Using an NTC device instead of RF1
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Hello Charlie
The link between power and inrush is not direct so I understand your question.
In low power designs (applications like mobile phone chargers up to 10 W) it is generally lower cost to replace the fuse with a resistor. The function is primarily to disconnect the AC supply from the power supply in the event of a catastrophic failure (for example bridge diode failing short circuit).
At these power level the inrush current is less of a concern as the impedance of the EMI filter, input capacitors etc limits the inrush current to below the maximum rating of the bridge rectifier diodes. Adding a fusible resistor only improves this by lowering the inrush current further. It also acts as part of the differential EMI filtering.
As the input power increases the loss in the resistor is unacceptable so a fuse is used instead. The increased input capacitance and lower impedance of the EMI stage now requires inrush limiting (to protect the diodes and other input stage components) and this is where an NTC would be used.
You asked earlier about resistor selection. We generally recommend 2 W wire wound types to handle the instantaneous dissipation seen when AC is applied. For example at 265 VAC (375 Vpk) and a 10 Ohm resistor the instantaneous peak power is 14 kW (V^2/R). Film construction resistors eventually fail in 230 VAC application. Some years ago I built a stress tester and attached is a photo of a 2 W film resistor that failed after about 20 cycles of AC being applied into 10 uF of capacitance (notice the black spots where the outer layer is damaged).
We always recommend flameproof types to prevent the possibility of fire (and meet safety requirements) when the resistor fails during a fault.
Cheers
PI-Chekov
If you have seperate fuse, you don't need RF1. Or you can use NTC to limit inrush current. Depending on your application, at 1W power range, you may not need to limit inrush current at all.