• # EEVblog #49 – Decibels (dB’s) for Engineers – A Tutorial

Are you a pessimist or an optimist? Dave explains dB’s and how they are useful for us engineering types.

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## EEVblog #1054 – How an Analog PC Joystick Works

How does a PC read an old school analog joystick? It might be more interesting ...

• What happened ?

I watched #49 and a few hours later it was gone. Now it’s back again. Was I hallucinating ?

• Andreas Dahl

alternative ending… 🙂

• Yeah, I need more sleep, my mind is going bonkers 🙂

• Oh and here’s a blog post at “Make” about the engineer who developed the NE555 timer chip.

http://blog.makezine.com/archive/2009/12/make_electronics_and_the_555_man.html

• walterdelbono

jaja…

awesome…

🙂

• Where I come from “jaja…” is easily interpreted as an equivalent to Bender’s (futurama) favourite line:

“Bite my shiny metal A..”

• Juanma

Hi David!

When you talk about dBm’s you say that the reference is one milliwatt, so -3dBm are 0.5 times a milliwatt, but in your video you write two times that

-3dBm = 0.5 W

Keep up the good work!

• Nice explanation of the decibel measure. I remember this from my study for my amateur radio license.

• That explains why my old stereo amp seemed to have its volume scale drawn “backwards”, with the numbers getting “smaller” as the volume went up… compared to normal amps where the volume starts at “0” and goes up to “11”.

The scale on the volume knob was showing me the number of dBs below the maximum power output of the amp, not how “loud” it is compared to being switched off.

• Andrew

Dave,

you got all your dBm’s wrong, by no less then three orders of magnitude 🙁 Which is, by the way, on of the great dangers of dB. If you get them wrong, it is usually wrong big time.

As you said, dBm is with reference to 1 mW. But then you equate -3 dBm with 0.5 W. 0.5 W would be 27 dBm, not -3 dBm. -3 dBm are 500

• I also have to take objection with your usage of dB both as a unit (right) and as a value

• Andrew

I am well aware that the anglo-american world likes to be sloppy with units and symbols, and likes to teach sloppiness right from the beginning.

That doesn’t mean it is a good idea to adopt. Rigor in notation is an aid not a burden when one anyhow has problems to sort ones thoughts.

I bet these guys wished they were a little bit less sloppy with their units and notation http://mars.jpl.nasa.gov/msp98/news/mco990930.html

• I am well aware that the anglo-american world likes to be sloppy with units and symbols, and likes to teach sloppiness right from the beginning.

That doesn

• Hallo Dave,

great tutorial. All of these rule of thumb values are rounded by the way…6db would be a ratio of 1.99526 (also rounded). Not trying to be a nitpicker. 😉

Greetings from Germany!

• Brian Hoskins

No no no Dave. When you’re an Engineer the glass is neither half empty or half full. The glass is twice as large as it needs to be 😉

Good blog. The only thing I have to add is that dBm is actually referenced to 1mW @ 600Ohms. I’m not aware that it’s ever used at different impedances, but that’s something to keep in mind.

Also, most multimeters that I’ve used only work in dBms. I’ve often wondered why this is, because I’ve more often found dBVs a more convenient expression.

The Agilent (or HP) 34401A can work in dBs, but you have to set the reference point first, it doesn’t to my knowledge use 1V as its reference. You can use it to do roll off measurements, but you have to take a reference at your centre frequency first. The only dB measurement the 34401A is capable of directly measuring in is dBm, and you can actually set different impedances as well. 600Ohm is default.

I have often found with other multimeters that they only take dBm measurements. Bizarre if you ask me, because I’d prefer dBV measurements most of the time!

Once again, good blog

Brian

• Strictly speaking it’s only dBu which is referenced to 600ohms. i.e. 1mW into 600ohms. dBm can be used on it’s own to mean just 1mW regardless of the impedance.

• Brian Hoskins

Dave,

I think you have that wrong. It is dBm that is referenced to 600Ohms. My understanding of it is as follows:

dBu is like dBV except it is referenced to 0.774V instead of 1V. dBu is not referenced to any impedance.

dBm is a power measurement referenced to 1mW, usually at 600 Ohms impedance (but can be referenced to any other impedance you want.)

dBu is the same as dBm when dBm is referenced to 600 Ohms. This is because the Square root of 600 Ohms x 1mW = 0.774V.

If I’m wrong, please show me how.

Brian

• Andrew

L_dBm is not in any way referred to 600 ?.

This L_dBm @ stuff is a crutch done by voltmeters, because L_dBm ia a power relation, but voltmeters really measure voltage, not power (voltage times current).

To convert the measured voltage into a power value the voltmeter either needs the current or an impedance. The convention is to throw an impedance |Z| at it. Then you have

P_2 = |V_2|**2 / |Z|
L_dBm = 10 log(P_2 / 1 mW)

This is kind of a voltmeter faking it for the convenience of the user, because it can’t measure the real power.

If your voltmeter can’t display L_dBm it is not the end of the world. Just run the above equation.

• Brian, you are not wrong. For many people and areas of the industry dBm will indeed be always referenced to 600ohms.
In other areas like RF for example it might always be referenced to 50ohms.
Yet in other areas (like in most of my experience) is it either not referenced to anything, or implies whatever system impedance you are using.

I don’t like to quote Wikipedia too much, but for example:
http://en.wikipedia.org/wiki/DBm
The only reference to 600ohms is in terms of dBu.

I’m sure you’d be able to find textbook references that work both ways. The Art of Electronics for example says it’s “1mW into some assumed load impedance, usually 50ohms, or 600ohms for audio”

I know quite a few people (and have done so myself) who will append the reference impedance to the dB value e.g. -3dBm(600R) so it’s absolutely clear that it’s specifically referenced to 600ohms.
If you don’t see any such reference then it’s usually (in my experience) assumed to be not referenced to any impedance.

As Andrew said, many voltmeters that display dBm are a classic example of this confusion, they have to assume 50 or 600ohms because they can’t measure true power.

YMMV.

• Brian Hoskins

Andrew / Dave,

Hmmmm okay. Well, my understanding of dBm seems to be correct because I wasn’t actually saying that it’s always referenced to 600 Ohms, I just meant that it’s *usually* referenced to 600 Ohms (and certainly almost always is with multimeters).

However, I do appear to be wrong in my interpretation of dBu. I thought dBu was a measure of magnitude, the same as dBV, except with a reference of 0.774V instead of 1V.

If I understand you correctly (Dave), you’re saying that dBu is in fact a power measurement, referenced permanently to 600Ohms?

I’m going to have to look this up now. I’ll check your link, thanks for that!

Brian

• All of these rule of thumb values are rounded by the way

• Dave,
Super GREAT video! I just had to watch it twice it was so good. I’m going to post a link to this one from my blog.
Only a master could explaining such Mathematics in such an easy to understand way. Normally people that try to explain things they themselves have not yet mastered tend to explain it in the most complicated way possible. Maybe they do this to make themselves seem or feel more intelligent. Your easy to understand video on dBs demonstrates you are a master in Electronics and Mathematics .
Todd

• Thanks Todd.
Master in electronics – in some ways, master in mathematics – never!
There is always more to learn in every area of electronics.

Yes, many people like to complicate things, and make the explanations so precise and complete that it bamboozles the beginner. I fully expected people to nit-pick my tutorial for not being rigid and precise enough (see Andrews post as an example, not that there’s anything wrong with that, he’s entitled to his opinion), but it’s water off a ducks back. If my “good enough” tutorials get the concept across to people, then that’s much more important than being rigid, precise and complicated.

Those who disagree are more than welcome to post a video response with their own tutorial, in fact I encourage them to!

• For what its worth, we actually hear audio close to what you have shown with the gain vs frequency plot. It just works out that we tend to perceive a factor of ten in audio power as sounding about twice as loud. Thats why they call it a “bell”. A fft on a log frequency scale shows the enormous dynamic range our ears have over magnitudes of power and frequency discrimination.

• TrentO

Dave,

As one of those beginner-wieners that this segment was directed towards, I sincerely thank you for all of your efforts. Your instructional videos have dramatically increased my understanding of electronics and electronics engineering as a profession. I consider my life enriched by the knowledge that you choose to share via this medium.

I feel compelled to write this, because of some of the negative comments left in this forum– much of which I believe is picayune-bullshit. I _am_ one of those guys that asked for a piece on dB’s and what they mean, and you delivered! For some dickhead to say that you’re “wrong” for using dB instead of ‘L’ is utter and complete nonsense. The tone of many of the professionals that participate here, have the effect of completely ‘turning-off’ people like me– perhaps those most representative of the audience at large. If the intent of these individuals are to force strict adherence to the raw standards and specific method of communication (and teaching) of the EE disciplines– may I suggest that they go back to university. It is not what we expect from watching videos on YouTube. I too would like to see the critics out there, produce a video explaining this better than Dave. Let’s SEE how many in the audience find the content informative AND entertaining enough to watch 20+ minutes– Dave pulls this off like a champ.

-Trent

• Thanks for the support Trent.
“picayune” I have to admit I had to look that one up, looks like it’s a Yanky saying!

• TrentO

Dave I must protest!!!

“Yanky” is not correct according to the EIA/TIA or ANSI published specification. “Yankee” or the correct shortened form, “Yank” is most appropriate. According to the formula–

Yankee = Log * 20 (British * Ass Savers * WWII / 1776)^2 / (Hated by * French) – (But ‘Pierre’ didn’t walk on the moon)

You will see that the use of “Yanky” infers that those of us from these-here United States are merely wankers… In reality, that could only apply to 50% of the general population (at most.)

I hope you will correct this oversight as your earliest convenience.

Sincerely,

-Trent

• Sean

Actually more of a Cajun saying I think as most of the usage is Louisiana and across the South (Not Yanks). ;^)

Thanks for the video, nice to have a refresher.

• Lionel

“Picayune” is a very tiny typeface. I’m not sure which usage came first…

• Ray Jones

Hi Dave,

I was a bit disappointed why you did not describe *why* for a voltage it is 20 x log10(ratio).

As you stated, dB is used to refer to power ratios.
Now to get power from a voltage, you need to square the voltage, and divide by the impedance.

So in reality it is 10 x log10 (VxV / reference).

It just so happens that logarithms make it real easy to skip the squaring part, simply by using 2 x 10 x log10 (V/reference).

As for dBm – I hardly every use 600ohms, 50ohms for RF thank you very much 🙂

0dBm however *always* is 1mW into the nominal impedance – that’s where the ‘m’ comes from.
However, the voltage observed will vary depending upon the impedance of the circuit under test. For RF this is 50 ohms, 600 for audio (phone lines)
A multimeter may have a dBm scale, but you will find it is assuming a 600ohm circuit impedance (and this was shown on the old moving coil meters)

I work on weather radars, and they have a huge range of dBm – some are +88dBm (50ohm) Transmitter power, and have a receiver sensitivity of -112dBm (50 ohm)
200dB difference in power or 10^20!!!

• Brian Hoskins

Hi Ray.

It has been my experience that pretty much nobody has an application for 600Ohms these days. Even in audio circles, 600Ohms seems to be a little used impedance. I do sometimes wonder where this figure came from in the first place! Maybe it’s to do with some legacy Electronics from years ago that did make use of 600Ohms impedance (like your telephone line example).

On that subject, it has also been my experience that there is nothing particularly special about 50Ohms in RF circles. I once spent a long time questioning this impedance value, assuming there was some special significance to it, but apparently there is not. 50 Ohms is still widely used and accepted in RF circles though, unlike the 600Ohms which I hardly ever see used in modern audio designs.

Brian

• Brian Hoskins

By the way, I do understand the need to use some accepted impedance value in RF designs (so that lines can be matched to limit reflections etc) but I never understood why it was chosen to be 50 Ohms and always assumed there must have been some special significance for it, which I now believe there is not.

Brian

• Jim

Choice of 50 ohm for RF is historically related to the properties of air dielectric coaxial cable.
Lowest attenuation occurs for 77 ohm cable, maximum power handling for 30 ohm cable.
50 ohm was chosen as a good compromise.

For more details see:
http://www.microwaves101.com/encyclopedia/why50ohms.cfm

Jim

• Brian Hoskins

Aha!!

Thanks Jim 🙂

• Jon

Thanks Ray, must confess I was left wondering about the difference – your comment explained it perfectly!

• George Herold

Thanks Ray, I was wondering when/if someone would mention this. For me dB is always power. (V^2 = power… the factor of 2)

Dave.. love the video blogs.

George H.

• Alex

!!!!!!!!!!!!!!!!!!!

Hello

YOu make mistake at 19:20 minutes, -3dB is not 0.5, but it’s 1/Sqrt(0.5)

!!!!!!!!!!!!!!!!!!!

• Alex

Ups, i didnt see you mention for power, so 10*Log….. 🙂

Great, keep doing great job, MAYBE you can “represent” PIC, ARM….

• Seis

Nice tutorial wonderful explanations about how much handy dBs are. Congratulations on your video blog.

Thanks Dave. I’m a Radio Amateur, but not an engineer. I love these types of tutorials and have listened to most of your video blogs. This one was particularly great (also liked the one on the Arduino).

Keep up the good work.

Oh…and from all us hams out there…yeah, 50 ohms is “it.” 🙂

• Cuno

The 600 ohm level comes from the telephone technologies.
HP had build a signal generator that the tech’s used to check the lines and frequency response.
The 0dB level choosen was simply the max output voltage of the generator. It is arbitrary but became a standard because the tech’s requested that newer Signal Generators had the same output so they could compare old and new measurements.
I read this history somewhere on the web.

The 600 ohms seem strange for audio but if you are dealing with long transmission lines this becomes important.

• hi. i’m total blind of this term db. but from what i got in the video stated db is a comparison to something else, ie its relative. and i think mathematic is not about comparison or relative, math is about absolution, 1+1=2, thats it. so this db thing, is actually a concept, not mathematic. its like the concept of length, some people use cm, some ft, inches or other. so if you said it should be compared to 1mA, 1mW, 600 ohm, 0.774V or some shit like that, i think that is your own preferences, it is specific to some particular community or field. now i think i can apply the db concept in mass, length, force etc in my mechanical eng knowledge, cant i? thanks alot for the info dave.

for those who want the super duper precise information on mathematical theoritical of db, i suggest you go to uni or buy some super duper electronic books. dave have mentioned/advised the art of electronic, GET ONE! and if you have any complain in it, go complain the author or any proffesor around!

i think this blog is more on practical, not theoritical or academic sh*t. i have 1-2 foot thick EE books and i never successfully finish them for soooo many years. simply by watching eevblog, releasing some tension in my synaptic networks, very good blog!

• Therian

thank you

• Awesome post! I think it would be great, and beneficial to most, if you could do a post on a list of things every Electrical/Electronics Engineer should know!

• vk6zgo

Dave, I think the frenetic pace of your blog left a few people bobbing in your wake!

I will try to toss them a lifebuoy (Or an anchor).

A 1kHz tone is applied from a 600 ohm source , at a level of 0dBm,to an
audio line amplifier,with 600 ohm input & output impedances.( I will use the letter “ Z” from now on)
The amplifier is terminated in 600ohms.

If a level meter set to high Z input is bridged across the input, it reads 0 on the dBm scale,& approx
774.6 mV on the voltage scale.

Using the power formula :- P=V^2/R this gives (774.6 x 10^-3)^2/600=10^3watts,or 1mW.

The meter is now bridged across the output, reading: +30dBm,& 24.495volts approx.

Again applying the power formula, output power is 1watt.

Using both dB formulas,

10 log 1/10^-3 = +30dB,

20 log24.495/774.6 x 10^-3 = +30dB

OK, at this point we decide we really want our amplifier to drive an 8ohm speaker instead, so we connect a (perfect) 600 ohm to 8 ohm transformer across the output.

The voltage across the 8 ohm termination reads approx 2.828 volts.

Using these values in the power formula still gives Pout=1w,so 10 log p1/p2 gives 30 dB of gain.
Let’s try 20 log v1/v2 —– 20 log 2.828/ 774.6^-3=11.248 dB???????
OK, we’ve learnt something— the voltage dB formula only works for equal impedances!
Some folks are a bit concerned that 600 ohms are not commonly used in modern audio equipment, & someone said, “What’s this about 774.6 mV”??.
Modern amplifiers have large reserves of gain,so do not have to be impedance matched for maximum power transfer,so designers found it was easier to make amplifiers with low Z balanced outputs,& simply bridge the existing 600 ohm loads across them,than to make amplifiers with 600ohm outputs.This maintained compatability, because as long as the following device saw 774.6mV across the input,it was quite happy.Terminated dB meters still read the level as dBm.
RF equipment commonly uses either 0dBm= 1mW in 50ohms,or 1mW in75 ohms.The cheap trick used with audio isn’t used with RF as there are other reasons for Z matching.

vk6zgo

I learned a few things here, and for that I thank you. It’s wonderful that you take the time – so much of your own time – to teach unseen stranger like me the “facts of life” as it pertains to electronics. Interesting, fun and informative.

Things are becoming clearer with every episode you make.

Rock on.

• chuck

At 14 min 12 seconds into the video you say that it’s 25db per decade.. but I don’t follow..

Isn’t the signal dropping 2.5 db every decade (10 hz)?

Or perhaps the screenshot doesn’t show clearly on the video?

• chethan

excellent..really helped.

• Ricardo

Nice explication… I like it

• This is one of the best explanations of dB’s I have ever seen… or as I like to think of it, the power of logarithmic scaling 🙂

I wish I had this video when I was learning this over 10 years ago 🙂 Not only did you explain it quite well but you backed it up with a solid explanation and illlustration of the benefits.

In other words you didn’t just say

“learn this, you will need to know it”

You said..

“learn this, you will need to know it, here is why you will WANT to know it”

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