Understanding Electrical Conduction in Wires

by Zvonko Fazarinc, Hewlett Packard Laboratories

Introduction

The topic at hand is studied in college courses on transmission lines and is commonly introduced by means of the four Maxwell's equations. These require considerable preparation in higher mathematics and in electromagnetics theory and are as such not a good starting point for majority of the population. We will try to explain the conduction phenomena in wires from first principles of Nature and thereby make them accessible to scientists, teachers, engineers, college students and high school students alike. In the process we will not sacrifice any scientific rigor or limit ourselves to trivial cases. The result should be a thorough comprehension of the concepts involved. As such it should become a reliable platform for teachers and students of these topics. It should serve as a firm foundation for practitioners and researchers who must deal with phenomena encountered in high frequency analog and digital circuits. For the layman the course should result in an understanding and appreciation of processes taking place inside the wires.

The visualization of underlying processes relies on a number of dynamic simulations and animations which are linked to the text. Their optimal presentation calls for some system properties that should be considered. The desire to reach the users of various operating systems has been addressed with the Java language. The wide range of performance levels is being faced with manual speed adjustment. The variety of presentation screens is being met with a selection of dynamic display sizes.

The course should be taken on-line with the textual and graphic components side by side. The animations and simulations are designed to appear in the left half of the screen. It is therefore recommended that you move your browser window to the far right and adjust its width to occupy about half of the screen. When encountering the red trigger points within the text, choose if you have 800 or more pixels of horizontal resolution and if your resolution is 600 or less. Of course, you may choose whichever you wish and you may even want to adjust the display window size to your liking.

To be able to follow the materials presented, the reader must know something about the potentials and currents , about the existence of electric charges and must accept the first principles of Nature at face value. You may acquire the necessary amount of this knowledge from the linked texts.

In order to introduce the topic we will first simulate the behaviour of electric signals in wires by using the electric current conduction model arising from Maxwell's equations. The mathematical model will be used only in the background and will in no way require its understanding. It will serve only as a substitute for an experimental laboratory. As such the model will address the question What if?, i.e. what happens if we impose certain conditions. After we will have identified some observational facts we will ask the question Why? and will try to gain an understanding of the physics of the observed phenomena from underlying mechanisms. We will look at the microscopic events taking place inside the wires and relate them to the externally observed behaviour. One behaviour specifically chosen to be illuminated is the quarter wave resonance which has been known to be the source of headaches for many young electrical engineers.

The reader who is unfamiliar with the transmission line theory and with the inductive and the capacitive quarter wave resonances on wires should start with the Mathematical Model of Conduction . Others may start with the Physical Model of Conduction . Once you have chosen your entry point you will be guided to sections and their subsections without the need for returning to this page.

Most sections contain one or more supportive dynamic presentations. The access links to them are red, labeled pushbuttons. The simulations are embedded in explanatory text which guides you through experiments deemed helpful in visualizing the phenomenon studied. For the reader's convenience in subsequent visits to this course all sections, their subsections as well as simulations are accessible directly through the linked list of contents shown below.