We describe a model of short-term synaptic depression that is derived from a circuit implementation. The dynamics of this circuit model is similar to the dynamics of some theoretical models of short-term depression except that the recovery dynamics of the variable describing the depression is nonlinear and it also depends on the presynaptic frequency. The equations describing the steady-state and transient responses of this synaptic model are compared to the experimental results obtained from a fabricated silicon network consisting of leaky integrate-and-fire neurons and different types of short-term dynamic synapses. We also show experimental data demonstrating the possible computational roles of depression. One possible role of a depressing synapse is that the input can quickly bring the neuron up to threshold when the membrane potential is close to the resting potential.