# How To Measure Noise Figure Using Noise Source ‘Note: This is an article written by an RF engineer who has worked in this field for over 40 years. Visit ABOUT to see what you can learn from this blog.’ 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.

Single-Stage Noise Figure Basics.

Multi-Stage Noise Figure Basics.

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.   $$1.7\times 10^{-14} µW/Hz$$

###### 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.

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: