Understanding OPERATIONAL AMPLIFIERS Noise! Your First Step to Becoming an Engineer | NEXTY Electronics, an Electronic Components and Semiconductor Trading Company

In OPERATIONAL AMPLIFIERS that handle minute signals, noise that mixes with the pure signals can become a problem.
There is noise generated by OPERATIONAL AMPLIFIERS itself and noise that is mixed in from outside, and it is necessary to understand which noise has the greater impact on the signals being handled and then take appropriate measures against each.
Here we will explain noise generated by OPERATIONAL AMPLIFIERS itself.

Noise generated by OPERATIONAL AMPLIFIERS

Noise from OPERATIONAL AMPLIFIERS can be broadly divided into the following two types:

Frequency-independent noise
Frequency-Dependent Noise

Frequency-independent noise

It is a noise that is independent of frequency, that is, it occurs randomly without correlation to frequency. When a graph is drawn with frequency on the horizontal axis and noise density on the vertical axis, it has flat characteristics and is called white noise.

Frequency-Dependent Noise

This noise is frequency-dependent, meaning that its magnitude changes depending on the frequency, and it is called 1/f noise (flicker noise) because it decreases in inverse proportion to the frequency.
The slope is 10dB/dec, and when both the horizontal and vertical axes are displayed logarithmically as shown in the figure below, it appears as a straight line.

As can be seen from the diagram above, the lower the frequency, the larger the frequency-dependent 1/f noise.
Conversely, as the frequency increases, the 1/f noise decreases and the frequency-independent white noise increases, resulting in a flat characteristic at high frequencies.
Here, the frequency at which 1/f noise and white noise switch places, that is, reach the same level, is called the corner frequency.
Although OPERATIONAL AMPLIFIERS itself has a bandwidth, if the bandwidth limited by the circuit using OPERATIONAL AMPLIFIERS is sufficiently higher than this corner frequency, 1/f noise can be almost ignored.

The graph above is the same as the previous one, but shown linearly instead of logarithmically.
The maximum value on the horizontal axis is 1 MHz, but because the total noise is the integration of the noise density, it can be seen that the impact of 1/f noise is smaller when viewed overall.

Noise Density

Above, we have naturally used the term "noise density," but for those who are not familiar with this term or the unit "V/√Hz," it may be difficult to understand.

What is noise density?

Noise is distributed over a wide frequency range, and in most cases the amount of energy varies depending on the frequency.
When analyzing noise, in order to determine which frequencies have high energy and which have low energy, the noise level is expressed as power (energy) per unit frequency, that is, per 1 Hz of bandwidth.
This is called noise power density and is expressed in W/Hz (power per 1 Hz).
However, in the world of electrical circuits, it is often more convenient to think of noise in terms of voltage rather than power, so noise voltage density is used.
Because power is proportional to the square of the voltage, noise voltage density has units of V/√Hz.
You might be thinking that if it is proportional to the square, then it should be V ² /Hz, and that is correct.
However, when it is written as V squared, you end up asking yourself how many V it actually is, and so you have to tap on a calculator, which is why the slightly unfamiliar expression V/√Hz is used.

About the noise level

We have explained noise density as a way to express the magnitude of noise at each frequency, but now we will explain how to express the overall magnitude of noise.
In the case of OPERATIONAL AMPLIFIERS, it is often expressed as an effective value (rms).
This is the sum of all noise components in a given frequency range.
In the case of voltage noise, if there are noise sources V1, V2, V3, etc. that are uncorrelated with each other, the total will be the sum of squares.

Noise sources V1, V2, etc. can be thought of as noise at each frequency, that is, noise density multiplied by bandwidth.
The noise density value at each frequency multiplied by the bandwidth (BW) to be calculated is the noise source, and the square sum of this value over the entire frequency range is the effective value (rms) of the noise.
If the bandwidth BW is 100 Hz and the frequency range is 10 kHz, the noise source is calculated every 100 Hz, and the square sum of 100 noise sources is taken.
In the case of white noise, the noise density is constant regardless of frequency, so it can be calculated by multiplying the noise density by the frequency range.
If we assume that the noise density is 10nV/√Hz and the noise up to 10kHz is