Steady-state Analysis Of Nonlinear Circuits Research Articles

Improving Efficiency of the Periodic Steady-State Analysis of Electronic Circuits Using Spectral Analysis

A key problem in the periodic steady-state analysis of electronic circuits is that the duration of transient processes in a circuit might be much larger than the period of a steady-state response. Thus, application of traditional transient methods becomes ineffective due to a huge amount of redundant computations, and special periodic-steady state methods should be used. The method for periodic steady-state analysis using the Kotelnikov-Shannon series is a time-domain method that has proved to be effective for a such type of circuits. In this method the unknown signals are expanded in the Kotelnikov-Shannon series and the derivatives of these signals are calculated as the derivatives of the series. A matrix form of the derivatives approximation leads to simple matrix expressions in a mathematical model.When using the method for periodic steady-state analysis of non-linear circuits using the Kotelnikov-Shannon series to find the steady-state response of a circuit, a time discretization step is chosen based on the spectral characteristics of the signals. As far as the goal of the method is to calculate the unknown signals in a circuit, a vicious circle occurs: to calculate the signals, the time discretization step has to be chosen, and to choose the time discretization step, the spectral characteristics of the signals have to be known, namely the upper frequency in these characteristics.In order to choose the time discretization step, we propose to calculate a partial transient response of a circuit for an input signal of the form of the Heaviside step function, which is usually used to obtain a step response of a linear circuit. The response is calculated with any method, suitable for solving a system of non-linear ordinary differential equations, which usually represents the mathematical model of a circuit. The upper frequency in the spectral characteristic of the partial transient response depends on the duration of the computational domain. The upper frequency versus the duration of the computational domain dependency can be approximated with a hyperbolic function. Thus, calculating few values of the upper frequency at different durations of the computational domain, the value of the upper frequency when the duration of the computational domain is equal to the period of a steady-state response can be forecasted using the hyperbolic approximation.

Autonomous Volterra Algorithm for Steady-State Analysis of Nonlinear Circuits

We present a novel algorithm, named autonomous Volterra (AV), that achieves efficient steady-state analysis of nonlinear circuits. With elegant analytic forms and availability of efficient solvers, AV constitutes a competitive steady-state algorithm besides the two mainstreams, namely, shooting Newton (SN) and harmonic balance (HB). Nonlinear systems are first captured in nonlinear differential algebraic equations, followed by expansion into linear Volterra subsystems. A key step of steady-state analysis lies in modeling each Volterra subsystem with autonomous nonlinear inputs. The steady-state solution of these subsystems then proceeds with a series of Sylvester equation solves, completely avoiding the guesses of initial condition and time stepping as in SN, as well as the uncertain length of Fourier series as in HB. Error control in AV is also straightforward by monitoring the norms of the Sylvester equation solutions. We further demonstrate that AV is readily parallelizable with superior scalability toward large-scale problems.

A Wavelet-Based Approach for Steady-State Analysis of Nonlinear Circuits With Widely Separated Time Scales

We propose a new wavelet method for steady-state analysis of nonlinear circuits. The new method inherits the robustness of wavelet-based technique in handling very strong nonlinear circuits while offering significant reduction of simulation costs for circuits with widely separated time scales

On the steady-state analysis of nonlinear circuits with frequency dependent parameters in wavelet domain

This letter introduces a new method for steady state analysis of nonlinear circuits with frequency dependent parameter components. The method enables treatment of distributed parameter components in a wavelet domain steady state circuit simulator. The method features thresholding of the convolution matrix in wavelet domain in order to reduce computational cost and is suitable for highly nonlinear circuits with distributed parameters under multitone excitations.

A wavelet-balance approach for steady-state analysis of nonlinear circuits

In this paper, a novel wavelet-balance method is proposed for steady-state analysis of nonlinear circuits. Taking advantage of the superior computational properties of wavelets, the proposed method presents several merits compared with those conventional frequency-domain techniques. First, it has a high convergence rate O(h/sup 4/), where h is the step length. Second, it works in time domain so that many critical problems in frequency domain, such as nonlinearity and high order harmonics, can be handled efficiently. Third, an adaptive scheme exists to automatically select proper wavelet basis functions needed at a given accuracy. Numerical experiments further prove the promising features of the proposed method in solving steady-state problems.

Symbolic Steady-State Analysis for Strongly Nonlinear Circuits and Systems

A symbolic method for steady-state analysis of nonlinear circuits and systems is presented. This method is based on the principle of the Equivalent Small Parameter method (the ESP method), which is...

Steady-state analysis of nonlinear circuits based on hybrid methods

Two efficient algorithms for calculating the steady-state responses of nonlinear circuits are proposed. They are based on both time-domain and frequency-domain approaches. A nonlinear circuit is partitioned into two subnetworks with substitution sources, and their responses are solved by a combined frequency-domain and time-domain method. The total response of the combined circuit can be calculated by an iterative technique based on either the Newton or the relaxation harmonic balance method. Since the methods are based on both time-domain and frequency-domain algorithms, they are called the Newton and the relaxation hybrid harmonic balance methods, respectively. The methods can be applied efficiently to strong nonlinear circuits containing high-Q subnetworks such as filter circuits and crystal oscillators. When a large-scale circuit is partitioned into large linear subnetworks and small nonlinear subnetworks, the method can also be applied efficiently. >

Use of multidimensional discrete Fourier transforms in the harmonic balance method

Time to frequency and frequency to time domain conversion algorithms needed in the steady-state analysis of non-linear circuits using the harmonic balance method become considerably complicated for multitone signal inputs. This paper shows that an efficient algorithm using the multidimensional discrete Fourier transform can be employed for a proper choice of the input signal frequencies.

Computation of the periodic steady-state response of nonlinear networks by extrapolation methods

The problem of computing the periodic steady-state response can be formulated as solving a nonlinear equation of the form <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z = F(z)</tex> where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F(z)</tex> Is the solution vector for the nonlinear network after one period of integration from the initial vector <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</tex> . The convergence of the sequence <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y_0 , y_1 , \cdots</tex> generated by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y_{r+1} = F(y_r)</tex> can be accelerated by extrapolation methods. This paper presents a unified analysis of three extrapolation methods: the scalar and vector <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\epsilon</tex> -algorithms and the minimum polynomial extrapolation algorithm. The main result of the paper is the theorem giving conditions for quadratic convergence of the extrapolation methods. To obtain this result the methods are studied for linear problems (where F is a linear function) and the error propagation properties are investigated. For autonomous systems a function called <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</tex> similar to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</tex> can be defined. In order to obtain quadratic convergence from the extrapolation methods, the derivatives of F and G must be Lipschitz continuous. The appendixes give sufficient conditions for the Lipschitz continuity. A discussion of practical problems related to the implementation of the extrapolation methods is based on the convergence theorem and the error analysis. The performance of the extrapolation methods is demonstrated and compared with other methods for steady-state analysis by four examples, two autonomous and two nonautonomous. Extrapolation methods are very easy to implement, and they are efficient for the steady-state analysis of nonlinear circuits with few reactive elements giving rise to slowly decaying transients.

Steady-state analysis of nonlinear circuits with periodic inputs

In the computer-aided analysis of nonlinear circuits with periodic inputs and a stable periodic response the steady-state periodic response is found for a given initial state by simply integrating the system equations until the response becomes periodic. In lightly damped systems this integration could extend over many periods making the computation costly. In this paper a Newton algorithm is defined which converges to the steady-state response rapidly. The algorithm is applied to several nonlinear circuits. The results show a considerable reduction in the amount of time necessary to compute the steady-state response. In addition, the initial iterates give information on the transient response of the system.