# Cascaded noise figure formula

In many electronic and RF systems, multiple components or stages (such as amplifiers, filters, and mixers) are cascaded together. These components introduce noise into the system. It's essential to understand how the noise accumulates through the stages. The Cascaded Noise Figure formula and calculator help engineers analyze and design these systems while considering noise performance.

Engineers use the formula to optimize the noise performance of a system. By carefully selecting components or adjusting their gain and noise figure, they can minimize the impact of noise on the overall system performance. This is crucial in applications where signal quality is critical, such as wireless communications or sensitive measurement equipment.

It is used to calculate the overall noise figure of a series (cascade) of interconnected electronic components, such as amplifiers or other signal processing devices. The noise figure (NF) measures how much the noise performance of a system degrades as a signal passes through multiple stages of amplification or processing.

The formula to calculate cascaded NF is given by following equation.

NF_{total} = NF_{1} + [(NF_{2} - 1)/G_{1}] +
[(NF_{3} - 1)/(G_{1} * G_{2})] + ... + [(NF_{n} - 1)/(G_{1} * G_{2}... * G_{n-1})]

Where,

NF_{total} = Total Noise figure of cascaded system

NF_{1}, NF_{2}, NF_{3}, ...., NF_{n} are noise figure
of each individual component or stage in the cascade.

G1, G2, G3, ...., Gn are the gains of each individual component or stage in the cascade.

## Cascaded Noise Figure Calculator

Following calculator can be used for 4-stage RF chain.

Cascaded noise figure calculation example :

INPUTS: F1 (dB) = 1 ,G1 (dB) = 10,F2 (dB) = 5 ,G2 (dB) = 10,F3 (dB) = 5 ,G3 (dB) = 10 ,F4 (dB) = 5 ,G4 (dB) = 10

OUTPUTS: Aggregate Noise Figure (linear) = 1.5 , Aggregate NF(dB)= 1.75

**Conclusion** : In summary, the Cascaded Noise Figure calculator and noise figure formula are valuable tools for engineers
and designers working on electronic and RF systems. They help in designing systems with optimized noise performance,
troubleshooting issues and ensuring compliance with industry standards.