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Help with OPA128 trans impedance amplifier.

opa128.TSCDear All,

I am trying to make a trans impedance amplifier using OPA-128. The attached schematic shows the circuit.

I want to measure nano-volts of current. The gain is 10^9 as I am using 1G-ohm resistor.
There is one 10pf capacitor in parallel to 1G resistor.

I have assembled the circuit on a pcb and put it in a metal box to save it from noise and all.

The problem is whenever I power on the circuit, the output goes to saturation most of the times.

I have tried to adjust offset using a 100K trim-pot but its not helping.

Sometimes the output is around 6V at no I/p and when i change the current at I/p the circuit works perfectly fine but I am not able to trim the offset to zero.
Other times the circuit remains in saturation and O/P voltage does not change with I/P current.

Please help me to remove this saturation problem. Also how can I make output zero at zero I/p current???

Regards

Manik