Surge limiter resistor

I was consulted by my colleague junior engineer, Teoh the other day, on what's the actual function of two big resistors prior to the input of linear regulator as circled in schematic below and how do we arrive at the resistance and power rating values.

The resistors indeed serves as surge limiting resistor. When the raw unregulated supply first applied to the circuit, the sudden ramp-up in supply voltage input would be taken as surge for the input capacitors; and the impedance across the input capacitors would be effectively near zero at that spur of moment. As the capacitors are deemed shorted to ground with the voltage surge, there could be large current surge due to short-circuit condition, if without a proper protection mechanism, this could blow up the capacitors; which is catastrophic failure. This method appears to be the most primitive way to limit the surge.

Another popular method would be using NTC thermistor, which might costs slightly higher, but actually induce less heat disspation because of the intrinsic characteristics of NTC thermistor, its resistance would decrease dramatically as the thermistor self-heats with steady-state current flow. The catch is, NTC thermistor needs cool off time prior to another power surge.

A brief reflective thought brought me to realization that in college time, we were not really taught of the electronics design practices to emphasize on safety and reliability. Engineers would only realize how important of all these practice to make the design survive the test of real world when they start to work.

OK, come back to Teoh's question. Let's take a look at the calculations of the resistance and power rating value in the above shown schematic.

Basically, the raw unregulated power supply input we used here is from normal car battery, i.e. 13.8V nominal +/-20%. That means min voltage @11.04V & max voltage @16.56V.

Take a look at the capacitor spec (the one nearest to the raw voltage supply), the max allowable surge current is slightly above 2A @ 1M frequency, which means fastest surge rise time of ~350ns.

So we would take 700mA as our targetted max allowable current.

Calculate the resistance value according to Ohm's law:

@16.56V, R= 16.56V/0.7A = ~24 ohm

@11.04V, R= 11.04V/0.7A = ~16 ohm

So, we would choose the higher resistance value to achieve lower power disspation; max power dissipation would then be V*V/R = 16.56*16.56/ 24 = ~11.4W.

We would choose the final resistance value to be 25 ohm, and thus the max power disspation is ~11W; we would parallel two resistors of 50 ohm each with power rating of 6W. Anyway, a quick thought on this would reveal that the resistors would be too big physically, and the continuous power loss for nothing during steady state doesn't look good. The use of NTC thermistor would be more appropriate as it dissipates negligible power loss at steady-state. In terms of economics of board space, it is more viable as well.