In the heart, rapid pacing rates may induce alternations in the strength of cardiac contraction, termed pulsus alternans. Often, this is due to an instability in the dynamics of intracellular calcium concentration, whose transients become larger and smaller at consecutive beats. This alternation has been linked experimentally and theoretically to two different mechanisms: an instability due to 1) a strong dependence of calcium release with sarcoplasmic reticulum (SR) load, together with a slow calcium reuptake into the SR or 2) to SR release refractoriness, due to a slow recovery of the ryanodine receptors (RyR2) from inactivation. The relationship between calcium alternans and refractoriness of the RyR2 has been more elusive than the corresponding SR Ca load mechanism. To study the former, we reduce a general calcium model, which mimics the deterministic evolution of a calcium release unit, to its most basic elements. We show that calcium alternans can be understood using a simple nonlinear equation for calcium concentration at the dyadic space, coupled to a relaxation equation for the number of recovered RyR2s. Depending on the number of RyR2s that are recovered at the beginning of a stimulation, the increase in calcium concentration may pass, or not, over an excitability threshold that limits the occurrence of a large calcium transient. When the recovery of the RyR2 is slow, this produces naturally a period doubling bifurcation, resulting in calcium alternans. We then study the effects of inactivation, calcium diffusion and release conductance for the onset of alternans.We find that the onset of alternans requires a well-defined value of diffusion while it is less sensitive to the values of inactivation or release conductance.PACS numbers: 47.55. 47.20.Ma, 68.03.Cd ionic models; ventricular arrhythmias; calcium alternans 1 Cardiac alternans is a dysfunction that has been identified as a risk factor for cardiac arrhythmias. During alternans, beat-to-beat alternations in action potential duration (APD) appear alongside alternations in cytosolic calcium concentration. Despite been tightly coupled, voltage clamp experiments have shown that, often, the originating mechanism for alternans stems from an instability in calcium handling. Two alternative scenarios may explain this instability, either a slow reuptake of calcium after a release, or a long refractory period in release. In this paper we study the conditions for alternans due to refractoriness in calcium release, by reducing the dynamics of calcium to a simple two-variable model. The model includes a nonlinear dependence of release with calcium concentration and a slow recovery from refractoriness. This simple model presents excitability with a threshold that depends on the state of the ryanodine receptors (RyRs), i.e., calcium sensitive channels through which calcium is released to the cytosol. Calcium alternans appears as a bifurcation in which only one out of every two pulses is able to cross this excitability limit.