Point-on-Wave (POW) is a new characteristic of voltage sag which has a significant influence on the sensitivity of some equipment. This paper investigates the Point of Inception (POI) and the Point of Recovery (POR) of the voltage sag signal due to symmetrical and unsymmetrical faults in power systems. The POI of voltage sag could be any point on the wave where the voltage sag starts. On the other hand, the POR depends on the circuit breaker fault clearing practice. Based on the actual fault clearing angles, three groups of voltage sag signals separated by 180o are identified and characterized. For single-phase faults there are three possible recovery points on the voltage wave. For double phase faults, six PORs are found at three instants of time. Nine possible PORs for three phase faults are obtained at nine different instants in time. This paper demonstrates that depending on the circuit breaker fault clearing time, the voltage sag duration increases significantly, and this can be harmful to some sensitive equipment. This paper also analyzes the current signals at different POI of corresponding voltage sag signals and detects some critical POI of voltage sags for which the highest transients in current signals occur. The analysis has been carried out on two different radial distribution systems for 25 voltage sag signals over a cycle with 150 intervals, for which simulation results are reported.