The present paper describes a microfluidic oscillator based on facing impinging jets and operating in laminar flow conditions. Using appropriate microchannel configurations, pulsatile liquid flows are generated at the microscale from steady and equal inlet flow conditions and without moving parts or external stimuli. An experimental campaign has been carried out, using oscillator structures manufactured in silicon using conventional microfabrication techniques. This allowed us to study in detail the impact of the main geometric parameters of these structures on the oscillation frequency. The observed range of regular oscillations was found to depend on the geometry of the output channels, with highly regular oscillations occurring over a very large range of Reynolds numbers (Re) when an expansion of the output channel is added. The evolution of the self-oscillating frequency was shown to be dependent on the distance separating the impinging jets and on the average speed of the jets. Direct numerical simulations have been performed using a spectral element method. The computed dye concentration fields and nondimensional self-oscillation frequencies compare well with the experiments. The simulations enable a detailed characterization of the self-oscillation phenomenon in terms of pressure and velocity fields.