# Noise-Figure Measurements using Spectrum Analyzer

**Gain Method:** Noise Figure (NF) can be measured, with a spectrum analyser, by using a procedure called Gain-Method. Note that following condition needs to be met by the Device-under-Test (DUT) for correct measurement:

- DUT (e.g., Receiver) output noise floor should be significantly higher than that of spectrum analyser itself. And this condition can be fulfilled for most of the spectrum analysers if ‘Gain+NF’ quantity of DUT is greater than 40 dB.

**Mathematical equation: **To develop the mathematical equation, follow these steps:

- Start with DUT input thermal noise floor, which we all know is -174 dBm/Hz.
- Therefore, a noiseless DUT having a gain of G
_{dB}, would produce an output noise density equal to: P_{NSD}= -174 dBm/Hz + G_{dB} - Now, incorporate the effects of noise added by a noisy-DUT to get:

P_{NSD}= -174 dBm/Hz + G_{dB}+ NF, where NF is the Noise-figure of DUT in dB. - Re-arrange above equation to get: NF= P
_{NSD}– (-174 dBm/Hz) – G_{dB} - Every Spectrum Analyser might not provide you output noise floor per Hz, however, we can always scale the measured noise to one Hz BW by using this equation:

P_{NSD}= (P_{noise})_{RBW }– 10*log10(RBW), where

RBW = spectrum analyser’s Resolution Bandwidth

(P_{noise})_{RBW}= DUT output Noise floor measured with spectrum analyser within a bandwidth of RBW. - So, the final equation for NF becomes:

NF= (P_{noise})_{RBW }– 10*log10(RBW) – (-174 dBm/Hz) – G_{dB}

**Step-by-Step NF measurement method with an example:**

**RBW:**Set the RBW of spectrum analyser at 10 kHz. (It is not necessarily to be 10kHz)**DUT Gain**:Let’s assume we have a Receiver with 40 dB small-signal gain. Note that we need to make sure that RX is not being driven into compression during gain measurements as we are using this Gain in NF calculations where input signal is thermal noise; and thermal noise can never drive a RX into compression! To measure the small-signal gain, just input a low-level CW signal (which is well below the input P1dB of RX) into RX and observe the output on spectrum analyser to calculate the RX gain. So, we have G_{ }_{dB }= 40 dB.**Spectrum analyser Noise floor:**Now just terminate the spectrum analyser input port at 50 ohms and measure spectrum analyser’s own noise floor.**DUT output Noise Floor:**Now terminate the RX input at 50 ohms and connect its output with spectrum analyser to measure RX output noise floor, (P_{noise})_{RBW}. Make sure that this noise floor is much higher than the spectrum own noise floor measured in previous step. Let’s assume this number comes out to be -80 dBm/10kHz.**Average Detector:**Another important point here is to make sure that you measure noise floor by using average detector of spectrum analyser while gain measurement needs to be done by employing peak detector of spectrum analyser. This is because algorithm being used in average detector is best to measure random noise.**RX NF:**NF= (P_{noise})_{RBW }– 10*log10(RBW) – (-174 dBm/Hz) – G_{dB. }After putting in the values, it becomes:

NF= -80 – 10*log10(10000) – (-174 dBm/Hz) – 40 = 14 dB

*Learn more about this topic by taking the complete course ‘**RF System Design of Receivers, Transmitters & Transceivers – RAHRF409’**. Watch the course videos for more detailed understanding. Also checkout other courses on RF system and IC design on **https://rahsoft.com/courses/**. **Rahsoft also provides a certificate on Radio Frequency. All the courses offer step by step approach.*

*Learn more about this topic by taking the complete course ‘*

*RF System Design of Receivers, Transmitters & Transceivers – RAHRF409’*

*. Watch the course videos for more detailed understanding. Also checkout other courses on RF system and IC design on*

*https://rahsoft.com/courses/*

*.*

*Rahsoft also provides a certificate on Radio Frequency. All the courses offer step by step approach.*

Tag:Gain Method, Noise Figure