TABLE OF CONTENTS Traveling wave effects were once the nearly exclusive domain of communications engineers and electric utility transmission line engineers. However, as variable frequency, pulse width modulated (PWM) motor drives have gone to higher and higher PWM frequencies, standingwave phenomena have appeared in motor circuits. Traveling waves are now of concern to many power electronics engineers, and an understanding of their effects is necessary for motor protection in installations with long cables or high PWM frequencies. In modern terms, a transmission line is any set of parallel or coaxial conductors of finite length, and they may be printed circuit conductors or miles of overhead wires.
Standing waves appear when a length of line is excited at a frequency for which the electrical line length is a significant part of an electrical wavelength. They result from the constructive and destructive interference of forward and reflected waves on the line. The behavior of the line can be determined by solving the applicable differential equations relating the line parameters to the exciting frequency. The solu-tion of the equations for a line with losses is rather complex and adds little to the practical considerations, so the lossless line will be analyzed instead.
In the lossless line, L is the series inductance per unit length, and C is the shunt capacitance. If a differential length, dx, is considered, the inductance for that length is L dx, and the voltage in that length is e = L dx( di
