Vol. 95
Latest Volume
All Volumes
PIERL 119 [2024] PIERL 118 [2024] PIERL 117 [2024] PIERL 116 [2024] PIERL 115 [2024] PIERL 114 [2023] PIERL 113 [2023] PIERL 112 [2023] PIERL 111 [2023] PIERL 110 [2023] PIERL 109 [2023] PIERL 108 [2023] PIERL 107 [2022] PIERL 106 [2022] PIERL 105 [2022] PIERL 104 [2022] PIERL 103 [2022] PIERL 102 [2022] PIERL 101 [2021] PIERL 100 [2021] PIERL 99 [2021] PIERL 98 [2021] PIERL 97 [2021] PIERL 96 [2021] PIERL 95 [2021] PIERL 94 [2020] PIERL 93 [2020] PIERL 92 [2020] PIERL 91 [2020] PIERL 90 [2020] PIERL 89 [2020] PIERL 88 [2020] PIERL 87 [2019] PIERL 86 [2019] PIERL 85 [2019] PIERL 84 [2019] PIERL 83 [2019] PIERL 82 [2019] PIERL 81 [2019] PIERL 80 [2018] PIERL 79 [2018] PIERL 78 [2018] PIERL 77 [2018] PIERL 76 [2018] PIERL 75 [2018] PIERL 74 [2018] PIERL 73 [2018] PIERL 72 [2018] PIERL 71 [2017] PIERL 70 [2017] PIERL 69 [2017] PIERL 68 [2017] PIERL 67 [2017] PIERL 66 [2017] PIERL 65 [2017] PIERL 64 [2016] PIERL 63 [2016] PIERL 62 [2016] PIERL 61 [2016] PIERL 60 [2016] PIERL 59 [2016] PIERL 58 [2016] PIERL 57 [2015] PIERL 56 [2015] PIERL 55 [2015] PIERL 54 [2015] PIERL 53 [2015] PIERL 52 [2015] PIERL 51 [2015] PIERL 50 [2014] PIERL 49 [2014] PIERL 48 [2014] PIERL 47 [2014] PIERL 46 [2014] PIERL 45 [2014] PIERL 44 [2014] PIERL 43 [2013] PIERL 42 [2013] PIERL 41 [2013] PIERL 40 [2013] PIERL 39 [2013] PIERL 38 [2013] PIERL 37 [2013] PIERL 36 [2013] PIERL 35 [2012] PIERL 34 [2012] PIERL 33 [2012] PIERL 32 [2012] PIERL 31 [2012] PIERL 30 [2012] PIERL 29 [2012] PIERL 28 [2012] PIERL 27 [2011] PIERL 26 [2011] PIERL 25 [2011] PIERL 24 [2011] PIERL 23 [2011] PIERL 22 [2011] PIERL 21 [2011] PIERL 20 [2011] PIERL 19 [2010] PIERL 18 [2010] PIERL 17 [2010] PIERL 16 [2010] PIERL 15 [2010] PIERL 14 [2010] PIERL 13 [2010] PIERL 12 [2009] PIERL 11 [2009] PIERL 10 [2009] PIERL 9 [2009] PIERL 8 [2009] PIERL 7 [2009] PIERL 6 [2009] PIERL 5 [2008] PIERL 4 [2008] PIERL 3 [2008] PIERL 2 [2008] PIERL 1 [2008]
2020-12-28
A Simple Matrix Approach for Computing the Equivalent Resistance and Unknown Components in Resistor Networks
By
Progress In Electromagnetics Research Letters, Vol. 95, 125-134, 2021
Abstract
A method is presented for computing the equivalent resistance and the unknown components of simple series and parallel resistor networks. The approach consists in taking the product of a simple 2×2 matrix (N-1) times, where N is the total number of components in the network. The matrix approach originates from the study of continued fractions. Numerical computations only require an algorithm that handles matrix multiplication.
Citation
Aris Alexopoulos, "A Simple Matrix Approach for Computing the Equivalent Resistance and Unknown Components in Resistor Networks," Progress In Electromagnetics Research Letters, Vol. 95, 125-134, 2021.
doi:10.2528/PIERL20102101
References

1. Saggese, A. and R. De Luca, "A fractal-like resistive network," Eur. J. Phys., 065006, 2014.
doi:10.1088/0143-0807/35/6/065006

2. Mungan, C. E. and T. C. Lipscombe, "Babylonian resistor networks," Eur. J. Phys., 531-537, 2012.
doi:10.1088/0143-0807/33/3/531

3. Fry, T. C., "The use of continued fractions in the design of electrical networks," Elec. Net., 463-498, 1929.

4. Kagan, M., "On equivalent resistance of electrical circuits," Am. J. Phys., Vol. 83, 53-63, 2015.
doi:10.1119/1.4900918

5. Cserti, J., "Application of the lattice Greens function for calculating the resistance of an infinite network of resistors," Am. J. Phys., Vol. 68, 896-906, 2000.
doi:10.1119/1.1285881

6. De Carlo, R. and P.-M. Lin, Linear Circuit Analysis: Time Domain, Phasor, and Laplace Transform Approaches, Oxford University Press, USA, 2001.

7. Baak, D. A. V., "Variational alternatives to Kirchhov's loop theorem in dc circuits," Am. J. Phys., Vol. 67, 36-44, 1999.
doi:10.1119/1.19188

8. Kreyszig , E., Advanced Engineering Mathematics, 5th Ed., Wiley & Sons, 1983.

9. Alexopoulos, A., "Binary circular inclusions in an effective medium approximation," Phys. Lett. A, 385-392, 2005.
doi:10.1016/j.physleta.2005.02.046

10. Alexopoulos, A., "Quantum scattering via the discretisation of Schrodinger's equation," Phys. Lett. A, Vol. 363, 66-70, 2007.
doi:10.1016/j.physleta.2006.10.099

11. Carmichael, R. D., The Theory of Numbers, and Diophantine Analysis, Dover, New York, 1959 .