# Noise Figure of a Cascaded System

Consider the problem of calculating Noise Figure of cascaded system. Such design problem is frequently encountered in electronics system design. For example connecting multiple amplifiers and then finally to an antenna.

Each of the component are specified in terms of their gain, noise factor and possible equivalent noise temperature. Following figure shows this.

In the diagram above, we have first two port network(like amplifier) which has gain G1, noise factor F1 and equivalent noise temperature Te1. It is cascaded with another system with gain G2, noise factor F2 and equivalent noise temperature Te2. The input to the first system is noise input power Ni at temperature Ti. Then after the first stage we have noise power N1 and after second stage we have noise power output No.

We want to find the overall circuit noise factor F and the overall noise temperature Te.

The noise factor N1 is the sum of noise factor due to the input noise temperature and due to the first stage. Hence,

And No will be due to N1 and due to the second stage,

Therefore the noise temperature of the cascaded system is,

Using the following known quantities,

we get,