Digital Circuit Boards: Mach 1 GHz

2.9 Waves that Transition between Lines with Different Characteristic Impedances

When a wave traveling along a transmission line reaches a change in characteristic impedance, some of the energy is reflected and some of it enters the termination. The termination can be a resistor or a second transmission line. If a wave traveling in Z₀ reaches a termination impedance Z_L, the fraction that is reflected is given by

2.5

where ρ is called the reflection coefficient. If Z_L equals zero, the reflection coefficient is simply − 1. The reflected wave is then the original wave reversed in polarity. If Z_L = Z₀, there is no reflection. If Z₀ is large, then the reflection coefficient is near unity meaning that the reflected wave has the same polarity as the arriving wave. In this case, the two waves add together, doubling the voltage at the point of reflection.

N.B.

The reflection coefficient is valid for all wave forms including sine waves and step functions.

The fraction of the wave that continues into the termination impedance is given by

2.6

where τ is called the transmission coefficient. If Z_L = Z₀ then τ is unity meaning that the transmitted wave is transferred without reflection to the new line or load. If Z_L is high compared to Z₀ then the voltage at the load is double the arriving ...