Equivalent Noise Temperature

Te = T0 × (NF − 1)

Quick answer

This calculator solves Te = T0 × (NF − 1) for Noise Temperature. With Reference Temperature 1.1 K, Noise Factor (linear) 2.35, the result is 1.485 K. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Noise Temperature
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Formula

Te = T0 × (NF − 1)

Description

Equivalent noise temperature provides an alternative way to express the noise contribution of a component by stating what temperature a matched resistor at the input would need to be to produce the same amount of noise. A perfect noiseless amplifier has Te = 0K. The standard reference temperature is T0 = 290K. This representation is preferred in radio astronomy and satellite communications where system noise temperatures are very low (cryogenic LNAs achieve Te < 10K). Noise temperature adds directly for cascaded stages (when properly referred to the same point).

Variables

  • Te — Equivalent noise temperature (K)
  • T0 — Reference temperature, standard 290K (K)
  • NF — Noise factor (linear, not dB)

Practical Notes

A 1 dB noise figure corresponds to Te = 75K. A 3 dB NF gives Te = 290K. Satellite LNAs operate at 40-70K noise temperature (0.5-0.8 dB NF). Radio telescopes use cryogenic receivers at 5-15K. The sky noise temperature at microwave frequencies is about 3K (cosmic microwave background) plus atmospheric contributions.

Symbols and units

Symbol Meaning Default unit Accepted units
Te Noise Temperature — K
T0 Reference Temperature — K
NF Noise Factor (linear) — —

Step by step

  1. 1. What you know: Reference Temperature 1.1 K, Noise Factor (linear) 2.35
  2. 2. The relation: Te = T0 × (NF − 1)
  3. 3. Substitute: T0 = 1.1 K, NF = 2.35
  4. 4. Result: Noise Temperature = 1.485 K

Worked examples

Minimum range

Given: Reference Temperature 0.055 K, Noise Factor (linear) 0.118

Result: Noise Temperature = -0.04851 K

Low range

Given: Reference Temperature 0.55 K, Noise Factor (linear) 1.18

Result: Noise Temperature = 0.099 K

Typical

Given: Reference Temperature 1.1 K, Noise Factor (linear) 2.35

Result: Noise Temperature = 1.485 K

High range

Given: Reference Temperature 1.76 K, Noise Factor (linear) 3.76

Result: Noise Temperature = 4.858 K

Maximum range

Given: Reference Temperature 17.6 K, Noise Factor (linear) 37.6

Result: Noise Temperature = 644.2 K

Solving for each variable

Solve for Noise Temperature

Reference Temperature 0.055 K, Noise Factor (linear) 0.118 → -0.04851 K

Solve for Reference Temperature

Noise Temperature 0.025 K, Noise Factor (linear) 0.118 → -0.02834 K

Solve for Noise Factor (linear)

Noise Temperature 0.025 K, Reference Temperature 0.055 K → 1.455

How Noise Temperature changes with Reference Temperature

Reference Temperature (input) Noise Temperature (result)
0.242 K 1.009 K
0.605 K 2.523 K
1.21 K 5.046 K
1.815 K 7.569 K
2.42 K 10.09 K
3.63 K 15.14 K
4.84 K 20.18 K
9.68 K 40.37 K
16.94 K 70.64 K
24.2 K 100.9 K

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Frequently asked questions

How do you calculate Equivalent Noise Temperature?

Use Te = T0 × (NF − 1). With Reference Temperature 1.1 K, Noise Factor (linear) 2.35, Noise Temperature works out to 1.485 K.

What is the formula for Equivalent Noise Temperature?

The formula is Te = T0 × (NF − 1). Equivalent noise temperature provides an alternative way to express the noise contribution of a component by stating what temperature a matched resistor at the input would need to be to produce the same amount of noise.

How do you find Reference Temperature when you know the other values?

Rearrange for Reference Temperature: with Noise Temperature 0.025 K, Noise Factor (linear) 0.118, Reference Temperature is -0.02834 K.

How do you find Noise Factor (linear) when you know the other values?

Rearrange for Noise Factor (linear): with Noise Temperature 0.025 K, Reference Temperature 0.055 K, Noise Factor (linear) is 1.455.

Related Concepts

All Signal & RF formulas →
Wavelength Free Space Path Loss Signal-to-Noise Ratio Nyquist Sampling Rate Link Budget Antenna Gain Skin Depth Friis Noise Figure (3-stage)

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