power consumption in digital applications (of the order of 0.35 / 0.4V), puts a limit on the voltage dynamic, and creates many problems with the stacked topologies. • Threshold voltage dependent on the channel length VTH = f(L) (short channel effects). • Low value of the output resistance of the MOS (r0) and gm limited by speed saturation, both causes contribute to achieving a low intrinsic gain gmr0 = 20 to 26dB. • Mismatch which brings offset effects on analog circuits. make the design of high performance analog circuits very difficult. Realizing lowpower circuits is fundamental in different contexts, and for different reasons: lowering the power dissipation gives the capability to reduce the batteries size in mobile devices (laptops, smartphones, cameras, measuring instruments, etc.), increase the life of remote sensing devices, satellites, space probes, also allows the reduction of the size and weight of the heat sink. The reduction of power dissipation allows the realization of implantable biomedical devices that do not damage biological tissue. For this reason, the analysis and design of low power and high precision analog circuits is important in order to obtain high performance in technological processes that are not optimized for such applications. Different ways can be taken to reduce the effect of the problems related to the technology: • Circuital level: a circuit-level intervention is possible to solve a specific problem of the circuit (i.e. Techniques for bandwidth expansion, increase the gain, power reduction, etc.). • Digital calibration: it is the highest level to intervene, and generally going to correct the non-ideal structure through a digital processing, these aims are based on models of specific errors of the structure. • Definition of new paradigms. This work has focused the attention on a very useful mixed-signal circuit: the pipeline ADC. The pipeline ADCs are widely used for their energy efficiency in high-precision applications where a resolution of about 10-16 bits and sampling rates above hundreds of Mega-samples per second (telecommunication, radar, etc.) are needed. An introduction on the theory of pipeline ADC, its state of the art and the principal non-idealities that affect the energy efficiency and the accuracy of this kind of data converters are reported in Chapter 1. Special consideration is put on low-voltage low-power ADCs. In particular, for ADCs implemented in deep submicron technology nodes side effects called short channel effects exist opposed to older technology nodes where undesired effects are not present. An overview of the short channel effects and their consequences on design, and also power consuption reduction techniques, with particular emphasis on the specific techniques adopted in pipelined ADC are reported in Chapter 2. Moreover, another way may be undertaken to increase the accuracy and the efficiency of an ADC, this way is the digital calibration. In Chapter 3 an overview on digital calibration techniques, and furthermore a new calibration technique based on Volterra kernels are reported. In some specific applications, such as software defined radios or micropower sensor, some circuits should be reconfigurable to be suitable for different radio standard or process signals with different charateristics. One of this building blocks is the ADC that should be able to reconfigure the resolution and conversion frequency. A reconfigurable voltage-scalable ADC pipeline capable to adapt its voltage supply starting from the required conversion frequency was developed, and the results are reported in Chapter 4. In Chapter 5, a pipeline ADC based on a novel paradigm for the feedback loop and its theory is described