Confusion about decibel - Page 1
Forum section: electronics / beginners

author: Laval
author_rank: Regular Contributor
timestamp: March 24, 2025, 01:33:44 am
content: Hello everyone.I'm a bit confused by the concept of decibel or rather by the way it is defined and used. I know what a logarithm is and what a logarithmic scale is and why it is used. The decibel is used to represent power ratios on a logarithmic scale, fine. If comparing powers then db = 10log10(p2/p1). Now, when comparing voltages, since p = v2/r, we getdb = 20log10(v2/v1) + 10log10(r1/r2)The second term here will be zero when r1 = r2 which is basically never the case with amplifier circuits. Yet, in many places (internet, datasheets and even textbooks) 20log10(v2/v1) is used. Of course, the power is always proportional to the square of the voltage but it also depends on the resistance (or impedance). You could define the gain in db as 20log10(v2/v1) but that no longer represents the same thing unless impedances are equal.Anyone can shed some light ?

author: showman
author_rank: Contributor
timestamp: March 24, 2025, 02:46:14 am
content: Quote from: Laval on March 24, 2025, 01:33:44 amYou might think you're confused, but that's not the case at all. In fact what I quoted really is the answer.

author: Andy Chee
author_rank: Super Contributor
timestamp: March 24, 2025, 03:26:27 am
content: Perhaps a thought experiment is in order.a) what dB increase in volts is required to change a loudspeaker from 60dB SPL to 70dB SPL?b) what dB increase in power is required to change a loudspeaker from 60dB SPL to 70dB SPL?

author: Laval
author_rank: Regular Contributor
timestamp: March 24, 2025, 09:17:10 am
content: Quote from: Andy Chee on March 24, 2025, 03:26:27 amSo it's just another scale chosen to preserve the variation while getting rid of the constant term with the impedances, thanks. So many sources implies so many different things.

author: Solder_Junkie
author_rank: Frequent Contributor
timestamp: March 24, 2025, 10:35:09 am
content: Another way to “unravel” dB measurements is to look at levels in dBm (dB referenced to a milliwatt) in radio frequency amplifiers and receivers.Assuming all the modules are designed for 50 Ohms, which many are, then trying to deal with millivolts, microvolts, peak to peak levels on an oscilloscope, Watts on a power meter… it is awkward. Now if you deal with levels in dBm, it all becomes a lot easier, an example for a receiver may include:Signal generator output: -73 dBmInput attenuator: 0 or 10 dBPre-amp: 0 or +12 dBMixer loss: 6 dBLocal oscillator level into mixer: + 7dBmIF amplifier gain 50 dBYou see how much easier it is with dB levels. The signal generator can be set to dBm, pre-amp and attenuators can be measured with a spectrum analyser (with tracking generator), oscillator levels can be measured with a spectrum analyser (they measure in dBm and are 50 Ohms), etc.SJ

author: Wallace Gasiewicz
author_rank: Super Contributor
timestamp: March 24, 2025, 12:33:52 pm
content: Decibel scales are analogous to the scales on a Slide Rule.A slide rule lets you multiply two numbers by adding their log 10.You add Decibel gains or loss to calculate input or output thru any number of devices.Get an old slide rule and look at it.

author: PGPG
author_rank: Frequent Contributor
timestamp: March 24, 2025, 01:25:02 pm
content: Quote from: Laval on March 24, 2025, 01:33:44 amIt is used because there is the assumption that changing a power doesn't change the impedance.I think no one cares about little cable dimension changes because of power dissipated in it that can lead to change its impedance from 50 ohm (or in TV systems 75 ohm) to some other value.Also speaker coil resistance changes not a l;ot if it gets higher temperature.

author: tggzzz
author_rank: Super Contributor
timestamp: March 24, 2025, 01:31:38 pm
content: Quote from: PGPG on March 24, 2025, 01:25:02 pmIt is usually valid in RF amplifiers, where the input and output impedances are the same. Hence it is valid.Where the impedances are not the same, e.g. audio amplifiers or opamps, it is not correct - but is commonly used since a scale -10 -20 -30 -40 is easier to interpret than 0.3 0.1 0.03 0.01 etc. Plus it ties in neatly with Bode plots and feedback/control loop stability.Summary dB=20log(V1/V2) ratio without constant impedance is wrong, but it is common and useful.

author: CaptDon
author_rank: Super Contributor
timestamp: March 24, 2025, 01:37:52 pm
content: When speaking in terms of decibel loss or gain most often we make a generalization that the impedences are equal. This assumption is made daily when working with 50 ohm R.F. transmission lines, also in the 75 ohm and 300 ohm common R.F. impedences. It is also common in 600 ohm audio systems. Sometimes when there is a low source impedance driving a very high load impedance where we are concerned about voltage levels and not power levels we think in a different way remembering a 10:1 voltage increase is a 20dB power increase where a 10:1 power increase is a 10dB power increase. I have seen people make mistakes in calculations in the audio preamplifier stages where they are usually only talking about voltage ratios where the input and output impedences may be different by a factor of ten to maybe ten thousand. I remember the little HP amplifier switches being marked 20dB and 40dB which was 10X or 100X voltage gains. Most people used those amplifiers ahead of an oscilloscope and were concerned more about the 10X and 100X voltage gains not the dB gain and many times forgot to terminate the amplifier output correctly which could approach a 20X or 200X voltage gain.