Preparing the books to read every day is enjoyable for many people. However, there are still many people who also don't like reading. This is a problem. But, when you can support others to start reading, it will be better. One of the books that can be recommended for new readers is computer aided analysis of electronic circuits algorithms and computational techniques. This book is not kind of difficult book to read. It can be read and understand by the new readers.

Computer-aided analysis of electronic circuits: Algorithms and computational techniques

In this paper, we present an approach to nonlinear model reduction based on representing a nonlinear system with a piecewise-linear system and then reducing each of the pieces with a Krylov projection. However, rather than approximating the individual components as piecewise linear and then composing hundreds of components to make a system with exponentially many different linear regions, we instead generate a small set of linearizations about the state trajectory which is the response to a "training input." Computational results and performance data are presented for an example of a micromachined switch and selected nonlinear circuits. These examples demonstrate that the macromodels obtained with the proposed reduction algorithm are significantly more accurate than models obtained with linear or recently developed quadratic reduction techniques. Also, we propose a procedure for a posteriori estimation of the simulation error, which may be used to determine the accuracy of the extracted trajectory piecewise-linear reduced-order models. Finally, it is shown that the proposed model order reduction technique is computationally inexpensive, and that the models can be constructed "on the fly," to accelerate simulation of the system response.

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A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices

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Elementary Numerical Analysis

f REEDA TM is a trademark of Michael Steer and registration has been applied for. PSpice probe, parts, device equations and digital files are trademarks of Microsim Corp. All other trademarks are the properties of their respective owners. Information contained in this work is believed to be reliable and obtained from sources that are also believed to be reliable. However, the authors do not guarantee the completeness or accuracy of any information contained herein and the authors shall not be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that the authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought.

Programmer's guide

In this paper, it is shown that Cauchy's method can be used effectively to interpolate/extrapolate narrow-band system responses. The given information can either be theoretical datapoints or measured experimental data over a band. For theoretical data extrapolation or interpolation, the sampled values of the function and, optionally, a few of its derivatives have been used to reconstruct the function. For measured data, only measured values of the parameter are used to create broadband information from limited data as derivative information is too noisy. Cauchy's method assumes that the parameter to be extrapolated/interpolated, as a function of frequency, is a ratio of two polynomials. The problem is to determine the order of the polynomials and the coefficients therein. The method of total least squares (TLS) has been used to solve the resulting matrix equation involving the coefficients of the polynomials. Typical numerical results have been presented to show that reliable interpolation/extrapolation can be done for various system responses.

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Application of the Cauchy method for extrapolating/interpolating narrowband system responses

A new method is proposed for dominant pole-zero (or pole-residue) analysis of large linear microwave circuits containing both lumped and distributed elements. The method is based on a multipoint Pade approximation. It finds a reduced-order rational s-domain transfer function using a data set obtained by solving the circuit at only a few frequency points. We propose two techniques in order to obtain the coefficients of the transfer function from the data set. The proposed method provides a more efficient computation of both transient and frequency domain responses than conventional simulators and more accurate results than the techniques based on single-point Pade approximation such as asymptotic waveform evaluation. >

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Pole-zero computation in microwave circuits using multipoint Pade approximation

A new type of sampled data filter consisting of transconductance elements, switches and capacitors, and called a transconductor switched-capacitor (TSC) filter is presented. Transconductance elements do not degrade their performance within a wide frequency range and tunable ones are available. The synthesis of TSC filters is explained on the basis of a signal flow graph realizing the general z-domain biquadratic transfer function. The transconductance elements employed as active devices are readily available in various technologies and are easily implemented and more suitable than operational amplifiers in a CMOS technology. Because the building blocks are not involved in any continuous feedback, frequency compensation is not necessary for stability purposes. The filter coefficients are determined by the clock pulse width and the transconductances, both of which can be tuned, and the integrator capacitors. This method can be easily generalized to the higher order filters. >

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Biquadratic transconductance switched-capacitor filters

A general purpose circuit simulation program, PL-AWE (piecewise linear asymptotic waveform evaluator) is developed especially for the analysis of VLSI circuits. PL-AWE uses the asymptotic waveform evaluation (AWE) technique, which is a new method to analyze linear(ized) circuits, and piecewise-linear (PL) models to represent nonlinear elements. AWE employs a form of Pade approximation rather than numerical integration to approximate the behavior of linear(ized) circuits in either the time or the frequency domain. The authors discuss the internal workings of the program, and indicate its effectiveness in terms of several illustrative examples. >

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Piecewise linear asymptotic waveform evaluation for transient simulation of electronic circuits

The number of active components in transconductance grounded capacitor filters is reduced. This reduction is possible in the case where capacitor loops and/or inductor cutsets exist in the LC-ladder prototype. A more significant reduction is obtained in the OTA-C (operational transductance amplifier-capacitor version). The number of OTAs is reduced to seven from 13 while the total capacitance value remains intact. It is also important to note that all transconductance elements or OTAs are identical except possibly one. The only drawback of this reduction is implementation of some floating capacitors instead of all grounded capacitors. >

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A reduction in the number of active components used in transconductance grounded capacitor filters

A new method is proposed for the transient analysis of circuits with large number of linear lumped elements and lossy coupled transmission lines, and with few mildly nonlinear terminations. The method combines the Volterra-series technique with Asymptotic Waveform Evaluation approach and corresponds to recursive analysis of a linear equivalent circuit. >

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M.A. Tan

Papers

Pole-zero computation in microwave circuits using multipoint Pade approximation

Biquadratic transconductance switched-capacitor filters

Piecewise linear asymptotic waveform evaluation for transient simulation of electronic circuits

A reduction in the number of active components used in transconductance grounded capacitor filters

Transient analysis of nonlinear circuits by combining asymptotic waveform evaluation with Volterra series