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I am using an TI TPS56121 buck converter and I have designed it to supply 4.6V at 5A. However, my load current can vary from 500mA up to 5A (the load normally runs at about 3.6A). How do I determine the current load value at which my design will no longer operate in CCM, but will begin operating in DCM (which is something that I do not want to happen)?

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It's a Synchronous Buck so it will always operate in CCM.

DCM occurs when the inductor current cannot go negative, effectively clipping the bottom of the inductor current waveform. The presence of a low-side FET (Synchronous topology) prevents this from happening by allowing negative inductor currents.

The problem with DCM is that by changing the inductor waveform it also changes the dynamic characteristics of the power stage, changing from a double pole (in CCM) to a dominant pole in (DCM), so you have to take care of compensation in a dual-mode. But you don't have this issue here with this device.

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