4 Impact Current Noise has on a Non-inverting Amp With Large Source Impedance

Generally, the f-squared noise is a concern for systems with large source resistance or large feedback resistance. Doing a simple analysis using your source impedance can lead you to believe that the f-squared current noise will translate to a large voltage noise. However, to fully understand the system performance you need to look at all the parasitic capacitance. Frequently, the parasitic are ignored because they are in the picofarad range and generally do not have a significant performance impact. However, in this case the source impedance is large and comparable to the capacitive reactance of the parasitic.

For example, the consider the OPA350 with a 100MΩ source impedance. At low frequencies this device has a current noise of 0.5fA/√Hz. Considering Table 1-1, the low frequency current noise must be negligible with a 100MΩ source impedance, but higher frequency current can be a concern as current noise increases to hundreds of femtoamps. The model for this circuit is shown in Figure 4-1. In this figure, the current noise sees a current divider. Some of the current will flow into the common mode capacitance and some will flow into the source. Furthermore, the source resistance generates a noise current which depends on the common mode capacitance. Keep in mind that the reactance of the common mode capacitance is significantly smaller than source resistance at higher frequencies (at 1kHz, $X_c=1/\left(2\pi \left(1kHz\right)\left(6.5pF\right)\right)=24M\Omega$ ). Thus, from a current divider perspective most of the current will flow in the common mode capacitance. Also note that any PCB parasitic capacitance on the non-inverting input will be in parallel with C_cm and will further reduce the reactance [ $X_{ccm}=1/\left(2\pi f\left(C_{cm}+C_{par}\right)\right)$ ].

For a better understanding of the interaction between the various sources and impedance in this circuit, it is useful to use superposition. First, look at the impact of the source resistor noise. Rs and the reactance of C_cm form a low pass filter. The noise voltage at the input of the amplifier will roll off at 245Hz ( $f_c=1/\left(2\pi R_s{C}_{cm}\right)=245Hz$ ). You can also consider that this noise voltage creates a noise current of $i_{Rs}=e_{nr}/\sqrt{{\left(R_s\right)}^2+{\left(X_{ccm}\right)}^2}$ (see Figure 4-2)

Considering the noise current from the amplifier (i_n) will flow from the amplifier into a current divider with the reactance of C_cm in parallel with R_s. Notice that at low frequencies the current noise flowing through the resistor is the same as the current from the amplifier. However, at higher frequencies the capacitive reactance of the common mode capacitor is small in comparison to the source resistance so most of the current from the amplifier flows through C_cm.

Figure 4-5 illustrates the overall noise for the OPA350 with a 100 MΩ source impedance. Notice that the output noise curve at low frequencies is mostly the thermal noise of the resistor. This makes sense according to Table 1-1, as the current noise at low frequency is 0.5fA/√Hz and 100 MΩ is low enough to minimize the impact of this low-level current noise. At higher frequencies however, you can expect the current noise to be more problematic as the noise is over 100fA/√Hz at 1MHz. However, this increase in current noise at higher frequencies is not seen by the load as the impedance of the common mode capacitor is small compared to the source impedance, so most of the current will in the common mode capacitance. In fact, the noise current flowing through the source impedance is mainly the thermal noise of the impedance ( $i_{np}\approx e_{nr}/R_s=1.28\mu V/100M\mathrm{\Omega }=12.8\mathrm{f}\mathrm{A}/\mathrm{r}\mathrm{t}\mathrm{H}\mathrm{z}$ ). Finally, notice that the amplifier output noise starts to roll-off at approximately 100Hz. This is because of the low pass filter formed by the source impedance and the common mode capacitance ( $f_c=1/\left(2\pi R_s{C}_{cm}\right)=245Hz$ ). Thus, the noise as well as any input signal will be attenuated by the filter from the source impedance and common mode capacitance.