INA241A: Current Sensing for very low power devices

Part Number: INA241A
Other Parts Discussed in Thread: INA241B

I have been trying to make a current sensor for a uA to mA consumption device, to be used instead of a current probe on an oscilloscope.

I am using a INA241B to sense the current on a 1.2V rail, but there is too much noise at the output. There is no place to change the feedback resistors and even add a capacitor at the feebcak line to reduce the noise at the output.

Will adding an output capacitor help to reduce the noise? If yes, what should be the recommended value?

The device is a bluetooth device and consumes from 100uA - 15mA current during normal operation. The inrush spikes are however in 100mAs range.