This brief presents an ultra-low-power generic fully tunable analog 1-D Gaussian kernel (GK) circuit, which is employed as an activation neuron for the radial basis function artificial neural network. In the proposed GK circuit, the maximum likelihood, center, and width of the Gaussian profile can be independently controlled. Besides, we have developed a mathematical model for the proposed GK circuit and further verified them experimentally. Thereby, the presented modeling can be employed to facilitate the off-chip learning of the neural network hardware. Fabricated in 180 nm CMOS process, the prototype demonstrates the full tunability of the proposed GK circuit and good agreement between the experimental measurements and mathematical model. The relative error of the measured width of the GK’s profile is less than 7 % compared to the value predicted by the presented mathematical model. The total power consumption is 13.5 nW with a supply voltage of 0.9 V, and the core circuit occupies 0.013 mm ² .