Fiber Optics - Absolute and decibel Power Gains

[Axis001]

Homework Statement

Problem is very simple but the textbook used for this class is complete garbage and has confused me to no end.

a) Convert the following absolute power gains (dBm) to decibel power gains (dB).
10^-3 dBm, 2^n dBm

b) Convert the following decibel power gains (dB) to absolute power gains (dBm).
-30 dB, 10n dB

Homework Equations

Power Level in dBm = 10log(P (in mW)/ 1 mW)
Power ratio in dB = 10log(P_2/P_1)

The Attempt at a Solution

a) 10^-3 -> 10log(10^-3) = -30 dB
2^n -> 10log(2^n) = 10n dB

b) Here is where I am having a issue with this problem. Part A is solvable according to my book by simply plugging the dBm value back into the same formula that is used to get it but if the same thing is attempted with the decibel power ratio of -30 well things don't go so well or make sense.

I am more or less looking for help explaining dBms and dBs and how they are related more than I am help solving this particular problem. Any help would be greatly appreciated.

 

[KataKoniK]

I understand your frustration with the textbook being confusing. However, I will try my best to explain the concept of dBm and dB in relation to power gains.

dBm is a unit of measurement for power, specifically power levels. It is a logarithmic unit that compares a given power level to 1 milliwatt (mW). The formula for converting from dBm to dB is correct, as you have shown in your attempt at a solution. In the case of 10^-3, the answer is -30 dB because 10^-3 is 0.001 and 10log(0.001) is -30 dB.

Now, moving on to decibel power gains (dB). This unit is used to compare two power levels. The formula for converting from dB to absolute power gains (dBm) is also correct. However, in this case, the power levels being compared are not specified. So, for the value -30 dB, we cannot convert it to dBm without knowing the reference power level. The same goes for the value 10n dB, as the power levels being compared are not specified.

In conclusion, dBm and dB are related in that they both measure power, but they are used in different contexts. dBm compares a power level to 1 mW, while dB compares two power levels. I hope this helps clarify things for you. Let me know if you have any further questions.