7 Amplifier Intrinsic Noise

The selection of the best chopper amplifier as well as the associated feedback network has a significant impact on the overall amplifier noise. This theory applies to both chopper and traditional amplifiers, and is pertinent background information for the discussions in the following sections. For full coverage of intrinsic noise see Amplifier Precision Labs.

Intrinsic noise refers to the noise generated by circuit components themselves. Amplifiers generate an intrinsic voltage and current noise that is specified in the data sheet. Using simulation or calculation it is possible to make accurate predictions on total RMS intrinsic noise for an amplifier. However, the resistors used in the feedback network and source impedance also generate an intrinsic noise. This noise can be calculated using the thermal noise equation.

where

e_n – the noise density generated by the resistor (nV/ $\sqrt{\mathrm{Hz}}$ )

k - Boltzmann’s constant 1.38 × 10^–23 J/K

R – Resistance in ohms

T – Absolute temperature in degrees Kelvin (K): T_K = T_C + 273.15

Two uncorrelated noise sources are added using the square-root sum of the squares as shown in Equation 8. When adding two noise sources, one noise source is considered to be insignificant compared to another when the larger noise source is at least three times the magnitude of the smaller source. For example, adding a
3nV/ $\sqrt{\mathrm{Hz}}$ noise source with 1nV/ $\sqrt{\mathrm{Hz}}$ gives a total noise of about 3.2nV/ $\sqrt{\mathrm{Hz}}$ , so the 1nV/ $\sqrt{\mathrm{Hz}}$ source is insignificant ( $\sqrt{{(3.0nV/\sqrt{Hz})}^2+{(1.0nV/\sqrt{Hz})}^2}=3.2nV/\sqrt{Hz}$ ).

where

e_nTotal – the total noise from combining e_n1 and e_n2

e_n1, e_n2 – two random uncorrelated noise sources

The noise model for an amplifier circuit is shown in Figure 7-1. The amplifier has a voltage noise source and current noise sources. These are specified in the amplifier data sheet. The current noise source is normally very low in CMOS amplifiers (i_bn < 100fA/ $\sqrt{\mathrm{Hz}}$ ) and can be neglected in most applications. Do not confuse the current noise source with current transients generated by the chopping calibration. Those transients do generate noise which is discussed in section Section 8. Aside from the amplifier noise sources each resistor has an associated noise source defined by Equation 7.

For the equivalent circuit, notice that the amplifier voltage noise source is located at the non-inverting input. Any noise from the source impedance is also at the non-inverting input and adds as the square-root sum of the squares (Equation 8). Additionally, the noise from the feedback network can be reflected to the non-inverting input as the parallel combination of R_f and R_g.

From a noise perspective, a circuit is generally considered to be optimized when the total noise is approximately equal to the amplifier noise. The idea is that you do not want to choose an amplifier for the excellent noise characteristics and use large noisy resistors that dominate the total noise. Therefore, to optimize the overall noise, the resistor noise is set to one-third of the amplifier noise (see Equation 9). Table 7-1 summarizes the maximum noise optimized equivalent feedback resistances for common chopper amplifiers.

The main trade-off involved in choosing a feedback network that can achieve the optimal thermal noise is the amplifier output current required to drive the feedback network. For example, the OPA388 has a voltage noise density of 7nV/ $\sqrt{\mathrm{Hz}}$ . The optimal noise feedback network for this case is 331Ω. Remember that this equivalent impedance is the parallel combination of R_f and R_g. When using this optimal feedback impedance, the load seen by the amplifier depends on the amplifier gain. Figure 7-2 shows the examples for a gain of 2V/V and a gain of 11V/V. Clearly, increasing the gain allows for a larger value of R_f and decrease of the overall amplifier loading.

The source impedance is frequently determined by the system requirements. For example, the source can be a sensor with a particular source impedance and the system designer does not have the flexibility to adjust the value. In this case, to minimize the overall system noise the source impedance is supposed to dominate the total noise and thus the amplifier noise is, in the best circumstance, one-third of the source impedance noise. However, in some cases it is not practical to find an amplifier with noise low enough for the source impedance noise to dominate. Figure 7-3 illustrates source resistance noise and recommended amplifier noise versus resistance.