When designing communication system one will come across the word Noise Factor and Noise Figure. If you look at amplifiers datasheet they are often quoted with Noise Factor(F) and Noise Figure(NF). So what are they?

A two port network such as amplifier circuit diagram is shown below.

Obviously the two port component(amplifier for example) have inherent noise source associated with them. The noise of the two port component is represented by Te. B is the bandwidth over which the component is designed to work with. G is the gain.

At the input we have a source(shown in circle). R is the source resistance. Pi is the total input power which is the sum of source power, Si and noise power Ni at the input. Similarly at the output we have a load resistor R. Po is the total output power which is the sum of signal power So and noise power No at the output.

The SNRi(Signal to Noise Ratio) at the input is Si/Ni and the SNRo at the output is So/No. The ratio of SNRo to SNRi is called the Noise Factor,

We can identify three cases as follows.

Suppose that the two port component has no noise. Then SNRo will be equal to SNRi in which case the noise factor, F is unity.

But there exist noise in the component so the output SNRo will decrease. This will then increase noise factor F.

This will not be met.

Hence the noise factor F will be generally greater than unity(>1).

By definition, the input noise power(Ni) is the noise power matched at resistor at temperature To = 290K(room temperature). That is,

Redefining Noise Factor

With the input noise power(Ni) defined as above, we can redefine the Noise Factor as follows.

The total output noise power in bandwidth B and through gain G is kToBG+Pint, where Pint is the output internal power that is generated by the two component internal network.

Therefore the above noise figure can be written as,

We can express noise factor F in dB and in this unit it is called Noise Figure.

A two port network such as amplifier circuit diagram is shown below.

Obviously the two port component(amplifier for example) have inherent noise source associated with them. The noise of the two port component is represented by Te. B is the bandwidth over which the component is designed to work with. G is the gain.

At the input we have a source(shown in circle). R is the source resistance. Pi is the total input power which is the sum of source power, Si and noise power Ni at the input. Similarly at the output we have a load resistor R. Po is the total output power which is the sum of signal power So and noise power No at the output.

The SNRi(Signal to Noise Ratio) at the input is Si/Ni and the SNRo at the output is So/No. The ratio of SNRo to SNRi is called the Noise Factor,

We can identify three cases as follows.

**Case 1: SNRi = SNRo**Suppose that the two port component has no noise. Then SNRo will be equal to SNRi in which case the noise factor, F is unity.

**Case 2: SNRi > SNRo**But there exist noise in the component so the output SNRo will decrease. This will then increase noise factor F.

**Case 3: SNRi < SNRo**This will not be met.

Hence the noise factor F will be generally greater than unity(>1).

**Input Noise Power(Ni)**By definition, the input noise power(Ni) is the noise power matched at resistor at temperature To = 290K(room temperature). That is,

Redefining Noise Factor

With the input noise power(Ni) defined as above, we can redefine the Noise Factor as follows.

The total output noise power in bandwidth B and through gain G is kToBG+Pint, where Pint is the output internal power that is generated by the two component internal network.

Therefore the above noise figure can be written as,

We can express noise factor F in dB and in this unit it is called Noise Figure.

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