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This paper describes a synapse circuit that approximately implements the dynamics of the dopamine (DA) modulated synapse proposed by Izhikevich (2007). The dynamics of the model, based on 'eligibility traces' generated according to a spike-timing-dependent plasticity (STDP) rule, ensure that causal pre-/postsynaptic spiking activity in the time preceding the reward, signaled by DA, leads to strengthening of the synaptic connections. The circuits are designed and fabricated in a 0.35 μm CMOS technology and the simulation results are presented. This circuit block is a good candidate for the development of neuromorphic VLSI architectures that implement brain-inspired computation using biologically plausible reinforcement learning strategies.