# Random Walks in Electrical Networks

Stefan Hollos and J. Richard Hollos

**Format and pricing:** Paperback 7.5 x 9.25 inch (66 pages) $9.95, pdf $7.95

**ISBN:** 9781887187473 (paperback)

**Publication date:** January 2024

Electrical network analysis is an old, mature and seemingly closed subject. But this is far from being true. It is part of the much broader subject of general network theory which is itself a branch of the mathematical subject of graph theory. This means that many of the powerful methods of graph theory can be applied to electrical network analysis.

Much of the work in this area has not made its way out of the confines of academic research. The electrical engineer is unlikely to be exposed to this way of doing network analysis in their undergraduate education. It is our belief that this way of doing network analysis is exciting, interesting and has practical benefits that have yet to be fully realized.

This book is our attempt to bring some of these nonstandard methods of network analysis to the attention of more engineers. We show how some of the traditional methods of doing network analysis can be turned into a problem involving a random walk on a graph. The book contains a variety of problems that are solved in detail using this method.

We have tried not to make this an academic book. It should be of interest to any engineer looking for new and more efficient ways to do network analysis. The only prerequisite for this book is a good knowledge of standard electrical network theory.

#### About the authors

Stefan Hollos and J. Richard Hollos are physicists and electrical engineers by training, and enjoy anything related to math, physics, engineering and computing. They are brothers and business partners at Exstrom Laboratories LLC in Longmont, Colorado.

## Table of Contents

**Preface****Nodal Analysis with a Voltage Source****Resistive Bridge Circuit****A Random Walk Interpretation****Equal Resistance Ladders****Resistance Lattices****Nodal Analysis with a Current Source****Consistency of Voltage and Current Source Analysis****Resistive Bridge Circuit with Current Source****Resistor Cube****Twin-T Notch Filter****Digital to Analog Conversion****Infinite Networks****Transmission Line****Software****References and Further Reading****Acknowledgements****About the Authors**

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Send comments to: Richard Hollos (richard[AT]exstrom DOT com)

Copyright 2023 by Exstrom Laboratories LLC