Since dBs are logs of ratios, you cannot do sums of squares on them, and take square roots. You would have to convert to numerics, do the rss, and then convert back to dBs.
Thus, given your example values: probe: 0.5 dB is roughly 6% tolerance cable: 0.1 dB is roughly 1.1% tolerance analyzer: 1 dB is roughly 12% tolerance RSS: = square root [ (0.06)^2 + (0.011)^2 + (0.12)^2 ] = 0.135 That corresponds to about 1.3 dB overall tolerance. Note that isn’t very far off from your 1.26 dB answer. However, to get that, you simply added the dB tolerances together (no rss) and then took a square root of the sum of dBs. When you add the dBs together, you are multiplying the tolerances. If you multiply the tolerances and take the cube root, it is as if you are taking a geometric mean. Geometric and arithmetic means are pretty close as long as the factors going into the product don’t vary much from each other. For instance, if the factors are identical, the geometric and arithmetic means are identical. Of course, that is a degenerate case where the concept of mean isn’t terribly useful. If you had two factors, say one and ten, the geometric mean would be 3.162, whereas the arithmetic mean would be 5.5. If the two factors are one and one hundred, then the geometric mean is ten, and the arithmetic mean is 50.5. You can see where this is going. Ken Javor Phone: (256) 650-5261 ________________________________ From: "Price, Edward" <[email protected]> List-Post: [email protected] List-Post: [email protected] List-Post: [email protected] Date: Tue, 8 Sep 2009 16:16:09 -0700 To: <[email protected]> Conversation: Measurement Uncertainty Subject: Measurement Uncertainty A quick question about calculating measurement uncertainty. For example, if I am doing a conducted emission test, and I know the calibration tolerance for each of the "modules" of my measurement system, how do I calculate an overall uncertainty figure? I have been under the assumption that, in the example I cite, that I have a tolerance for my probe (say +/- 0.5 dB), my cable (+/- 0.1 dB) and my analyzer (+/- 1 dB). I have been using an "rms" calculation, where I square each of the tolerances, sum them, and take the square root. Thus, square root of 1.6 dB equals 1.26 dB uncertainty. I recently had a customer say that this method implied that I was using "rectangular" shape factors, and thus, I should be taking the cube root of the sum. Rectangular? Cube root? Ed Price [email protected] <blocked::mailto:[email protected]> WB6WSN NARTE Certified EMC Engineer Electromagnetic Compatibility Lab Cubic Defense Applications San Diego, CA USA 858-505-2780 Military & Avionics EMC Is Our Specialty - This message is from the IEEE Product Safety Engineering Society emc-pstc discussion list. To post a message to the list, send your e-mail to <[email protected]> All emc-pstc postings are archived and searchable on the web at http://www.ieeecommunities.org/emc-pstc Graphics (in well-used formats), large files, etc. can be posted to that URL. Website: http://www.ieee-pses.org/ Instructions: http://listserv.ieee.org/request/user-guide.html List rules: http://www.ieee-pses.org/listrules.html For help, send mail to the list administrators: Scott Douglas <[email protected]> Mike Cantwell <[email protected]> For policy questions, send mail to: Jim Bacher <[email protected]> David Heald <[email protected]> - This message is from the IEEE Product Safety Engineering Society emc-pstc discussion list. To post a message to the list, send your e-mail to <[email protected]> All emc-pstc postings are archived and searchable on the web at http://www.ieeecommunities.org/emc-pstc Graphics (in well-used formats), large files, etc. can be posted to that URL. Website: http://www.ieee-pses.org/ Instructions: http://listserv.ieee.org/request/user-guide.html List rules: http://www.ieee-pses.org/listrules.html For help, send mail to the list administrators: Scott Douglas <[email protected]> Mike Cantwell <[email protected]> For policy questions, send mail to: Jim Bacher <[email protected]> David Heald <[email protected]>
