A Methodology to Derive a Symbolic Transfer Function for Multistage Amplifiers

In this paper, a simple while effective methodology to calculate the symbolic transfer function of a multistage amplifier with frequency compensation is proposed. Three general amplifier models are introduced and analyzed, which represent basic topologies found in the literature. For these amplifier models, the symbolic transfer function is derived and specific strategies for the zero and non-dominant pole expressions are presented. The methodology is suited for hand calculations and yields accurate results while offering more intuition into the operation of the widely adopted frequency compensation solutions discussed in the literature. The effectiveness of the proposed approach is validated through various typical cases of study

Performance enhancement in the desing of amplifier and amplifier-less circuits in modern CMOS technologies.

In the context of nowadays CMOS technology downscaling and the increasing demand of high performance electronics by industry and consumers, analog design has become a major challenge. On the one hand, beyond others, amplifiers have traditionally been a key cell for many analog systems whose overall performance strongly depends on those of the amplifier. Consequently, still today, achieving high performance amplifiers is essential. On the other hand, due to the increasing difficulty in achieving high performance amplifiers in downscaled modern technologies, a different research line that replaces the amplifier by other more easily achievable cells appears: the so called amplifier-less techniques. This thesis explores and contributes to both philosophies. Specifically, a lowvoltage differential input pair is proposed, with which three multistage amplifiers in the state of art are designed, analysed and tested. Moreover, a structure for the implementation of differential switched capacitor circuits, specially suitable for comparator-based circuits, that features lower distortion and less noise than the classical differential structures is proposed, an, as a proof of concept, implemented in a ΔΣ modulator

An improved reversed miller compensation technique for three-stage CMOS OTAs with double pole-zero cancellation and almost single-pole frequency response

This paper presents an improved reversed nested Miller compensation technique exploiting a single additional feed-forward stage to obtain double pole-zero cancellation and ideally single-pole behavior, in a three-stage Miller amplifier. The approach allows designing a three-stage operational transconductance amplifier (OTA) with one dominant pole and two (ideally) mutually cancelling pole-zero doublets. We demonstrate the robustness of the proposed cancellation technique, showing that it is not significantly influenced by process and temperature variations. The proposed design equations allow setting the unity-gain frequency of the amplifier and the complex poles' resonance frequency and quality factor. We introduce the notion of bandwidth efficiency to quantify the OTA performance with respect to a telescopic cascode OTA for given load capacitance and power consumption constraints and demonstrate analytically that the proposed approach allows a bandwidth efficiency that can ideally approach 100%. A CMOS implementation of the proposed compensation technique is provided, in which a current reuse scheme is used to reduce the total current consumption. The OTA has been designed using a 130-nm CMOS process by STMicroelectronics and achieves a DC gain larger than 120 dB, with almost single-pole frequency response. Monte Carlo simulations have been performed to show the robustness of the proposed approach to process, voltage, and temperature (PVT) variations and mismatches

Fully-Digital Rail-to-Rail OTA with Sub-1,000 μm2 Area, 250-mV Minimum Supply and nW Power at 150-pF Load in 180nm

A fully-digital operational transconductance amplifier (DIGOTA) architecture for tightly energy-constrained low-cost systems is presented. A 180nm DIGOTA testchip exhibits an area below the 1,000-μm2 wall, and 2.4-nW power under 150pF load, and a minimum supply voltage Vmin of 0.25 V. In the 0.3-0.5 V supply range, DIGOTA improves the areanormalized small (large) signal energy FoM by at least 836X (267X) over prior sub-500mV OTAs, while reducing area by 27-85X. The low-Vmin and nW-power features are shown to enable direct harvesting at the mm scale

High-speed Time-interleaved Digital-to-Analog Converter (TI-DAC) for Self-Interference Cancellation Applications

Nowadays, the need for higher data-rate is constantly growing to enhance the quality of the daily communication services. The full-duplex (FD) communication is exemplary method doubling the data-rate compared to half-duplex one. However, part of the strong output signal of the transmitter interferes to the receiver-side because they share the same antenna with limited attenuation and, as a result, the receiver’s performance is corrupted. Hence, it is critical to remove the leakage signal from the receiver’s path by designing another block called self-interference cancellation (SIC). The main goal of this dissertation is to develop the SIC block embedded in the current-mode FD receivers. To this end, the regenerated cancellation current signal is fed to the inputs of the base-band filter and after the mixer of a (direct-conversion) current-mode FD receiver. Since the pattern of the transmitter (the digital signal generated by DSP) is known, a high-speed digital-to-Analog converter (DAC) with medium-resolution can perfectly suppress main part of the leakage on the receiver path. A capacitive DAC (CDAC) is chosen among the available solutions because it is compatible with advanced CMOS technology for high-speed application and the medium-resolution designs. Although the main application of the design is to perform the cancellation, it can also be employed as a stand-alone DAC in the Analog (I/Q) transmitter. The SIC circuitry includes a trans-impedance amplifier (TIA), two DACs, high-speed digital circuits, and built-in-self-test section (BIST). According to the available specification for full-duplex communication system, the resolution and working frequency of the CDAC are calculated (designed) equal to 10-bit (3 binary+ 2 binary + 5 thermometric) and 1GHz, respectively. In order to relax the design of the TIA (settling time of the DAC), the CDAC implements using 2-way time-interleaved (TI) manner (the effective SIC frequency equals 2GHz) without using any calibration technique. The CDAC is also developed with the split-capacitor technique to lower the negative effects of the conventional binary-weighted DAC. By adding one extra capacitor on the left-side of the split-capacitor, LSB-side, the value of the split-capacitor can be chosen as an integer value of the unit capacitor. As a result, it largely enhances the linearity of the CADC and cancellation performance. If the block works as a stand-alone DAC with non-TI mode, the digital input code representing a Sinus waveform with an amplitude 1dB less than full-scale and output frequency around 10.74MHz, chosen by coherent sampling rule, then the ENOB, SINAD, SFDR, and output signal are 9.4-bit, 58.2 dB, 68.4dBc, and -9dBV. The simulated value of the |DNL| (static linearity) is also less than 0.7. The similar simulation was done in the SIC mode while the capacitive-array woks in the TI mode and cancellation current is set to the full-scale. Hence, the amount of cancelling the SI signal at the output of the TIA, SNDR, SFDR, SNDRequ. equals 51.3dB, 15.1 dB, 24dBc, 66.4 dB. The designed SIC cannot work as a closed-loop design. The layout was optimally drawn in order to minimize non-linearity, the power-consumption of the decoders, and reduce the complexity of the DAC. By distributing the thermometric cells across the array and using symmetrical switching scheme, the DAC is less subjected to the linear and gradient effect of the oxide. Based on the post-layout simulation results, the deviation of the design after drawing the layout is studied. To compare the results of the schematic and post-layout designs, the exact conditions of simulation above (schematic simulations) are used. When the block works as a stand-alone CDAC, the ENOB, SINAD, SFDR are 8.5-bit, 52.6 dB, 61.3 dBc. The simulated value of the |DNL| (static linearity) is also limited to 1.3. Likewise, the SI signal at the output of the TIA, SNDR, SFDR, SNDRequ. are equal to 44dB, 11.7 dB, 19 dBc, 55.7 dB

Design of event-driven automatic gain control and high-speed data path for multichannel optical receiver arrays

The internet has become the ubiquitous tool that has transformed the lives of all of us. New broadband applications in the field of entertainment, commerce, industry, healthcare and social interactions demand increasingly higher data rates and quality of the networks and ICT infrastructure. In addition, high definition video streaming and cloud services will continue to push the demand for bandwidth. These applications are reshaping the internet into a content-centric network. The challenge is to transform the telecom optical networks and data centers such that they can be scaled efficiently, at low cost. Furthermore, from both an environmental and economic perspective, this scaling should go hand in hand with reduced power consumption. This stems from the desire to reduce CO2 emission and to reduce network operating costs while offering the same service level as today. In the current architecture of the internet, end-users connect to the public network using the access network of an internet service provider (ISP). Today, this access network either reuses the legacy copper or coaxial network or uses passive optical network (PON) technologies, among which the PON is the most energy efficient and provides the highest data rates. Traffic from the access network is aggregated with Ethernet switches and routed to the core network through the provider edge routers, with broadband network gateways (BNGs) to regulate access and usage. These regional links are collectively called the metro network. Data centers connect to the core network using their own dedicated gateway router. The problem of increasing data rates, while reducing the economic and environmental impact, has attracted considerable attention. The research described in this work has been performed in the context of two projects part of the European Union Seventh Framework Programme (FP7), which both aim for higher data rates and tight integration while keeping power consumption low. Mirage targets data center applications while C3PO focuses on medium-reach networks, such as the metro network. Specifically, this research considers two aspects of the high-speed optical receivers used in the communication networks: increasing dynamic range of a linear receiver for multilevel modulation through automatic gain control (AGC) and integration of multiple channels on a single chip with a small area footprint. The data centers of today are high-density computing facilities that provide storage, processing and software as a service to the end-user. They are comprised of gateway routers, a local area network, servers and storage. All of this is organized in racks. The largest units contain over 100 000 servers. The major challenges regarding data centers are scalability and keeping up with increasing amounts of traffic while reducing power consumption (of the devices as well as the associated cooling) and keeping cost minimal. Presently, racks are primarily interconnected with active optical cables (AOCs) which employ signal rates up to 25 Gb/s per lane with non-return-to-zero (NRZ) modulation. A number of technological developments can be employed in AOCs of the future to provide terabit-capacity optical interconnects over longer distances. One such innovation is the use of multilevel modulation formats, which are more bandwidth-efficient than traditional NRZ modulation. Multilevel modulation requires a linear amplifier as front-end of the optical receiver. The greater part of this dissertation discusses the design and implementation of an AGC system for the data path of a linear transimpedance amplifier (TIA). The metro network is the intermediate regional network between the access and core network of the internet architecture, with link lengths up to 500 km. It is estimated that in the near future metro-traffic will increase massively. This growth is attributed mainly to increasing traffic from content delivery networks (CDNs) and data centers, which bypass the core network and directly connect to the metro network. Internet video growth is the major reason for traffic increase. This evolution demands increasingly higher data rates. Today, dense wavelength division multiplexing (DWDM) is widely recognized as being necessary to provide data capacity scalability for future optical networks, as it allows for much higher combined data rates over a single fiber. At the receiver, each wavelength of the demultiplexed incoming light is coupled to a photo diode in a photo diode array which is connected to a dedicated lane of a multichannel receiver. The high number of channels requires small physical channel spacing and tight integration of the diode array with the receiver. In addition, active cooling should be avoided, such that power consumption per receiver lane must be kept low in order not to exceed thermal operation limits. The second component of this work presents the development of an integrated four-channel receiver, targeting 4 × 25 Gb/s data rate, with low power consumption and small footprint to support tight integration with a p-i-n photo diode array with a 250 μm channel pitch. Chapter 1 discusses the impact of increasing data rates and the desire to reduce power consumption on the design of the optical receiver component, in wide metropolitan area networks as well as in short-reach point-to-point links in data centers. In addition, some aspects of integrated analog circuit design are highlighted: the design flow, transistor hand models, a software design tool. Also, an overview of the process technology is given. Chapter 2 provides essential optical receiver concepts, which are required to understand the remainder of the work. Fundamentals of feedback AGC systems are discussed in the first part of Chapter 3. A basic system model is presented in the continuous-time domain, in which the variable gain amplifier (VGA) constitutes the multistage datapath of a linear optical receiver. To enable reliable reception of multilevel modulation formats, the VGA requires controlled frequency response and in particular limited time-domain overshoot across the gain range. It is argued that this control is hard to achieve with fully analog building blocks. Therefore, an event-driven approach is proposed as an extension of the continuous-time system. Both the structural and behavioral aspects are discussed. The result is a system model of a quantized AGC loop, upon which the system-level design, presented in Chapter 4, is based. In turn, Chapter 5 discusses the detailed implementation of the various building blocks on the circuit level and presents experimental results that confirm the feasibility of the proposed approach. Chapter 6 discusses the design and implementation of a 4 × 25 Gb/s optical receiver array for NRZ modulation with a small area footprint. The focus lies on the input stages and techniques to extend bandwidth and dynamic range are presented. Measurement results for NRZ and optical duobinary (ODB) modulation are presented, as well as the influence of crosstalk on the performance. Finally, Chapter 7 provides an overview of the foremost conclusions of the presented research and includes suggestions for future research. Two appendices are included. Appendix A gives an overview of the general network theorem (GNT), which is used throughout this work and which has been implemented numerically. The results from Appendix B, the analysis of a two-stage opamp compensated with capacitance multipliers, were used to design a building block for the AGC system

Time-domain optimization of amplifiers based on distributed genetic algorithms

Thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Electrical and Computer EngineeringThe work presented in this thesis addresses the task of circuit optimization, helping the designer facing the high performance and high efficiency circuits demands of the market and technology evolution. A novel framework is introduced, based on time-domain analysis, genetic algorithm optimization, and distributed processing. The time-domain optimization methodology is based on the step response of the amplifier. The main advantage of this new time-domain methodology is that, when a given settling-error is reached within the desired settling-time, it is automatically guaranteed that the amplifier has enough open-loop gain, AOL, output-swing (OS), slew-rate (SR), closed loop bandwidth and closed loop stability. Thus, this simplification of the circuit‟s evaluation helps the optimization process to converge faster. The method used to calculate the step response expression of the circuit is based on the inverse Laplace transform applied to the transfer function, symbolically, multiplied by 1/s (which represents the unity input step). Furthermore, may be applied to transfer functions of circuits with unlimited number of zeros/poles, without approximation in order to keep accuracy. Thus, complex circuit, with several design/optimization degrees of freedom can also be considered. The expression of the step response, from the proposed methodology, is based on the DC bias operating point of the devices of the circuit. For this, complex and accurate device models (e.g. BSIM3v3) are integrated. During the optimization process, the time-domain evaluation of the amplifier is used by the genetic algorithm, in the classification of the genetic individuals. The time-domain evaluator is integrated into the developed optimization platform, as independent library, coded using C programming language. The genetic algorithms have demonstrated to be a good approach for optimization since they are flexible and independent from the optimization-objective. Different levels of abstraction can be optimized either system level or circuit level. Optimization of any new block is basically carried-out by simply providing additional configuration files, e.g. chromosome format, in text format; and the circuit library where the fitness value of each individual of the genetic algorithm is computed. Distributed processing is also employed to address the increasing processing time demanded by the complex circuit analysis, and the accurate models of the circuit devices. The communication by remote processing nodes is based on Message Passing interface (MPI). It is demonstrated that the distributed processing reduced the optimization run-time by more than one order of magnitude. Platform assessment is carried by several examples of two-stage amplifiers, which have been optimized and successfully used, embedded, in larger systems, such as data converters. A dedicated example of an inverter-based self-biased two-stage amplifier has been designed, laid-out and fabricated as a stand-alone circuit and experimentally evaluated. The measured results are a direct demonstration of the effectiveness of the proposed time-domain optimization methodology.Portuguese Foundation for the Science and Technology (FCT

High performance CMOS integrated circuits for optical receivers

Optical communications is expanding into new applications such as infrared wireless communications; therefore, designing high performance circuits has gained considerable importance. In this dissertation a wide dynamic-range variable-gain transimpedance amplifier (TIA) is introduced. It adopts a regulated cascode (RGC) amplifier and an operational transconductance amplifier (OTA) as the feed forward gain element to control gain and improve the overload of the optical receiver. A fully-differential variable-gain TIA in a 0.35µm CMOS technology is realized. It provides a bit error rate (BER) less than 10-12 for an input current from 6µA-3mA at 3.3V power supply. For the transimpedance gain variation, from 0.1kΩ to 3kΩ, -3dB bandwidth is higher than 1.7GHz for a 0.6pF photodiode capacitance. The power dissipations for the highest and the lowest gains are 8.2mW and 24.9mW respectively. A new technique for designing uniform multistage amplifiers (MA) for high frequency applications is introduced. The proposed method uses the multi-peak bandwidth enhancement technique while it employs identical, simple and inductorless stages. It has several advantages, such as tunability of bandwidth and decreased sensitivity of amplifier stages, to process variations. While all stages of the proposed MA topology are identical, the gain-bandwidth product can be extended several times. Two six-stage amplifiers in a TSMC 0.35µm CMOS process were designed using the proposed topology. Measurements show that the gain can be varied for the first one between 16dB and 44dB within the 0.7-3.2GHz bandwidth and for the second one between 13dB and 44dB within a 1.9-3.7GHz bandwidth with less than 5.2nV/√Hz noise. Although the second amplifier has a higher gain bandwidth product, it consumes more power and occupies a wider area. A technique for capacitance multiplication is utilized to design a tunable loop filter. Current and voltage mode techniques are combined to increase the multiplication factor (M). At a high input dynamic range, M is adjustable and the capacitance multiplier performs linearly at high frequencies. Drain-source voltages of paired transistors are equalized to improve matching in the current mirrors. Measurement of a prototype loop filter IC in a 0.5µm CMOS technology shows 50µA current consumption for M=50. Where 80pF capacitance is employed, the capacitance multiplier realizes an effective capacitance varying from 1.22nF up to 8.5nF