Question:

Published on: 24 July, 2024

**Define SNR and Noise Figure. Why is the noise performance of the first stage of a cascade receiver so important? If each stage of a two – stage cascade amplifier has a gain of 10 dB and noise figure of 10 dB, calculate the total noise figure in dB. **

Answer:

**SNR (Signal to noise ratio)**

In the communication systems, the comparison of signal power with the noise power at the same point is important, to ensure that the noise at that point is not excessively larger. It is defined as the ration of the signal power to the noise power at the same point.

**Noise figure:**

The noise facto can be expressed in term of decibels. The representation of noise factor in decibel is known as noise figure.

The noise figure \(F_{dB}=10logF\)

The noise figure \(F=10log\frac{S/Nattheinput}{S/Nattheoutput}=10log\left(\frac{S}{N}\right)_i-10log\left(\frac{S}{N}\right)_0\)

Hence noise figure \(F_{dB}=log\left(\sfrac{S}{N}\right)_idB-log\left(\sfrac{S}{N}\right)_0dB\)

For two stage cascade amplifier noise factoris

\(F=\frac{F_1G_1G_2kT_0B+G_2\left(F_2-1\right)kT_0B}{G_1G_2kT_0B}=F_1+\frac{\left(F_2-1\right)}{G_1}=10+\frac{\left(10-1\right)}{10}=10.9\)

The noise figure \(F_{dB}=10logF=10log10.9=10.37dB\)

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