Cascaded Noise Factor of RF system

For components like op-amps, we specify noise in terms of equivalent voltages and current. But at system level its difficult to account for noise contributions of each component in each sub-system. Instead we use another term widely know as Noise Factor (F) of a sub-system.

Block Diagram - Noise contributions

Cascaded Noise Factor in RF

In above diagram, we have noise contributions by each sub-block as (Fn-1)kTB.
Sub block has gains G1, G2 and G3.
Sub-block has individual noise contribution as F1, F2 and F3.
k is Boltzman constant,
T is temperature (degrees Kelvin) and
B is frequency bandwidth (in Hz).

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Rest of our calculations are based on the equivalent noise Factor of the system with cascaded components. In order to calculate total noise factor, we will need to refer the noise back at the input of the system. Block diagram below shows the Total Noise contributions.

Block Diagram: N access noise contributions at the input of system.

Cascaded Noise Factor in RF

Total noise factor at the input of the system is calculated with formula below:
Total Noise Factor of cascaded system with 3 blocks is below
Ftotal = F1+(F2-1)/G1+ (F3-1)/(G1G2)


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