#136: What is a dB, dBm, dBu, dBc, etc. on a Spectrum Analyzer?

or in this video we're going to try to answer the question what is DBM or DB mu or DB mV and why do we use these various units on a spectrum analyzer now of course to answer that question the first question we need to address ourselves with is what is a DB a DB or a decibel is a logarithmic expression of the ratio of two power levels and the general equation is just like this it's ten times the log base ten of the ratio between two power levels we'll call it P 1 and P 2 it's important to note that it's the logarithm base 10 not the natural log which on your calculator is typically Ln that's usually spelled out the capital letters log4 the log base 10 so we're going to ask the question what is a DB and why do we use them and how can you relate them to things like volts and watts and things like that that you're used to looking at or dealing with with an oscilloscope that electronics the definition for a decimal or a DB is at 10 times the log of the ratio of two power levels not voltage levels but power levels so we have a look at it this way as a couple of examples so let's say p1 is a quantity of 1 say one watt p2 is 1 watt the ratio between them is 1 if you punch that into your calculator the log of the value 1 gives you zero so zero times 10 is zero let's say that P p1 was twice the value of p2 the ratio would then be 2 that would be 3 dB you'd do that in your calculator if p1 was 10 times the value of p2 the ratio would be 10 and I would be 10 DB now there's a let's say the p1 was 1/2 the value of p2 then the ratio would be 1/2 and that would be minus 3db so what you can see here is that a factor of two increase was a plus three D be a factor of two decrease or one half was minus 3 dB so just take some oddball numbers like 7 point 2 4 P 1 1 point 6 4 P 2 the ratio is four point five and if you punch that into your calculator you get 6.5 DB as it is the ratio between these two power levels so a couple of other interesting things is if you take a look at say let's say that p1 was a hundred times p2 that would be 20 DB a thousand times that's 30 DB so you can see for these three cases say from ten to a hundred to a thousand we multiply by 10 10 10 so we go from 1 to 10 to a hundred to a thousand each of those is multiplying by 10 but the DB value is increased linearly by tens of 10 20 and 30 so while one way to think about that is that logarithms will turn multiplication and division into an addition and subtraction that's kind of the reason why we use logarithms years and years ago before we had calculators ok the other convenient thing about this is that logarithms can be used to express or to view large variations and ratios and to be able to see them on a reasonable scale we can we can see for example that we have a ratio of 10 to one or a hundred to one I'm going to view them on the same scale it's just going from zero to 10 to 2230 so even if we had a thousand to one ratio we want to look also another quantity that had 100 to one ratio we could see them on the same scale very easily and we'll see if we try to look at things linearly without using this logarithm expression that that would be very tough to see we're going to look at the the scope in a little while and you'll see a really good example of that so here's a quick example of how these large variations and ratios can be expressed on a reasonable scale on an oscilloscope the relaxes so that the displayed voltage is linear so I've got a sine wave here and if I reduce its amplitude by 10 dB we can see that how small that signal got by reduce it by another 10 DB okay now I can still see it if I reduce it by another 10 DB so that's 30 DB lower and I can just barely see it if I go to say 40 DB I can't even see that change on this same scale okay so I can really get you know typically about 30 DB maybe a little bit a little bit more on a scope screen to be able to see that on the same scale let's move the signal over to the spectrum analyzer I'll turn the spectrum analyzer on and turn the time domain off so there's that signal represented in the frequency domain on a spectrum analyzer if I cut its amplitude by 10 DB alright I can still see it very easily 20 DB 30 DB even 40 DB very easy to see that signal still on the screen so even if I go 50 DB 60 DB or even 70 DB 70 DB is starting to be way down in the noise there but that is now 70 DB is a factor of 10 million okay so I've made that signal 10 million times lower in power and I can still see it would be no way to see that on an oscilloscope screen so this is why DBS are used when looking on a spectrum analyzer because it allows us to view maybe large signals in the presence of or excuse me be able to simultaneously view large signals and small signals on the same scale even if the power of those signals varies by tremendous amount so we can see if this signal was sitting up here at full power if I had another signal that was sitting down here 60 DB down I'd be able to see that which would be very very difficult or impossible to do if the scale was linear so that's why we use dB so let's look at a couple of examples of how we use them and where so these other units come from like DPM and DBU and that kind of thing now we stated earlier that since the DB is a ratio it's not an absolute quantity like a watt or a volt so for example we can say that hey this signal that we're looking at is 3 DB greater than that one okay because that's a ratio but we cannot say that this signal is 3 DB that doesn't make any sense because DB is in 2 unit or isn't an absolute value DP is always a ratio so how do we use it to measure absolute quantities so in order to measure an absolute quantity we must specify or imply a reference like we did here saying 3 DB greater than some value right so an example we can always say that hey this signal is twice as big as X or the signal is half the size of Y all right knowing the reference okay the ratio then becomes an absolute value because if we know what this value is if the signal is twice as big of it we know how big that signal is so once we know the reference or we imply a reference okay then we can turn a DB into essentially an absolute value and this is where the suffix comes in on the DBS so when you see say DBM that's implying that the reference is a milli Watt and you see DB you it's implying the references of microwatt and typically the W is omitted if the with that being omitted the the assumption is and the convention is is that we're talking about power so that would be watts if you see you know typically if you're not going to be specifying a reference as a power level in watts but you're going to express it in volts then that typically would show up here so DBM V the reference is a millivolt so we're going to say that this signal is x times larger than a millivolt where x times smaller than a microwatt or x times larger or smaller than a milli watt so the suffix then can turn a DB into an absolute quantity like DBM so DBM is an absolute quantity that says we're going this power level is x times larger or smaller than a milli watt so we can calculate that out to a specific quantity so that's where these particular values come in so let's run some examples on the instrument and show you what we're talking about okay let's use this example that we have on the screen this is a 10 megahertz signal that's measuring just about 950 milli volts peak-to-peak so if we run that calculation that 10 megahertz signal at 950 million to peak it is being terminated into 50 ohms that's kind of an important thing too and we're going to be measuring and comparing power levels they all have to be with respect to the same load so in this case we're going to consider 50 ohms so if the peak to peak voltage is 950 millivolts we need to calculate the RMS voltage in order to calculate power so that's simply the peak to peak voltage divided by two times the square root of 2 so if we do that calculation the RMS voltage is 336 millivolts therefore the power in the 50 ohm load is equal to the RMS voltage squared divided by the load resistance so that's 0.33 6 squared divided by 50 or 2.25 6 millions so to express this value in DBM the reference is a milli watt so we basically say the value in DBM is equal to 10 times the log of 2 point 2 5 6 milliwatts divided by a milli watt that's a reference and that gives us 3 point 5 3 DBM so let's see if that will that's what we have we'll move the signal over to the spectrum analyzer intimate and turn the spectrum analyzer on we'll turn off the analog trace and so there's the signal we're seeing on the scope we took a look at the measurement there goes right at 3.5 DBM that's pretty darn close point zero 3 DBM different but so that is basically what our answer is if we want to express that value in DB U or DB relative to a microwatt then we would just run the calculation here to say it's 10 times the log of two point two five six times 10 to the minus three that's milli watts divided by a microwatt which is one times 10 to the minus six and that would give us 33 point 5 3 DBM so we'll hit the amplitude key here change the vertical units I'll use the knob here to change that to DB microwatts or DB u we take a look there we are thirty three point five and we expected 33 point five three that's basically the same number so now you can see how those numbers relate to the voltage that we measured on the scope so what about comparing voltage ratios can we use DBS for that well a DB like I said by definition relates to power so we have to calculate it against power but we can still kind of do this so here's how it works so if we're going to compare power levels we're going to basically take the voltages of interest and compute the power so the power from voltage number 1 is V 1 squared divided by R the power of our reference value is V 2 squared over R now we're going to assume an equal R for this for this video which is almost always the case so let's simplify this equation so when you have a fraction over a fraction you can invert and multiply so that's the same as 10 times the log of V 1 squared over R times R over V 2 squared the RS cancel out so you're left with 10 times the log of V 1 squared over V 2 squared that's the same as 10 times the log of V 1 over V 2 that will quantity squared now you may remember from your high school algebra that when you have the logarithm of a quantity that has an exponent the exponent can come outside and multiply against the front so that would be the same as having two times ten times log of v1 over v2 and that's why we wind up seeing the expression work of computing logs with respect to voltages where it's 20 times the log when you're comparing a voltage ratio it's ten times the log I need to a power ratio 20 times the log to the voltage ratio and again this is all assuming an equal load impedance ok the equal are all right now in our case we have this 950 milli volt peak-to-peak signal and that can be expressed say in DB relative to a millivolt or DBM V we have to compute the you know use the RMS value that we computed on the previous page so we say the DBM V is 20 times the log of the RMS value of that which is 336 millivolts divided by a millivolt and that gives us fifty point two five DBM V let's take a look let's change the unit here we were looking at about 3.5 DBM before let's move this unit down to DB Envy and we're looking at 50 point 5 DV M V and that's basically what we calculated so you may ask well what about DBC you know I always see DBC when we're talking about spectrum analyzers what does that mean what's the reference there well DBC basically means that it's decibels relative to some carrier power level now this is very very common in RF applications because what this might do is to say how large is a distortion component with respect to my main signal okay so we often will call that D B C or D B relative to a carrier level let's take a look at how we might use that on this analyzer here so I've got this signal coming in here that set you know 10 megahertz about three and a half DBM and let's change the span I want to change my stop frequency here out to 30 megahertz and in doing that what I can see now is I see the my fundamental signal here okay ten megahertz plus 3.5 DBM I also see I look carefully here I can see there's a another tone down here it's actually the second harmonic coming out of my signal generator and that guy is down at Oh minus 53 minus 53 minus 54 DBM or so so that's the absolute power level of it but what might what might be important to me is how far down is that with respect to my carrier we can set the markers up here to be relative what reading markers so if I set that to be a relative or Delta reading marker what that will do is it will take this measurement here okay as my reference level and now when I go to make the other measurement here that shows that me shows it to me as DBC DBC means it's decibels relative to the carrier which is my reference point over here so it tells me that the second harmonic is in this case about 57 DB down from the carrier and that's typically what we'll need to know we'll typically use the absolute value for the carrier measurement and then use relative values or DBC values to look at other components with respect to our carrier level so that's what DBC means it's looking at other power levels with respect to some other level that you might be looking at as your reference on screen so I hope this video gave you a little bit of an idea of what the various amplitude units are that you'll find on a spectrum analyzer and why we use decibels in the first place or a logarithmic exper representation of amplitude on a spectrum analyzer you know the expression analyzer gives us so much dynamic range makes it easy to see signals that are a million times or 10 million times lower in power than another signal for example that would be impossible to see on the linear display that you get out of oscilloscope screen so we use a rhythmic representation of the power level to make it easy to visualize these things with to each other anyway thanks again for watching and oscillator

Channel: w2aew

Views: 252,225

Rating: 4.9698281 out of 5

Keywords: W2AEW, Tek, Tektronix, Decibel (Unit), dB, dBm, dBu, dBmV, dBuV, dBc, oscilloscope, spectrum analyzer, MDO4000B, mixed domain oscilloscope, amplitude, relative, reference, dynamic range, attenuation, gain, calculation, units, basics, tutorial

Id: 1mulRI-EZ80

Length: 17min 41sec (1061 seconds)

Published: Sat Mar 22 2014

Reddit Comments

[u/mahibak]

Thank you very much for this video. I never knew the relationship between V and dBm, and I now know that dBc exists!

Why is it written dBm, if it's really dBmW? just to save time writing it?

I also saw on the wikipedia page for high-sensitivity GPS that they can receive signals as low as -130 dBm, how impressive is that? I don't really have any idea how low that is, as I am still in EE school.

Thank you for your work!

[u/TheSignalPath]

And the full review of this instrument (nearly 2 hours long) featuring the measurement of an entire up-converter system can be found here: https://www.youtube.com/watch?v=gyzwS5Ozb7U&list=UUKxRARSpahF1Mt-2vbPug-g