  Neural processing systems typically represent data using leaky integrate and
fire (LIF) neuron models that generate spikes or pulse trains at a rate
proportional to their input amplitudes. This mechanism requires high firing
rates when encoding time-varying signals, leading to increased power
consumption. Neuromorphic systems that use adaptive LIF neuron models overcome
this problem by encoding signals in the relative timing of their output spikes
rather than their rate. In this paper, we analyze recent adaptive LIF neuron
circuit implementations and highlight the analogies and differences between
them and a first-order sigma-delta feedback loop. We propose a new sigma-delta
neuron circuit that addresses some of the limitations in existing
implementations and present simulation results that quantify the improvements.
We show that the new circuit, implemented in a 1.8 V, 180 nm CMOS process,
offers up to 42 dB signal-to-distortion ratio and consumes orders of magnitude
lower energy. Finally, we also demonstrate how the sigma-delta interpretation
enables mapping of real-valued recurrent neural network to the spiking
framework to emphasize the envisioned application of the proposed circuit.
