How To Measure Noise Figure Using Noise Source

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Noise Figure is an important RF parameter as well as a myth if you do not clearly understand it.

It is a measure of how much a device degrades the Signal to Noise Ratio (SNR), with lower values indicating better performance.

It is one of the terms that a lot of RF people have difficulty to really understand and apply.

You should visit these very helpful articles related to Noise Figure before keeping on reading this article:

Single-Stage Noise Figure Basics.

Multi-Stage Noise Figure Basics.

Cascade Noise Figure Analysis, A 9-Stage Receiver Design Using Spreadsheet.

Receiver Cascade Noise Figure Universal Spreadsheet Template-Overview And Application.

In this article we will discuss how to calculate the Noise Figure of a receiver design using the most popular measuring tool, Noise Source.

Before starting, we need to display 2 formulas below:

 

1.   Definition of Noise Factor (F) and Noise Figure (NF):

 

$$\text {Noise Factor (F)} = {{{S_{in}/N_{in}}\over {S_{out}/N_{out}}}={SNR_{in}\over SNR_{out}}}$$

It is always greater than 1.

And simply,

$${Noise Figure (NF_{dB})}=10log(F)$$

$$=log(SNR_{in})-log(SNR_{out})$$

Noise Figure is always greater than 0 dB.

 

Q.  If \(S_{in}/N_{in}=1530\) and \(S_{out}/N_{out}=680\), then,

      1.  What is the Noise Factor (\(F\))?

           Ans.   2.25

      2.  What is the Noise Figure (\(NF_{dB}\))?

           Ans.   3.5 dB

 

2.   The Basic Equation:

 

$$F=F_{1}+{{F_{2}-1}\over G_{1}}+{{F_{3}-1}\over{G_{1}G_{2}}}+{{F_{4}-1}\over{G_{1}G_{2}G_{3}}}$$

$$+{{F_{5}-1}\over{G_{1}G_{2}G_{3}G_{4}}}+….$$

 

Q.  If a simple receiver design has 4 stages with parameters as follows:

       Stage 1, RF Amplifier (LNA):  Gain=27 dB, Noise Figure=1.2 dB

       Stage 2, Mixer:  Gain=-7 dB, Noise Figure=8 dB

       Stage 3, IF Amplifier:  Gain=28 dB, Noise Figure=6 dB

       Stage 4, Demodulator:  Gain=53 dB, Noise Figure=12 dB

       Then, 

       What is the Noise Figure (\(NF_{dB}\))?

       Ans.   4.29 dB

Refer to Multi-Stage Noise Figure Basics.

And use the Universal Spreadsheet Template.

 

3. Excess Noise Ratio (ENR)

 

 

The Y-factor technique involves the use of a noise source that has a pre-calibrated Excess Noise Ratio (ENR). This is defined as:

$$ENR={{T_{on(S)}-T_{off(S)}}\over T_0}$$

Because noise power is proportional to noise temperature, it can also be stated:

$$ENR={{N_{on(S)}-N_{off(S)}}\over N_0}$$

or in decibel terms as:
$$ENR_{dB} = 10 log({{T_{on(S)}-T_{off(S)}}\over T_0})$$

$$= 10 log({{N_{on(S)}-N_{off(S)}}\over N_0})$$

\(T_{on(S)}\) and \(T_{off(S)}\) are the noise temperatures of the noise source in its ON and OFF states.

\(N_{on(S)}\) and \(N_{off(S)}\) are the noise output power levels of the noise source in its ON and OFF states.

\(T_0\) is the reference temperature \(290°K\).

\(N_0\) is the noise output power level at \(290°K\).

Even though \(T_{off(S)}\) and \(T_0\) are usually two different temperatures, the calibrated ENR of a noise source is always referenced to \(T_{off(S)}= T_0 = 290°K\) and,

$$ENR={{T_{on(S)}\over T_0} -1}$$

$$={{N_{on(S)}\over N_0} -1}$$

Also,

$$N_{on(S)}=N_0(ENR+1)$$

And,

$$T_{on(S)}=T_0(ENR+1)$$

or in decibel terms as:
$$ENR_{dB} = 10 log({{T_{on(S)}\over T_0} -1})$$

$$=10log({{N_{on(S)}\over N_0} -1})$$

 

We will explain how to correct for the common situation where \(T_{off(S)}\) is higher or lower than the reference temperature \(290°K\) in another articles.

 

Q.  In the table above “Example of ENR of Noise Source”,

      1.  What is \(T_{on(S)}\) in °K at 3 GHz?

           Ans.   \(1,245.9°K\)

      2.  What is \(N_{on(S)}\) in µW/Hz at 3 GHz?

           Ans.   \(1.7\times 10^{-14} µW/Hz\)

           Refer to Single-Stage Noise Figure Basics.

 

4. Y-factor

Y-factor is a ratio of two noise power levels at circuitry ouput, one measured with the noise source ON, \(N_{on}\), and the other with the noise source OFF, \(N_{off}\):

$$Y={N_{on}\over N_{off}}$$

Q.  If \(N_{off}=-112 dBm/Hz\) and \(N_{on}=-100 dBm/Hz\), then how much is Y?

Ans.   15.85

Refer to dB, dBm, dBW, dBc Basics.

 

 

5. Calculating Noise Figure Using Noise Source:

 

 

Below is a handy equation to calculate the Noise Figure of a circuitry using noise source.

$$NF_{dB}=ENR_{dB}-10Log(Y-1)$$

The data of \(ENR_{dB}\) are typically provided in dB by manufacturer. We only need to measure \(N_{on}\) and \(N_{off}\) to calculate the Noise Figure of the circuitry.

But how was this equation derived?

When the noise source is OFF, the noise presented at the input port is thermal noise \(N_0\).

If the total gain and Noise Factor of a receiver circuitry are G and F, respectively, then the measured noise at the output port is \(N_{off}\) and,

$$N_{off}=GN_0+G(F-1)N_0=GFN_0$$

\(G(F-1)N_0\) is the noise added by the circuitry.

When the noise source is ON, the noise power \(N_{on}\) at the output port is,

$$N_{on}=G(N_{on(S)})+G(F-1)N_0$$

$$=GN_0(ENR+1)+G(F-1)N_0$$

$$=GN_0(ENR+F)$$

So,

$$Y={N_{on}\over N_{off}}={{GN_0(ENR+F)}\over {GFN_0}}$$

$$={{ENR+F}\over F}={{ENR\over F}+1}$$

And,

$$F={ENR\over {Y-1}}$$

$${10logF}=10log{ENR\over {Y-1}}$$

Therefore,

$$NF_{dB}=ENR_{dB}-10Log(Y-1)$$

 

Example: 

If the ENR of noise source is 15 dB and the measured \(N_{off}=-95 dBm/Hz\) and \(N_{on}=-83 dBm/Hz\), then how much is the Noise Figure \(NF_{dB}\) ?

Ans:   

\(N_{off}=-95 dBm/Hz=3.16×10^{-10} mW/Hz\)

\(N_{on}=-83 dBm/Hz=5.01×10^{-9} mW/Hz\)

So,

$$Y={N_{on}\over N_{off}}={5.01×10^{-9}\over 3.16×10^{-10}}=15.85$$

And,

$$NF_{dB}=ENR_{dB}-10Log(Y-1)$$

$$=15-10Log(15.85-1)$$

$$=15-11.72$$

$$=3.28dB$$

 

Q. If the ENR of noise source is 12 dB and the measured \(N_{off}=-103 dBm/Hz\) and \(N_{on}=-93 dBm/Hz\), then how much is the Noise Figure \(NF_{dB}\) ?

Ans:   2.46 dB

 

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References:

https://cdn.rohde-schwarz.com/pws/dl_downloads/dl_application/application_notes/1ma178/1MA178_2e_NoiseFigure.pdf

http://literature.cdn.keysight.com/litweb/pdf/5952-3706E.pdf

https://www.maximintegrated.com/en/app-notes/index.mvp/id/2875

https://www.ieee.li/pdf/viewgraphs/noise_figure_measurements.pdf

http://www.noisewave.com/faq.pdf

 

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