This paper presents a SAR converter based mixed-signal multiplier for the feature extraction of neural signals using quadratic operators. After a thorough analysis of design principles and circuit-level aspects, the proposed architecture is explored for the implementation of two quadratic operators often used for the characterization of neural activity, the moving average energy (MAE) operator and the nonlinear energy operator (NEO). Programmable chips for both operators have been implemented in a HV-180 nm CMOS process. Experimental results confirm their suitability for energy computation and action potential detection and the accomplished area×power performance is compared to prior art. The MAE and NEO prototypes, at a sampling rate of 30kS/s, consume 116 nW and 178 nW, respectively, and digitize both the input neural signal and the operator outcome, with no need for digital multipliers.