In a three stage cascade amplifier, each stage has a gain of 10 dB and noise figure of 10 dB. The overall noise figure is

Three-Stage Cascade Amplifier and Overall Noise Figure Calculation

Problem Statement: In a three-stage cascade amplifier, each stage has a gain of 10 dB and a noise figure of 10 dB. We are tasked with calculating the overall noise figure of this cascade system.

Solution:

To calculate the overall noise figure (F_overall) of a cascade amplifier, we use Friis's formula for noise figure in cascaded systems:

Friis's Formula:

F_overall = F₁ + ^{(F₂ - 1)}/_G1 + ^{(F₃ - 1)}/_{G1 × G2} + ...

Where:

• F_n = Noise figure of the nth stage (in linear scale).
• G_n = Gain of the nth stage (in linear scale).

Step 1: Convert Gains and Noise Figures from dB to Linear Scale

The given gain (G) and noise figure (F) for each stage are 10 dB:

• G = 10 dB → G (linear) = 10^G(dB)/10 = 10^10/10 = 10.
• F = 10 dB → F (linear) = 10^F(dB)/10 = 10^10/10 = 10.

Step 2: Apply Friis's Formula

Since there are three stages, Friis's formula for the overall noise figure becomes:

F_overall = F₁ + ^{(F₂ - 1)}/_G1 + ^{(F₃ - 1)}/_{G1 × G2}

Substitute the values for F₁, F₂, F₃, G₁, and G₂:

• F₁ = 10 (linear).
• F₂ = 10 (linear).
• F₃ = 10 (linear).
• G₁ = G₂ = 10 (linear).

Thus:

F_overall = 10 + ^{(10 - 1)}/₁₀ + ^{(10 - 1)}/_{10 × 10}

F_overall = 10 + 0.9 + 0.09

F_overall = 10.99

Final Answer: The overall noise figure of the three-stage cascade amplifier is 10.99 (linear scale).