Equilibrium propagation (EqProp) and its adaptations for spiking neural networks (SNN) are presented as biologically plausible alternatives to back-propagation (BP) which describe a potential low-energy means of learning complex tasks in neuromorphic hardware. These algorithms are conducive to extremely efficient analog computing approaches, but a detailed analog circuit implementation and architectural outline have not yet been presented. Furthermore, current theoretical analog designs of EqProp have not addressed synapse circuit-level implementations capable of simultaneous sensing and weight updates for real-time learning. To this end, we have designed and simulated a circuit-level implementation of a spiking EqProp neuron and synapse in CMOS 65 nm technology capable of concurrent inference and weight updates for real-time learning.