  Here we describe a multi-compartment neuron circuit based on the
Adaptive-Exponential I&F (AdEx) model, developed for the second-generation
BrainScaleS hardware. Based on an existing modular Leaky Integrate-and-Fire
(LIF) architecture designed in 65 nm CMOS, the circuit features exponential
spike generation, neuronal adaptation, inter-compartmental connections as well
as a conductance-based reset. The design reproduces a diverse set of firing
patterns observed in cortical pyramidal neurons. Further, it enables the
emulation of sodium and calcium spikes, as well as N-Methyl-D-Aspartate (NMDA)
plateau potentials known from apical and thin dendrites. We characterize the
AdEx circuit extensions and exemplify how the interplay between passive and
non-linear active signal processing enhances the computational capabilities of
single (but structured) on-chip neurons.
