ISRO EC 2023 Q.42: solution and answer

ISRO 2023 · ECQ.42 · 1 mark · MCQ

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

(A)
10.99
(B)
10
(C)
1.09
(D)
10.9

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Answer and solution

ANSWER

The overall noise figure is $10.99$ (option A).

Official answer: ASource: ISRO's revised and final answer key of 16 February 2024

Convert from dB to ratios: gain $G = 10 dB \Rightarrow 10$ and noise factor $F = 10 dB \Rightarrow 10$ for every stage.
Use Friis' formula for a cascade: $F = F_{1} + \frac{F _{2} - 1}{G _{1}} + \frac{F _{3} - 1}{G _{1} G _{2}}$ .
Substitute: $F = 10 + \frac{10 - 1}{10} + \frac{10 - 1}{10 \times 10} = 10 + 0.9 + 0.09$ .
So $F = 10.99$ as a ratio (about $10.41 dB$ ). The options are plain ratios, so the answer is $10.99$ .
Other options: $10$ ignores the later stages, $10.9$ drops the third-stage term, and $1.09$ is not even above a single stage's factor.

KEY IDEA

Convert dB values to plain ratios, then apply Friis' formula: each later stage's excess noise $(F_{k} - 1)$ is divided by the total gain ahead of it.

WATCH OUT FOR

Adding or using the dB values directly in Friis' formula, or stopping at the first stage's $F_{1} = 10$ and ignoring the later stages' small contributions ( $0.9$ and $0.09$ ).

From the ISRO EC 2023 paper. Every question of this paper · The full paper (PDF, ISRO) · All 2 ISRO Noise & shielding (IN) questions, with notes