Undergraduate Research Projects
Design and Simulation of Fractional-Order Analog Filters
Electronic filter circuits are ubiquitous in signal processing, used in nearly all applications that need to remove unwanted characteristics from a signal. This ranges from removing power line noise to improve the quality of electroencephalogram (EEG) recordings during research on brain activity to selecting the correct frequency band to hear your favorite radio station in your car. The introduction of fractional-calculus into these circuits has yielded filters with magnitude and phase characteristics that are not realizable using traditional design techniques. For example, the stopband of a fractional-order filter can be designed to achieve -20(n+a) dB/decade of attenuation, where n is the integer order of the filter and 0<a<1 is the fractional step (not easily implemented with traditional integer order design techniques). These filters offer greater design flexibility than their integer order counter-parts, meaning they can be designed to meet the exact specifications of target applications.
Research Problem: The circuit theory to design and realize fractional-order filters remains largely undeveloped. In this project students will work to generalize and optimize the design process to realize a fractional-filter from a set of target specifications, the process to analyze their stability, and the topologies for their realization using fractional-order components or integer-order emulation circuits.
Role of Student in Research: Application of optimization search routines to approximate fractional-order lowpass, highpass, bandpass, and bandreject responses necessary to meet attenuation specifications; implementation of electrical circuit topologies to realize fractional-order transfer functions; approximation of fractional-order components; circuit simulation and physical realization of designed fractional filter circuits.
Software/Equipment: Students will use MATLAB to implement optimization routines to design and visualize the filter responses, Cadence circuit simulator to verify the circuit functionality, and measurement of physical filter circuits using network analyzer to validate their operation.
Design and Implementation of Fractional-Order Elements by Resistive-Capacitive Elements with Distributed Parameters (RC-EDP)
Fractional-order circuits and systems are typically designed using fractional-order capacitors or inductors before their simulation and realization. Although fractional-order elements (FOEs) can be approximated using integer-order realizations, there are currently no FOEs that are commercially available, compact, feature wide frequency range operability, and can be electronically tuned. Using resistive-capacitive elements with distributed parameters (RC-EDP) is being actively investigated. However, further research is required to develop this design technique, incorporating the fabrication technology properties; which limit the accuracy of the phase and magnitude response and the usable frequency bandwidth of these designs.
Research Problem: Research is required to investigate the influences of fabrication technology parameters including phenomena at the layer boundaries and parasitic influences of metallic contacts on the RC-EDP design. Analyses will focus on thick-film technology, which has currently been utilized for RC-EDP fabrication and expand to include thin-film and CMOS technologies. Different technologies have different layer properties which are expected to impact the frequency limits of the RC-EDP. Students will also investigate possibilities of tuning the fractional-order, pseudocapacitance, and frequency range of these devices for each technology.
Role of Student in Research: Familiarization with RC-EDP design software, simulation models of RC-EDP, and properties of thick-, thin-film and CMOS technology with respect to the fabrication of RC-EDPs. Measurements of available thick-film samples of RC-EDPs, analysis of their properties, design of their simulation models. Investigation of deviations from the target impedance characteristics and finding methods of improving the design and fabrication process.
Software/Equipment: Students will use RC-EDP design software that provides electrical and geometrical properties of the layer structure of these elements, Cadence OrCAD circuit simulation software for modeling device impedance properties, and impedance analyzers to measure device samples
Design and Implementation of Impedance Transformation Circuits for Realizing Fractional-Order Elements
It is necessary to explore different techniques to realize Fractional Order Elements (FOEs) to understand their different features in terms of realizing specific fractional-order properties (fractional-orders, pseudo-capacitances, frequency ranges), design complexity, and sensitivity to process variations to name a few. Current designs of fractional-order systems often integrate FOEs approximated by RC networks. However, requiring fractional-orders that are close to zero (0) or unity (1) results in very high ratios in the values of resistors and capacitors which is a limitation on the practical implementations. Methods that reduce these ratios to realize FOEs with practical component values or even active devices without passives are needed to continue advancing FOEs that can be easily integrated into circuits and systems.
Research problem: Impedance converters are active circuits that transform the impedance of a seed element to a desired target impedance, widely used in active designs to emulate inductive characteristics that can be designed on-chip. Research is required to characterize how integer-order impedance converters can be expanded to fractional-order, the limitations of frequency band and fractional-orders that can be practically realized, and their experimental validation.
Role of the Student in Research: Design and validation of impedance converters functionality and their generalization to fractional-order; performance optimization based on targeted frequency bands; experimental validation using active circuit elements.
Software/Equipment: Students will use Cadence circuit simulators to implement and validate their grounded and floating impedance converter functionalities; measure implemented circuits in time and frequency domains using oscilloscopes/function generators and network analyzers.
Fractional-order Emulators for Characterizing Measurement Accuracy
Systems that can be modelled by fractional-order impedances are widely observed in biology. The fractional-order parameters of these systems are obtained from experimental impedance data that are fit to an expected mathematical model based on an underlying physical theory that predicts the impedance. These parameters can be tracked over time to identify changes in the observed system, which is useful for monitoring the health of batteries and identifying pathologies in biological tissues. However, characterizing new instruments for measuring fractional-order impedances is particularly challenging due to the time-dependent behavior of materials with these properties. Therefore, there is a need for reliable emulators of impedance properties representative of real-world systems that preserve their electrical properties over time. The availability of these emulators will enable comparison of various measurement techniques and estimation methods to evaluate them in terms of simplicity, accuracy and in case of biological tissues the time required to perform the measurements.
Research problem: Electrical emulators for fractional-order systems have been presented, but they are limited to specific cases which are not representative of the full range of impedances in expected applications. Therefore, there is a need to define and implement a set of universal fractional-order electrical emulators to support for further development of fractional-order measurement techniques.
Role of the Student in Research: Measurement of biological samples with fractional-order impedances, design of circuit topologies to emulate the range of measured impedances, and simulation/experimental validation of proposed circuit topologies.
Software/Equipment: Students will measure the properties of material and tissues, design emulators to replicate these measurements, and validate their designs using Cadence circuit simulators, and if required perform optimization to achieve greater emulation accuracy. The experimental measurements in time and frequency domain will be performed using mainly the network analyzers, function generators and oscilloscopes.
Alternatives to Direct Fractional-Order Impedance Measurements
Impedance spectroscopy (IS) is a useful and convenient analytical tool in material research to characterize material (solid or liquid) properties by relatively simple electrical measurements, and is widely used to characterize materials with fractional-order properties. However, in many cases measurements at very low frequencies are required; with low frequencies referring to measures in the low Hz and mHz range. For this level of precision, expensive equipment is typically required along with long measurement times; which limits its adoption for measuring time-varying systems.
Research problem: Alternatives to impedance analyzers for characterizing material impedance use the transient response of the sample. The sample can be driven as a one-port network by a current or voltage waveform with the excited response directly measured in the time domain or the sample can be used as a component of two-port network that suitably transforms its impedance to a transfer function can be measured. From both methods, the fractional-order characteristics can be estimated, but this requires models of the responses derived from the fractional-order perspective and circuits to apply the necessary excitations and measure the resulting responses.
Role of the Student in Research: Theoretical development of mathematical methods to determine impedance of tested samples without using an impedance analyzer, design of circuits to collect the transient and/or frequency response based on the proposed method, and their experimental validation.
Software/Equipment: Students will use Cadence circuit simulators to observe the time and frequency behavior of measurement circuits with fractional-order impedances, collect time-domain and frequency domain responses using oscilloscopes and network analyzers, and apply signal processing routines in MATLAB to extract fractional-order impedances from collected responses.