3.3. Internal noise of an op-amp

Op-amps are used to amplify a tiny signal from a sensor or other device. Noise is added to this tiny signal and amplified by an op-amp. Therefore, noise contributes to a reduction in the sensitivity and accuracy of a sensor.
The noise related to an op-amp is divided into external noise caused by electromagnetic interference and external parts and internal noise. This section focuses on the internal noise of an op-amp.

Two types of internal noise are defined as equivalent input noise:

• Frequency-dependent 1/f noise: Thermal noise generated by resistors and shot noise generated by free-moving carriers in a semiconductor
• Frequency-independent white noise: Flicker noise caused by crystal defects and burst noise

Figure 3-9 shows the noise frequency characteristics of the op-amp, and Figure 3-10 shows an example of the measured equivalent input noise voltage. Figure 3-10 compares Toshiba’s TC75S51 general-purpose op-amp and TC75S67 low-noise op-amp.
The general-purpose op-amp has a white noise of roughly 30 nV/√Hz and a corner frequency of 300 Hz whereas the low-noise op-amp has a white noise of roughly 6 nV/√Hz and a corner frequency of 100 Hz.

Both 1/f noise and white noise appear at the inputs of an op-amp and are defined as equivalent input noise voltage. The equivalent input noise is amplified by a gain and appears at the output. In particular, care is required as to low-frequency noise because its voltage is dependent on frequency.

To amplify a tiny signal, multiple amplifiers are sometimes connected in a cascade in order to prevent abnormal oscillation. Let’s consider how each amplifier stage affects the noise that appears at the output of the cascade amplifier.
Figure 3-11 shows a three-stage cascade amplifier.
As shown in Figure 3-11, the output signal power (P_Sout3) and the output noise power (P_Nout3) can be calculated as follows.
As you see, the input noise (P_Nin) and the equivalent input noise (P_N1) of the first-stage amplifier have the greatest impact on the output noise.

The output signal power (P_Sout3) and the output noise power (P_Nout3) are expressed by the following equations:

P_Sout3 = G₁ × G₂ × G₃ × P_Sin
P_Nout3 = G₁ × G₂ × G₃ × (P_Nin+P_N1) + G₂ × G₃ × P_N2 + G₃ × P_N3

Therefore, the noise factor (F), a measure of noise, is calculated as follows:

The equivalent input noise of the second-stage amplifier (P_N2) is divided by the first-stage gain (G₁) whereas the equivalent input noise of the third-stage amplifier (P_N3) is divided by the first-stage and second-stage gains (G₁ and G₂). Therefore, the input noise of the successive stages of amplifiers has progressively less impact on the output P_Nout3.
As indicated by this example, a low-noise amplifier should be used at the first stage to reduce the effect of its noise.