how a tetra repeater works

I want to extend the radio coverage and I need to install a repeater to pick up the signal and broadcast it except I’m confused about how it works:
the repeater has a gain = 90 dbm and an output power = 37 dbm. for example the repeater receives a signal equal to -50dbm in this case how its output power will be calculated:
case 1: output power = received signal (-60dbm) + gain (90dbm)
-50+90=40 dbm = 10 watt
case 2: it suffices to capture a signal (greater than the minimum reception limit) so that the repeater to amplify it to its maximum power which is for this repeater equal to 37 dbm

You’ve got yourself tied up with gain figures - if you have a 37dBm output - that’s 5 Watts in understandable units. Your input sensitivity - as for the weak signals, means a likely sensitivity figure around -75-90dBm? so in voltage terms, very little. What are you confused about in practice? You will lose a little going through the filters on in and out, and perhaps if you have a combiner for single antenna operation, that’s another loss - but the point for practical use is that a repeater with decent antenna in the best place beats a semi-duplex radio in performance because of where the antenna is - the filter/combiner losses are known, but so much better performance, the losses are manageable. You pick the output power to be a balance between the input and output path. If all your users are in vehicles with decent antennas an 10-25W output, receive signal strength will be higher, and the path length a little greater. That might need a higher power output to make the in and out paths the same. If your paths are shorter because of low power, hand-held radios, there could be no point in using a high power ouput - they could hear the repeater, but the repeater wouldn’t be reciprocal, it wouldn’t hear them. The lower power output would also make the filtering more efficient.

What are you struggling with?

I believe the original poster is asking about how repeaters work and gave two possible scenarios. The short answer is that case 2 more accurately describes how a repeater works.

Case 1 would describe how an amplifier would work. However, a repeater is not an amplifier.

Well, it does sort of make sense - but just isn’t how we normally talk about it? Paul

High Level Overview of how all digital repeaters work:

  1. Signal with a high enough signal to noise ratio (i.e. the detector circuit can make out that it is a valid signal) is received and demodulated into a serial data stream (receiver)
  2. Forward error correction is applied (optional step and depending on the protocol it may or may not be performed)
  3. Serial data is then sent to the transmitter, modulated and transmitted

High Level Overview of how all analog repeaters work:

  1. Signal which opens squelch is received and demodulated into line level audio
  2. Demodulated line level audio is modulated and transmitted

Pretty basic functional overview. In both cases the serial data and audio are normalized so the received signal value has zero correlation to the transmitted signal value. There is at least one repeater on the market which is theoretically capable of performing DSP enhancement on a received signal to clean up analog audio but in practice it is not used.