What is thermal noise of resistor?

Resistance is the basic component we have encountered earliest, there is an introduction of resistance in the textbook, Figure 1-20 shows the common chip resistor, thermistor and straight insert/color ring resistor, the resistance value can be read through the color ring of the resistor.

 

Figure 1-20 Various types of Resistors

We learned the resistance related content in middle school, and later we often hear that the resistance has noise, so where does the noise of the resistance come from? The noise of the resistance usually refers to thermal noise (also called Johnson noise), the characteristic is that even the resistor is not connected to the circuit, even without current passing through the resistor, there will be voltage changes at both ends of the resistor, this is the thermal noise of the resistor.

Within the working bandwidth of the system, the thermal noise of the resistor can be considered as white noise (or broadband noise). When the two ends of the resistor are open, the effective value (root mean square value) of the thermal noise can be calculated by formula (1-4):

Where k is the Boltzmann constant, k = 1.38 * 10-23J / K, T is the Kelvin thermodynamic temperature, R is the resistance value, and B is the equivalent noise bandwidth of the system.

 

For example:

When the temperature is 27 ℃ (300 Kelvin), the thermal noise voltage effective value of 10KΩ resistor in 100KHz bandwidth circuit is 4uV; under the same environment, if the resistance is 20KΩ, the thermal noise voltage effective value is 5.8uV.

From the formula, we can see that the larger the resistance, the greater the noise, and the noise increases with the increase of the resistance value. One of the reasons why we seldom use large resistors in our amplifying circuits is to reduce noise. Similarly, noise is also related to temperature, however, noise is not sensitive to temperature, because the thermal thermodynamic temperature is used in the formula. When the temperature changes to tens or dozens of degrees Celsius, the effect on noise is not very significant.

For example, in the above example, the noise at both ends of the resistor is basically the same at 17 ℃ and 27 ℃.

However, in the application of using resistance to measure current (current passing through the resistance, measuring the voltage at both ends of the resistance, the voltage divided by the resistance value is the current value), increasing the resistance will actually improve the accuracy of current collection. This is because the larger the resistance, the larger the voltage generated by the current passing through the resistance, which will improve the accuracy of current detection. If the resistance is too large, the voltage shared by the resistance will be large, so that the voltage shared by the system behind the resistance will be low, which requires engineers to carefully weigh.