Designing non-linear single OP-AMP circuits: A cook-book approach

The inherent saturation non-linearity of the op amp is used to design circuits having a wide variety of useful non-linear v-i characteristics. These circuits are made of one op amp and 3 or 4 linear resistors which are passive under a rather mild assumption derived from the 3-port paramountcy condition. Explicit design formulae are given for each prototype circuit and numerous examples are given and validated by actual measurements.     

An efficient interval method for global analysis of non-linear resistive circuits

A new method for finding the set of all operating points of non-linear resistive circuits is suggested. It takes into account the fact that the circuit equations are in the so-called separable form where any equation f_i(x) is the sum of terms f_ij(x_j), each term depending on a single variable. The method is based on the introduction of an approximation of every real non-linear function f_ij(x_j) by an appropriate linear interval function, i.e. by a real linear function having an additive interval term. The parameters of the linear interval approximations are dynamically updated at each iteration of the computational process. Numerical experiments show that the computational efficiency of the new method is vastly superior to that of other known methods for global analysis, especially for circuits of large size. © 1998 John Wiley & Sons, Ltd.     

An interval method for finding all operating points of non-linear resistive circuits

A new method for finding the set of all d.c. operating points of non-linear electronic circuits is suggested. it is applicable in the case where the circuit equations are written in the hybrid-representation form. In the general case, the non-linear elements involved may be described by non-monotone continuous characteristics. The method suggested is based on interval analysis techniques. Unlike other non-interval methods, this approach guarantees that all operating points will be found within prescribed accuracy in a finite number of steps. The computational efficiency of the present method is illustrated by a numerical example.     

Small-signal harmonic analysis of non-linear circuits

An approximate harmonic analysis method for non-linear circuits is introduced. the method solves the steady state, time domain representation as well as the frequency response of non-linear circuits. It allows simulation of non-ideal switched capacitor circuits composed of any kinds of linear components and non-linear transistors as switches. All switches must have the same period, but they can be opened and closed at any time. the method proposed may also be applied to mixer analysis for the case of strong LO and weak RF signals. Examples are given to demonstrate that the method is efficient and sufficiently fast to be used in circuit design. the simulation results show good agreement with those obtained by harmonic balance and transient analysis.     

Curve-search algorithm for DC analysis of non-linear electronic circuits

The solution of the original DC analysis problem is reformulated as a search for a certain point in functional space which belongs to the curve in the same space. the generalized matrix equation of the hyperplane normal to this curve is easily derived and a new iterative algorithm is presented. Some critical situations arising in non-linear circuit simulation and the behaviour of the new approach in these cases are considered. Six application examples are given.     

A discrete-time approach to the steady state analysis and optimization of non-linear autonomous circuits

In this paper a method for the steady state analysis and optimization of non-linear autonomous circuits is described. After discretizing the linear part of the circuit, a system of non-linear algebraic equations is obtained. the final formulation is written entirely in the discrete-time domain, making it unnecessary to repeatedly take direct and inverse DFTs during the solution process. Furthermore, it is shown that the resulting formulation may be viewed as a generalization of the harmonic balance equations. an analytic method for computing the exact partial derivatives of the resulting equations with respect to the samples of the variables, the oscillation period and the circuit element values is described, making the proposed approach efficient for both analysis and optimization. Different globally convergent techniques for solving the non-linear system of equations are described, with emphasis on an algorithm based on fast simulated diffusion. Selected application examples are provided to validate the proposed approach.     

Efficient frequency-domain modelling and simulation of nonuniform coupled transmission lines: application in transient analysis of VLSI circuits

A new method of analysis of the transients in nonuniform lossy multiconductor transmission lines with frequency-dependent parameters is presented. The terminations may be nonlinear, and the interconnections networks are arbitrary. The method of the solution is based on steplines approximation of the nonuniform transmission lines and quasitransverse electromagnetic mode (quasi-TEM) assumptions. Using steplines approximation, the system of coupled nonuniform transmission lines is subdivided into an arbitrarily large number of coupled uniform lines (steplines) with different characteristics. Then, using the modal decomposition method, the system of coupled partial differential equations for each step is decomposed into a number of uncoupled ordinary telegraph equations, which are then solved in the frequency domain. Thereafter each step of the system is modelled as a linear filter with frequency-dependent coefficients. The terminations for linear and nonlinear cases are then modelled as linear or nonlinear systems. Finally, the transfer matrix of the system is obtained. Some examples from the literature are then solved to demonstrate the validity of the method. The method proposed here is very fast and can easily be implemented using general-purpose software packages like MATLAB.     

An interpolation model to accelerate the frequency-domain response calculation of grounding systems using the method of moments

The transient characteristics of grounding systems are essential for their designs and related electromagnetic-compatibility problems in power systems. Although the method of moments (MoM) is a popular way to analyze the characteristics of grounding systems, it is time-consuming. In this paper, a two-stage method is presented to construct fitted models of the frequency-domain responses of grounding systems to accelerate the calculations of the MoM. In the first stage, the adaptive model-based parameter estimation is used to adaptively choose the most valuable frequency sampling points to construct the initial fitted functions, and then the fitted functions are adjusted in the second stage by comparing the fitted results with those computed by the first principle model at some points. The validation was achieved by a comparison of the numerical results and those obtained by inverse fast Fourier transformation.     

Harmonic balance method applied to the numerical electrical physical modelling of two-terminal,non-linear microwave circuits in the frequency domain

A numerical frequence-domain modelling of two-terminal, non-linear microwave circuits is presented. It basically relies on a process allowing the solution of the frequency-domain curcuit harmonic balance equations while accounting for the semiconductor device by means of an accurate numerical macroscopic physical model. In its present state of development, the model allows the study of a single two-terminal device circuit operating in harmonic mode. Its capabilites are illustrated by means of the results of a study devoted to the optimization of the load curcuit configuration of a millimetre-wave avalanche diode frequency multiplier. The influence of the output load impedance level on the circuit output RF performance has been investigated for different input power levels in direct frequency multiplication mode and in the presence of additional circuit tunings at low harmonic rank idler frequencies.     

A generalized fault diagnosis method in dynamic analogue circuits

Fault diagnosis of analogue circuits is essential for analogue and mixed‐signal systems testing and maintenance. A new method is proposed in this paper for multiple fault diagnosis of linear analogue circuits in frequency domain. The Woodbury formula is applied to the modified nodal equation to construct the fault diagnosis equation, which relates the limited measured circuit responses with the multiple faults inside the circuit in a linear way. A recently developed ambiguity group locating technique is modified here to identify the faulty parameters directly. Computation cost is reduced compared to combinatorial search in traditional fault verification methods. Only one node is needed for voltage measurement, but multiple excitations on accessible nodes are required for fault identification. Parameter evaluation can provide the exact solution to the deviated values of faulty parameters. The faulty parameter deviations can have any finite values. Example circuits are provided to illustrate the proposed method. Two other methods for multiple analogue fault diagnosis sharing the same mechanism as the method proposed in this paper are also briefly described. The proposed method is extremely effective for the circuit with very limited accessible nodes and is also computationally efficient. Copyright © 2002 John Wiley & Sons, Ltd.     

A method for fault diagnosis in linear electronic circuits

A method for fault location and parameter identification in linear AC and DC circuits with limited accessible terminals for excitation and measurement is developed in this paper. Fault location is based on a derived relationship having a general meaning. It requires analyses of the circuit with nominal parameters and distinct excitations as well as measurements of some node voltages in the circuit with perturbed parameters. The fault parameter is identified using a formula obtained on the basis of the Woodbury expression. A decomposition technique is suggested enabling us to apply the method for multiple fault diagnosis. Several numerical examples illustrate the proposed approach and show its effectiveness. Copyright © 2000 John Wiley & Sons, Ltd.     

Analysis of non-linear dynamical circuits and systems under the influence of thermal noise

In some electronic systems, such as cryoelectronic circuits, random noise has to be taken into consideration for modelling and simulation. After theoretical considerations an algorithm for the simulation of non-linear circuits with random noise is developed. Methods for global analysis of non-linear dynamical systems, such as Lyapunov exponents and the Poincaré map, are applied to systems with noise. the developed algorithms are applied to the cryoelectronic circuit of the ideal DC-SQUID model. Several non-linear effects which occur through noise are explained.     

A space-domain preconditioned spectral method for non-linear boundary value problems

A novel spectral procedure for the numerical solution of non-linear boundary value problems is presented. The discrete spectral equations are solved by an iterative algorithm using space-domain preconditioning. The preconditioning operator is obtained by spatial weighting (or windowing) of the exact differential operator. Convergence behaviour of the iterative solution is investigated using an eigenvalue analysis. Theoretical estimates for the convergence rate and accuracy are compared with that achieved in a numerical application—a non-linear boundary value problem from semiconductor device modelling. The method combines the infinite-order exponential accuracy of spectral discretizations with the sparse structure of finite difference equations. This offers numerical advantages in comparison to previously developed Fourier–Galerkin algorithms, particularly important for physically ill-conditioned and strongly non-linear problems. The tradeoff of achievable accuracy versus computer time is easily controlled, thus making essential speed-ups possible for moderate accuracy requirements.     

A new vector frequency modulation method for power conversion circuits

This paper presents an effective PWM method for power conversion circuits. The proposed method is called Vector Frequency Modulation (VFM) in this paper. VFM is different from conventional PWM methods. Although VFM is based on the concept of the space voltage vector, all necessary calculations of the periods of the voltage vectors can be performed without using traditional equations. The voltage vectors are classified into two groups, zero vectors and nonzero vectors. Instead of the complicated equations, a very simple algorithm is employed in VFM. One vector period is fixed and the zero vectors are distributed among the nonzero vectors in the ratio determined by the command voltage or frequency. The action of VFM is performed in software, and no modulation‐wave oscillators, comparators, and up‐down counters are needed. First, a reversible chopper is modulated by VFM and a 2‐kW DC motor is driven by the chopper. The motor speed is regulated by modern control theory. Next, a three‐phase inverter is modulated by VFM and a 2.2‐kW induction motor is driven by the inverter. Experimental results are presented to demonstrate that VFM is useful for power conversion circuits. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 174(1): 59–68, 2011; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.20982