The short-term stability of passive atomic frequency standards, particularly ones operated sequentially, is often limited by local oscillator noise via intermodulation effects. This article describes an experimental demonstration of the intermodulation effect on the frequency stability of a continuous atomic fountain standard usually imperceptible under normal operating conditions. To make the effect observable, we increase the phase instability of the microwave field interrogating the clock transition. We measure the frequency stability of the locked, commercial local oscillator, for both square-wave phase modulation and squarewave frequency modulation of the microwave field. The observed degradation of the stability depends on the modulation frequency in a way that agrees with our earlier theoretical predictions. Most significantly, no degradation is observed when the modulation frequency is made equal to the Ramsey linewidth. When no extra phase noise is added, the frequency instability, currently 2.0×10 −13 at 1 s, is limited only by atomic shot-noise. This shows the potential to reduce it via the use of a higher atomic flux.