A describing function study of saturated quantization and its application to the stability analysis of multi-bit sigma delta modulators

Just as their single-bit counterparts, multi-bit sigma delta modulators exhibit nonlinear behavior due to the presence of the quantizer in the loop. In the multi-bit case this is caused by the fact that any quantizer has a limited output range and hence gives an implicit saturation effect. Due to this, any multi-bit modulator is prone to modulator overloading. Unfortunately, until now, designers had to rely on extensive time-domain simulations to predict the overloading level, because there is no adequate analytical theory to model this effect. In this work, we have developed such an analytical theory based on multiple input describing function analysis. This way, we obtained expressions for the signal gain, the noise gain and the variance of the quantization noise. Here, both the case of DC as well as sinusoidal signals was considered. These results were used for the stability analysis of multi-bit Sigma Delta modulators, which allows to predict the overloading level. Code implementing the proposed expressions is available for download at http://cas1.elis.ugent. be/cas/en/download

A low hardware complexity time domain quantizer for wideband multibit - ADCs

This paper presents proof of concept of a low hardware complexity time domain quantizer (TDQ) for wideband multibit countinuous time (CT) ΣΔ ADCs. Besides rendering multi-level quantization of the input signal, the proposed scheme generates a two-level loop feedback signal for the modulator. The two-level feedback eliminates the errors emanating from component mismatches in the feedback digital-to-analog converter (DAC) due to process variations. The complete scheme is modeled using Simulink (MATLAB) and is validated through simulation. A 2nd order ΣΔ modulator incorporating the proposed TDQ achieves a dynamic range of 45.7 dB for a bandwidth of 10 MHz and an input sine-wave of -5.78 dBFS amplitude

Oversampled analog-to-digital converter architectures based on pulse frequency modulation

Mención Internacional en el título de doctorThe purpose of this research work is providing new insights in the development of voltage-controlled oscillator based analog-to-digital converters (VCO-based ADCs). Time-encoding based ADCs have become of great interest to the designer community due to the possibility of implementing mostly digital circuits, which are well suited for current deep-submicron CMOS processes. Within this topic, VCO-based ADCs are one of the most promising candidates. VCO-based ADCs have typically been analyzed considering the output phase of the oscillator as a state variable, similar to the state variables considered in __ modulation loops. Although this assumption might take us to functional designs (as verified by literature), it does not take into account neither the oscillation parameters of the VCO nor the deterministic nature of quantization noise. To overcome this issue, we propose an interpretation of these type of systems based on the pulse frequency modulation (PFM) theory. This permits us to analytically calculate the quantization noise, in terms of the working parameters of the system. We also propose a linear model that applies to VCO-based systems. Thanks to it, we can determine the different error processes involved in the digitization of the input data, and the performance limitations which these processes direct to. A generic model for any order open-loop VCO-based ADCs is made based on the PFM theory. However, we will see that only the first-order case and a second order approximation can be implemented in practice. The PFM theory also allows us to propose novel approaches to both single-stage and multistage VCObased architectures. We describe open-loop architectures such as VCO-based architectures with digital precoding, PFM-based architectures that can be used as efficient ADCs or MASH architectures with optimal noise-transfer-function (NTF) zeros. We also make a first approach to the proposal and analysis of closed loop architectures. At the same time, we deal with one of the main limitations of VCOs (especially those built with ring oscillators), which is the non-linear voltage to- frequency relation. In this document, we describe two techniques mitigate this phenomenon. Firstly, we propose to use a pulse width modulator in front of the VCO. This way, there are only two possible oscillation states. Consequently, the oscillator works linearly. To validate the proposed technique, an experimental prototype was implemented in a 40-nm CMOS process. The chip showed noise problems that degraded the expected resolution, but allowed us to verify that the potential performance was close to the expected one. A potential signal-to-noise-distortion ratio (SNDR) equal to 56 dB was achieved in 20 MHz bandwidth, consuming 2.15 mW with an occupied area equal to 0.03 mm2. In comparison to other equivalent systems, the proposed architecture is simpler, while keeping similar power consumption and linearity properties. Secondly, we used a pulse frequency modulator to implement a second ADC. The proposed architecture is intrinsically linear and uses a digital delay line to increase the resolution of the converter. One experimental prototype was implemented in a 40-nm CMOS process using one of these architectures. Proper results were measured from this prototype. These results allowed us to verify that the PFM-based architecture could be used as an efficient ADC. The measured peak SNDR was equal to 53 dB in 20 MHz bandwidth, consuming 3.5 mW with an occupied area equal to 0.08 mm2. The architecture shows a great linearity, and in comparison to related work, it consumes less power and occupies similar area. In general, the theoretical analyses and the architectures proposed in the document are not restricted to any application. Nevertheless, in the case of the experimental chips, the specifications required for these converters were linked to communication applications (e.g. VDSL, VDSL2, or even G.fast), which means medium resolution (9-10 bits), high bandwidth (20 MHz), low power and low area.El propósito del trabajo presentado en este documento es aportar una nueva perspectiva para el diseño de convertidores analógico-digitales basados en osciladores controlados por tensión. Los convertidores analógico-digitales con codificación temporal han llamado la atención durante los últimos años de la comunidad de diseñadores debido a la posibilidad de implementarlos en su gran mayoría con circuitos digitales, los cuales son muy apropiados para los procesos de diseño manométricos. En este ámbito, los convertidores analógico-digitales basados en osciladores controlados por tensión son uno de los candidatos más prometedores. Los convertidores analógico-digitales basados en osciladores controlados por tensión han sido típicamente analizados considerando que la fase del oscilador es una variable de estado similar a las que se observan en los moduladores __. Aunque esta consideración puede llevarnos a diseños funcionales (como se puede apreciar en muchos artículos de la literatura), en ella no se tiene en cuenta ni los parámetros de oscilación ni la naturaleza determinística del ruido de cuantificación. Para solventar esta cuestión, en este documento se propone una interpretación alternativa de este tipo de sistemas haciendo uso de la teoría de la modulación por frecuencia de pulsos. Esto nos permite calcular de forma analítica las ecuaciones que modelan el ruido de cuantificación en función de los parámetros de oscilación. Se propone también un modelo lineal para el análisis de convertidores analógico-digitales basados en osciladores controlados por tensión. Este modelo permite determinar las diferentes fuentes de error que se producen durante el proceso de digitalización de los datos de entrada y las limitaciones que suponen. Un modelo genérico de convertidor de cualquier orden se propone con la ayuda de este modelo. Sin embargo, solo los casos de primer orden y una aproximación al caso de segundo orden se pueden implementar en la práctica. La teoría de la modulación por frecuencia de pulsos también permite nuevas perspectivas para la propuesta y el análisis tanto de arquitecturas de una sola etapa como de arquitecturas de varias etapas construidas con osciladores controlados por tensión. Se proponen y se describen arquitecturas en lazo abierto como son las basadas en osciladores controlador por tensión con moduladores digitales en la etapa de entrada, moduladores por frecuencia de pulsos que se utilizan como convertidores analógico-digitales eficientes o arquitecturas en cascada en las que se optimizan la distribución de los ceros en la función de transferencia del ruido. También se realiza una aproximación a la propuesta y el análisis de arquitecturas en lazo cerrado. Al mismo tiempo, se aborda una de las problemáticas más importantes de los osciladores controlados por tensión (especialmente en aquellos implementados mediante osciladores en anillo): la relación tensión-freculineal que presentan este tipo de circuitos. En el documento, se describen dos técnicas cuyo objetivo es mitigar esta limitación. La primera técnica de corrección se basa en el uso de un modulador por ancho de pulsos antes del oscilador controlado por tensión. De esta forma, solo existen dos estados de oscilación en el oscilador, se trabaja de forma lineal y no se genera distorsión en los datos de salida. La técnica se propone de forma teórica haciendo uso de la teoría desarrollada previamente. Para llevar a cabo la validación de la propuesta teórica se fabricó un prototipo experimental en un proceso CMOS de 40-nm. El chip mostró problemas de ruido que limitaban la resolución, sin embargo, nos permitió velicar que la resolución ideal que se podrá haber obtenido estaba muy cercana a la resolución esperada. Se obtuvo una potencial relación señal-(ruido-distorsión) igual a 56 dB en 20 MHz de ancho de banda, un consumo de 2.15 mW y un área igual a 0.03 mm2. En comparación con sistemas equivalentes, la arquitectura propuesta es más simple al mismo tiempo que se mantiene el consumo así como la linealidad. A continuación, se propone la implementación de un convertidor analógico digital mediante un modulador por frecuencia de pulsos. La arquitectura propuesta es intrínsecamente lineal y hace uso de una línea de retraso digital con el fin de mejorar la resolución del convertidor. Como parte del trabajo experimental, se fabricó otro chip en tecnología CMOS de 40 nm con dicha arquitectura, de la que se obtuvieron resultados notables. Estos resultados permitieron verificar que la arquitectura propuesta, en efecto, podrá emplearse como convertidor analógico-digital eficiente. La arquitectura consigue una relación real señal-(ruido-distorsión) igual a 53 dB en 20 MHz de ancho de banda, un consumo de 3.5 mW y un área igual a 0.08 mm2. Se obtiene una gran linealidad y, en comparación con arquitecturas equivalentes, el consumo es menor mientras que el área ocupada se mantiene similar. En general, las aportaciones propuestas en este documento se pueden aplicar a cualquier tipo de aplicación, independientemente de los requisitos de resolución, ancho de banda, consumo u área. Sin embargo, en el caso de los prototipos fabricados, las especificaciones se relacionan con el ámbito de las comunicaciones (VDSL, VDSL2, o incluso G.fast), en donde se requiere una resolución media (9-10 bits), alto ancho de banda (20 MHz), manteniendo bajo consumo y baja área ocupada.Programa Oficial de Doctorado en Ingeniería Eléctrica, Electrónica y AutomáticaPresidente: Michael Peter Kennedy.- Secretario: Antonio Jesús López Martín.- Vocal: Jörg Hauptman

A Continuous-Time Delta-Sigma Modulator for Ultra-Low-Power Radios

The increasing need of digital signal processing for telecommunication and multimedia applications, implemented in complementary metal-oxide semiconductor (CMOS) technology, creates the necessity for high-resolution analog-to-digital converters (ADCs). Based on the sampling frequency, ADCs are of two types: Nyquist-rate converters and oversampling converters. Oversampling converters are preferred for low-bandwidth applications such as audio and instrumentation because they provide inherently high resolution when coupled with proper noise shaping. This allows to push noise out of signal band, thus increasing the signal-to-noise ratio (SNR). Continuous time delta-sigma ADCs are becoming more popular than discrete-time ADCs primarily because of inherent anti-aliasing filtering, reduced settling time and low-power consumption. In this thesis, a 2nd-order 4-bits continuous-time (CT) delta-sigma modulator (DSM) for radio applications is designed. It employs a 2nd-order loop filter with a single operational amplifier. Implemented in a 65-nanometer CMOS technology, the modulator runs on a 0.8-V supply and achieves a SNR of 70dB over a 500-kHz signal bandwidth. The modulator operates with an oversampling ratio (OSR) of 16 and a sampling frequency of 16MHz. In the first chapter the principles of ΔΣ modulators are analysed, introducing the differences between discrete-time (DT) modulators and continuous-time (CT) modulators. In the next chapter the techniques to design a ΔΣ modulators for ultra-low-power radios are presented. The third chapter talks over the design of the operational amplifier, which appears inside the loop filter. In the fourth chapter the performance of the complete ΔΣ modulator, which employs a flash quantizer, is shown. Finally, in the last chapter, a performance analysis is carried out replacing the flash quantizer with an asynchronous SAR quantizer. The analysis shows that a further reduction of the quantizer power consumption of about 40% is possible. The conjunction of this replacement with the power-saving technique implemented in the loop filter appears relevant

VCO-based ADCs Design Techniques for Communication Systems

This work presents a novel technique to implement voltage-controlled oscillator based continuous-time Delta-Sigma analog-to-digital converters (VCO-based CT-ΔΣ ADCs) in closed-loop configuration. Over the past years there has been an upward trend in the use of these type of converters for instrumentation, audio and communication applications. The reason is that they are mostly digital and thus benefit from advances in deep-submicron CMOS processes. VCO-based ADCs have been widely studied in a great deal of papers and it is known that one of its main drawbacks is the non-linearity it presents. To overcome this issue, to place the VCO within a closed-loop is usually done to attenuate its input magnitude level. However, to do so it is needed a digital-to-analog converter (DAC) as in a conventional CT-ΔΣ, therefore it is required for the DAC to be simple and it cannot present a high number of elements, being the latter a bottleneck for implementing VCOs with a high number of inverters. This works presents a technique that enables to use VCOs with severals inverters while keeping the same number of DAC elements as before. Based upon previous theoretical studies of the VCO-based ADCs which model it as a pulse frequency modulation encoder, this new technique is analyzed and linear models are developed in order to study its viability at system level. Moreover, how impairments related to a real implementation affect the use of this technique are also analyzed. The contributions proposed in this document are focused but not limited to communication applications.Máster Universitario en Ingeniería de Sistemas Electrónicos y Aplicaciones. Curso 2018/201

Design of Highly Efficient Analog-To-Digital Converters

The demand of higher data rates in communication systems is reflected in the constant evolution of communication standards. LTE-A and WiFi 802.11ac promote the use of carrier aggregation to increase the data rate of a wireless receiver. Recent DTV receivers promote the concept of full band capture to avoid the implementation of complex analog operations such as: filtering, equalization, modulation/demodulation, etc. All these operations can be implemented in a robust manner in the digital domain. Analog-to-Digital Converters (ADCs) are located at the heart of such architectures and require to have larger bandwidths and higher dynamic ranges. However, at higher data rates the power efficiency of ADCs tends to degrade. Moreover, while the scale of channel length in CMOS devices directly benefits the power, speed and area of digital circuits, analog circuits suffer from lower intrinsic gain and higher device mismatch. Thus, it has been difficult to design high-speed ADCs with low-power operation using traditional architectures without relying on increasingly complex digital calibration algorithms. This research presents three ADCs that introduce novel architectures to relax the specifications of the analog circuits and reduce the complexity of the digital calibration algorithms. A low-pass sigma delta ADC with 15 MHz of bandwidth is introduced. The system uses a low-power 7-bit quantizer from which the four most significant bits are used for the operation of the sigma delta ADC. The remaining three least significant bits are used for the realization of a frequency domain algorithm for quantization noise improvement. The prototype was implemented in 130 nm CMOS technology. For this prototype, the use of the 7-bit quantizer and algorithm improved the SNDR from 69 dB to 75 dB. The obtained FoM was 145 fJ/conversion-step. In a second project, the problem of high power consumption demanded from closed loop operational amplifiers operating at Giga hertz frequency is addressed. Especially the dependency of the power consumption to the closed loop gain. This project presents a low-pass sigma delta ADC with 75 MHz bandwidth. The traditional summing amplifier used for excess loop compensation delay is substituted by a summing amplifier with current buffer that decouples the power consumption dependency with the closed loop gain. The prototype was designed in 40 nm CMOS technology achieving 64.9 dB peak SNDR. The operating frequency was 3.2 GHz, the total power consumption was 22 mW and FoM of 106 fJ/conversion-step. In a third project, the same approach of decoupling the power consumption requirements from the closed loop gain is applied to a pipelined ADC. The traditional capacitive multiplying DAC used in the residual amplifier is substituted by a current mode DAC and a transimpedance amplifier. The prototype was implemented in 40 nm CMOS technology achieving 58 dB peak SNDR and 76 dB SFDR with 200 MHz sampling frequency. The ADC consumes 8.4 mW with a FoM of 64 fJ/Conversion-step

Design of a Time Based Analog to Digital Converter

Analog to digital converter (ADC) plays a very important role in any mixed analog/digital system. Because digital CMOS technology can take advantage of technology scaling, system designers try to increase the percentage of the digital part of the system. This means moving the ADC more and more towards the input of the system which results in making the role of the ADC more and more critical. With technology scaling, the switching characteristics of MOS transistors offer superb timing accuracy at high frequencies. This makes the time based analog to digital converter (TADC) a good alternative to the conventional ADCs in sub-micron region. In this thesis, an all digital TADC structure is proposed. This TADC is based on an analog to time converter (ATC), followed by a time to digital converter (TDC). The TDC is based on sigma-delta modulation. A non-linear multi-bit internal quantizer in sigma-delta modulator is used to counteract the nonlinearity introduced when the VCO is used as the ATC. The novel TADC also uses an implicit sample and hold (S/H) circuit to reduce area. Dynamic element matching (DEM) is used to improve the robustness of the system against random mismatch in the multi-bit quantizer. Both first and second order sigma-delta modulator TADC are proposed. Simulations and measurements on the proposed TADC are provided. Measurements, from a prototype chip fabricated using 0.13um CMOS technology, show that the first order TADC has achieved a dynamic range of 11 bits for a bandwidth of 2MHz. While simulation results show a dynamic range of 12 bit. Simulations show that the second order TADC has achieved a dynamic range of 12bit for a bandwidth of 20MHz