Power and Voltage decibels formulas. - Page 1
Forum section: electronics / beginners

author: Rene
author_rank: Regular Contributor
timestamp: February 10, 2015, 07:27:36 am
content: Hey guys.Quick question. If decibels are meant to be used as a way to represent a simple ratio between two values, then why do we have to have two separate decibel formulas for representing power and voltage ratios?Power: db = 10Log(p1/p2)Voltage: db = 20Log(v1/v2)Please note thatI am awareof how we end up with the 20Log(v1/v2) formula when calculating voltage dbs, the technical reason for how we derive that formula is not the real question. This is more of a philosophical question I guess.For example, a 6 inch banana is 3db bigger than a 3 inch banana (no dirty thoughts please). This is because db = 10Log(6/3) = 3db. As you can see, I easily managed to convey the fact that one banana is twice as big as the other banana without having to resort to adding any additional factors to the equation. just keeping it simple I guess.So why can't the same not be done with Voltage? Why can't I just say that a 20 volt signal is twice as big as a 10 volt signal by simply doing db = 10Log(20/10) = 3db. What exactly is the point for complicating things and say that a doubling in voltage is db = 20Log(20/10) = 6db just because power = v^2/R.Why not keep it simple and let 3db be doubling of a value all the time and forgo the technicalities of power = v^2/R?Probably a stupid question but just curious.Thanks.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: February 10, 2015, 07:39:09 am
content: A matter of convention: power works well in dB (it's a more invariant measure, not depending on system impedance, or any system at all i.e. free propagating waves), but voltage arguably less so. So it gets the 20 and power gets the 10.To use your analogy directly:If a square is 3dB longer, how many dB has its area increased by? If a cube, the volume?Tim

author: LabSpokane
author_rank: Super Contributor
timestamp: February 10, 2015, 08:10:45 am
content: Pure convention. It all goes back to the definition of the Bel back in the 20s. The Bel was defined as a ratio of powers. It proved too large to not have everything be 0.nnn so the decibel was begat and thus the 10 multiplier.I'll see if I have a copy of the Bell Labs Technical Journal where it was introduced. Alcatel used to have a free archive, but it's now been paywalled behind IEEE. I think it was 1925 or thereabouts. The big deal in telephony then was power transfer just due to the devices they had to work with. Impedance matching was a big deal then. Today, with high impedance inputs, we try to maximize the signal level transfer, in order to maximize the SNR.Thus, we have a 20 instead of 10, even though we really care about the "voltage transfer" if you will.

author: LabSpokane
author_rank: Super Contributor
timestamp: February 10, 2015, 06:48:31 pm
content: Oops, the "transmission unit" was adopted in 1922.The BSTJ introduced the "transmission unit" in publication in 1924 here:https://archive.org/details/bstj3-3-400Here's the article that introduced the word "decibel" in 1929:https://archive.org/details/bstj8-1-1Recommended reading! It's fun to read the early Bell Labs journals and see the foundations of electrical engineering developed.

author: AG6QR
author_rank: Frequent Contributor
timestamp: February 10, 2015, 07:36:05 pm
content: Quote from: Rene on February 10, 2015, 07:27:36 amYour bigger banana may be twice as long, but if all dimensions are scaled simultaneously, it has four times the surface area, and eight times the volume.So if you want to maintain the fact that the two bananas differ by 3dB, then your dB formula for comparing two bananas must be different depending on whether you are given two lengths, two volumes, or two surface areas.That's what we do with signals. We might say that signal "A" is 3dB bigger than signal "B". That's true regardless of what thing about the signals we're measuring. If we measure the power of signal "A", we'll know that the power of signal "B" is half that of signal "A". But if we measure the voltage, the ratio is about 0.7.

author: KM4FER
author_rank: Regular Contributor
timestamp: February 10, 2015, 10:36:07 pm
content: By far the best explanation of dB I have ever read can be found here:http://www.edn.com/design/test-and-measurement/4423318/How-to-Think-in-dBearl...

author: Yansi
author_rank: Super Contributor
timestamp: February 10, 2015, 10:42:29 pm
content: No conventions here. The only convention is the times 10 before the logarithm.As you have already mentioned, because power depends on the voltage squared, as it is well known, logarithm of something squared is the same as twice logarithm of the "something".a = log b² = 2 log bSimple mathematics.Note: Look up what is the Np unit. (Neper) :-)

author: LabSpokane
author_rank: Super Contributor
timestamp: February 10, 2015, 11:04:10 pm
content: The convention is that the decibel was a ratio of *powers*. It could have been defined equally as a ratio of voltages, or currents. It is a contrived unit. And whether or not to use base 10 or natural logarithms was a topic of discussion in the papers referenced above.And the original poster already explained that he understood logarithms...