Noise Figure (NF) Basics: What Is It & How To Use It To Help You Design A Receiver – Single Stage.

Noise Figure (NF): a myth as well as an important RF parameter.

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

There are complicated formulas involved to get you very confused once you work through them.

And you might have difficulty to apply them properly to design a receiver.

When designing circuits for use with extremely weak signals, noise is an important consideration.

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

The noise contribution of each device in the signal path must be low enough that it will not significantly degrade the Signal to Noise Ratio.

I’ll show you those easy and common RF concepts and you will eventually be able to design and complete RF projects and salable products in a very short time without making a lot of mistakes.

I’ll also provide a few resources for those of you who would like to learn more advanced details.

What is “kTB”?
Before discussing Noise Factor and Noise Figure, we need to know better about receiver noise.

First thing we need to know is there is a thermal noise everywhere in the space and this is the minimal noise power we need to face and handle.

No way we can get rid of it.

Receiver design would have been much easier if this basic noise did not exist.

All other types of noise are not desirable and we should do our best to minimize them.

Usually we express noise in watts since it’s one type of power.

The amplitude of this thermal noise power is:

Thermal Noise=k(Joules/˚K)×T(˚K)×B(Hz)

Where k is Boltzmann’s constant in Joules/˚K, T is temperature in °Kelvin (°K), and B is the bandwidth in Hz.

If,
k=1.38×10−23
T=290°K(equivalent to 17°C or 62.6°F)
And,
B=1Hz
Then,
Thermal Noise =1.38×10−23×290×1
=4.002×10−21W/Hz
=4.002×10−18mW/Hz

If we convert it to dBm, then,
4.002×10−18mW/Hz=10log(4.002×10−18)
=6.0−180=−174dBm/Hz
This is the amount of thermal noise power in a 1 Hz bandwidth @17°C and you should remember this number by heart before working with Noise Figure.

Thermal Noise and Temperature:

The table below shows the thermal noise per hertz versus temperature:

As you can see in this table, the thermal noise difference between these 2 extreme temperature -40°C and 75°C is only

−173.2−174.9=1.7dBm

Therefore, for the sake of convenience, we usually take the middle number 17°C (290°K) & -174 dBm as references.

Thermal Noise and Operation Frequency Bandwidth:

For a 1 MHz of bandwidth,

Thermal Noise=−174dBm+10log(1×106)

=−114dBm

We will wrap up “thermal noise” with 2 questions to test how much you know about this term. You must know it thoroughly before continuing to see this important parameter “Noise Figure” that we will discuss below:

Q1:  How many dBm per hertz is the thermal noise at -25°C?

Ans.     -174.7 dBm

Q2: How many dBm is the total thermal noise with a bandwidth of 250 kHz at 65°C?

Ans.     -119.3 dBm


Signal to Noise Ratio (SNR)
 


Receiver sensitivity is a measure of the ability of a receiver to demodulate and get information from a weak signal. We quantify sensitivity as the lowest signal power level from which we can get useful information.

The weakest signal a receiver can discriminate is a function of how much thermal noise the receiver adds to the signal. The signal to noise ratio is the most convenient way of quantifying this effect.

For input signal to noise ratio,

SNRin=Sin/Nin

Where Sin is the input signal level and Nin is the input noise level.

For output signal to noise ratio,

SNRout=Sout/Nout

Where Sout is the output signal level and Nout is the output noise level.

Since kTB is everywhere, Sout/Nout can never be better than Sin/Nin. Therefore, the best situation you can have is:

Sout/Nout=Sin/Nin, (SNRout=SNRin)
 
Noise Factor (F) &
Noise Figure (NF)
We need to define these two terms “Noise Factor” and “Noise Figure” before going further.

Noise Factor (F)=Sin/NinSout/Nout=SNRinSNRout
Noise factor is a measure of how the the signal to noise ratio is degraded by a device.

You need to remember this definition by heart before you are able to work with Noise Figure.

A perfect electronic circuitry (which does not exist) would have a noise factor of 1.

In the real world , it is always greater than 1.

And simply,

=log(SNRin)−log(SNRout)

Noise Figure is always greater than 0 dB.

I would like to explain these 2 important terms using 3 examples below and I hope you will take time to follow through every single one step.

Example #1
If the electronic circuitry is transparent, then gain is 0, internal noise level Nckt is also 0.

Ans.

Since Sin=Sout and Nin=Nout

Noise Factor (F) = 1    and

Noise Figure (NF)=10log(1)=0

This type of circuit almost does not exist.

Example #2
If the electronic circuitry is a 6 dB resistor π network attenuator (-6 DB), what is the Noise Factor?

Ans.

Both Sin and Nin have 6 dB of losses, so

Sout=(1/4)Sin and supposedly,

Nout=(1/4)Nin

But the minimal thermal noise anywhere is kTB.

So,
Nout=kTB
Therefore,
Noise Factor (F)=Sin/NinSout/Nout
=Sin/kTB(1/4)Sin/kTB=4
And,
Noise Figure (NF)=10log(4)=6dB
The noise figure is exactly the same as the attenuation 6dB, as expected.

Example #3

An amplifier has a gain of 12 dB and the noise figure is 3 dB,

(a) what is the noise level per Hz (in dBm) at the output port, and

(b) what is the extra noise per Hz (in dBm) created in this amplifier?




Ans.

(a).
Since,
So,

Sout=16×Sin

Sin/Nin16Sin/Nout=1.995

Therefore, the noise level (in dBm) at the output port is:

=10log31.9+10logkTB=15.0−174

=−159.0dBm

(b).

And

Nout=16×Nin+(x+1)kTB=(17+x)kTB

F=Sin/kTB16Sin/(17+x)kTB=2

After few steps of operation

x=15

So the extra noise (in dBm) created in this amplifier is:

15kTB=15×4.0×10−18mW

=6.0×10−17mW=−162.2dBm

 

Okay, time to wrap up this article. Do you like to know if you really understand what Noise Figure is and how to use it? Find out from these 2 questions:

Q1:  An LNA has a gain of 20 dB. If the measured noise level at the output port is -152 dBm/Hz, then what is the NF of this amplifier?

Ans.    2 dB

Q2:  The NF of an amplifier is 1.0 dB and the operation frequency bandwidth is 200 kHz,  if the measured output port noise level is -132 dBm, what is the gain of this amplifier?

Ans. 18 dB

Leave a message 

Message List