Shown here are curve traces for a 20 mA CCR. The top left trace demonstrates that if the input voltage goes negative the CCR will break down at about -0.5 V and would require a reverse protection diode. As the voltages goes positive the CCR turns on very fast, often as soon as the voltage crosses the zero intersect. The bottom right trace shows that at 0.5 V the CCR is already at 25 % of the regulating current.