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MCP1755 has Power Good Output (PWRGD) output pin which is open drain. In page 15 of data-sheet it says

The PWRGD pin may be pulled up to VIN or VOUT. Pulling up to VOUT conserves power when the device is in Shutdown (SHDN = 0V) mode.

1) How should I connect this pin. Should I leave it as not connected or pull it up to Vout pin with 10K. (I will not monitor the operation of converter I want only proper 3.3v regulation).

2) What is the exact purpose of this pin. Should we connect it to an ADC to see the operating condition if we want.

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Connect it through 10k to Vout. The pin is just a logic output, you can see from the second block diagram on page 3 of your datasheet that it's the output of a comparator. It would not be connected to an ADC. The pin could be used to drive a LED, the datasheet shows that it has sufficient current capability: 1mA is enough for an indicator.

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Connect PWRGD through 10k to Vout.

On page 5,6,7 the manufacturer tells you how to connect it. You can find it in AC/DC Characteristics.

Example:

Electrical Specifications: Unless otherwise specified, all limits are established for VIN = VR + 1V, Note 1, ILOAD = 1 mA, COUT = 1 µF (X7R), CIN = 1 µF (X7R), TA = +25°C, tr(VIN) = 0.5 V/µs, SHDN = VIN, PWRGD = 10K to VOUT. Boldface type applies for junction temperatures, TJ (Note 7) of -40°C to +125°C.

As for SHDN. As a manufacturer tells you it's used to enable or disable the conversor.

Also if you are going to use this circuit as a simple conversor I would switch to a MCP1755S if you can.

Hope this helps you

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