# Noise of a current source

Precision current sources are critical electronics in atomic physics. They can serve as power supply for diode lasers or drive a coil to generate a precise magnetic field. We sometimes need to have the load grounded in experiments to prevent short-circuit on the conductive optical table. This demand is often achieved by using an instrumentation amplifier(INA). The current flow through a sensing resistor and the voltage drop on that resistor is sampled by INA and feedback to the output stage. We find AD8429 from Analog Devices a great INA choice for a bi-polar current source with the input noise density as low as $1nV/\sqrt{Hz}$.

When facing with extremely noise sensitive application, we should have a second look at our design. In our old design, the $Gain=1$ is set without gain setting resistor attached. This seemed very convenient because we do not want gain drift. The mismatch of the temperature coefficient of the on-chip resistors and the external gain setting resistor will sure cause terrible gain drift. In fact, the total input referred noise of an INA should include the output noise part attenuated from the feedback network. The AD8429 has a very decent input noise density $1nV/\sqrt{Hz}$, but a relative higher output noise density $45nV/\sqrt{Hz}$. When the INA runs at $Gain=1$, the total input referred noise is dominated by the unattenuated output noise of the chip. The result is nearly  $45nV/\sqrt{Hz}$ noise density on the input after RMS summing of the two kinds of noise!

An easy way to fix this is to increase the gain of the INA. In our configuration, a $200m\Omega$ current sensing resistor is used under the maximum current 5A(1V voltage drop). If we can amplifier that to 10V, which is still inside the rail of the INA, the output noise contribution will also be greatly reduced to 1/10. However, it is difficult to just place a resistor on that chip due to the temperature drift mentioned before. Instead, I find AD8228, which has a pair of internal matched gain setting resistors, providing $Gain=10$ and $Gain=100$ through simply opening or shorting the gain setting pins. For its fixed gain, the noise density of AD8228 referred in the datasheet includes the output noise contribution on the input noise. This means that the $15nV/\sqrt{Hz}$ should be the final input referred noise density of AD8228 under $Gain=10$ setting. Definitely much better than $45nV/\sqrt{Hz}$!