A two-stage LNA has the following parameters:
a) Stage 1: Gain , Noise Figure
b) Stage 2: Gain , Noise Figure .
Calculate the overall noise figure of the amplifier.

Ask by Hardy Hills. in India

Mar 29,2025

Question

A two-stage LNA has the following parameters:
a) Stage 1: Gain , Noise Figure
b) Stage 2: Gain , Noise Figure .
Calculate the overall noise figure of the amplifier.

Ask by Hardy Hills. in India

Mar 29,2025

UpStudy AI · Accepted Answer

**Step 1: Convert gains and noise figures from dB to linear scale**

For Stage 1:  
- Gain:  
  $$
  G_1 = 10^{\frac{10}{10}} = 10
  $$
- Noise Figure:  
  $$
  NF_1 = 10^{\frac{2}{10}} \approx 10^{0.2} \approx 1.585
  $$

For Stage 2:  
- Gain:  
  $$
  G_2 = 10^{\frac{8}{10}} \approx 10^{0.8} \approx 6.31
  $$
- Noise Figure:  
  $$
  NF_2 = 10^{\frac{3}{10}} \approx 10^{0.3} \approx 1.995
  $$

**Step 2: Apply the Friis formula for cascaded stages**

The overall noise figure in linear scale is given by
$$
NF_{\text{total}} = NF_1 + \frac{NF_2 - 1}{G_1}
$$

Substitute the values:
$$
NF_{\text{total}} = 1.585 + \frac{1.995 - 1}{10}
$$
$$
NF_{\text{total}} = 1.585 + \frac{0.995}{10}
$$
$$
NF_{\text{total}} = 1.585 + 0.0995 \approx 1.6845
$$

**Step 3: Convert the overall noise figure back to dB**

The overall noise figure in dB is found by
$$
NF_{\text{total,dB}} = 10 \log_{10}(NF_{\text{total}})
$$
$$
NF_{\text{total,dB}} = 10 \log_{10}(1.6845)
$$

Calculating:
$$
\log_{10}(1.6845) \approx 0.226
$$
$$
NF_{\text{total,dB}} \approx 10 \times 0.226 \approx 2.26\,\mathrm{dB}
$$

**Final Answer:**

The overall noise figure of the amplifier is approximately $$ 2.26\,\mathrm{dB} $$.
The overall noise figure of the amplifier is approximately $$ 2.26\,\mathrm{dB} $$.

A two-stage LNA has the following parameters:
a) Stage 1: Gain , Noise Figure
b) Stage 2: Gain , Noise Figure .
Calculate the overall noise figure of the amplifier.

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A two-stage LNA has the following parameters: a) Stage 1: Gain , Noise Figure b) Stage 2: Gain , Noise Figure . Calculate the overall noise figure of the amplifier.

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A two-stage LNA has the following parameters:
a) Stage 1: Gain , Noise Figure
b) Stage 2: Gain , Noise Figure .
Calculate the overall noise figure of the amplifier.