Nonlinear theory plays an indispensable role in analysis, design and optimization of electric/electronic circuits because almost all circuits in the real world are modeled by nonlinear systems. Also, as the scale and complexity of circuits increase, more effective and systematic methods for the analysis, design and optimization are desired. The goal of this special section is to bring together research results from a variety of perspectives and academic disciplines related to nonlinear electric/electronic circuits.This special section includes three invited papers and six regular papers. The first invited paper by Kennedy entitled “Recent advances in the analysis, design and optimization of digital delta-sigma modulators” gives an overview of digital delta-sigma modulators and some techniques for improving their efficiency. The second invited paper by Trajkovic entitled “DC operating points of transistor circuits” surveys main theoretical results on the analysis of DC operating points of transistor circuits and discusses numerical methods for calculating them. The third invited paper by Nishi et al. entitled “Some properties of solution curves of a class of nonlinear equations and the number of solutions” gives several new theorems concerning solution curves of a class of nonlinear equations which is closely related to DC operating point analysis of nonlinear circuits. The six regular papers cover a wide range of areas such as memristors, chaos circuits, filters, sigma-delta modulators, energy harvesting systems and analog circuits for solving optimization problems.The guest editor would like to express his sincere thanks to the authors who submitted their papers to this special section. He also thanks the reviewers and the editorial committee members of this special section for their support during the review process. Last, but not least, he would also like to acknowledge the editorial staff of the NOLTA journal for their continuous support of this special section.

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Digital Delta-Sigma Modulators (DDSMs) are almost univerally used in integrated circuits for wireless communications and digital audio, particularly in fractional-N frequency synthesizers and oversampled digital-to-analog converters (DACs). A DDSM is a nonlinear dynamical system which reduces the wordlength of an oversampled digital signal without significantly degrading the SNR in the signal band. DDSMs can exhibit a number of behaviors that are characteristic of nonlinear dynamical systems such as oscillation, coexisting steady-state solutions, sensitivity to initial conditions, and sensitivity to the input. This paper explains the root cause of deterministic spurious and idle tones in DDSMs—short periodic cycles—and describes strategies to eliminate them. The use of a DDSM simplifies the design of analog circuitry in a mixed-signal system. By reducing the bus width in a prescribed way, a DDSM can also permit more efficient downstream digital signal processing—in terms of power and speed—with negligible degradation in performance.

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Finding a circuit's dc operating points is an essential step in its design and involves solving systems of nonlinear algebraic equations. Of particular research and practical interests are dc analysis and simulation of electronic circuits consisting of bipolar junction and field-effect transistors (BJTs and FETs), which are building blocks of modern electronic circuits. In this paper, we survey main theoretical results related to dc operating points of transistor circuits and discuss numerical methods for their calculation.

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This paper gives several theorems on solution curves of a class of nonlinear equations consisting of n variables and (n-1) equations. In particular we give a remarkable theorem on the rank of a Jacobian matrix associated with the above equations. For the proof of these theorems the Ω-matrix, which one of the authors defined previously, and the irreducible matrix play a definitely important role. As the result we show that the solution curves consist of only two types of curves.

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The peculiar features of the memristor, a fundamental passive two-terminal element characterized by nonlinear relationship between charge and flux, promise to revolutionize integrated circuit design in the next few decades. Besides its most popular potential applications, ultra-dense non-volatile memories and brain-simulating systems, much research has been lately devoted to their use in chaotic circuits. Although the physical memristor is inherently-asymmetric, complementary behaviors arise in devices with opposite polarity. In this work we demonstrate that this makes it feasible to devise a number of practical realizations of a monotone-increasing odd-symmetric charge-flux nonlinearity suitable for chaos-based applications through the sole use of physical memristors of the kind recently fabricated at Hewlett-Packard Labs. Confirmation for such claim is obtained through comparison of chaotic behavior of two modified Chua's oscillators, in which the nonlinear diode is replaced in one case with an artificial memristor with symmetric nonlinearity and in the other case with one of the proposed symmetric memristor combinations.

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In this paper we propose the use of fractional capacitors in the Tow-Thomas biquad to realize both fractional lowpass and asymmetric bandpass filters of order 0<α₁+α₂≤2, where α₁ and α₂ are the orders of the fractional capacitors and 0<α_1,2≤1. We show how these filters can be designed using an integer-order transfer function approximation of the fractional capacitors. MATLAB and PSPICE simulations of first order fractional-step low and bandpass filters of order 1.1, 1.5, and 1.9 are given as examples. Experimental results of fractional low pass filters of order 1.5 implemented with silicon-fabricated fractional capacitors verify the operation of the fractional Tow-Thomas biquad.

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This paper presents a novel automated microwave filter tuning method based on successive optimization of zeros of reflection characteristics. We develop an optimization procedure to determine how much adjusting screws of a filter should be rotated. The proposed method consists of two stages; coarse and fine tuning stages. In the first stage, called coarse tuning, the phase response error of the target filter is minimized so that the filter roughly approximates almost-ideal bandpass characteristics. Then in the second stage, called fine tuning, we optimize the position of zeros of reflection characteristics. Performance of the proposed tuning procedure is evaluated through some experiments of actual filter tuning.

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This paper addresses a problem of designing decentralized sigma-delta modulators for quantized control, i.e., feedback control subject to quantized signal constraints. The sigma-delta modulators to be considered here have a limited information structure so as to be implemented in a decentralized manner, which poses a challenging design problem. We first analytically derive a solution to the problem such that the resulting quantized feedback system optimally approximates the corresponding unquantized system. Next, the performance is demonstrated by a numerical simulation and an experiment for the stabilization problem of a seesaw-cart system.

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This paper presents a sub-0.3V CMOS full-wave rectifier for energy harvesting devices. By adopting a body-input comparator with simple bias circuit, combining with body bias technique, the lowest input voltage amplitude can be reduced to 0.28V when using a standard CMOS 0.18µm process. Moreover, the voltage drop of negative voltage converter can be reduced to enhance the output voltage efficiency by adopting the proposed body bias technique. In combination with minimum reverse current and simple bias circuit in the proposed comparator, the proposed active rectifier can achieve the peak voltage conversion efficiency of over 96% and the maximum power efficiency of approximately 94%.

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This paper presents novel shortest paths searching system based on analog circuit analysis which is called sequential local current comparison method on alternating-current (AC) circuit (AC-SLCC). Local current comparison (LCC) method is a path searching method where path is selected in the direction of the maximum current in a direct-current (DC) resistive circuit. Since a plurality of shortest paths searching by LCC method can be done by solving the current distribution on the resistive circuit analysis, the shortest path problem can be solved at supersonic speed. AC-SLCC method is a novel LCC method with orthogonal frequency division multiplexing (OFDM) communication on AC circuit. It is able to send data with the shortest path and without major data loss, and this suggest the possibility of application to various things (especially OFDM communication techniques).

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Complex-valued Associative Memory (CAM) has an inherent property of rotation invariance. Rotation invariance produces many undesirable stable states and reduces the noise robustness of CAM. Constant terms may remove rotation invariance, but if the constant terms are too small, rotation invariance does not vanish. In this paper, we eliminate rotation invariance by introducing large constant terms to complex-valued neurons. We have to make constant terms sufficiently large to improve the noise robustness. We introduce a parameter to control the amplitudes of constant terms into projection rule. The large constant terms are proved to be effective by our computer simulations.

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We present a simple neuron model that shows a rich property in spite of the simple structure derived from the simplification of the Hindmarsh-Rose, the Morris-Lecar, and the Hodgkin-Huxley models. The model is a typical example whose characteristics can be discussed through the concept of potential with active areas. A potential function is able to provide a global landscape for dynamics of a model, and the dynamics is explained in connection with the disposition of the active areas on the potential, and hence we are able to discuss the global dynamic behaviors and the common properties among these realistic models. The obtained outputs are broadly classified as simple oscillations, spiking, bursting, and chaotic oscillations. The bursting outputs are classified as with spike undershoot and without spike undershoot, and the bursts without spike undershoot are classified as with tapered and without tapered. We show the parameter dependence of these outputs and discuss the connection between these outputs and the potential with active areas.

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