Ali, a 25 year old male from Pakistan asks on May 27, 2008,

In microwave transmission sometimes we use power in positive e.g +13db and sometimes in negative like -13 db. What is the difference? How can we choose the right power? Please inform.viewed 13373 times

When we describe power in dB (decibels), it is relative to some reference level, like 1 Watt (W) or 1 milliWatt (mW). If the power in dBW is positive, it means it is greater than 1 W. If the power in dBW is negative, it means it is less than 1 W. And if the power in dBW is 0, it means the power is 1 W. Similarly for dBmW: if the power in dBm is positive, the power is more than 1 mW.

It's a bit like per cent in that respect. For example, 1.1 W is 10% up from 1 W, and 0.9 W is down 10% (i.e. it's -10%) from 1 W. However, decibels are not the same as per cent!

decibels are actually based on logarithms. The dB measure of power is 10 log (P/Pref), where P is the power and Pref is the reference power level. Suppose 1 W is the reference, and you have a 10 W signal. In dBW, that is 10 log(10/1) = 10 dBW. On the other hand, a signal of 0.1 W is 10 log(0.1/1) = -10 dBW.

A common rule of thumb is that doubling the power of a signal adds 3 dB, and that halving the power subtracts 3 dB. To see this, consider a signal of power P Watts, or 10 log(P) in dBW. Now double the power to 2P. In dBW, it is now 10 log(2P) = 10 log(2) + 10 log(P) = 3 + 10 log(P). This is approximate, but close.

Let's look at the specific values you mentioned. A power of 13 dB is 20 times the power of the reference level, so it's 20 W if you are using dBW, or 20 mW if you are using dBmW. Similarly, a power of -13 dB is 1/20 Watt (0.5 Watt) or 1/20 mW, depending on whether it's dBW or dBm.

Finally, an example. Some wireless personal area networks under development have restrictions on transmitter power. In any 3 kHz bandwidth, they are limited to +8 dBm. That's more than 1 mW and less than 10 mW. Taking the antilog, we see that the limitation is about 6.3 mW in any 3 kHz.

Note: All submissions are moderated prior to posting.

If you found this answer useful, please consider making a small donation to science.ca.

- Canadian Nuclear Safety Commission Educational Resources
- National Inventors Hall of Fame
- JUMP Math
- Society for Canadian Women in Science and Technology
- SciQuest e-Solutions for Science
- Natural Sciences and Engineering Research Council of Canada
- Manning Awards for Innovation
- Royal Society of Canada
- Geological Survey of Canada
- Canadian Networks of Centres of Excellence
- Canadian Landscapes at Natural Resources Canada
- Canadian Association of Physicists
- A Century of Innovation
- Understanding Science
- AlphaGalileo
- National Film Board of Canada Youth Science
- PICS Climate Insights 101
- Canadian Association for Girls in Science
- Virtual Library for the History of Science
- The Chemical Institute of Canada
- Canadian Biotechnologist 2.0
- ISI Highly Cited Scientists
- Deep River Science Academy
- Journal of the History of Canadian Science
- Wikipedia
- Innovation Canada
- Mars Society
- Nobel Prize Archive
- science.gc.ca
- Online Science & Engineering Encyclopedia
- CurioCity
- Canadian Nuclear FAQ
- Association of Science Communicators
- Astrofiles
- Wilderness Astronomy