A signal is traveling down a transmission line that is lossy

A signal is traveling down a transmission line that is lossy. When the signal decays to 20% of the original signal you need to add a repeater to the line to boost the signal by a factor of 5 to the original signal level. A new repealer is developed that could boost the signal by a factor of 20 so you only need a repeater when the signal reached 5% of original signal. What would the cost of this new repeater need to be to make it cost effect compared to the original repeater?

Solution

No, Over a given transmission line length, the total cost would be the same using new repeater and the old repeater. So there is no cost advantage.

Amplifying the signal by 5x that\'s decayed to 20% of the original level will introduce less noise than
amplifying the signal by 20x after it\'s decayed to 5% of the original level.
So, the old repeater has a signal to noise advantage.