Thermal Noise Calculator Formulae & Equations

- formulae & calculations associated with RF or thermal noise and a simple to use voltage and dBm calculator.

As noise is a very important factor in many electronics / RF applications and circuits, it is important to be able to calculate the values for noise under the conditions.

There are many equations that enable the prediction of thermal noise levels.

The thermal noise calculations can be undertaken relatively easily in most instances. While some integration may be required in some instances, there are straightforward equations for most calculations required.

Thermal noise calculator

The thermal noise calculation below provides an easy method of determining the various thermal noise values that may be required.


Thermal Noise Calculator

     

Enter Values:

Temperature:   °Celsius
Resistance:   Ohms, Ω (not required for dBm calculation).
Bandwidth:   Hz
 
 
 
 

Results:

Noise voltage:   μV RMS
Noise power:   dBm


Basic thermal noise calculation and equations.

Thermal noise is effectively white noise and extends over a very wide spectrum. The noise power is proportional to the bandwidth. It is therefore possible to define a generalised equation for the noise voltage within a given bandwidth as below:

Basic noise formula used for calculating thermal noise

Where:
    V = integrated RMS voltage between frequencies f1 and f2
    R = resistive component of the impedance (or resistance) Ω
    T = temperature in degrees Kelvin
      (Kelvin is absolute zero scale thus Kelvin = Celsius + 273.16)
    f1 & f2 = lower and upper limits of required bandwidth

For most cases the resistive component of the impedance will remain constant over the required bandwidth. It therefore possible to simplify the thermal noise equation to:

Equation or formula to calculate the noise voltage:  V = square root (4 k t b r)

Where:
    B = bandwidth in Hz

Thermal noise calculations for room temperature

It is possible to calculate the thermal noise levels for room temperature, 20°C or 290°K. This is most commonly calculated for a 1 Hz bandwidth as it is easy to scale from here as noise power is proportional to the bandwidth. The most common impedance is 50 Ω.

Popular noise calculation for room temperature and in a 1Hz bandwidth

Thermal noise power calculations

While the thermal noise calculations above are expressed in terms of voltage, it is often more useful to express the thermal noise in terms of a power level.

To model this it is necessary to consider the noisy resistor as an ideal resistor, R connected in series with a noise voltage source and connected to a matched load.

Thermal noise = k T B

Note: it can be seen that the noise power is independent of the resistance, only on the bandwidth.

This figure is then normally expressed in terms of dBm.

Thermal noise in a 50 Ω system at room temperature is -174 dBm / Hz.

It is then easy to relate this to other bandwidths: because the power level is proportional to the bandwidth, twice the bandwidth level gives twice the power level (+3dB), and ten times the bandwidth gives ten times the power level (+10dB).


Bandwidth
(Δf) Hz
Thermal Noise Power
dBm
1
-174
10
-164
100
-154
1k
-144
10k
-134
100k
-124
200k (GSM channel)
-121
1M (Bluetooth channel)
-114
5M (WCDMA channel)
-107
10M
-104
20M (Wi-Fi channel)
-101

By Ian Poole


<< Previous   |   Next >>


Share this page


Want more like this? Register for our newsletter








A Guide to RF Amplifier Envelope Tracking
A Guide to RF Amplifier Envelope Tracking

Ian Poole
Envelope tracking is a key technology that is used in association with RF...
Read more . .

USA bookstore UK bookstore
Guidebooks for electronics engineers
Training
Online - Effective Spectrum Analyzer Measurements
Learn how to make spectrum analyzer measurements at RF and microwave frequencies

More training courses

Books for electronics engineers
Whitepapers
New External Power Supply Regulations Are Coming in 2016
In this whitepaper, power supply experts CUI look at the standards & requirements for power supplies around the globe that will hit the industry by 2016.

More whitepapers










Radio-Electronics.com is operated and owned by Adrio Communications Ltd and edited by Ian Poole. All information is © Adrio Communications Ltd and may not be copied except for individual personal use. This includes copying material in whatever form into website pages. While every effort is made to ensure the accuracy of the information on Radio-Electronics.com, no liability is accepted for any consequences of using it. This site uses cookies. By using this site, these terms including the use of cookies are accepted. More explanation can be found in our Privacy Policy