Tower Mounted Amplifier - Mathematical Principles

Mathematical Principles

In a receiver, the receiving path starts with the signal originating at the antenna. Then the signal is amplified in further stages within the receiver. It is actually not amplified all at once but in stages, with some stages producing other changes (like changing the signal's frequency).

The principle can be demonstrated mathematically; the receiver's noise figure is calculated by modularly assessing each amplifier stage. Each stage consists of a noise figure (F) and an amount of amplification, or gain (G). So amplifier number 1 will be right after the antenna and described by and . The relationship of the stages is known as the Friis formula.

System Noise Figure = F_1 + \frac{ F_2 - 1 }{ G_1 } + \frac{ F_3 - 1 }{ G_1 \times G_2 } + \cdots + \frac{ F_n - 1 }{ G_1 \times G_2 \times G_3 \times \cdots \times G_{ n-1 } }

Note that:

  1. The first amplifier will set the temperature ; nothing reduces its contribution to the total.
  2. The second amplifier's temperature will also influence the total but it is reduced (divided) by the gain of the first amplifier .
  3. The third amplifier's temperature is influencing even less, as it is reduced by its preceding amplifier gains, .
  4. And so on until N stages.

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