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LM5145: ILIM current RDSON sensing temperature coefficient

Alika Ah New
Prodigy 30 points

Part Number: LM5145
Other Parts Discussed in Thread: CSD18563Q5A

Hi, I see that the LM5145 includes a temperature coefficient of +4500ppm/C to help track the RDSON temperature variation of the low side MOSFET. I'm trying to make sure that our current limit will be the same at higher temperatures, but I need some help understanding how the math works. Can you help me work through this example?

If our low side MOSFET is CSD18563Q5A, the RDSON vs temperature is shown in the chart below. Given that the gate drivers from the LM5145 drive VGS at 7.5V, this means RDSON is 6mOhm at 25C and 10.5mOhms at 125C. 

Using the formula R_ILIM = (I_OUT - I_L / 2) / I_RDSON x RDSON, with a desired current limit I_OUT = 14A, peak to peak inductor ripple current I_L = 3A, I_RDSON = 200uA, and RDSON = 6mA at 25C from the chart above. That works out to R_ILIM = 375 ohms to have a current limit of 14A at 25 C. 

Now if I am trying to figure out what the current limit I_OUT would be at 125 C, I can rearrange the formula to be:

I_OUT = (R_ILIM x I_RDSON / RDSON) + I_L / 2

To double check this at 25C => I_OUT = (375 x 0.0002 / 0.006) + 3/2 = 14 A

Now trying to solve for the current limit at 125C, is it increasing the I_RDSON by +4500ppm/C as shown in the math below?

TC = 4500 ppm/C x (125C-25C) = 0.45

I_RDSON = 200uA x (1+0.45) = 290 uA

Let's say the R_ILIM has a TC of 100ppm/C, then at 125C, it would have resistance of 378.75 ohms.

Using this in the formula above, with RDSON @ 125C = 10.5mOhm

This would give I_OUT = (378.75 x 0.00029 / 0.0105) + 3/2 = 12A

Is my math above right? If not, can you help me work through the math correctly?

I would like to make sure I understand the current limits at higher temperatures, because if we're designing for a 14A limit, but actually getting a limit of 12A at higher temperatures, we will need to redesign our circuit a bit. Do you have any suggestions on ways we can make this more consistent across different temperatures? Is there another MOSFET that matches this temperature coefficient better?

Thank you!