EEVblog #49 - Decibels (dB's) for Engineers - A Tutorial

hi welcome to the EEV blog an electronics engineering video blog of interest to anyone involved in electronics design I'm your host Dave Jones hi today we're going to talk about DB's decibels because I've had a few people comment about what exactly I mean when I talk about DB's in my blog I might say the minus 3 DB bandwidth of an oscilloscope or something like that or I might say something 6 DB down or I might say the roll-off of an amplifier is a minus 20 DB per decade or something like that but what does that mean because beginners seem to get confused with DBS they seem to think there's some weird you know who abstract mathematical thing that's all complex and but no D B's are really easy they're one of the easiest concepts in electronics so what the heck is a DB well a DB is a decibel what the hell's a decibel well a decibel is 1/10 of a Bell because deci is a 1 live means 1/10 and a Bell is a very old unit which nobody gives a toss about anymore but decibels are important because it gives us engineers a way of expressing large values and numbers and working with large values of numbers without making it really cumbersome the first thing you have to learn about the DB is that it's not really a unit like our volts or ohms or amps or something like that the a DB is a ratio it is just a it's a it's a ratio of two numbers basically so it's like saying something is half of something else it's point five times you know if I've got one volt and something is 0.5 times that one volt right point five is a ratio just like a DB and in this case point five is actually minus 6 dB instead of being linear like saying point five we say minus 6 DB because DBS are a logarithmic ratio it has to do with logarithms now I go into logarithms and all the math and all that sort of crap but there are some advantages as you'll see to talking in terms of DBS instead of 0.5 or one ten-thousandth or 1 million times a 1 one billionth of something you're better off talking in terms of DB when it comes to engineering and really that's all there is to it d B's are easy it's just a ratio of one number to another number usually a reference number a reference level like 1 volt or you know 1 milliwatt or something like that as we'll go into but D B's are no more complex and that is just another way a more convenient way sometimes of expressing a ratio of two numbers now there's two different types of formula one is only for power when you're talking in terms of what's okay power is the formula the DB ratio is 10 times log of power 1 divided by power 2 now this power 2 is actually can actually be a reference level in fact that's basically what it is you're comparing this number to this reference value and it gives you a ratio a power ratio in DBS and the same for magnitude voltage and current the ratio in DBS is equal to 20 times log voltage or current on the second voltage or current and once again this is the bottom one is a reference value that you're working from and that's all there is to it these two formulas you can do everything in DBS in engineering and that's all you need to know simple and of course there's different types of logarithms when we're talking about DBS we're always talking in terms of a base 10 logarithm not a natural logarithm to base e ok let's go through a simple example that you might get in typically in electronics let's say you've got an amplifier we're like this and you feed in a fixed amplitude sine wave it's conk let's just assume it's absolutely constant over all frequencies the amplitude is constant okay and you measure the amplitude of the output sine wave aren't with either a multimeter on oscilloscope or anything you like now watch it let's say you measure that at one kilohertz that's your reference level for example and you might measure one volt okay so remember the v2 over here is your reference level so that's one volt okay whoop one volt and let's say you wind up the frequency on your function generator and it goes to 100 kilohertz or something like that and you might measure a value now of 0.5 volts okay so that's ooh that's your other number so now you've got these two numbers and you want to compare them well obviously the signal is down by 0.5 okay it's you know it's 1/2 right and that's a very convenient number to work with but it doesn't sound very funky right in electronics you've got to have things we talk in terms of DB and because it's just nice up when things get more complex so let's convert it to DBS you got point 5 volts on one volt okay and you do log 20 times log of that and it's actually equal you'll find if you get out your calculator which you won't have to do which we'll talk about okay it's actually minus 6 minus 6 DB so you can say that that signal is minus 6 DB at that frequency compared to the other frequency or in other engineering parlance you say it's 6 DB down ok let's take a look at an example where DB start becoming useful okay let's say that we've got a system here with three amplifiers in series ok three amplifiers cascaded and the first one has a gain of times two okay the next one has a game of type gain of times 10 and next one has a gain of times 31 point six now if you want to work out what's the total gain out from input to output okay you've got to multiply these together and well that's not too hard okay with these numbers but they could be weird they could be harder numbers okay and you've got to multiply them you get a total gain of 632 but if you convert these to DBS you'll find it's actually easier so if you convert these ratios into DB's times 2 is actually 6 dB if you use the formula which we had before times 10 is actually 20 DB and times 31.6 happens to be 30 DB and where we multiplied these before the good thing the really neat thing about DBS is that now you just add them together 6 plus 20 plus 30 is 56 DB and that's your total gain is and if you actually convert 50 6 DB back into using that formula in Reverse back into a ratio you get 632 and that's the advantage of DBS is that you can actually instead of multiplying things you add them in DBS and the same as dividing things in in regular ratios in DBS you subtract them so it's easier to do calculations and the numbers are smaller and more manageable let's take a look at a really good example we can see the benefit of DBS and in this case it's DB scaling now this is a spectrum analyzer you're probably familiar with the spectrum analyzer it displays amplitude versus frequency now if you've got say a 1 megahertz signal into your spectrum analyzer you expect to see a line on the display like that and if it's 1 volt amplitude you expect to see a vault now what you might want to do is while I typical thing with the spectrum analyzers you want a view where the noise floor is now let's say the noise floor is at 10 micro volts for example ah now 10 microvolts okay that's one 100,000 of one volt so if you've got a linear axes on your volts display like this you have to divide this into a hundred thousand little you know things and then your noise is going to be so far down here it's it's one 100,000 okay it's less than the width of the one fiber on the tip of this pen it's tiny okay so you can't possibly see it you won't be able to display large values there sorry small values of noise in at the out on the same scale as large values now here's where DBS come in if you convert that into if you make this into a log scale okay in DBS and DB v okay one vote okay that's zero DB is your reference level and then you divide into -10 DB minus 20 and so on and you get down to say minus 100 down here now a hundred thousand 10 micro volts which we were looking at before is actually if you convert it it's actually minus 100 DB so you will actually be able to see it you'll see your noise down here and you'll see your signal like that and bingo it allows you d be scaling allows you to view small signals at the same in the same space as large signals and that's the real benefit of DB's one of the huge benefits okay let's give you yet another example of a frequency response of an amplifier which is a very typical application and let's say you want to plot the frequency response okay you've seen the frequency response of an amplifier it might look something like that okay now if you know it rolls off at some low frequency and it rolls off at some high frequency and it's gain is pretty much constant at you know one or one volt say right in that you know somewhere in the middle now this and actually span frequency responses of amplifiers can span very large ranges or what we call lots of decades now it can span anywhere you know from basically 1 Hertz up to say 1 megahertz and that is six decades if you try and plot six decades if you have one megahertz up here if you divide that once again into a million little things you can't see anything down at this end down here if your signal starts rolling off at you know 10 Hertz or something like that it's kind of your actual response is going to look something like this and you're actually going to see something like that now you can't see any detail down here so what you do is you compress it using decibels into what are called decades so that's one Hertz okay one Hertz and then you go to ten Hertz and then you go to a hundred Hertz and then you go to one kilohertz and then you go to 10 kilohertz a hundred and so on these are decades and if you have this scale your x-axis in DBS or what you call it or what they call a log scale as opposed to a linear scale then it allows you to once again show our detail at the extreme ends of your frequency spectrum so it allows you to once again view large numbers in the presence of small numbers and that's the beauty of DB's now I actually put up two real screenshots here for you of two frequency responses now you can see this first one this is using a linear scale and well look at that right from 0 to 1 megahertz it's you know what is that right it's certainly not linear like that is not a straight line and you can't see any detail down at zero megahertz right or zero Hertz you can't see any detail at all but if you take that same at the exact same frequency response and you plot it on a log axes or a DB axes with six decades like this bingo that's the exact same data and you can see that it starts rolling off at about a hundred Hertz and goes down and in this case it's 25 DB down there we go we're using the jargon 25 DB down at around about that one Hertz figure and you can see it's about 20 DB down at one megahertz and you'll notice that the slopes of those lines are actually straight they're linear when you plot them on a logarithmic axes go figure and that allows you to say - that allows you to easily determine the roll-off of an amplifier in this case it's going to be about our 20 odd DB per decade and there you go okay let's look at some rules of thumb some ways you can work with DBS without using your silly calculator okay these are numbers ratios which you should remember which will make working with DBS real easy for you now if you're talking in terms of magnitudes which is uh probably most I do say most of the time in electronics when you're dealing with voltages and and signal levels and things like that you'll be dealing with magnitude so but you'll be using the 20 log formula to remember that now what you have to remember - 3 DB is not point 707 which is 1 on the square root of 2 you may have seen that before it might be familiar to you now that's what's called the half power point and we'll actually see that down here - 3 DB for a power is not quite a factor of 0.5 now it's called the half power point because the basically if that voltage into a resistor is going to be half the power what it is at if you put one volt into a into the same resistor so that's why they call it the half power point and they use that for things to determine like the minus 3 DB bandwidth of an oscilloscope or an amplifier they use it's kind of an industry convention to use the half power point but it's actually not 0.707 times the voltage now the other one you've got to remember is 6 DB now - 6 DB is not 0.5 so it's half of something ok now similarly plus 6 DB equals 2 times something so if something's double something else if you eat you know if 2 volts is twice as high as 1 volt then it's 6 dB easy and the same thing with minus 20 DB it's not point 1 and conversely so it's 1/10 of something conversely plus 20 DB equals 10 times something or an order of magnitude bigger so something there's another engineering buzzword for you order of magnitude is ten times bigger or one tenth now that's real easy to do now okay why why do you have to remember these because it allows you to do simple basic calculations let's say if something is a thousand times bigger than something else in magnitude okay don't get out your calculator and plug in a thousand and do the log and everything no you can just add DB's remember plus 20 DB is 10 times so 20 each decimal point 40 60 so a thousand equals 60 DB easy and the same thing with let's say you had one milli volt okay one milli volt is same thing 20 40 60 DB equals minus 60 DB piece of cake now if you're talking in terms of power okay or intensity like sound intensity or something like that then minus 3 DB is half the power or the same width plus 3 DB equals double the power twice the power and minus 10 is one-tenth the power and same again +10 DB equals 10 times the power simple rules of thumb you don't need your damn calculator think you can do D B's in your head and you can impress people because a lot of people just don't realize that he can do D B's simply by you know how many decimal places and adding them up and remembering a few simple things now I mentioned before that D B's are just a ratio they don't have any units and you might see something like this you might see minus 6 dB well what does that mean on its own well it actually means absolutely nothing it's a useless bit of information because you can assume it's a magnitude for example in which case is going to be not point 5 but not point 5 of what I mean half a rabbit what you know it could be anything so it's useless bit of information so you can actually get a reference which are pens to the end of it in this case you might see minus 6 DB V and in this case V is actually an industry standard thing and it's one volt so in this case minus 6 DB equals not 0.5 minus 6 DB V use nor point 5 volts and the same thing again you can Owosso that actually means something on its own it's actually got inherent value because there's a reference attached to the end of it and you might also see something like minus 3 DB m in this case M is an industry standard reference for 1 milli watt so it's minus 3 DB relative to 1 milli watt which is going to be not 0.5 milli Watts like that easy and there's a whole slew of these industry standard terms out there there's you know this one probably a couple of doesn't stand at once but there's hundreds or you can even make up your own I've made up stuff that I'm sure nobody's ever done before so just go check him out DB references now there's only one tricky thing with logs that you have to remember we have to be aware of you've got to be aware of whether you're working with a power or a magnitude in this case DB V as well engine is a volt sorts of magnitude so you know you've got to use the 20 log formula you know you're dealing with that formula but if you see DBM as I said is milli watt so it's a power so you know you're going to be working with the 10 log formula so you know just be careful cuz that's really the only major trap with D B's so start using D B's in your everyday life as well take the classic half a glass of water is it half full or is it half empty are you an optimist or a pessimist well I'm an engineer so it's 6 DB down Cheers and yes check it out this is a triple five time a t-shirt in the cool it's part of the new EE vblog merchandise pick yourself up one

Channel: EEVblog

Views: 196,270

Keywords: db, db's, decibels, log, logorithm, logorithmic, scale, engineering, electronics, amplifier, response, frequency, bode, plot, tutorial, how

Id: mLMfUi2yVu8

Length: 20min 48sec (1248 seconds)

Published: Sat Dec 12 2009