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I had been trying to build a low current sensor using a jfet but it is not able to sense anything. Further how do I eliminate the background noise from the given setup
You cannot see the pA signal because the noise is high. If the signal is varying only slowly (low frequency) you can consider a chopper stabilized amplifier. If your signal is periodic, you may be able to design a averaging setup. Essentially everything boils down to the nature of the signal. Perhaps you can consider a mosfet instead of a jfet that can provide higher input impedance.
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