Limiting Cases

The force-wave reflectance of an infinite impedance (rigid wall or ``open circuit'') is

$$\hat{\rho}(s) = \frac{R(s) - R_0}{R(s)+R_0} = \frac{\infty - R_0}{\infty +R_0} = 1$$

Similarly, the force-wave reflectance of a zero impedance (free termination, frictionless surface, or ``short circuit'') is

$$\hat{\rho}(s) = \frac{0 - R_0}{0+R_0} = -1$$

For velocity waves, we obtain the opposite results: rigid terminations are inverting, and free terminations are non-inverting.