How to set the carrier output power of Bi-directional Amplifier?

Question

If a bi-directional amplifier is used for a multi carrier trunked radio radio network is at 10watts which equal to +40dBm.
If each carrier is set at +20dBm at the output port of the amplifier, then what is the maximum number of carriers can be work together at +20dBm level at the same time by the BDA and not to degrading the signal output of each carrier at +20dBM.
How to calculate????? What other criterias define or affect the output power of the BDA setting???

Answer 1

When I first started to answer, off the top of my head, I was going to say that each carrier added twice the power (+3 dB) to the total, but that was wrong thinking.

I looked it up in "Reference Data for Radio Engineers". There are several tables, charts, and a couple of formulas for deriving the answer. It depends on the voice power in each channel and statistics on how many channels are active at one time. The whole discussion takes a page starting on page 30-31 (for the 5th edition 1970).

For max. talker volume (6 dB);

P = P0 + 10*log(N) + deltaC

- deltaC comes from a chart that depends on number of channels and speech power.
- P0 is the average speech power from a statistical distrbution.
- N is the number of channels.
- "log" is log base 10

In your case:
40 dBm = -9.75 + 10*log(N) + deltaC

Since both N and deltaC are a function of N, it must be solved iterratively.

(49.75 - deltaC)/10 = log(N)
4.975 - deltaC/10 = log(N)

With this setup, according to the deltaC chart, you could get over 2000 channels on the line. The chart only goes up to 2000, but the equation was starting to converge just above 2000.

Intuitively this seems a bit high, but 10 Watts is quite a bit of power for a cable system, so maybe that's right.

This is all based on 25% of the channels being active at-a-time. It is also based on a "flat" transmission line (equalized with pre-emphasis or post equalization).

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There is another possible way to look at the problem.
It might be written as:
40 = 20 + 10*log(N) + deltaC
IF the power of carrier can be assumed to be the max. power of the individual channel. In which case:
2 - deltaC/10 = logN

In this case N works out to be less than 10 channels, which is closer to the 'off-the-top-of-my-head' 6 channel initial guess based on adding 3 dB per channel.

.

Answer 2

A 40 dBm amplifier can be used up to about 28 dBm total power with mixed carriers (12 dB headroom). BUT distortion will occur, its a question of how much you can tolerate. I would think four carriers at 20 dBm , totaling 26 dBm, would be a limit.

Answer 3

47.2