David Cerny

Efficient algorithm for solving systems of circuit differential-algebraic equations with reliable divergence suppression in DC and time domains

Although many simulation tools contain advanced algorithms for the solution of the systems of differential-algebraic nonlinear equations, some classes of circuits still cause serious problems. These are typically the circuits with strong negative feedbacks, flip-flop circuits, the blocks that are characterized by macromodels with unusual elements, and large distributed amplifiers and oscillators. In the paper, a very efficient and reliable algorithm for solving the circuit differential-algebraic equations is characterized first, which is based on a sophisticated arrangement of the Newton interpolation polynomial. After that, a novel method is introduced for improving the convergence with four suggested criteria that are being compared. Unlike the similar algorithms focused on an operating point analysis only, the proposed method also works in a transient analysis. All the four criteria are thoroughly tested on nine problematic circuits - six of them often diverge in the operating point analysis, and three of them diverge at some points during the transient analysis. The results confirm extraordinary robustness of the proposed method, even circuits with a large memelement hysteresis can be solved.

A more efficient arrangement of the sparse LU factorization for the large-scale circuit analysis

In the paper, an efficient and reliable algorithm for solving the circuit nonlinear algebraic-differential equations based on a sophisticated arrangement of Newton interpolation polynomial is characterized first. After that, a novel method is introduced for improving the convergence with four suggested criteria that are being compared. Unlike the similar algorithms focused on an operating point analysis only, the proposed method also works in a transient analysis. For enhancing the efficiency of repeated solutions of linear systems necessary in the Newton-Raphson method, a novel modification of the Markowitz criterion is suggested, which is compatible with the fast modes of the LU factorization. The modified criterion consists in an estimation of probabilities of the fill-in enlargement. The probabilities are determined for all columns of the system matrix before the LU factorization, where the column probability is calculated as the average value of the probabilities for all the column elements. Finally, the columns are reordered so that first and last should be those with the minimum and maximum probabilities, respectively. As a verification of this fundamental proposal of the paper, a comprehensive set of numerical tests has been carried out.

Multiobjective optimization with an asymptotically uniform coverage of Pareto front

This paper suggests an enhancement of an existing method for the multiobjective optimization known as GAM (goal attainment method). In our proposal, the GAM algorithm is combined with a mechanism that automatically provides a set of parameters (weights, coordinates of the reference point) for which the method generates noninferior solutions uniformly spread over a suitably selected part of the Pareto front. The resulting set of solutions is then presented in a suitable graphic form so that the solution representing the most satisfactory tradeoff can be easily chosen. The whole algorithm was implemented as a program and tested on several RF design examples (video, low-noise, and power amplifiers), whose optimization results are also presented. For a comparison, the first design example was also solved by another method known as WMM (weighted metrics method).

A flexible algorithm for solving systems of circuit differential-algebraic equations with integrated Fortran 95 compiler for modeling

Although many simulation tools contain advanced algorithms for the solution of the systems of differential-algebraic nonlinear equations, some classes of circuits still cause serious problems. In the paper, a very flexible and reliable algorithm for solving the circuit differential-algebraic equations is characterized first, which is based on a sophisticated arrangement of the Newton interpolation polynomial. After that, a reliable method is introduced for improving the convergence with four possible criteria. Unlike the similar algorithms focused on an operating point analysis only, the proposed method also works in a transient analysis. Moreover, for an ability of the procedure to model practically arbitrary electronic device, a subset of the Fortran 95 programming language was integrated to the circuit simulator with a power to differentiate functions symbolically.

Functional chaining mechanism allowing definable models of electronic devices

Fast and stable processing optimized for given simulation problem is essential for any modern simulator. It is characteristic for electronic circuit analysis that complexity of simulation is given by circuit size and used device models. Implementation of electronic device models in program SPICE uses traditional functional paradigm allowing fast computation but further modification of model can be questionable. In this article, we propose modification of standard procedure inserting functional computation layer into the process. It allows on-the-fly modification of standard models and own functional definition during circuit definition without a loss in computational performance. It also gives a possibility of functional chaining mechanism and improves mapping performance of circuit variables to device models.

Comparing the steady-state procedures based on epsilon-algorithm and sensitivity analysis

Although many programs have built-in various methods for finding the steady state nowadays, their actual implementations are often quite unsatisfactory regarding algorithm efficiency and reliability. We improved and checked procedures built on both ϵ-algorithm and sensitivity analysis in time domain. First of all, it was clearly demonstrated that increasing demands on the overall numerical accuracy do not lead to an excessive number of necessary integration steps and therefore LU factorizations correspondingly. This feature is especially significant for the suggested procedure based on the ϵ-algorithm. Furthermore, the practical experiments confirmed that a proposed arrangement of the extrapolation method is greatly insensitive to its order, which is even more important because a program user is unable to estimate the appropriate order for complicated circuits well. The properties of the methods are demonstrated using rectifier, C-class amplifier, and LNA for which exceptional attention was given to checking the insensitivity of the extrapolation to its order.

Adaptive sparse matrix indexing technique for simulation of electronic circuits based on λ-calculus

In this paper, a fundamentally new approach to computer-aided design and simulation of electrical circuits based on a use of λ-calculus for circuit device model representation and dynamic sizeable containers for sparse matrix simulation indexation indices is presented. This approach differs from traditional procedure where the entire simulation was performed over the matrix or matrix system assembled by modified nodal analysis (MNA). Turning device model definitions using λ-calculus to functionals allowed to reduce an effort required for their specification and opened new possibilities for simulation evaluation. Considering MNA matrix as second-order tensor system holding the functional definition of original sparse matrix entries allows to imagine these dependencies as chains with respect to a model definition and global dependencies between their defining inner functions. In this particular case, standard indexing methods would be a waste of memory during a computation, this problem occurs when huge sparse matrices enter the simulation. Therefore, new optimized indexing technique for non-zero matrix entries and variable size container types for those indexation vectors is proposed.

An improved model of high-voltage power LDMOSFET and its usage in multi-objective optimization of radio-frequency amplifiers

In the paper, a set of improvements of the semiempirical MOSFET model is suggested to ensure required accuracy for simulating power electronic circuits. The enhancement of the precision was arranged by incorporating the more accurate Grove-Frohman equations into the semiempirical model because the contemporary short-channel-oriented models BSIM and EKV are inappropriate for characterizing the power transistors. The ability of the modified model to characterize power devices was confirmed by successful processes of extracting its parameters for medium- and high-power transistors, and a demonstration of this process for an SIPMOS power transistor is also shown in the paper. Finally, a multi-objective optimization of a C-class radio-frequency power amplifier with LDMOSFET is demonstrated as well as an analogous procedure for a low-noise preamplifier. In the two examples in time and frequency domains, resulting three-and two-dimensional Pareto fronts are presented in convenient graphic forms for a comfortable selection of a tradeoff by a user.

Efficient procedure for solving circuit algebraic-differential equations with modified sparse LU factorization improving fill-in suppression

In the paper, an efficient and reliable algorithm for solving the circuit algebraic-differential equations is characterized first, which is based on a sophisticated arrangement of the Newton interpolation polynomial. For enhancing the efficiency of repeated solutions of linear systems necessary in the Newton-Raphson method, a novel modification of the Markowitz criterion is suggested, which is compatible with the fast modes of the LU factorization. The modified criterion consists in an estimation of probabilities of the fill-in enlargement. The probabilities are determined for all columns of the system matrix before the LU factorization, where the column probability is calculated as the average value of the probabilities for all the column elements. Finally, the columns are reordered so that first and last should be those with the minimum and maximum probabilities, respectively. As a verification of the proposed algorithm, a comprehensive set of numerical tests has been performed.

New approach for enhancing efficiency of computer aided design in circuit simulation

All versions of SPICE can perform various kinds of analysis such as operating point, sensitivity, and transient analyses, and many others. The algorithms used for computations are based on an iterative numerical solution of nonlinear differential equations. This paper gives a simple overview about these algorithms, their principles, function and disadvantages. It introduces a novel approach and implementation of implicit and explicit algorithms for solving the differential equations in circuit design with the aim to improve the reliability and efficiency of the solution. Furthermore, it presents a comparison between the standard SPICE algorithm and the new developed ones.