The study presents an oscillator circuit for a spike neural network with the possibility of firing rate coding and sigmoid-like activation function. The circuit contains a switching element with an S-shaped current-voltage characteristic and two capacitors; one of the capacitors is shunted by a control resistor. The circuit is characterised by a strong dependence of the frequency of relaxation oscillations on the magnitude of the control resistor. The dependence has a sigmoid-like form and we present an analytical method for dependence calculation. Finally, we describe the concept of the spike neural network architecture with firing rate coding based on the presented circuit for creating neuromorphic devices and artificial intelligence.