# Resistor Noise Calculator

Created by Wei Bin Loo
Reviewed by Wojciech Sas, PhD and Adena Benn
Last updated: Dec 21, 2022

We have prepared this resistor noise calculator to help you to calculate the RMS noise signal generated by resistors. This concept and formula will help you calculate the amount of unwanted noise signals the resistor produces when operating.

This article will help you understand what is the resistor noise and how to calculate it using the resistor noise formula. We will also demonstrate resistor noise calculation to help you understand the concepts.

## What is the resistor noise?

Resistor noise is AC noise signals that a resistor produces when it is operating. This is often an annoying phenomenon as the noise is usually unwanted. The motion of the electrons generates the resistor noise within the resistors.

In general, there are 2 types of resistor noise, namely thermal noise and current noise. **Thermal noise is usually the main contributor to resistor noise.**The movement of electrons causes thermal noises. As the temperature increases, the motion of electrons increases, hence increasing the thermal noise produced. However, current noise decreases when the frequency and movement of electrons increases, unlike thermal noise.

Also, thermal noise increases with a larger resistance value, whereas current noise decreases when resistance increases.

## How to calculate the resistor noise? The resistor noise formula

To understand the resistor noise calculation and RMS noise voltage formula (you met something similar at our RMS voltage calculator, let's take the following resistor and conditions as our example:

• Boltzmann's constant, $k =1.380649\times10^{-23}\ \mathrm{J/K}$;
• Resistance, $R=20000\ \mathrm{Ω}$;
• Temperature, $T =293.15\ \mathrm{K} = 20\ \degree\mathrm{C}$;
• Bandwidth, $ΔF = 1000\ \mathrm{Hz}$.

This calculation requires four steps:

1. Determine the resistance of the resistor:

The resistance of the resistor is usually listed on the resistor. If it's not there, you can find it using our resistor color code calculator The $R$ for our resistor is $20000\ \mathrm{Ω}$.

1. Determine the temperature:

This is the temperature that the resistor is operating in. Do keep in mind that the temperature of the resistor will change. Usually, the longer it works, the higher its temperature. In our example, the $T$ is equal to $293.15\ \mathrm{K}$.

1. Determine the bandwidth:

The bandwidth is the frequency of the radio signal: meet this quantity at our frequency calculator. The $ΔF$ in our example is $1000\ \mathrm{Hz}$.

1. Calculate the resistor noise signal using the RMS noise voltage formula:

The last step is to calculate the resistor noise, $E$, using the thermal noise formula below:

$E = \sqrt{4\cdot R \cdot k\cdot T\cdot ΔF}$

According to the thermal noise formula, the resistor noise in our example is $569\times 10^{-9}\ \mathrm{V}$ or $569\ \mathrm{nV}$.

1. Calculate the noise level $L_{\mathrm{u}}$:

You can calculate the noise level $L_{\mathrm{u}}$ using the formula below:

$L_{\mathrm{u}} = 20\cdot \log_{10}\left(\frac{V}{V_0}\right)$

where $V_0 = 0.77459667 \ \mathrm{V}$, which is the reference voltage for noise level $L_\mathrm{u}$.

1. Calculate the noise level $L_\mathrm{v}$:

You can calculate the noise level $L_\mathrm{v}$ using the formula below:

$L_\mathrm{v} = 20 \cdot \log_{10}\left(\frac{V}{V_0}\right)$

where $V_0 = 1\ \mathrm{V}$ is the reference voltage for noise level $L_\mathrm{v}$.

## Why are low noise resistors better?

Now that we understand what resistor noise is and its calculation let's discuss why it is better to have a low noise resistor. There are more reasons than the one you may think by reading our signal to noise ratio calculator.

Having a low noise resistor is essential when using them as input resistors within an amplifier circuit. This is because every input signal, including the noise generated by the resistors, will be fully amplified. This will cause the unwanted signal to be amplified, and extra energy will be wasted.

Usually, resistors with thin films and metal foils produce lower resistor noise. On the other hand, resistors with thick films and carbon composition generate the most unwanted noise signal while operating.

## FAQ

### What is a resistor?

A resistor is an electrical component that is built for creating resistance in the flow of an electric current. Creating resistance limits the electric current going through the circuit, creates voltage division, generates heat from electric current, etc.

### What is Boltzmann constant?

Boltzmann constant is created and named after Ludwig Boltzmann, an Austrian scientist. It is equal to 1.380649×10-23 JK−1. The Boltzmann constant relates the gas particle's relative kinetic energy to the temperature of the gas.

### What is resistance in electronics?

In electronics, we define resistance as a characteristic of a material that opposes the current flow in an electrical circuit. The unit for this measure is ohms. Conductors have low resistance, whereas insulator has high resistance. In general, the higher the resistance, the lower the current flow, given a constant voltage.

### What is bandwidth in electronics?

The definition of bandwidth in electronics is the frequency of a radio signal. It is usually measured in hertz, which is the number of oscillations per second.

### What is the noise level Lᵥ given a voltage of 2V?

The noise level Lᵥ will be 2 dBV. This is because the reference voltage for noise level Lᵥ is 1V. You can perform the calculation using this formula: Lᵥ = 20 ⋅ log₁₀(V / V₀), where V₀ = 1 V is the reference voltage for noise level Lᵥ.

Wei Bin Loo
Resitance (R)
Ω
Temperature (T)
°F
Bandwidth (ΔF)
Hz
Resistor noise (E)
μV
Noise level Lᵤ
dBu
Noise level Lᵥ
dBV
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