How to Calculate Noise Figure for Cascaded Stages (Example Questions – Part 2)

Example 2:

Calculate the total NF for the below-given diagram:

To calculate the total noise figure for this cascaded stage, we’re going to calculate the total noise factor.

The linear expression for total noise factor is equal to the noise factor of the first block in the linear domain plus the noise factor of the second block minus one over the gain of the first block:

We don’t need F3 because we have only two stages. The above expression is linear, but the parameters are in the log domain, so we have to convert them to linear.

Use this formula in order to convert from log domain to linear domain:The noise factor of the second stage is divided by the gain of the first stage, and it has less contribution. Most of the contribution is coming from the first stage. Therefore, the first stage is important in calculating the noise figure.

The total noise factor is converted to log scale to get the total noise figure:It can be seen from here that this value is close to the noise figure of the first stage. The second one is 10 dB, but we just see some part of it at the output, mostly coming from the first noise figure.

Going further with more blocks, the noise factor is going to be divided by a large value that’s why the noise figure contribution of the subsequent stage is less after the second or third stage and is negligible. Hence, you can say these values are very small, and you don’t have to calculate them.

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