Overview

You can't see electrons, current, or voltages in ordinary conductors. Only through mathematics can we see electronics in action. Our interest is not electronics as a whole, but in just one very specialized area of electronics. This area, high data-rate transmission, can be seen through the application of a particular set of mathematics. That set probably doesn't exactly coincide with the set that you have been using. While the mathematics used to describe microwaves is not totally new, it might be a bit rusty from disuse. So here is a refresher on some of the applicable mathematics.

At microwave frequencies, you cannot directly measure many parameters needed for your designs. Rather, you make measurements and then mathematically extract the needed information. How is that done? This chapter tells you. It covers concepts and procedures needed to read and use the material presented in this book.

First, we refresh the most basic complex number operations, and then we cover fundamental matrix manipulations. This material is used in the description of scattering, or S, parameters.

Why, you may ask, do we need to study this? For several reasons. Your real-time oscilloscope is not likely to be capable of a bandwidth of more than a few gigahertz. A really good time-domain reflectometer (TDR) may have an effective bandwidth of six or seven gigahertz. Network analyzers capable of 50-gigahertz bandwidth are readily available. And, not only can they measure this range, they can achieve accuracies orders of magnitudes better than either the oscilloscope...