Analisis Sensitivitas Parameter Rangkaian RLC Menggunakan Runge-Kutta Adaptif untuk Akurasi Numerik Optimal

David Eka Putra; Reski Yulian Fauzan; Amran Paso Salmeno

doi:10.55382/jurnalpustakaai.v5i3.1432

Penulis

David Politeknik Negeri Padang
Fauzan Politeknik Negeri Padang
Amran Politeknik Negeri Padang

DOI:

https://doi.org/10.55382/jurnalpustakaai.v5i3.1432

Kata Kunci:

rangkaian RLC, Runge-Kutta adaptif, RFK45, simulasi numerik, analisis sensitivitas.

Abstrak

This study investigates the numerical performance and parameter sensitivity of a RLC circuit solved using the adaptive Runge-Kutta-Fehlberg (RKF45) method. The mathematical model is formulated as a second-order ordinary differential equation and numerically integrated using RKF45 with local error control, then compared with the classical fourth-order Runge-Kutta (RK4) method using a fixed time step. Validation against the analytical steady-state solution shows that RKF45 achieves high accuracy with a lower Root Mean Square Error (RMSE ? 1.39×10??) while requiring 40% fewer integration steps than RK4. A sensitivity analysis based on normalized sensitivity coefficients is performed for ±10% variations of the R, L, and C parameters. The results reveal that inductance is the most dominant parameter influencing oscillatory dynamics, followed by capacitance, while resistance contributes mainly to damping. The sensitivity ranking is found to |. Overall, the findings display that RKF45 offers an efficient and accurate approach for RLC transient simulation and parameter sensitivity evaluation, making it suitable for applications that require high-precision dynamic analysis.

Unduhan

Data unduhan belum tersedia.

Referensi

M. Yang, J. Liu, Y. Xiao, and H. Liao, “14.4 nW fourth-order bandpass filter for biomedical applications,” Electron. Lett., vol. 46, no. 14, pp. 973–974, Jul. 2010, doi: 10.1049/el.2010.1520.

S. Saad, F. Haddad, and A. Ben Hammadi, “A Compact and Tunable Active Inductor-Based Bandpass Filter with High Dynamic Range for UHF Band Applications,” Sensors, vol. 25, no. 10, p. 3089, May 2025, doi: 10.3390/s25103089.

J. Hope, Z. Aqrawe, M. Lim, F. Vanholsbeeck, and A. McDaid, “Increasing signal amplitude in electrical impedance tomography of neural activity using a parallel resistor inductor capacitor (RLC) circuit,” J. Neural Eng., vol. 16, no. 6, p. 66041, Nov. 2019, doi: 10.1088/1741-2552/ab462b.

C. K. Alexander and M. N. O. Sadiku, Fundamentals of Electric Circuits, 5th ed. New York: McGraw-Hill Education, 2013.

A. S. Sedra and K. C. Smith, Microelectronic Circuits, 7th ed. New York: Oxford University Press, 2015.

M. T. Hlaing, W. W. Aung, and T. T. Htwe, “Application of Laplace Transform for RLC Circuit,” Int. J. Sci. Eng. Appl., vol. 8, no. 8, pp. 317–319, Aug. 2019, doi: 10.7753/IJSEA0808.1014.

A. Wilmer III and G. B. Costa, “Solving second-order differential equations with variable coefficients,” Int. J. Math. Educ. Sci. Technol., vol. 39, no. 2, pp. 238–243, Mar. 2008, doi: 10.1080/00207390701464709.

E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, 2nd ed., vol. 8. Berlin, Heidelberg: Springer-Verlag, 1993.

T. A. Kee and R. Ranom, “Comparison Of Numerical Techniques In Solving Transient Analysis of Electrical Circuits,” ARPN J. Eng. Appl. Sci., vol. 13, no. 1, pp. 314–320, 2018.

J. Kafle, B. K. Thakur, and I. B. Bhandari, “Application of Numerical Methods for the Analysis of Damped Parallel RLC Circuit,” J. Inst. Sci. Technol., vol. 26, no. 1, pp. 28–34, Jun. 2021, doi: 10.3126/jist.v26i1.37814.

Y. Workineh, H. Mekonnen, and B. Belew, “Numerical methods for solving second-order initial value problems of ordinary differential equations with Euler and Runge-Kutta fourth-order methods,” Front. Appl. Math. Stat., vol. 10, Feb. 2024, doi: 10.3389/fams.2024.1360628.

A. G. Shaikh, U. Keerio, W. Shaikh, and A. H. Sheikh, “Numerical higher-order Runge-Kutta methods in transient and damping analysis,” Int. J. Adv. Appl. Sci., vol. 9, no. 10, pp. 174–179, Oct. 2022, doi: 10.21833/ijaas.2022.10.020.

K. P. Patel, R. R. Mehta, and C. L. Parikh, “Simulation of Series RLC Circuit Using MATLAB Computer Program: Study Effect of Variable Component on Frequency Response,” Paripex – Indian J. Res., vol. 4, no. 10, 2015.

D. Biolek, V. Biolková, Z. Kolka, and Z. Biolek, “SPICE Modeling of Analog Circuits Containing Constant Phase Elements,” in 2023 Communication and Information Technologies (KIT), Oct. 2023, pp. 1–6, doi: 10.1109/KIT59097.2023.10297047.

A. Saltelli, S. Tarantola, F. Campolongo, and M. Ratto, Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models. Chichester: John Wiley & Sons, Ltd, 2004.