# Thermal Noise Floor Calculator

Enter the following:

• Temperature in either Kelvin or Celsius
• Bandwidth
• Noise Figure in dB

## Formula

Noise FloordBm = 10*Log10(kTB/(1 mW)) + NF

where,

• T = Temperature in Kelvin
• B = Bandwidth in Hz
• k = Boltzmann’s constant
• NF = Noise Figure

In a radio receiver, the noise floor is the level below which a signal will not be detected. In practice, a signal has to be a few dB higher than this floor before it can be detected. This level is called the Minimum Detectable Signal level or the receiver sensitivity.

As the equation above indicates, the noise floor is directly proportional to the operating temperature, bandwidth and the noise figure.

Receivers for example those used in radio astronomy, have to be very sensitive in order to detect very weak signals. At the NRAO for instance, receivers are cryogenically cooled to reduce the temperature and therefore the noise floor.

Reducing the bandwidth requires high quality analog filtering followed by digital filtering. However the limit to this is the bandwidth of the actual signal being observed.

Finally, the noise figure of the receiver is dependent on the quality of its design. Typically the first low noise amplifier makes the biggest contribution to reducing the noise.

Often times there’s not much you can do about the receiver itself as it cannot be modified internally. In this case one approach to improving noise floor is to add a LNA to the front end of the receiver (shown in the picture below).

Here a Hydrogen Line LNA is added in front of a software-defined radio receiver. More details on the configuration and experiment.

## Example Noise Floor Calculation

Let’s calculate the noise floor of a LoRa receiver system.

For a temperature of 25oC, 125 kHz Bandwidth and a noise figure of 10 dB, the noise floor is -113 dBm. Increasing the antenna cable length will directly impact the noise figure and increase the noise floor. Note that this is not the signal level at which the LoRa signal will be detected. As mentioned, there’s a requirement to include the SNR which typically increases with modulation order and complexity.

## Johnson Noise

Thermal noise is also called Johnson or Nyquist-Johnson noise. This noise results from thermal agitation of electrons. It’s present in all electronic devices and depending on the magnitude can mask a signal of interest and therefore prevent detection.