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LMZ35003: Stability with ceramic Cout and constant current load

Part Number: LMZ35003
Other Parts Discussed in Thread: TPS2561

My customer has designed this into a product, providing 5V power to four channels of USB 5V. Vin=12V. Their design uses a number of 47uF ceramic output caps. Webench shows an adequate phase margin. When they overload the USB switches, which puts them into a constant current mode, the LMZ35003 appears to oscillate at a frequency around 40KHz, This appears to be a large signal oscillation defined by periods of switching and no switching. Below is an example of the resulting waveform. Load current on the LMZ with this short in place is around 0.5A.

Yellow is the output voltage of the USB switch as it is shorted. Green is the LMZ output voltage showing the load transient response and resulting oscillatory ripple. Blue is a field probe near the LMZ device attempting to look at the internal switching behavior.

Please provide your thoughts on this. Do you think it appears to be a stability issue? We have added additional ceramic caps to the 5V LMZ output without affecting the problem. The load switch is the TPS2561.

Thanks, Mark.