An internal unsteady compressible flowfield of a pulsed jet actuator (PJA) is simulated by unsteady Reynolds-averaged Navier–Stokes (URANS) and large-eddy simulation (LES) frameworks. The PJA’s feedback loops are short enough to have non-negligible jet switching time compared to the oscillation period. The results show that within a range of inlet pressure (which is the only control parameter) where the jet goes from subsonic to supersonic regime, the oscillation frequencies and the exit velocity waveform predicted by LES are in better agreement with the measured data than those predicted by URANS. Although URANS is able to capture the flowfield inside the feedback loops, it fails to predict the exit jet dynamics, unlike LES. This indicates the importance of a proper resolution of turbulence in the interaction region where jet switching occurs. Using LES data, it is found that the total jet switching time remains constant as the inlet pressure changes. It is also found that only the part of the jet switching period that ends at the first moment when the jet attaches to the opposite wall is involved in the oscillation period. Therefore, a new lumped model is proposed to estimate the oscillation frequency, which also explains the trend observed for the low inlet pressure values.