SummaryHardware realizations of neural networks can pave the way towards a new generation of processors due to the biological role model being superior in terms of speed and energy‐efficiency compared to today's processors. This can be achieved by deriving novel design principles for circuits being obtainable when replicating and investigating real biological neural networks in depth. This has, for example, been done by utilizing the Hindmarsh‐Rose model, offering a rich repertoire of neuronal firing patterns. Our aim is to synthesize a theoretical, equivalent electrical circuit of the Hindmarsh‐Rose model being well interpretable in terms of biology, since this supports the derivation of design principles from biology and can serve as a basis for a systematic circuit simplification. We do this by starting from a linearized model because this allows for a systematic approach and then first derive a linear and afterwards a nonlinear equivalent electrical circuit. The resulting circuit has a structure similar to conductance‐based models, where a deployed negative impedance converter can be seen as a deeper modeling of ion pump activity. Simulation results of the proposed circuits show the functionality of the equivalent circuits.