# Spectrum Analyzer Noise Figure Measurement

### Noise figure is a key parameter for many RF circuits and systems and here we describe how to measure noise figure with a spectrum analyzer.

Noise figure is an important parameter in many RF applications. Often it is not possible t be able to use a dedicated noise figure meter and in these circumstances it is important to know how to measure noise figure with a spectrum analyzer.

Using a spectrum analyzer to measure noise figure can be a very useful option as one of these test instruments is more likely to be available.

## Noise figure measurement basics

Noise figure measurements are important in many RF circuits and blocks or systems because the limit of sensitivity of a radio or wireless receiver is limited by noise. In an ideal system this would be limited by noise picked up at the antenna, but in reality all systems generate some noise themselves.

Noise figure can be applied to a single circuit like an RF amplifier, or a mixer, or it can be applied to a complete system like a radio receiver, etc.

In order to measure noise figure using spectrum analyser it is necessary to look at the theory and formulas a little.

$F=\frac{\frac{{S}_{i}}{{N}_{i}}}{\frac{{S}_{o}}{{N}_{o}}}=\frac{\frac{{S}_{i}}{kTB}}{\frac{{S}_{i}G}{{N}_{o}}}$

Therefore:

$F=\frac{{N}_{o}}{GkTB}$

Where:
N = noise power output
G = device gain
k = Boltmann's constant - 1.374 x 10-23 joule/°C
T = temperature in °Kelvin, i.e. 290° is room temperature
B = bandwidth in Hz
F = Noise factor (Note: noise figure is the noise factor expressed in decibels)

It is possible to convert the formula so that it provides the noise performance in terms of noise figure.

$NF=10{\mathrm{log}}_{10}\left(FGkTB\right)-10{\mathrm{log}}_{10}\left(G\right)-10{\mathrm{log}}_{10}\left(kTB\right)$

It is possible to see how the different constituents contribute to the noise figure. The factor:

$10{\mathrm{log}}_{10}\left(FGkTB\right)$   relates to the noise power output .

The factor: $10{\mathrm{log}}_{10}\left(G\right)$   relates to the gain.

And finally the factor: $10{\mathrm{log}}_{10}\left(kTB\right)$   relates to the noise input.

This noise figure equation can be further reorganised. It is necessary to accommodate the bandwidth of the spectrum analyzer ebcuse the noise is proportional to bandwidth. Therefore the formula can reorganised as follows:

$NF=10{\mathrm{log}}_{10}\left({N}_{o}\right)-10{\mathrm{log}}_{10}\left(G\right){-}_{174}dB-10{\mathrm{log}}_{10}\left(B\right)$

Again it is possible to see the contributing factors:

$10{\mathrm{log}}_{10}\left({N}_{o}\right)$   is the noise output.

The factor: $10{\mathrm{log}}_{10}\left(G\right)$   results from the gain.

And the factor: $-174dB-10{\mathrm{log}}_{10}\left(b\right)$   is the equivalent noise input in bandwidth B.

In some instances it may be necessary to add some factors to accommodate for the real responses, etc of the analyser against the theoretical requirements for making noise figure measurements with a spectrum analyzer:

• Filter:   As the filter response of the spectrum analyzer cannot be a completely rectangular shape – the response is curved. This means that the noise power bandwidth and the resolution bandwidth are not exactly the same. A typical figure quoted for some analyzers was that the filter bandwidth was around 1.2 times the resolution bandwidth which equates to an adjustment of 0.8 dB.
• Noise level:   The averaging effect of the video filters, etc on analogue spectrum analyzers tended to give a reading that was around 2.5 dB below the RMS noise level. This also needs to be accommodated.

The overall adjustment is around +1.7 dB (i.e. 2.5 - 0.8). However most modern spectrum analyzers will have corrections for these discrepancies and the makers literature or help material should be consulted regarding them as they will vary slightly between spectrum analyzers and manufacturers..

To make the noise figure measurements required, the spectrum analyzer should have a noise floor that is 6dB lower than the noise emanating from the device under test. As this will typically be an amplifier, its noise level is likely to be greater. If not a further low noise amplifier can be added after the device under test to bring the noise level up - note that the noise will tend to be at the input to the device under test if it is an amplifier.

The noise figure can then be calculated as:

$NF=N-\left({G}_{d}+{G}_{amp}\right)-10{\mathrm{log}}_{10}B+174dB+1.7dB$

Where:
N = noise power output
Gd = Gain of device under test in dB
Gamp = Gain of additional amplifier in dB
B = Bandwidth in Hz

In this way the noise figure can be measured with a knowledge of the device gain, measurement bandwidth and noise power output.

## Noise figure measurement procedure

The procedure for measuring noise figure using this test method is quite straightforward. It consists of a number of simple stages:

1. Measure system gain:   One of the key elements in the noise figure equation is the figure for the system gain. This needs to be measured by the system. Typically this is achieved by using a signal generator fed into the device under test. The gain can be measured simply by measuring the signal level directly from the output of the signal generator and then with the amplifier in circuit. The gain is simple the output divided by the input.
2. Measure noise power:   The next step in measuring the noise figure using a spectrum analyzer is to disconnect the signal generator and terminate the input to the device under test with a resistance equal to its characteristic impedance.

With the lower signal level, i.e. just the noise power from the device, the input attenuator level of the spectrum analyser may need to be adjusted, e.g. to 0dB, and sufficient video averaging applied to obtain a good reading for the noise level.
3. Calculate noise figure:   Using readings for the average noise power and the bandwidth for the analyzer, these can be substituted in the equation above to give the noise figure for the device under test.

## Spectrum analyzer noise figure measurements

There are many reasons for using a spectrum analyzer to make noise figure measurements.

• Uses available equipment:   One of the most important reasons for using a spectrum analyser to measure noise figure is that it can utilise equipment that is available. It is a simple and easy test and does not require hunting around for a specialised item of test instrumentation like a noise figure meter that may not be available.
• Wide frequency range:   Spectrum analyser noise figure measurements can be made at any frequency within the range of the spectrum analyser. As many spectrum analyzers have a very wide range, it enables noise figure measurements to be made on almost any frequency required. A variety of frequencies can be used for different devices without changes to the test configuration.
• Frequency selective noise figure measurements:   Measurements can be made to be frequency selective, independent of device bandwidth and spurious responses.

Using a spectrum analyser may not as accurate as those obtained when using a dedicated noise figure meter, but this is very dependent upon the spectrum analyser and the measurement method used. The "Y" factor method is often accepted as being equally as accurate as that of a specialised noise figure meter, but requires the use of a noise source. Some spectrum analyzers have software built in to run these tests.