## Resistor NetworksSeptember 26, 2016 While most audio signal processing is now done using digital circuitry, it's often easier in some cases to implement simple audio filters using venerable analog circuit techniques. While using an analog bandpass filter in a recent circuit design, I ran into the common problem of needing an uncommon resistance value to hit the desired frequency. I did what most electrical engineers do in that case, I used a parallel combination of two resistors. The problem could have been solved, also, by a series combination of two resistors. In my case, a parallel combination of a 470 k-ohm and a 1 meg-ohm resistor gave a resistance of 320 k-ohms, close enough to my desired 330 k-ohms. The formulas for calculating series and parallel resistance are found in the figure, below.
R of a regularly shaped piece of a material with resistivity ρ, cross-sectional area A and length L, as shown in the figure, is just R = ρ (L/A).
## References:- A.E. Kennelly, "Equivalence of triangles and three-pointed stars in conducting networks", Electrical World and Engineer, vol. 34 (1899), pp. 413-414. An early tutorial can be found at Robert D. Evans, "Analytical Solutions," The Electrical Journal, vol. XVI, January-December, 1919, pp. 345-349 (via Google Books).
- D. Atkinson and F. J. van Steenwijk, "Infinite resistive lattices," Amer. Jour. Phys., vol. 67, no. 6 (June, 1999), pp. 486-492. A PDF copy can be found, here.
- N.Sh. Izmailian, and R. Kenna, "A generalised formulation of the Laplacian approach to resistor networks," arXiv, June 19, 2014.
- M. Owaidat, "On the uniform tiling with electrical resistors," arXiv, May 25, 2013.
- J. H. Asad, "Infinite Body Centered Cubic Network of Identical Resistors," Arxi, February 19, 2013.
- Jihad H. Asad, "Exact Evaluation of The Resistance in an Infinite Face-Centered Cubic Network," Arxiv, October 7, 2012.
- J. H. Asad, "Infinite Face Centered Cubic Network of Identical Resistors," Arxiv, May 5, 2012.
- Jozsef Cserti, Gabor Szechenyi and Gyula David, "Uniform tiling with electrical resistors," Arxiv, March 7, 2011.
- J. H. Asad, R. S. Hijjawi, A. J. Sakaji and J. M. Khalifeh, "Resistance Calculation for an infinite Simple Cubic Lattice- Application of Green's Function,", May 1,2009.
- J. H. Asad, A. J. Sakaji, R. S. Hijjawi and J. M. Khalifeh, "On the resistance of an Infinite Square Network of Identical Resistors- Theoretical and Experimental Comparison," arXiv, April 3, 2009.
- R. S. Hijjawi, J. H. Asad, A. J. Sakaji, M. Al-Sabayleh and J. M. Khalifeh, "Infinite Simple 3D Cubic Lattice of Identical Resistors (Two Missing Bonds)," arXiv, March 24, 2009.
- Yakov M. Strelniker, Shlomo Havlin, Richard Berkovits, and Aviad Frydman, "Resistance distribution in the hopping percolation model," arXiv, June 7, 2005.
- Thomas Lam, "Electrical Resistor Networks," Notices of the American Mathematical Society, vol. 63, no. 8 (September, 2016), pp. 875f., DOI: http://dx.doi.org/10.1090/noti1420 (PDF file).
Linked Keywords: Audio signal processing; digital; electronic circuit; circuitry; audio filter; analog electronics; analog circuit; bandpass filter; resistance; frequency; electrical engineering; electrical engineer; parallel combination; resistor; series combination; ohm; k-ohm; meg-ohm; formula; calculation; conductance; multiplicative inverse; reciprocal; Inkscape; physics; physical; material; resistivity; cross-sectional area; length; inverting; network analysis; analysis of resistor networks; terminal; Y-Delta transform; transformation; Arthur Edwin Kennelly; doctoral advisor; thesis advisor; Vannevar Bush; Massachusetts Institute of Technology; MIT; node; algebra; experimentalist; equation; potentiometer; variable resistor; measurement; measure; errors and residuals in statistics; instrumentation; multimeter; digital volt-ohm-milliamp meter; infinity; infinite; lattice graph; square grid graph; two-dimensional space; experiment; experimental; pi; analysis; scientific literature; publish; arXiv; origin; rational number; irrational number; transcendental number; computer simulation; modeling; Voronoi diagram; nearest neighbor; three-dimensional space; electrical percolation. |
RSS Feed
## Google Search
Latest Books by Dev Gualtieri
- Soybean Graphene - March 23, 2017
- Income Inequality and Geometrical Frustration - March 20, 2017
- Wireless Power - March 16, 2017
- Trilobite Sex - March 13, 2017
- Freezing, Outside-In - March 9, 2017
- Ammonia Synthesis - March 6, 2017
- High Altitude Radiation - March 2, 2017
- C.N. Yang - February 27, 2017
- VOC Detection with Nanocrystals - February 23, 2017
- Molecular Fountains - February 20, 2017
- Jet Lag - February 16, 2017
- Highly Flexible Conductors - February 13, 2017
- Graphene Friction - February 9, 2017
- Dynamic Range - February 6, 2017
- Robert Boyle's To-Do List for Science - February 2, 2017
- Nanowire Ink - January 30, 2017
- Random Triangles - January 26, 2017
- Torricelli's law - January 23, 2017
- Magnetic Memory - January 19, 2017
- Graphene Putty - January 16, 2017
- Seahorse Genome - January 12, 2017
- Infinite c - January 9, 2017
- 150 Years of Transatlantic Telegraphy - January 5, 2017
- Cold Work on the Nanoscale - January 2, 2017
- Holidays 2016 - December 22, 2016
- Ballistics - December 19, 2016
- Salted Frogs - December 15, 2016
- Negative Thermal Expansion - December 12, 2016
- Verbal Cues and Stereotypes - December 8, 2016
- Capacitance Sensing - December 5, 2016
- Gallium Nitride Tribology - December 1, 2016
- Lunar Origin - November 27, 2016
- Pumpkin Propagation - November 24, 2016
- Math Anxiety - November 21, 2016
- Borophene - November 17, 2016
- Forced Innovation - November 14, 2016
- Combating Glare - November 10, 2016
- Solar Tilt and Planet Nine - November 7, 2016
- The Proton Size Problem - November 3, 2016
- Coffee Acoustics and Espresso Foam - October 31, 2016
- SnIP - An Inorganic Double Helix - October 27, 2016
- Seymour Papert (1928-2016) - October 24, 2016
- Mapping the Milky Way - October 20, 2016
- Electromagnetic Shielding - October 17, 2016
- The Lunacy of the Cows - October 13, 2016
- Random Coprimes and Pi - October 10, 2016
- James Cronin (1931-2016) - October 6, 2016
- The Ubiquitous Helix - October 3, 2016
- The Five-Second Rule - September 29, 2016
- Resistor Networks - September 26, 2016
- Brown Dwarfs - September 22, 2016
- Intrusion Rheology - September 19, 2016
- Falsifiability - September 15, 2016
- Fifth Force - September 12, 2016
- Renal Crystal Growth - September 8, 2016
- The Normality of Pi - September 5, 2016
- Metering Electrical Power - September 1, 2016
### Deep ArchiveDeep Archive 2006-2008
Blog Article Directory on a Single Page |

Copyright © 2017 Tikalon LLC, All Rights Reserved.

Last Update: 03-23-2017