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I have a constant current LED Driver (LM3410) that effectively functions as a switching voltage regulator to provide enough voltage for LEDs in series. When I power it with a relatively low voltage it lights up the light strip pretty well, although under the current it should be regulating at. If I increase the input voltage so that the current output is higher, the strip turns on fine for about a half second then starts flickering (slow at first then fast, maybe 5hz to 20hz).

I followed most of the recommendations in the datasheet so I'm pretty sure I'm using good capacitors and resistors (high enough voltage and values) but I'm somewhat unsure about the Inductor. The Inductor is 8.2uH but the SRF is unspecified and I'm worried it may not be compatible with the two available frequencies of the Driver. Current is about 1.5 A and the Inductor is rated for 2 A.

Can someone tell me what the reasons usually are for a switching regulator to flicker it's power supply when input voltage changes like in this scenario?

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I suspect the inductor is probably not suitable - it needs to be rated for the current (if it saturates, the inductance drops and the circuit won't work properly) and have a higher SRF than the operating frequency. You definitely need to know the specs of your inductor. Purchase one with a datasheet, and check it's suitable for use with the part.

Another possible problem is thermal issues if you have a high current design (what is the current?) but don't have a good PCB layout as recommended in the datasheet (large solid plane underneath the IC)

One last thing is make sure the DIM pin is not floating - tie it to Vin.

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