Calculate transmitting power of the Transmitter

Question

I cannot get a hold of my professor and I'm stuck tyring to understand how to solve this problem. It's not homework or an assignment I'm preparing my self for a test.

So as the title states I need to calculate the transmitting power of the transmitter if we Increase said power? for 20db or 3db.

There is very little explanation in the book about this the first are given and go as follows:

Initial step:
$$ dB = 10 \cdot log_{10} \bigg( \frac{P1}{P0} \bigg)$$

First step: $$ 20dB = 10 \cdot log_{10} \bigg( \frac{P1 + x}{P0} \bigg)$$

Third step:
$$ \frac{20dB}{10} = log_{10}\bigg( \frac{P1 + x}{P0} \bigg) $$

That's it only thing that they added was:
P1 = Transmitting power,
P0 = Reference power?

Can anyone please give me a better detailed explanation about this how to solve it. The problem does not provide and information regarding values of P and what the hell is that x in First step.

Answer 1

dB is defined in your first equation. All you need to do is to calculate what power ratio corresponds to 20 dB. If you substitute dB = 20, and solve for P1/P0, you get P1/P0 = 10^2 = 100. Therefore P1 = 100P0. If dB = 3, then substitute that value into the first equation and again solve for P1/P0. You get P1/P0 = 10^.3 = 1.995 which is usually rounded to 2. So 3 dB corresponds to a power ratio of 2. Therefore P1/P0 = 2 and thus P1 = 2P0.