Generation of State Equations for Circuits with Excess Elements

Marin, Mihai Eugen; Staicu, Ciprian-Stefan; Gheorghe, Alexandru Gabriel; Constantinescu, Florin

doi:10.1109/isfee51261.2020.9756144

Cited by 2 publications

(2 citation statements)

References 8 publications

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“…As an example, for the circuit with excess state quantities (capacitor loop and inductor cut-set circuit) and without sources for simplicity, in Figure 7 [8,9], the state equations are obtained:…”

Section: Circuits With Excess State Quantitiesmentioning

confidence: 99%

Electrical Circuits as Dynamical Systems

Gheorghe¹,

Marin²

2023

Qualitative and Computational Aspects of Dynamical Systems

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An electrical circuit containing at least one dynamic circuit element (inductor or capacitor) is an example of a dynamic system. The behavior of inductors and capacitors is described using differential equations in terms of voltages and currents. The resulting set of differential equations can be rewritten as state equations in normal form. The eigenvalues of the state matrix can be used to verify the stability of the circuit. The most fitted numerical methods to integrate electrical circuit differential equations are the Euler Method (Forward and Backward), the Trapezoidal Rule, and the Gear Method of second to sixth degree, for circuits having stiff equations. These methods are implemented, with adjustable time-step integration, in the majority of circuit simulation software, such as SPICE. The analytical solution can also be computed, for small-size circuits, applying the Laplace Transform. It is interesting to compare the graphical presentation of numerically and analytically obtained solutions. While the numerical methods can be used for both linear and nonlinear circuits, the Laplace Transform is mostly used for linear circuits. A method of using it for nonlinear circuits is also presented.

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Section: Circuits With Excess State Quantitiesmentioning

confidence: 99%

Electrical Circuits as Dynamical Systems

Gheorghe¹,

Marin²

2023

Qualitative and Computational Aspects of Dynamical Systems

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“…Although the existing symbolic pole/zero analysis methods [8][9][10][11][12][13][14][15][16][17][18][19][20][21] incorporate some types of approximations during the calculation of transfer function, they suffer from some Disclaimer/Publisher's Note: The statements, opinions, and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions, or products referred to in the content.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Root Simplification in Operational Amplifiers using an Ensemble Heuristic-Metaheuristic Algorithm

Behmanesh-Fard¹,

Yazdanjouei²,

Shokouhifar³

et al. 2023

Preprint

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Symbolic pole/zero analysis is an important step when designing an analog operational amplifier. Generally, a simplified symbolic analysis of analog circuits suffers from NP-hardness, i.e., an exponential growth of the number of symbolic terms of the transfer function with the circuit size. In this study, we present a mathematical model combined with a heuristic-metaheuristic solution method for the symbolic pole/zero simplification in operational transconductance amplifiers (OTA). At first, the circuit is symbolically solved and an improved root splitting method is applied to extract symbolic poles/zeroes from the exact expanded transfer function. Then, a hybrid algorithm based on heuristic information and a metaheuristic technique using simulated annealing is performed for the simplification of the derived symbolic pole/zero expressions. The developed method has been tested on three analog OTAs. The obtained results show the effectiveness of the proposed method to achieve accurate simplified symbolic pole/zero expressions with the least complexity.

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Generation of State Equations for Circuits with Excess Elements

Cited by 2 publications

References 8 publications

Electrical Circuits as Dynamical Systems

Electrical Circuits as Dynamical Systems

Mathematical Root Simplification in Operational Amplifiers using an Ensemble Heuristic-Metaheuristic Algorithm

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