Current–Mode Fractional–Order Electronically Controllable Integrator Design

This contribution presents a design of a current–mode fractional–order electronically controllable integrator which can be used as a building block for a design of fractional–order (FO) circuits. The design is based on a 2nd–order Follow–the–Leader–Feedback topology which is suitably approximated to operate as an integrator of a fractional order. The topology is based on Operational Transconductance Amplifiers (OTAs), Adjustable Current Amplifiers (ACAs) and Current Follower (CF). The proposed structure offers the ability of the electronic control of its fractional order and also the electronic control of the frequency band. Simulations in Cadence IC6 (spectre) and more importantly experimental measurements were carried out to support the proposal. If wider bandwidth where the approximation is valid is required, a higher order structure must be used as also shown in this paper by utilization of a 4th–order FLF topology

Arbitrarily Tunable Phase Shift in Low-Frequency Multiphase Oscillator

A special electronically tunable multiphase oscillator with arbitrarily and continuously adjustable phase shifts is introduced. Our design assumes to set the phase around the asymptotical limit of 180.. These features cannot be easily achieved in a standard way, i.e., any simple single-phase oscillator supplemented by a first-order adjustable all-pass (AP) section (shifter). The proposed design uses an electronically linearly tunable quadrature oscillator with a frequency range from 0.98 up to 12.54 kHz. It also offers multiples of 45. as the initial setting of the phase shift tuning region. The example of operation shows the adjustment of the phase shift at a specific frequency (10 kHz) within the range of +/- 45 degrees. and around -180 degrees, -135 degrees, and -90 degrees. This variability is not available in standard cases without the use of several AP sections. The current value of the phase shift of the presented oscillator is electronically controlled and does not influence the oscillation frequency and condition of oscillation. Output levels of produced signals are not influenced by this tuning process and are in the range of several hundreds of mV. Two applications of the oscillator are proposed. The first one focuses on low-bitrate modulation systems [phase shift keying (PSK)] while in the second one, our circuit represents a source of phase-adjustable signals in acoustic experiments. Discrete passive elements and active devices (special multipliers having current output terminals, unity-gain differential voltage buffers) fabricated in 0.35 mu m I3T25 ON Semiconductor 3.3 V CMOS process are used in experimental verification

Analog Implementation of Fractional-Order Elements and Their Applications

With advancements in the theory of fractional calculus and also with widespread engineering application of fractional-order systems, analog implementation of fractional-order integrators and differentiators have received considerable attention. This is due to the fact that this powerful mathematical tool allows us to describe and model a real-world phenomenon more accurately than via classical “integer” methods. Moreover, their additional degree of freedom allows researchers to design accurate and more robust systems that would be impractical or impossible to implement with conventional capacitors. Throughout this thesis, a wide range of problems associated with analog circuit design of fractional-order systems are covered: passive component optimization of resistive-capacitive and resistive-inductive type fractional-order elements, realization of active fractional-order capacitors (FOCs), analog implementation of fractional-order integrators, robust fractional-order proportional-integral control design, investigation of different materials for FOC fabrication having ultra-wide frequency band, low phase error, possible low- and high-frequency realization of fractional-order oscillators in analog domain, mathematical and experimental study of solid-state FOCs in series-, parallel- and interconnected circuit networks. Consequently, the proposed approaches in this thesis are important considerations in beyond the future studies of fractional dynamic systems

Collective analog bioelectronic computation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 677-710).In this thesis, I present two examples of fast-and-highly-parallel analog computation inspired by architectures in biology. The first example, an RF cochlea, maps the partial differential equations that describe fluid-membrane-hair-cell wave propagation in the biological cochlea to an equivalent inductor-capacitor-transistor integrated circuit. It allows ultra-broadband spectrum analysis of RF signals to be performed in a rapid low-power fashion, thus enabling applications for universal or software radio. The second example exploits detailed similarities between the equations that describe chemical-reaction dynamics and the equations that describe subthreshold current flow in transistors to create fast-and-highly-parallel integrated-circuit models of protein-protein and gene-protein networks inside a cell. Due to a natural mapping between the Poisson statistics of molecular flows in a chemical reaction and Poisson statistics of electronic current flow in a transistor, stochastic effects are automatically incorporated into the circuit architecture, allowing highly computationally intensive stochastic simulations of large-scale biochemical reaction networks to be performed rapidly. I show that the exponentially tapered transmission-line architecture of the mammalian cochlea performs constant-fractional-bandwidth spectrum analysis with O(N) expenditure of both analysis time and hardware, where N is the number of analyzed frequency bins. This is the best known performance of any spectrum-analysis architecture, including the constant-resolution Fast Fourier Transform (FFT), which scales as O(N logN), or a constant-fractional-bandwidth filterbank, which scales as O (N2).(cont.) The RF cochlea uses this bio-inspired architecture to perform real-time, on-chip spectrum analysis at radio frequencies. I demonstrate two cochlea chips, implemented in standard 0.13m CMOS technology, that decompose the RF spectrum from 600MHz to 8GHz into 50 log-spaced channels, consume < 300mW of power, and possess 70dB of dynamic range. The real-time spectrum analysis capabilities of my chips make them uniquely suitable for ultra-broadband universal or software radio receivers of the future. I show that the protein-protein and gene-protein chips that I have built are particularly suitable for simulation, parameter discovery and sensitivity analysis of interaction networks in cell biology, such as signaling, metabolic, and gene regulation pathways. Importantly, the chips carry out massively parallel computations, resulting in simulation times that are independent of model complexity, i.e., O(1). They also automatically model stochastic effects, which are of importance in many biological systems, but are numerically stiff and simulate slowly on digital computers. Currently, non-fundamental data-acquisition limitations show that my proof-of-concept chips simulate small-scale biochemical reaction networks at least 100 times faster than modern desktop machines. It should be possible to get 103 to 106 simulation speedups of genome-scale and organ-scale intracellular and extracellular biochemical reaction networks with improved versions of my chips. Such chips could be important both as analysis tools in systems biology and design tools in synthetic biology.by Soumyajit Mandal.Ph.D