In this paper, we design a mixed-signal Integrate-And-Fire (IAF) neuron with two approaches for the refractory period mechanism. The two approaches, one digital and one analog, have been designed to behave equivalently, except for the use of external programming signals. Neurons using both refractory blocks have been simulated using a 65nm CMOS process and their performances have been quantified in terms of area and power consumption. We find that although the analog refractory block can be made smaller than the digital counterpart by using a smaller capacitor, the digital block performs better in terms of power consumption and programming precision.