I'm having a difficult time trying to solve something that should be very easy.
I have the following:
40dBm - 6 dB + 10dB - Lprop > -100dBm
Now, the answer should be Lprop < -144dB, but I'm getting messed up with the signs.
I'm trying to move the -100dBm to the left part of the inequation and I think there is where I'm doing it wrong. If I move it to the other part with a + signus, then I'm adding dBm with dBm and, that doesn't make sense, as they would be mW^2 and Lprop is unitless.
What should happen somehow is that I would need to substract dBm - dBm in order to get dB, but I can't figure this out.
Could someone make the solution of this step by step and providing as much information as posible? That would be of great help thank you!
40dBm - 6 dB + 10dB - Lprop > -100dBm
are you solving for Lprop?
-Lprop > -100dBm - 40dBm + 6dB - 10dB
-Lprop > -144 dBm - 4dB
Lprop < 144dBm + 4dB
40dBm - 6 dB + 10dB - Lprop > -100dBm
Your dBm's will never cancel out... regardless of what side you bring them too.
Do you have to convert your dB's to dBm's first??
hmmm....
To solve the equation, let's break down each term and simplify step by step.
Given equation:
40dBm - 6dB + 10dB - Lprop > -100dBm
Step 1: Combine the dBm terms on the left side of the equation.
40dBm - 6dB + 10dB = (40 - 6 + 10) dB = 44 dBm
So now, the equation becomes:
44 dBm - Lprop > -100 dBm
Step 2: Move the -100 dBm to the right side by adding it with the opposite sign. Remember that adding a negative value is the same as subtracting.
44 dBm - Lprop + 100 dBm > 0
Step 3: Simplify the equation by combining the dBm terms.
(44 + 100) dBm - Lprop > 0
144 dBm - Lprop > 0
Step 4: Now, rearrange the equation to isolate Lprop by subtracting 144 dBm from both sides. Remember to change the sign when moving to the other side of the equation.
- Lprop > -144 dBm
Step 5: To solve for Lprop, multiply both sides by -1. Remember that when multiplying or dividing by a negative number, the inequality sign flips.
Lprop < -(-144) dBm
Lprop < 144 dBm
Therefore, the correct solution to the inequality is Lprop < 144 dBm.
Note: In dB calculations, you can perform addition and subtraction directly. However, dBm represents power in decibels relative to 1 milliwatt. It is not a unit, but rather a power measurement with a reference. When adding or subtracting dBm values, the dBm terms can be directly combined, while dB terms need to be converted to dBm or vice versa if necessary.