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I'm designing a PCB that will utilize USB-C to supply power (5V/3A) to my board and have a few questions:

  1. What are the requirements to ensure a 5V/3A (15 W) supply to my device if I know nothing about the supply (i.e which default current supply case will occur if I'm charging from a laptop or other supply in which Rp is not known)?

  2. Is it possible to ensure a 5V/3A delivery of power without a USB-C Configuration Channel Controller or USB Power Delivery IC? Ideally I'd like to implement the basic layout seen below and tap from VBUS.

Standard Supply to Sink Connection

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in which Rp is not known

This is the entire idea of Type-C basic connectivity. Your device must use some voltage comparator to determine the voltage level of Rp:Rd divider. That's how you "know" what the Rp is. Your device can take 3A only if you sense about 1.6V at one of CC pin, which corresponds to 10k - 5.1k voltage divider. To sense this condition, you can either use TWO analog comparators (maybe one comparator will suffice if charging-only function, not sure), or use a single CC-controller IC that does this job.

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