Fast Circuit Boards

Appendix ASine Waves in Circuits

A.1 Introduction

The material in this appendix is a fast review of linear circuit theory. This material is needed when applying the Smith chart to matching impedances. This theory describes the voltages and currents that result when sine waves at a fixed frequency are used to excite a network of linear components. Complex notation is used so that the phase relations in RLC networks can be analyzed as a function of frequency. The concepts of impedance, admittance, resistance, conductance, reactance, and susceptance are introduced. If the reader needs a slower pace, there are many texts available with problem sets. Working problems is an important part of learning this material and keeping it fresh.

A.2 Unit Circle and Sine Waves

On a simple grid of vertical and horizontal lines, label the center point as zero. This point is called the origin. Draw a circle with the center in mid page. This is called the unit circle. The horizontal line that goes through the origin is the x axis, the vertical line that goes through the origin is the y axis. The top of the circle is a y value of 1. The bottom is −1. The far left point has a y value of 0 and an x value of −1. Number the grid of lines so that every point on the circle can be given an x and y value from 0 to ±1.

Now draw a radial line from the origin to the circle at the point where y = 0.5. The radius is the hypotenuse of a triangle formed by the x and y distances. Note that any point on the circle ...