![solve for i decibel scale solve for i decibel scale](https://www.engineeringtoolbox.com/docs/documents/341/decibel_scale.png)
You are transmitting a carrier at 350 kbit, and want to transmit a carrier at 800 kbit.Now you can solve the second problem – how to best resize a carrier given Y margin. But that is close enough for quick estimates. It’s not really equal to 2 it is 3 dB = 10 0.3 = 1.995. “3 dB equals double the power” is just an estimate. Why isn’t that 1024 kbit? Because I wasn’t entirely honest with you. So we can transmit a 1021.57 kbit carrier. Remember that we’re using log base 10, so a = 10. To solve for P2, we need to convert decibels back to a linear scale. If you’ve been paying attention, you know that 3 dB means “double the power”, so the quick answer is P2 = 512 * 2 = 1024 kbit. How large can I make this carrier if I want to have 0 dB margin? My maximum safe transmit power, which we determined early by a 1-dB compression test, is -12 dBm. My modem is transmitting at -15 dBm, and has a C/N which is exactly what we need for reliable service. I have a carrier P1 that is 512 kbit in size. Modems often express transmit power in dBm. Which you use – dBW or dBm – does not matter as long as all your inputs are using the same scale. Converting between these two scales is easy just add or subtract 30 dB. I commonly work with dBW (where P2 is expressed in Watts of power and P1 is 1 W) or dBm (where P2 is expressed in milliwatts of power, and P1 is 1 mW).
![solve for i decibel scale solve for i decibel scale](https://c8.alamy.com/comp/KE4W39/the-decibel-scale-sound-level-KE4W39.jpg)
When this happens we write them as “dBX”, where X is the reference.
![solve for i decibel scale solve for i decibel scale](https://lifeinlifts.files.wordpress.com/2018/09/common-decibel-levels-chart.png)
Old carrier is 512 kbit, and new carrier is 768 kbit.ĭecibels are sometimes expressed as relative to some reference. Let’s use IP rate in kbit instead of Hertz (both carriers must use the same modulation and encoding we must compare apples to apples). This means you can compare P1 and P2 in any equivalent terms. They only tell you how two signals relate to one another. Now we have an answer to the first question – what is the difference in power between two carriers? Now I’ll take a moment to explain a few more things before answering the second question.ĭecibels are relative on their own, they do not express an absolute value. We might be able to use a smaller antenna or BUC. Let’s start with a 500 kHz carrier and reduce it to 375 kHz: The same math works for a smaller carrier. That means a larger antenna or transmitter (BUC) on the transmitting side, or a larger antenna on the receiving side. So if I want to transmit this carrier, I must improve that carrier’s C/N by 1.5 dB somehow. So we’ll need 1.5 dB more power to transmit the new carrier P2. What if the math isn’t so easy? Let’s say my old carrier is 685 kHz in size, and I want to increase to 976 kHz.ġ0 * log (976/685) = 10 * log (1.425) = 1.54 dB Which is logical if you want to transmit a carrier that is twice as big as your current carrier, you need twice the power. So, if one carrier is 800 kHz in size, and another is 400 kHz in size, what is the difference in power between the two carriers? Remember that 0 dB does not mean “no power”, it is just another point on the scale. The scale can run negative as well, so a carrier transmitted at 0 dB is half the power of that 3 dB carrier, and at -3 is one-quarter the power. And a carrier transmitted at 9 dB is four times as powerful as that 3 dB carrier. A carrier transmitted at 6 dB is twice as powerful as a carrier transmitted at 3 dB. The handy rule of thumb of the decibel scale is this: 3 dB means twice the power. Since this is base 10, we can be express this without the explicit base: Where P1 and P2 are the two signals to be compared. A decibel is the base 10 logarithm of the ratio of the power of two signals, times 10: We know two of three variables P1, P2, and Y, and we want to solve for the missing one.įirst, the basics. How large can I make my new carrier P2? Or if Y is negative, how small?