# Noise in Cascaded Stages with Example

The concept of noise in cascaded stages is similar to that of linearity, where the aim was to find the total IIP3. Read about __Non-linearity in Cascaded stages.__

Here we need to find the total Noise Figure, NF. If we have n-number of Blocks as shown below, we can write the total NF as:

In previous examples for NF, we calculated NF in terms of Rs (source resistance). However, in this formula, we don’t have R_{s}, therefore changing the equation in terms of R_{s,} we get:

Showing the output resistance R_{out} in the circuit, Av is the gain, and V_{in} is the input voltage. The circuit for Block 1 can be modeled as:

The resistance of the source is now R_{out} which in turn becomes the source for Block 2 and goes so on until the last Block. For the first Block, the source is Vs, and for the second Block, the source is the voltage that is produced by Block one. The input resistance for Block 2 is R_{out1} which is the output resistance of Block 1.

The available power is calculated for Block one using the below equation:

The first part of the equation is similar to that derived in the previous examples. It is additionally multiplied by the source resistance over output resistance for Block one to get the available power in the particular Block.

Similarly, available power for Block 2 can be calculated as:

### Why NF of stage 1 is important?

In the total NF calculation formula, we can notice that the NF for block 1 is without any attenuation, whereas other Blocks are divided by the gains of further stages. We can say that the effect of noise decreases after stage 1. At every stage, it reduces and eventually goes to 0.

We can conclude that the noise figure for the first stage is the most dominant one. Hence, this is the reason when any RF system is designed, and the first stage noise has to be selected such that it has less effect on the whole system. Sometimes the noise from other sources is ignored as they are quite small compared to stage 1.

**Example – Find the NF for the cascaded stages**

This system has two stages of MOS transistor, and we are going to find out the NF for this cascaded system.

From the previous section we know that the formula for calculating total Noise Figure NF is:**Noise Figure for stage 1:** the only noise source we have is from the stage 1 transistor channel noise.

**Noise Figure for stage 2:**

There is no voltage division and R_{in} is going to infinity.

As we discussed before that noise figure of second stage is significantly smaller and can be ignored. Therefore NF can be written as: