A 45nm CMOS DESIGN OF NEUROMORPHIC SYSTEM

Neuromorphic computing has become an emerging field in wide range of applications. Its challenge lies in developing a brain-inspired architecture that can emulate human brain and can work for real time applications. In this report a flexible neural architecture is presented which consists of 128 X 128 SRAM crossbar memory and 128 spiking neurons. For Neuron, digital integrate and fire model is used. All components are designed in 45nm technology node. The core can be configured for certain Neuron parameters, Axon types and synapses states and are fully digitally implemented. Learning for this architecture is done offline. To train this circuit a well-known algorithm Restricted Boltzmann Machine (RBM) is used and linear classifiers are trained at the output of RBM. Finally, circuit was tested for handwritten digit recognition application. Future prospects for this architecture are also discussed.

EXPERIMENTAL AND COMPUTATIONAL STUDIES OF ELECTROMAGNETIC CLOAKING AT MICROWAVES

An invisibility cloak is a device that can hide the target by enclosing it from the incident radiation. This intriguing device has attracted a lot of attention since it was first implemented at a microwave frequency in 2006. However, the problems of existing cloak designs prevent them from being widely applied in practice. In this dissertation, we try to remove or alleviate the three constraints for practical applications imposed by loosy cloaking media, high implementation complexity, and small size of hidden objects compared to the incident wavelength. To facilitate cloaking design and experimental characterization, several devices and relevant techniques for measuring the complex permittivity of dielectric materials at microwave frequencies are developed. In particular, a unique parallel plate waveguide chamber has been set up to automatically map the electromagnetic (EM) field distribution for wave propagation through the resonator arrays and cloaking structures. The total scattering cross section of the cloaking structures was derived based on the measured scattering field by using this apparatus. To overcome the adverse effects of lossy cloaking media, microwave cloaks composed of identical dielectric resonators made of low loss ceramic materials are designed and implemented. The effective permeability dispersion was provided by tailoring dielectric resonator filling fractions. The cloak performances had been verified by full-wave simulation of true multi-resonator structures and experimental measurements of the fabricated prototypes. With the aim to reduce the implementation complexity caused by metamaterials employment for cloaking, we proposed to design 2-D cylindrical cloaks and 3-D spherical cloaks by using multi-layer ordinary dielectric material (εr>1) coating. Genetic algorithm was employed to optimize the dielectric profiles of the cloaking shells to provide the minimum scattering cross sections of the cloaked targets. The designed cloaks can be easily scaled to various operating frequencies. The simulation results show that the multi-layer cylindrical cloak essentially outperforms the similarly sized metamaterials-based cloak designed by using the transformation optics-based reduced parameters. For the designed spherical cloak, the simulated scattering pattern shows that the total scattering cross section is greatly reduced. In addition, the scattering in specific directions could be significantly reduced. It is shown that the cloaking efficiency for larger targets could be improved by employing lossy materials in the shell. At last, we propose to hide a target inside a waveguide structure filled with only epsilon near zero materials, which are easy to implement in practice. The cloaking efficiency of this method, which was found to increase for large targets, has been confirmed both theoretically and by simulations.

Transformer modeling ATP : internal faults & high-frequency discretization

Power transformers are key components of the power grid and are also one of the most subjected to a variety of power system transients. The failure of a large transformer can cause severe monetary losses to a utility, thus adequate protection schemes are of great importance to avoid transformer damage and maximize the continuity of service. Computer modeling can be used as an efficient tool to improve the reliability of a transformer protective relay application. Unfortunately, transformer models presently available in commercial software lack completeness in the representation of several aspects such as internal winding faults, which is a common cause of transformer failure. It is also important to adequately represent the transformer at frequencies higher than the power frequency for a more accurate simulation of switching transients since these are a well known cause for the unwanted tripping of protective relays. This work develops new capabilities for the Hybrid Transformer Model (XFMR) implemented in ATPDraw to allow the representation of internal winding faults and slow-front transients up to 10 kHz. The new model can be developed using any of two sources of information: 1) test report data and 2) design data. When only test-report data is available, a higher-order leakage inductance matrix is created from standard measurements. If design information is available, a Finite Element Model is created to calculate the leakage parameters for the higher-order model. An analytical model is also implemented as an alternative to FEM modeling. Measurements on 15-kVA 240?/208Y V and 500-kVA 11430Y/235Y V distribution transformers were performed to validate the model. A transformer model that is valid for simulations for frequencies above the power frequency was developed after continuing the division of windings into multiple sections and including a higher-order capacitance matrix. Frequency-scan laboratory measurements were used to benchmark the simulations. Finally, a stability analysis of the higher-order model was made by analyzing the trapezoidal rule for numerical integration as used in ATP. Numerical damping was also added to suppress oscillations locally when discontinuities occurred in the solution. A maximum error magnitude of 7.84% was encountered in the simulated currents for different turn-to-ground and turn-to-turn faults. The FEM approach provided the most accurate means to determine the leakage parameters for the ATP model. The higher-order model was found to reproduce the short-circuit impedance acceptably up to about 10 kHz and the behavior at the first anti-resonant frequency was better matched with the measurements.

Direction finding in the presence of a more realistic environment model

Direction-of-arrival (DOA) estimation is susceptible to errors introduced by the presence of real-ground and resonant size scatterers in the vicinity of the antenna array. To compensate for these errors pre-calibration and auto-calibration techniques are presented. The effects of real-ground constituent parameters on the mutual coupling (MC) of wire type antenna arrays for DOA estimation are investigated. This is accomplished by pre-calibration of the antenna array over the real-ground using the finite element method (FEM). The mutual impedance matrix is pre-estimated and used to remove the perturbations in the received terminal voltage. The unperturbed terminal voltage is incorporated in MUSIC algorithm to estimate DOAs. First, MC of quarter wave monopole antenna arrays is investigated. This work augments an existing MC compensation technique for ground-based antennas and proposes reduction in MC for antennas over finite ground as compared to the perfect ground. A factor of 4 decrease in both the real and imaginary parts of the MC is observed when considering a poor ground versus a perfectly conducting one for quarter wave monopoles in the receiving mode. A simulated result to show the compensation of errors direction of arrival (DOA) estimation with actual realization of the environment is also presented. Secondly, investigations for the effects on received MC of λ/2 dipole arrays placed near real-earth are carried out. As a rule of thumb, estimation of mutual coupling can be divided in two regions of antenna height that is very near ground 0

Development of room temperature operating single electron transistor using FIB etching and deposition technology

The single-electron transistor (SET) is one of the best candidates for future nano electronic circuits because of its ultralow power consumption, small size and unique functionality. SET devices operate on the principle of Coulomb blockade, which is more prominent at dimensions of a few nano meters. Typically, the SET device consists of two capacitively coupled ultra-small tunnel junctions with a nano island between them. In order to observe the Coulomb blockade effects in a SET device the charging energy of the device has to be greater that the thermal energy. This condition limits the operation of most of the existing SET devices to cryogenic temperatures. Room temperature operation of SET devices requires sub-10nm nano-islands due to the inverse dependence of charging energy on the radius of the conducting nano-island. Fabrication of sub-10nm structures using lithography processes is still a technological challenge. In the present investigation, Focused Ion Beam based etch and deposition technology is used to fabricate single electron transistors devices operating at room temperature. The SET device incorporates an array of tungsten nano-islands with an average diameter of 8nm. The fabricated devices are characterized at room temperature and clear Coulomb blockade and Coulomb oscillations are observed. An improvement in the resolution limitation of the FIB etching process is demonstrated by optimizing the thickness of the active layer. SET devices with structural and topological variation are developed to explore their impact on the behavior of the device. The threshold voltage of the device was minimized to ~500mV by minimizing the source-drain gap of the device to 17nm. Vertical source and drain terminals are fabricated to realize single-dot based SET device. A unique process flow is developed to fabricate Si dot based SET devices for better gate controllability in the device characteristic. The device vi parameters of the fabricated devices are extracted by using a conductance model. Finally, characteristic of these devices are validated with the simulated data from theoretical modeling.

DISTRIBUTED APPROACH FOR SOLVING OPTIMAL POWER FLOW PROBLEMS IN THREE-PHASE UNBALANCED DISTRIBUTION NETWORK

The objective of this report is to study distributed (decentralized) three phase optimal power flow (OPF) problem in unbalanced power distribution networks. A full three phase representation of the distribution networks is considered to account for the highly unbalance state of the distribution networks. All distribution network’s series/shunt components, and load types/combinations had been modeled on commercial version of General Algebraic Modeling System (GAMS), the high-level modeling system for mathematical programming and optimization. The OPF problem has been successfully implemented and solved in a centralized approach and distributed approach, where the objective is to minimize the active power losses in the entire system. The study was implemented on the IEEE-37 Node Test Feeder. A detailed discussion of all problem sides and aspects starting from the basics has been provided in this study. Full simulation results have been provided at the end of the report.

MODELING AND PROTOCOL DESIGN FOR EMERGING WIRELESS SYSTEMS

Mobile Mesh Network based In-Transit Visibility (MMN-ITV) system facilitates global real-time tracking capability for the logistics system. In-transit containers form a multi-hop mesh network to forward the tracking information to the nearby sinks, which further deliver the information to the remote control center via satellite. The fundamental challenge to the MMN-ITV system is the energy constraint of the battery-operated containers. Coupled with the unique mobility pattern, cross-MMN behavior, and the large-spanned area, it is necessary to investigate the energy-efficient communication of the MMN-ITV system thoroughly. First of all, this dissertation models the energy-efficient routing under the unique pattern of the cross-MMN behavior. A new modeling approach, pseudo-dynamic modeling approach, is proposed to measure the energy-efficiency of the routing methods in the presence of the cross-MMN behavior. With this approach, it could be identified that the shortest-path routing and the load-balanced routing is energy-efficient in mobile networks and static networks respectively. For the MMN-ITV system with both mobile and static MMNs, an energy-efficient routing method, energy-threshold routing, is proposed to achieve the best tradeoff between them. Secondly, due to the cross-MMN behavior, neighbor discovery is executed frequently to help the new containers join the MMN, hence, consumes similar amount of energy as that of the data communication. By exploiting the unique pattern of the cross-MMN behavior, this dissertation proposes energy-efficient neighbor discovery wakeup schedules to save up to 60% of the energy for neighbor discovery. Vehicular Ad Hoc Networks (VANETs)-based inter-vehicle communications is by now growingly believed to enhance traffic safety and transportation management with low cost. The end-to-end delay is critical for the time-sensitive safety applications in VANETs, and can be a decisive performance metric for VANETs. This dissertation presents a complete analytical model to evaluate the end-to-end delay against the transmission range and the packet arrival rate. This model illustrates a significant end-to-end delay increase from non-saturated networks to saturated networks. It hence suggests that the distributed power control and admission control protocols for VANETs should aim at improving the real-time capacity (the maximum packet generation rate without causing saturation), instead of the delay itself. Based on the above model, it could be determined that adopting uniform transmission range for every vehicle may hinder the delay performance improvement, since it does not allow the coexistence of the short path length and the low interference. Clusters are proposed to configure non-uniform transmission range for the vehicles. Analysis and simulation confirm that such configuration can enhance the real-time capacity. In addition, it provides an improved trade off between the end-to-end delay and the network capacity. A distributed clustering protocol with minimum message overhead is proposed, which achieves low convergence time.

HIGH PERFORMANCE, LOW COST SUBSPACE DECOMPOSITION AND POLYNOMIAL ROOTING FOR REAL TIME DIRECTION OF ARRIVAL ESTIMATION: ANALYSIS AND IMPLEMENTATION

This thesis develops high performance real-time signal processing modules for direction of arrival (DOA) estimation for localization systems. It proposes highly parallel algorithms for performing subspace decomposition and polynomial rooting, which are otherwise traditionally implemented using sequential algorithms. The proposed algorithms address the emerging need for real-time localization for a wide range of applications. As the antenna array size increases, the complexity of signal processing algorithms increases, making it increasingly difficult to satisfy the real-time constraints. This thesis addresses real-time implementation by proposing parallel algorithms, that maintain considerable improvement over traditional algorithms, especially for systems with larger number of antenna array elements. Singular value decomposition (SVD) and polynomial rooting are two computationally complex steps and act as the bottleneck to achieving real-time performance. The proposed algorithms are suitable for implementation on field programmable gated arrays (FPGAs), single instruction multiple data (SIMD) hardware or application specific integrated chips (ASICs), which offer large number of processing elements that can be exploited for parallel processing. The designs proposed in this thesis are modular, easily expandable and easy to implement. Firstly, this thesis proposes a fast converging SVD algorithm. The proposed method reduces the number of iterations it takes to converge to correct singular values, thus achieving closer to real-time performance. A general algorithm and a modular system design are provided making it easy for designers to replicate and extend the design to larger matrix sizes. Moreover, the method is highly parallel, which can be exploited in various hardware platforms mentioned earlier. A fixed point implementation of proposed SVD algorithm is presented. The FPGA design is pipelined to the maximum extent to increase the maximum achievable frequency of operation. The system was developed with the objective of achieving high throughput. Various modern cores available in FPGAs were used to maximize the performance and details of these modules are presented in detail. Finally, a parallel polynomial rooting technique based on Newton’s method applicable exclusively to root-MUSIC polynomials is proposed. Unique characteristics of root-MUSIC polynomial’s complex dynamics were exploited to derive this polynomial rooting method. The technique exhibits parallelism and converges to the desired root within fixed number of iterations, making this suitable for polynomial rooting of large degree polynomials. We believe this is the first time that complex dynamics of root-MUSIC polynomial were analyzed to propose an algorithm. In all, the thesis addresses two major bottlenecks in a direction of arrival estimation system, by providing simple, high throughput, parallel algorithms.

DESIGN AND IMPLEMENT DYNAMIC PROGRAMMING BASED DISCRETE POWER LEVEL SMART HOME SCHEDULING USING FPGA

With the development and capabilities of the Smart Home system, people today are entering an era in which household appliances are no longer just controlled by people, but also operated by a Smart System. This results in a more efficient, convenient, comfortable, and environmentally friendly living environment. A critical part of the Smart Home system is Home Automation, which means that there is a Micro-Controller Unit (MCU) to control all the household appliances and schedule their operating times. This reduces electricity bills by shifting amounts of power consumption from the on-peak hour consumption to the off-peak hour consumption, in terms of different “hour price”. In this paper, we propose an algorithm for scheduling multi-user power consumption and implement it on an FPGA board, using it as the MCU. This algorithm for discrete power level tasks scheduling is based on dynamic programming, which could find a scheduling solution close to the optimal one. We chose FPGA as our system’s controller because FPGA has low complexity, parallel processing capability, a large amount of I/O interface for further development and is programmable on both software and hardware. In conclusion, it costs little time running on FPGA board and the solution obtained is good enough for the consumers.

Bluetooth Enabled Ad-hoc Networks: Performance Evaluation of a Self-healing Scatternet Formation Protocol

Bluetooth wireless technology is a robust short-range communications system designed for low power (10 meter range) and low cost. It operates in the 2.4 GHz Industrial Scientific Medical (ISM) band and it employs two techniques for minimizing interference: a frequency hopping scheme which nominally splits the 2.400 - 2.485 GHz band in 79 frequency channels and a time division duplex (TDD) scheme which is used to switch to a new frequency channel on 625 μs boundaries. During normal operation a Bluetooth device will be active on a different frequency channel every 625 μs, thus minimizing the chances of continuous interference impacting the performance of the system. The smallest unit of a Bluetooth network is called a piconet, and can have a maximum of eight nodes. Bluetooth devices must assume one of two roles within a piconet, master or slave, where the master governs quality of service and the frequency hopping schedule within the piconet and the slave follows the master’s schedule. A piconet must have a single master and up to 7 active slaves. By allowing devices to have roles in multiple piconets through time multiplexing, i.e. slave/slave or master/slave, the Bluetooth technology allows for interconnecting multiple piconets into larger networks called scatternets. The Bluetooth technology is explored in the context of enabling ad-hoc networks. The Bluetooth specification provides flexibility in the scatternet formation protocol, outlining only the mechanisms necessary for future protocol implementations. A new protocol for scatternet formation and maintenance - mscat - is presented and its performance is evaluated using a Bluetooth simulator. The free variables manipulated in this study include device activity and the probabilities of devices performing discovery procedures. The relationship between the role a device has in the scatternet and it’s probability of performing discovery was examined and related to the scatternet topology formed. The results show that mscat creates dense network topologies for networks of 30, 50 and 70 nodes. The mscat protocol results in approximately a 33% increase in slaves/piconet and a reduction of approximately 12.5% of average roles/node. For 50 node scenarios the set of parameters which creates the best determined outcome is unconnected node inquiry probability (UP) = 10%, master node inquiry probability (MP) = 80% and slave inquiry probability (SP) = 40%. The mscat protocol extends the Bluetooth specification for formation and maintenance of scatternets in an ad-hoc network.

MULTIDIMENSIONAL OPTIMAL DROOP CONTROL FOR WIND RESOURCES IN DC MICROGRIDS

Two important and upcoming technologies, microgrids and electricity generation from wind resources, are increasingly being combined. Various control strategies can be implemented, and droop control provides a simple option without requiring communication between microgrid components. Eliminating the single source of potential failure around the communication system is especially important in remote, islanded microgrids, which are considered in this work. However, traditional droop control does not allow the microgrid to utilize much of the power available from the wind. This dissertation presents a novel droop control strategy, which implements a droop surface in higher dimension than the traditional strategy. The droop control relationship then depends on two variables: the dc microgrid bus voltage, and the wind speed at the current time. An approach for optimizing this droop control surface in order to meet a given objective, for example utilizing all of the power available from a wind resource, is proposed and demonstrated. Various cases are used to test the proposed optimal high dimension droop control method, and demonstrate its function. First, the use of linear multidimensional droop control without optimization is demonstrated through simulation. Next, an optimal high dimension droop control surface is implemented with a simple dc microgrid containing two sources and one load. Various cases for changing load and wind speed are investigated using simulation and hardware-in-the-loop techniques. Optimal multidimensional droop control is demonstrated with a wind resource in a full dc microgrid example, containing an energy storage device as well as multiple sources and loads. Finally, the optimal high dimension droop control method is applied with a solar resource, and using a load model developed for a military patrol base application. The operation of the proposed control is again investigated using simulation and hardware-in-the-loop techniques.

CHARACTERIZATION OF ELECTRODEPOSITED POLYANILINE BIOSENSOR PLATFORM FOR ESCHERICHIA COLI O157:H7 DETECTION

Amperometric electrodeposition has been used to obtain uniform, conductive, and repeatable polyaniline (PANi) thin films for use in nano scaled biochemical sensors. This report describes the characterization of these films. Techniques such as ellipsometry were used to test repeatability of the deposition and the uniformity of the deposited thin films. Raman spectroscopy was utilized to confirm the composition of the deposited PANi thin films. Fluorescence microscopy was used to determine the immobilization of antibodies to the PANi thin films using biotin-avidin interactions, as well as the density of active binding sites. Ellipsometry results demonstrated that biomolecules could be immobilized on PANi films as thin as 9nm. Evidence from the Raman spectroscopy demonstrated the conductive nature of the PANi films. The fluorescence microscopy demonstrated that antibodies could be immobilized on PANi films, although the experiment also demonstrated a low density of binding sites. The characterization demonstrates the utility of the PANi thin films as a conductive interface between the inorganic sensor platform and biochemical molecules.

Automatic Food Intake Assessment Using Camera Phones

Obesity is becoming an epidemic phenomenon in most developed countries. The fundamental cause of obesity and overweight is an energy imbalance between calories consumed and calories expended. It is essential to monitor everyday food intake for obesity prevention and management. Existing dietary assessment methods usually require manually recording and recall of food types and portions. Accuracy of the results largely relies on many uncertain factors such as user's memory, food knowledge, and portion estimations. As a result, the accuracy is often compromised. Accurate and convenient dietary assessment methods are still blank and needed in both population and research societies. In this thesis, an automatic food intake assessment method using cameras, inertial measurement units (IMUs) on smart phones was developed to help people foster a healthy life style. With this method, users use their smart phones before and after a meal to capture images or videos around the meal. The smart phone will recognize food items and calculate the volume of the food consumed and provide the results to users. The technical objective is to explore the feasibility of image based food recognition and image based volume estimation. This thesis comprises five publications that address four specific goals of this work: (1) to develop a prototype system with existing methods to review the literature methods, find their drawbacks and explore the feasibility to develop novel methods; (2) based on the prototype system, to investigate new food classification methods to improve the recognition accuracy to a field application level; (3) to design indexing methods for large-scale image database to facilitate the development of new food image recognition and retrieval algorithms; (4) to develop novel convenient and accurate food volume estimation methods using only smart phones with cameras and IMUs. A prototype system was implemented to review existing methods. Image feature detector and descriptor were developed and a nearest neighbor classifier were implemented to classify food items. A reedit card marker method was introduced for metric scale 3D reconstruction and volume calculation. To increase recognition accuracy, novel multi-view food recognition algorithms were developed to recognize regular shape food items. To further increase the accuracy and make the algorithm applicable to arbitrary food items, new food features, new classifiers were designed. The efficiency of the algorithm was increased by means of developing novel image indexing method in large-scale image database. Finally, the volume calculation was enhanced through reducing the marker and introducing IMUs. Sensor fusion technique to combine measurements from cameras and IMUs were explored to infer the metric scale of the 3D model as well as reduce noises from these sensors.

USING PROBABILISTIC GRAPHICAL MODELS TO DRAW INFERENCES IN SENSOR NETWORKS WITH TRACKING APPLICATIONS

Sensor networks have been an active research area in the past decade due to the variety of their applications. Many research studies have been conducted to solve the problems underlying the middleware services of sensor networks, such as self-deployment, self-localization, and synchronization. With the provided middleware services, sensor networks have grown into a mature technology to be used as a detection and surveillance paradigm for many real-world applications. The individual sensors are small in size. Thus, they can be deployed in areas with limited space to make unobstructed measurements in locations where the traditional centralized systems would have trouble to reach. However, there are a few physical limitations to sensor networks, which can prevent sensors from performing at their maximum potential. Individual sensors have limited power supply, the wireless band can get very cluttered when multiple sensors try to transmit at the same time. Furthermore, the individual sensors have limited communication range, so the network may not have a 1-hop communication topology and routing can be a problem in many cases. Carefully designed algorithms can alleviate the physical limitations of sensor networks, and allow them to be utilized to their full potential. Graphical models are an intuitive choice for designing sensor network algorithms. This thesis focuses on a classic application in sensor networks, detecting and tracking of targets. It develops feasible inference techniques for sensor networks using statistical graphical model inference, binary sensor detection, events isolation and dynamic clustering. The main strategy is to use only binary data for rough global inferences, and then dynamically form small scale clusters around the target for detailed computations. This framework is then extended to network topology manipulation, so that the framework developed can be applied to tracking in different network topology settings. Finally the system was tested in both simulation and real-world environments. The simulations were performed on various network topologies, from regularly distributed networks to randomly distributed networks. The results show that the algorithm performs well in randomly distributed networks, and hence requires minimum deployment effort. The experiments were carried out in both corridor and open space settings. A in-home falling detection system was simulated with real-world settings, it was setup with 30 bumblebee radars and 30 ultrasonic sensors driven by TI EZ430-RF2500 boards scanning a typical 800 sqft apartment. Bumblebee radars are calibrated to detect the falling of human body, and the two-tier tracking algorithm is used on the ultrasonic sensors to track the location of the elderly people.

DESIGN AND IMPLEMENTATION OF HOME USE PORTABLE SMART ELECTRONICS

The widespread of low cost embedded electronics makes it easier to implement the smart devices that can understand either the environment or the user behaviors. The main object of this project is to design and implement home use portable smart electronics, including the portable monitoring device for home and office security and the portable 3D mouse for convenient use. Both devices in this project use the MPU6050 which contains a 3 axis accelerometer and a 3 axis gyroscope to sense the inertial motion of the door or the human hands movement. For the portable monitoring device for home and office security, MPU6050 is used to sense the door (either home front door or cabinet door) movement through the gyroscope, and Raspberry Pi is then used to process the data it receives from MPU6050, if the data value exceeds the preset threshold, Raspberry Pi would control the USB Webcam to take a picture and then send out an alert email with the picture to the user. The advantage of this device is that it is a small size portable stand-alone device with its own power source, it is easy to implement, really cheap for residential use, and energy efficient with instantaneous alert. For the 3D mouse, the MPU6050 would use both the accelerometer and gyroscope to sense user hands movement, the data are processed by MSP430G2553 through a digital smooth filter and a complementary filter, and then the filtered data will pass to the personal computer through the serial COM port. By applying the cursor movement equation in the PC driver, this device can work great as a mouse with acceptable accuracy. Compared to the normal optical mouse we are using, this mouse does not need any working surface, with the use of the smooth and complementary filter, it has certain accuracy for normal use, and it is easy to be extended to a portable mouse as small as a finger ring.