Two amplifiers are connected in cascade, each having a gain of 10 dB and a noise temperature of

step 1 To solve this problem, let us write the given data first. So here the value of amplifier first g

Two amplifiers are connected in cascade, each having a gain...

Two amplifiers are connected in cascade, each having a gain of $10 \mathrm{~dB}$ and a noise temperature of $200 \mathrm{~K}$. Calculate $(a)$ the overall gain and $(b)$ the effective noise temperature referred to input.

Key Concepts

Gain Conversion from dB to Linear

Gain expressed in decibels (dB) is a logarithmic measure where conversion to linear scale is necessary for direct multiplication across stages. The conversion is done using the formula G_linear = 10^(G_dB/10). This linear gain is essential for calculating the overall system gain and for combining noise contributions in a cascade of amplifiers.

Amplifier Cascading

When multiple amplifiers are connected in series (cascade), their individual gains multiply to give the overall system gain. However, noise contributions from each stage must be carefully accounted for because the noise added by early stages is much more influential than that added by later stages. This cascading effect highlights the importance of positioning low-noise amplifiers at the beginning of the chain to minimize the effective noise figure or noise temperature seen at the input.

Friis Formula for Noise Temperature

The Friis formula for noise temperature (or noise figure) in cascaded systems quantifies the contribution of each stage toward the overall noise performance of the chain. It states that the effective noise temperature referred to the input is the noise temperature of the first stage plus the noise temperatures of successive stages, each divided by the cumulative gain of all preceding stages. This principle is crucial for determining how noise from multiple amplifiers aggregates in a cascaded system.

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