Data Model Documentation
Sources of noise

Sources of noise

Key Concepts

Noise factor, noise figure, noise temperature, and noise power are all related values that describe the noise contributed to a signal.

Noise factor: For an input signal with a reference noise temperature (often 290 K), the noise factor is a unitless metric that describes the ratio of the output noise power of the element to the output noise power that would result if the element added no noise. In other words, the noise factor is the ratio of the input carrier-to-noise to the output carrier-to-noise, assuming an input with the reference noise temperature. A noise factor of 1 indicates the element contributes no noise. For more details, see here.

Noise figure: The noise factor expressed in dB:

noise_figure = 10 * log10(noise_factor)

A noise figure of 0 indicates the element contributes no noise. For more details, see here.

Noise temperature: The noise contributed by the element, in kelvin. For more details, see here.

Antenna noise temperature: The noise received by an antenna from itself and its environment, in kelvin. This depends on factors such as:

  • The target: For example, the noise temperature is higher when pointing directly at the sun versus at the Earth
  • The environment along the pointing direction: Humidity, clouds, and rain can increase the noise temperature
  • The internal components of the antenna: May contribute unwanted energy to the signal
  • Note: This does not refer to the physical temperature at the antenna site. For more details, see here.

Reference temperature: The noise factor and noise temperature are related through the reference temperature. Given a noise factor in linear units and a reference temperature in K, the noise temperature, in K, can be computed as:

noise_temperature = (noise_factor - 1) * reference_temperature

A reference temperature of 290 K is commonly used.

System noise temperature: The total noise temperature of the antenna and receive signal processing chain. To compute the noise across the signal processing chain, sum the first component’s noise temperature with each subsequent component’s noise temperature divided by the cumulative gain of all preceding components. For example, for a receive chain that contains an antenna followed by a low-noise amplifier and a filter, the noise temperature of the signal processing chain, in K, would be:

signal_processing_chain_noise_temperature = 
  (amplifier_noise_temperature / 1) 
  + (filter_noise_temperature / gain_of_amplifier)

where the gain is in linear units.

Then, the system noise temperature, in K, can be calculated as:

system_noise_temperature = antenna_noise_temperature + signal_processing_chain_noise_temperature

For more details, see the Friis equation for noise temperature.

Noise power: The equivalent power of a noise temperature over a given bandwidth. The noise power, in watts, can be calculated as:

N = k * T * B

where

  • k is Boltzmann’s constant, in joules per kelvin (1.381×10−23 J/K)
  • T is the system noise temperature, in K
  • B is the signal bandwidth, in Hz

This is a relevant value when computing metrics like the carrier-to-noise in a link budget. For more details, see here.

Corresponding Fields in NMTS

NMTS models these concepts in the antenna and in each element of the signal processing chain.

Antenna

Amplifiers

Filters

The system noise temperature is not directly specified in a field in NMTS. Rather, the noise temperature of the antenna and each element of the signal processing chain is modeled individually. A model consumer can use these values to compute the system noise temperature.

Using these sources of noise in link budget calculations

Recall that the noise power, in watts, can be calculated as:

N = k * T * B

where

  • k is Boltzmann’s constant, in joules per kelvin (1.381×10−23 J/K)
  • T is the system noise temperature, in K
  • B is the carrier bandwidth, in Hz

For more details, see here.

Expressing this value in dB:

Np = 10 * log10(k * T * B)

For this example link budget, the power at the receiver of the link can be summarized as, in dBW:

Pr = EIRP - L + Gr

where

  • EIRP is the effective isotropic radiated power of the transmit antenna, in dBW
  • L is the total loss across the link, in dB
  • Gr is the receive antenna’s gain in the direction of the link, in dB

The carrier-to-noise can then be calculated as, in dB:

C/N = Pr - Np

Therefore,

C/N = EIRP - L + Gr - 10 * log10(k * T * B)

Alternatively, expanding this equation yields:

C/N = EIRP - L + Gr - 10 * log10(k) - 10 * log10(T) - 10 * log10(B)

where

  • EIRP is the effective isotropic radiated power of the transmit antenna, in dBW
  • Gr is the receive antenna’s gain in the direction of the link, in dB
  • L is the total loss across the link, in dB
  • k is Boltzmann’s constant, in joules per kelvin (1.381×10−23 J/K)
  • T is the system noise temperature, in K
  • B is the carrier bandwidth, in Hz
Antennas