Day 5

Traveling wave in a coax cable (zero reflection)

The dots represent electrons in a coaxial cable. The color scale represents charge density (red is positive, blue is negative). The top colored line represents the inner wire. The lower colored line represents the outer cylinder. Each conductor (top and bottom) carries a traveling longitudinal wave. There are regions of high voltage difference between the inner wire and the outer cylinder, and accompanying regions of high electrical current. When oscillating charges reach the terminating resistor, energy is dumped into the resister.

Standing waves in a coax cable (100% reflection)

If the inner wire is disconnected from the outer cylinder, charge builds up at the end of the cable. We call this an infinite terminating impedance. There is a voltage anti-node. The incoming voltage wave is reflected and the sum of incident and reflected waves creates a standing wave. There is no sign flip to the voltage wave upon reflection.

When the inner wire is shorted to the outer cable, charge cannot build up at the end of the cable. We call this zero terminating impedance. There is a voltage node. The incoming voltage wave is reflected and the sum of incident and reflected waves makes a standing wave. The sign of the incoming voltage wave is flipped upon reflection.

The stretched string is a useful mechanical analog to the coax cable. But there is not a one-to-one analog between the voltage waves in a coax and the displacement waves in a stretched string. Please compare to these stretched-string animations, courtesy of Dr. Dan Russell, Grad. Prog. Acoustics, Penn State.

For the mechanical analogy to be useful (especially for predicting reflections and transmissions at impedance mismatches), one must compare dψ/dx of the stretched string to voltage in the coax cable.