Wave digital simulation of passive systems in linear state‐space form

This paper deals with wave digital modeling of passive state‐space models. The set of differential equations must be of linear state‐space form, but all parameters can be time‐variant and/or nonlinear. For such state‐space models, a canonical internally passive reference circuit is presented and used for deriving wave digital structures. In order to show the usability, special solutions for important basic linear time‐variant models are compared with wave digital simulation results. Moreover, the wave digital modeling of a nonlinear and time‐variant oscillator is discussed. Especially for a lossless oscillator an implementation is proposed, which preserves energy under finite‐arithmetic conditions. This is verified by comparing simulation results with the analytical solution of a gravity pendulum. Copyright © 2009 John Wiley & Sons, Ltd.     

Exact solutions of cyclically symmetric oscillator equations with non-linear coupling. Part II: Coupling with phase shift

Several authors have found very simple exact limit cycle solutions in cyclically symmetric systems of N oscillator equations with linear coupling in zero order of a perturbation parameter and non-linear coupling in first order. In contrast with such solutions in most other non-linear systems, each of these limit cycles is an exact normal mode of the unperturbed equations with no change in frequency or addition of higher harmonics. In Part I of this paper it was shown that the construction and analysis of such systems of equations are substantially simplified if the equations are expressed in terms of the normal mode co-ordinates of the unperturbed system. the effects of the cyclic symmetry, as well as those of a higher symmetry shared by previous authors' models, were studied. It is shown here that similar results can be obtained in systems if the coupling involves a phase shift. the phase shift places added conditions on the systems, so that some sets of equations, shown to have the simple limit cycle solutions, no longer have them after shift is introduced. the methods of the earlier paper, however, can be used to find families of systems with phase shifts which have such solutions. A result in Part I, that frequencies in a system with the higher symmetry mentioned above are unchanged from those of the unperturbed system, is not valid if phase shifts are introduced.     

Identification of the parameters of the high‐frequency equivalent circuit of PM synchronous motor based on genetic algorithm

This paper presents an identification technique of parameters of a high‐frequency equivalent circuit of permanent magnet synchronous motors (PMSM) driven by a PWM inverter. The high‐frequency oscillatory currents such as leakage current to the motor frame (common‐mode current) and high‐frequency oscillatory line current (normal‐mode current) are generated by switching instants of inverter transistors. The parameters of the high‐frequency equivalent circuit of PMSM which can simulate the oscillating current are identified by means of genetic algorithm. It is shown that the high‐frequency equivalent circuit with identified parameters can generate the oscillating current by some simulation results. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn, 167(4): 57–66, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20717     

A current‐mode 1kHz/10kHz low‐voltage integrated analogue PLL for lock‐in portable applications

We present a low‐supply voltage (2V) low‐power consumption (500W) analogue phase‐locked loop (PLL), working at two low frequencies (1 and 10kHz), to be used in an integrated lock‐in amplifier. An externally settable control bit allows the switching operation between the two different frequencies. The circuit has been designed in a standard 0.6–m CMOS technology and differs from the standard analogue PLL architectures for the current mode implementation of both the loop filter and of the oscillator. Three different locked waveforms (sinusoidal, triangular, squared) can be obtained at the PLL output. Simulation results, obtained through the use of PSPICE and using accurate transistor models, will be proposed. The pull‐in ranges are about ±250Hz around 1 and ±1.3kHz around 10kHz, with pull‐in times of about 10 and 4ms, respectively. Copyright © 2003 John Wiley & Sons, Ltd.     

CMOS current‐steering DAC architectures based on the triple‐tail cell

In this paper two novel current‐steering digital‐to‐analog converter (DAC) architectures, exploiting the triple‐tail cell as switching element, are presented. The proposed solutions are theoretically analysed and design equations are carried out. The two architectures show better performance than the classical binary‐weighted solution and it is shown that they can profitably substitute the binary sub‐DAC section in a segmented topology. Theoretical results are compared with behavioural‐level simulations and confirm the effectiveness of the proposed architectures. Copyright © 2007 John Wiley & Sons, Ltd.     

Frequency–amplitude relations for cross‐coupled voltage‐controlled oscillator

Dependence of frequency on amplitude and control bias is considered for the cross‐coupled voltage‐controlled oscillator. Closed form expressions are derived for frequency of oscillation as a function of amplitude, for positive and negative control bias voltages. Theory of nonlinear ordinary differential equations is utilized to show that the capacitance–voltage relation is the main cause of frequency shift with amplitude. Furthermore, the case of small amplitudes relative to control voltage is analyzed, and a closed form expression is derived for dependence of frequency on amplitude. This relation is then verified using the concept of effective capacitance. The effective capacitance approach is also used to extend the analysis to large voltage swings. Dependence of frequency on tuner control voltage is calculated for both bias polarities. Implications of the aforementioned equations for voltage‐controlled oscillator performance are discussed. Numerical calculations and simulations are used to compare and verify the closed form equations, showing good agreement. Copyright © 2012 John Wiley & Sons, Ltd.     

Exact solutions of cyclically symmetric oscillator equations with non-linear coupling

Kaplan and Yardeni have found very simple exact limit cycle solutions in cyclically symmetric systems of N oscillator equations with linear coupling in zero order of a perturbation parameter and non-linear coupling in first order. In contrast with such solutions in other non-linear systems, each of these limit cycles is a normal mode of the unperturbed equations, with no change in frequency. the sources of this simple behaviour are studied here with the equations expressed in terms of the normal mode co-ordinates of the unperturbed system rather than in the original co-ordinates. It is found that the simplicity of the Kaplan-Yardeni solutions arises partly from an additional symmetry of the perturbation terms beyond the cyclic symmetry and partly from the specific choices of the perturbations. Extension of their systems to arbitrary N leads to the result that all such sets of equations have similar simple limit cycles. More general cyclically symmetric sets of equations are also discussed, with limit cycle solutions whose frequencies are shifted from the zero-order values by easily calculated amounts or with solutions which are linear combinations of zero-order normal modes.     

Design and performance study of phase‐locked loop using fractional‐order loop filter

The present work reports the realization of an analog fractional‐order phase‐locked loop (FPLL) using a fractional capacitor. The expressions for bandwidth, capture range, and lock range of the FPLL have been derived analytically and then compared with the experimental observations using LM565 IC. It has been observed that bandwidth and capture range can be extended by using FPLL. It has also been found that FPLL can provide faster response and lower phase error at the time of switching compared to its integer‐order counterpart. Copyright © 2014 John Wiley & Sons, Ltd.     

Two‐dimensional non‐stationary numerical model for MSM structures

In this paper the solution of the non‐stationary model for MSM structures is obtained numerically. The two‐dimensional model consists of three singularly perturbed non‐linear partial differential equations. The alternating‐direction method for discretization in time and the non‐oscillatory streamline upwind method on a piecewise uniform grid for discretization in space are used to eliminate the interior and boundary layer oscillations. The described model is used for the analysis of the time response of a GaAs n‐type MSM structure to a Heaviside function form of the applied voltage. For the stationary case the I–V characteristic of the structure is determined. The numerical results confirm that the applied method is convenient for solving convection–diffusion problems. Copyright © 1999 John Wiley & Sons, Ltd.     

Uniqueness of the asymptotic behaviour of autonomous and non-autonomous,switched and non-switched,linear and non-linear systems of dimension 2

An explicit criterion is given which guarantees that the solutions of a system of two first-order differential equations have a unique asymptotic behaviour as t'→ + ∞. the equations are allowed to be time-dependent, with isolate discontinuities (switching), and non-linear. In particular, continuously differentiable and piecewise linear systems, as far as the dependence on the state variables is concerned, are considered. the particular case of a linear system switched back and forth between two 2 × 2 matrices is treated in detail, with an outline of an algorithm to decide on the converence to zero of the solutions. The case of switching between N matrices is a straightforward generalization that is, however, not covered in this paper. It is shown that the problem of unique asymptotic behaviour of piecewise linear systems can always be treated by considering such switched linear systems. Furthermore, an example shows that even some continuously differentiable systems may be reduced to this case. Finally, the connection with the work of Brayton and Tong on the stability of differential equations, also using sets of matrices, is given.     

Improved switching mode oscillators employing generalized switching lines

The present work proposes an unusual method for controlling the activation of the switches of switching mode oscillators. The proposed method is in fact a tool for developing switching mode oscillators that are controlled by full variable feedback. The methods developed in the present article rely on characterizing the switching procedure by intentionally moulding the related switching line (the switching line is the line in the state space, where the switches change polarity). The switching line in most of the switching mode oscillators is relatively simple. For example, in many cases the switch changes state in accordance with the output current sign. Hence, the line ‘output current’ is zero, is the switching line in this case. Relatively many advantages are attained by the present moulding of the switching line. For example, oscillators that oscillate even with very low‐quality factor (large load) are obtainable. The proposed method enables a simple way for controlling the output voltage and the frequency of the switching mode oscillator. Furthermore, current limiter property of the oscillator output can be obtained by the method, even in cases where the original oscillator is inherently a voltage source. The output impedance is also made controllable by the method. The successfully improved characteristics are demonstrated by investigating a particular structure, namely, a switching mode series resonant oscillator. Copyright © 2000 John Wiley & Sons, Ltd.     

M‐matrices and global convergence of discontinuous neural networks

The paper considers a general class of neural networks possessing discontinuous neuron activations and neuron interconnection matrices belonging to the class of M‐matrices or H‐matrices. A number of results are established on global exponential convergence of the state and output solutions towards a unique equilibrium point. Moreover, by exploiting the presence of sliding modes, conditions are given under which convergence in finite time is guaranteed. In all cases, the exponential convergence rate, or the finite convergence time, can be quantitatively estimated on the basis of the parameters defining the neural network. As a by‐product, it is proved that the considered neural networks, although they are described by a system of differential equations with discontinuous right‐hand side, enjoy the property of uniqueness of the solution starting at a given initial condition. The results are proved by a generalized Lyapunov‐like approach and by using tools from the theory of differential equations with discontinuous right‐hand side. At the core of the approach is a basic lemma, which holds under the assumption of M‐matrices or H‐matrices, and enables to study the limiting behaviour of a suitably defined distance between any pair of solutions to the neural network. Copyright © 2006 John Wiley & Sons, Ltd.     

A generalized family of memristor‐based voltage controlled relaxation oscillator

Recently, memristive oscillators are a significant topic in the nonlinear circuit theory where there is a possibility to build relaxation oscillators without existence of reactive elements. In this paper, a family of voltage‐controlled memristor‐based relaxation oscillator including two memristors is presented. The operation of two memristors‐based voltage relaxation oscillator circuits is demonstrated theoretically with the mathematical analysis and with numerical simulations. The generalized expressions for the oscillation frequency and conditions are derived for different cases, where a closed form is introduced for each case. The effect of changing the circuit parameters on the oscillation frequency and conditions is investigated numerically. In addition, the derived equations are verified using several transient PSPICE simulations. The power consumption of each oscillator is obtained numerically and compared with its PSPICE counterpart. Furthermore, controlling the memristive oscillator with a voltage grants the design an extra degree of freedom which increases the design flexibility. The nonlinear exponential model of memristor is employed to prove the oscillation concept. As an application, two examples of voltage‐controlled memristor‐based relaxation oscillator are provided to elaborate the effect of the reference voltage on the output voltage. This voltage‐controlled memristor‐based relaxation oscillator has nano size with storage property that makes it more efficient compared with the conventional one. It would be helpful in many communication applications.     

Small‐signal analysis of interleaved dual boost converter

This paper presents a systematic development of steady‐state, small‐signal models of interleaved dual boost converter operating in a continuous current mode. These models are derived by employing the well‐known signal flow graph method. This signal flow graph approach provides a means to directly translate the switching converter into its equivalent graphic model, from which a complete behaviour of the converter can easily be studied. Steady‐state performance, small‐signal characteristic transfer functions are derived using Mason's gain formula. The bode plots of audiosusceptibility, input impedance, output impedance, and control‐to‐output transfer functions are determined and illustrated using MATLAB for different values of load resistances, duty ratios. Small‐signal frequency responses obtained from the signal flow graph method are validated with PSPICE simulator results. To validate the signal flow graph modelling equations, sample steady‐state experimental results are provided. Copyright © 2001 John Wiley & Sons, Ltd.     

A minimum five‐component five‐term single‐nonlinearity chaotic jerk circuit based on a twin‐jerk single‐op‐amp technique

A minimum 5‐component 5‐term single‐nonlinearity chaotic jerk circuit is presented as the first simplest chaotic jerk circuit in a category that a single op‐amp is employed. Such a simplest circuit displays 5 simultaneous advantages of (1) 5 minimum basic electronic components, (2) 5 minimum algebraic terms in a set of 3 coupled first‐order ordinary differential equations (ODEs), (3) a single minimum term of nonlinearity in the ODEs, (4) a simple passive component for nonlinearity, and (5) a single op‐amp. The proposed 5‐term single‐nonlinearity chaotic jerk circuit and a slightly modified version of an existing 6‐term 2‐nonlinearity chaotic jerk circuit form mirrored images of each other. Although both mirrored circuits yield 2 different sets of the ODEs, both sets however can be recast into a pair of twin jerk equations. Both mirrored circuits are therefore algebraically twin 5‐component chaotic jerk circuits, leading to a twin‐jerk single‐op‐amp approach to the proposed minimum chaotic jerk circuit. Two cross verifications of trajectories of both circuits are illustrated through numerical and experimental results. Dynamical properties are also presented.     

A common‐mode replica compensated inductor–capacitor voltage‐controlled oscillator for mixed‐signal system‐on‐chip applications

A novel 1.57 GHz complementary metal–oxide semiconductor inductor–capacitor voltage‐controlled oscillator with the common‐mode replica compensation is introduced for mixed‐signal system‐on‐chip applications. In order to alleviate power line disturbances, the center tap node of differential symmetric inductor and the replica biasing circuit are adopted in the differential voltage regulating unit to reduce power supply sensitivity. In addition, this proposed design also leads to low tuning gain and low power dissipation. The post‐layout simulation results under the Taiwan Semiconductor Manufacturing Company's mixed‐signal 0.18 µm 1P6M process show that the proposed design achieves power supply rejection of ?68.6 dB at low frequencies and 1.2 MHz/V pushing sensitivity. It exhibits phase noise of ?130.6 dBc/Hz at a 1 MHz offset from a 1.57 GHz carrier yet dissipates only 5.58 mW under a 1.8 V power supply. Copyright © 2011 John Wiley & Sons, Ltd.     

Non‐unique solutions in drift diffusion modelling of phototransistors

We report non‐unique solutions for the potential in a Drift Diffusion (DD) model of a two terminal phototransistor. These solutions are present under bias without illumination, and persist until high illumination levels. It is well known that the DD equations can yield non‐unique solutions for pn structures which contain three or more junctions and two terminals with applied biases greater than k_BT log 2 where k_BT is the thermal energy at a temperature T, but DD models of phototransistors under illumination have been less well studied. The implicit belief is that one needs to artificially impose a potential in the base of the phototransistor in order to obtain a unique solution. We show here that this is only necessary because of a weakness in the numerical methods used to solve the equations, and describe two methods which circumvent this for which we show that this problem does not occur. These methods are used to investigate the operation of GaAs and In_0·53Ga_0·47As homojunction phototransistors, including the influence of the position of the illumination region and base doping. Copyright © 2000 John Wiley & Sons, Ltd.     

A frequency‐domain approach to the analysis of stability and bifurcations in nonlinear systems described by differential‐algebraic equations

A general numerical technique is proposed for the assessment of the stability of periodic solutions and the determination of bifurcations for limit cycles in autonomous nonlinear systems represented by ordinary differential equations in the differential‐algebraic form. The method is based on the harmonic balance (HB) technique, and exploits the same Jacobian matrix of the nonlinear system used in the Newton iterative numerical solution of the HB equations for the determination of the periodic steady state. To demonstrate the approach, it is applied to the determination of the bifurcation curves in the parameters' space of Chua's circuit with cubic nonlinearity, and to the study of the dynamics of the limit cycle of a Colpitts oscillator. Copyright © 2007 John Wiley & Sons, Ltd.     

Parameter identification of simplified common‐mode equivalent circuit for inverter‐fed motor drive systems by applying computer‐aided optimization software

This paper deals with common‐mode (CM) electromagnetic interference (EMI) in an inverter‐fed motor drive system. A simplified CM equivalent circuit including π‐type equivalent circuit for the motor winding is proposed by using the waveform of the common‐mode current flowing in the ground conductor. Moreover, a parameter identification method applying the computer‐aided software modeFRONTIER is proposed to decide objectively the circuit parameters of the proposed simplified equivalent circuit. Validity and effectiveness of the proposed equivalent circuit are confirmed by comparing the measured impedance characteristics with the calculated ones. Finally, the possibility of a nonlinear phenomenon is discussed in this system. It is shown that the accuracy of simulation result can be improved by introducing the nonlinear element. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Design equations for fractional‐order sinusoidal oscillators: Four practical circuit examples

Four practical sinusoidal oscillators are studied in the general form where fractional‐order energy storage elements are considered. A fractional‐order element is one whose complex impedance is given by Z = a(jω)^±α, where a is a constant and α is not necessarily an integer. As a result, these oscillators are described by sets of fractional‐order differential equations. The integer‐order oscillation condition and oscillation frequency formulae are verified as special cases. Numerical and PSpice simulation results are given. Experimental results are also reported for a selected Wien‐bridge oscillator. Copyright © 2007 John Wiley & Sons, Ltd.