Questions on Levels [Archive]

Adrian Tuddenham[_2_]

November 19th 10, 09:41 AM

PStamler > wrote:

> On Nov 18, 8:39*pm, Randy Yates > wrote:
> > > * 1. If you backtrack to 0 dB from this wikipedia article
> > > * *http://en.wikipedia.org/wiki/Line_level
> > > * the reference levels for dBu and dBV are 0.775 VRMS and 1 VRMS,
> > > * respectively. Is this correct? Are the reference levels I've given
> > > * here exact?
>
> No and yes, respectively. The reference level for dBu is actually
> 0.77459666924148337703585307995648V, according to my calculator --
> that's the voltage equivalent of 1mW into a 600 ohm load. The
> reference level for dBV is exactly 1V.
>
> > > * 2. Is there a standard for converting from dBFS to dBu? If so, *
> > > what is it?
>
> No. There's an informal standard used in the film industry and in many
> broadcast applications of +4dBu = -20dBFS, but it's never been
> codified as an official standard. The informal standard, though, is (I
> believe) based on an rms scale -- in other words, a tone that would
> read 0 VU on a VU meter calibrated to +4dBu would be -20dBFS. Correct
> me if I'm wrong on that last bit, but that's what I think is the case.

The optimum reference headroom (the difference between reference level
and full-scale level) would vary according to the application and the
equipment used. With lots of bits to spare, 20dB would be fine, but if
you were recording to 16-bit CD standards, you would have thrown away
20dB of your potential dynamic range and dropped your signal/noise ratio
to around 45 dB for average levels. (Digital noise sounds horrible, much
worse than analogue noise, so you really do want to keep clear of it.)

For something like A.M. broadcasting, a reference headroom of around 12
dB is more common and that is also quite satisfactory for 16-bit
recordings provided you are prepared to control the gain intelligently
on the very loudest passages. If part of the chain is in mono, there is
the further complication that two stereo channels can add to give any
level from much lower to 6dB higher, depending on coherence and phase.

For professional use, the system of marking the beginning of a recording
with a burst of reference tone (or a series of squeaks if equalisation
is involved) is the simplest way of ensuring the correct playback or
copying level.

--
~ Adrian Tuddenham ~
(Remove the ".invalid"s and add ".co.uk" to reply)
www.poppyrecords.co.uk

Arny Krueger

November 19th 10, 01:41 PM

"dizzy" > wrote in message

> Randy Yates wrote:
>
>> One other question: is there a specification on the
>> absolute maximum signal voltage magnitude for a line
>> level output?
>
> Most preamps will put out close to 10 VRMS, considering
> the typical +/- 15V power-supply rails...

One word: tubes.

Mike Rivers

November 19th 10, 02:14 PM

On Nov 18, 9:39*pm, Randy Yates > wrote:

> > * the reference levels for dBu and dBV are 0.775 VRMS and 1 VRMS,
> > * respectively. Is this correct? Are the reference levels I've given
> > * here exact?

Exact for dBV, close enough for engineering purposes for dBu.

> > * 2. Is there a standard for converting from dBFS to dBu?

No. This is a great point of confusion. You can't directly convert
them because they describe different kinds of units. It's like
converting the number of apples in a bushel to the number of potatoes
in a bushel. There are a few conventions, however, but mostly there's
things that you choose for yourself, not a standard to which a
manufacturer adheres. Back when people had VU meters and digital
recorders had readable meter scales and an adjustable input level
control, there was often a mark typically somewhere between -16 and
-20 dBFS on the digital meter that was the recommended point
corresponding to 0 VU. But it's rare to see that any more. If you're
working with 24-bit converters and material with fairly high dynamic
range, I'd recommend 0 VU (at whatever level that represents) provides
a record level of -20 dBFS. But it's up to you.

> One other question: is there a specification on the absolute maximum
> signal voltage magnitude for a line level output?

No specification or standard, but since most gear you'll find today
operates from a +/- 15 volt power supply, it's rare to find a maximum
output level before clipping much higher than +24 dBu. There are
exceptions, of course.

You'll find some discussion of these issues in the Gozintas and
Gozoutas and Meter Madness articles in the Technical Articles section
of my web site. http://mikeriversaudio.wordpress.com

Randy Yates

November 19th 10, 03:01 PM

Hi Paul,

Thank you for your answers. Comments below.

PStamler > writes:

> On Nov 18, 8:39Â*pm, Randy Yates > wrote:
>> > Â* 1. If you backtrack to 0 dB from this wikipedia article
>> > Â* Â*http://en.wikipedia.org/wiki/Line_level
>> > Â* the reference levels for dBu and dBV are 0.775 VRMS and 1 VRMS,
>> > Â* respectively. Is this correct? Are the reference levels I've given
>> > Â* here exact?
>
> No and yes, respectively. The reference level for dBu is actually
> 0.77459666924148337703585307995648V, according to my calculator --
> that's the voltage equivalent of 1mW into a 600 ohm load.

Ah, that's right - it's the voltage level that corresponds to 0 dBm (1
mW) when delivering to a 600 ohm load.

> The reference level for dBV is exactly 1V.

Got it.

>> > Â* 2. Is there a standard for converting from dBFS to dBu? If so, Â* what is it?
>
> No. There's an informal standard used in the film industry and in many
> broadcast applications of +4dBu = -20dBFS, but it's never been
> codified as an official standard. The informal standard, though, is (I
> believe) based on an rms scale -- in other words, a tone that would
> read 0 VU on a VU meter calibrated to +4dBu would be -20dBFS. Correct
> me if I'm wrong on that last bit, but that's what I think is the case.

There seems to be no universal agreement, but you are close to what this
guy says (under "Here come the numbers..."):

+22dBu = 0dBFS ==> +4dBu = -18dBFS.

I'm still not sure if that's FS sine or FS square.
--
Randy Yates % "Remember the good old 1980's, when
Digital Signal Labs % things were so uncomplicated?"
% 'Ticket To The Moon'
http://www.digitalsignallabs.com % *Time*, Electric Light Orchestra

Randy Yates

November 19th 10, 03:09 PM

Mike Rivers > writes:

> On Nov 18, 9:39Â*pm, Randy Yates > wrote:
>
>> > Â* the reference levels for dBu and dBV are 0.775 VRMS and 1 VRMS,
>> > Â* respectively. Is this correct? Are the reference levels I've given
>> > Â* here exact?
>
> Exact for dBV, close enough for engineering purposes for dBu.

Right. As Paul said, dBu reference is the voltage corresponding
to 1 mW into 600 ohms. I knew this - just temporarily forgot (:o).

>> > Â* 2. Is there a standard for converting from dBFS to dBu?
>
> No. This is a great point of confusion. You can't directly convert
> them because they describe different kinds of units. It's like
> converting the number of apples in a bushel to the number of potatoes
> in a bushel.

Well, yeah, I didn't mean that way. What I meant to ask is if
there is a standard way to map the full-scale output of a DAC
(or input of an ADC) to a specific voltage voltage level.

> There are a few conventions, however, but mostly there's things that
> you choose for yourself, not a standard to which a manufacturer
> adheres. Back when people had VU meters and digital recorders had
> readable meter scales and an adjustable input level control, there was
> often a mark typically somewhere between -16 and -20 dBFS on the
> digital meter that was the recommended point corresponding to 0 VU.

And 0 VU correspondings to +4dBu?

> But it's rare to see that any more. If you're working with 24-bit
> converters and material with fairly high dynamic range, I'd recommend
> 0 VU (at whatever level that represents) provides a record level of
> -20 dBFS. But it's up to you.

That's the same translation Paul mentioned: +4dBu = -20 dBFS.

No one has yet answered the question about whether it's FS sine
or FS square.

>> One other question: is there a specification on the absolute maximum
>> signal voltage magnitude for a line level output?
>
> No specification or standard, but since most gear you'll find today
> operates from a +/- 15 volt power supply, it's rare to find a maximum
> output level before clipping much higher than +24 dBu. There are
> exceptions, of course.

Thank you, Mike.

> You'll find some discussion of these issues in the Gozintas and
> Gozoutas and Meter Madness articles in the Technical Articles section
> of my web site. http://mikeriversaudio.wordpress.com

OK, great. Thanks for the pointers, Mike.
--
Randy Yates % "Midnight, on the water...
Digital Signal Labs % I saw... the ocean's daughter."
% 'Can't Get It Out Of My Head'
http://www.digitalsignallabs.com % *El Dorado*, Electric Light Orchestra

Mike Rivers

November 19th 10, 03:10 PM

On 11/19/2010 10:01 AM, Randy Yates wrote:

> +22dBu = 0dBFS ==> +4dBu = -18dBFS.
> I'm still not sure if that's FS sine or FS square.

dBFS is a peak level. But since good peak reading meters
(and good average reading meters as well) are pretty rare,
generally we look at the RMS value of a sine wave when
expressing levels.

I determine the maximum input level experimentally by
feeding in a sine wave, watching the digital meter, and
looking at the RMS value of the sine wave when the overload
light just comes on. To be more accurate, I'll record a bit
and examine the level for clipping, boosting the input level
incrementally until I'm sure I'm reaching full scale on peaks.

For outputs, I'll use a program to generate a 0 dBFS sine
wave, play it, and read the RMS level of the output.

--
"Today's production equipment is IT based and cannot be
operated without a passing knowledge of computing, although
it seems that it can be operated without a passing knowledge
of audio." - John Watkinson

http://mikeriversaudio.wordpress.com - useful and
interesting audio stuff

Randy Yates

November 19th 10, 03:22 PM

Mike Rivers > writes:

> On 11/19/2010 10:01 AM, Randy Yates wrote:
>
>> +22dBu = 0dBFS ==> +4dBu = -18dBFS.
>> I'm still not sure if that's FS sine or FS square.
>
> dBFS is a peak level.

That's not the way I understand it. Am I wrong? It's
no different than dBu or dBV - just a different "reference"
level. Thus it would be an RMS measure.

> But since good peak reading meters (and good average reading meters as
> well) are pretty rare, generally we look at the RMS value of a sine
> wave when expressing levels.

So you're saying then it's FS sine.
--
Randy Yates % "Maybe one day I'll feel her cold embrace,
Digital Signal Labs % and kiss her interface,
% til then, I'll leave her alone."
http://www.digitalsignallabs.com % 'Yours Truly, 2095', *Time*, ELO

Scott Dorsey

November 19th 10, 03:29 PM

In article >, Randy Yates > wrote:
>One other question: is there a specification on the absolute maximum
>signal voltage magnitude for a line level output?

No, and that's the problem. The standards are average and not peak standards,
and so the amount of headroom required over average is not defined.

For me, I'd like to see 20 dB over average level before clipping, maybe more.
Unfortunately a lot of "pro audio" gear does not do this.

I believe your questions are answered by IEC 60027-3, and by AES standard
AES-R2-1998. Peak-reading standards are in AES-R7-2006.
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

Scott Dorsey

November 19th 10, 03:41 PM

PStamler > wrote:
>On Nov 18, 8:39=A0pm, Randy Yates > wrote:
>> > =A0 1. If you backtrack to 0 dB from this wikipedia article
>> > =A0 =A0http://en.wikipedia.org/wiki/Line_level
>> > =A0 the reference levels for dBu and dBV are 0.775 VRMS and 1 VRMS,
>> > =A0 respectively. Is this correct? Are the reference levels I've given
>> > =A0 here exact?
>
>No and yes, respectively. The reference level for dBu is actually
>0.77459666924148337703585307995648V, according to my calculator --
>that's the voltage equivalent of 1mW into a 600 ohm load. The
>reference level for dBV is exactly 1V.
>
>> > =A0 2. Is there a standard for converting from dBFS to dBu? If so, =A0 =
>what is it?
>
>No. There's an informal standard used in the film industry and in many
>broadcast applications of +4dBu =3D -20dBFS, but it's never been
>codified as an official standard. The informal standard, though, is (I
>believe) based on an rms scale -- in other words, a tone that would
>read 0 VU on a VU meter calibrated to +4dBu would be -20dBFS. Correct
>me if I'm wrong on that last bit, but that's what I think is the case.

This is sort of like asking if there is a standard for converting pounds
to feet. They aren't measuring the same thing. If you know something
specific about the item being measured, you can make some good estimates,
but you need to know something more.
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

Scott Dorsey

November 19th 10, 03:45 PM

In article >, Randy Yates > wrote:
>> No. There's an informal standard used in the film industry and in many
>> broadcast applications of +4dBu = -20dBFS, but it's never been
>> codified as an official standard. The informal standard, though, is (I
>> believe) based on an rms scale -- in other words, a tone that would
>> read 0 VU on a VU meter calibrated to +4dBu would be -20dBFS. Correct
>> me if I'm wrong on that last bit, but that's what I think is the case.
>
>There seems to be no universal agreement, but you are close to what this
>guy says (under "Here come the numbers..."):
>
> +22dBu = 0dBFS ==> +4dBu = -18dBFS.
>
>I'm still not sure if that's FS sine or FS square.

That's assuming a sine wave.

Unfortunately if you use that standard and you record a trumpet with peaks
at 0 dBu, you'll clip the hell out of your converters.

This is because trumpets aren't making sine waves.
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

Klay_Anderson

November 19th 10, 03:54 PM

On Nov 19, 8:29*am, (Scott Dorsey) wrote:
> In article >, Randy Yates > wrote:
>
> >One other question: is there a specification on the absolute maximum
> >signal voltage magnitude for a line level output?
>
> No, and that's the problem. *The standards are average and not peak standards,
> and so the amount of headroom required over average is not defined. *
>
> For me, I'd like to see 20 dB over average level before clipping, maybe more.
> Unfortunately a lot of "pro audio" gear does not do this.
>
> I believe your questions are answered by IEC 60027-3, and by AES standard
> AES-R2-1998. *Peak-reading standards are in AES-R7-2006.
> --scott
>

The nice thing about standards is that there are so many of them.

I have posted a JPEG scan of a level scales card I picked up some time
ago a convention. It shows the relationship of 0.775Vrms to most
known standard scales.

See: http://www.klay.com/klay/world_audio_levels.jpg

Text "Klay" to 50500 for contact info

-.- .-.. .- -.-- / .- - / -.- .-.. .- -.-- / -.. --- - / -.-. --- --
Yours truly,

Mr. Klay Anderson, D.A.,Q.B.E.

PStamler

November 19th 10, 05:45 PM

On Nov 19, 7:41*am, "Arny Krueger" > wrote:
> "dizzy" > wrote in message
>
>
>
> > Randy Yates wrote:
>
> >> One other question: is there a specification on the
> >> absolute maximum signal voltage magnitude for a line
> >> level output?
>
> > Most preamps will put out close to 10 VRMS, considering
> > the typical +/- 15V power-supply rails...
>
> One word: tubes.

And two more words: differential outputs.

With higher supply voltages (like +/- 21V) there are several common
opamps which will (just) put out +24dBu. Use a pair of them as a
differential output and you get +30dBu max output. Or you can use a
higher-supply-voltage discrete circuit or, as Arny says, tubes.

Peace,
Paul

Randy Yates

November 19th 10, 07:01 PM

(Scott Dorsey) writes:

> In article >, Randy Yates > wrote:
>>One other question: is there a specification on the absolute maximum
>>signal voltage magnitude for a line level output?
>
> No, and that's the problem. The standards are average and not peak standards,
> and so the amount of headroom required over average is not defined.
>
> For me, I'd like to see 20 dB over average level before clipping, maybe more.
> Unfortunately a lot of "pro audio" gear does not do this.
>
> I believe your questions are answered by IEC 60027-3, and by AES standard
> AES-R2-1998. Peak-reading standards are in AES-R7-2006.
> --scott

Excellent information - thanks Scott!
--
Randy Yates % "With time with what you've learned,
Digital Signal Labs % they'll kiss the ground you walk
% upon."
http://www.digitalsignallabs.com % '21st Century Man', *Time*, ELO

David Nebenzahl

November 19th 10, 10:02 PM

On 11/19/2010 7:45 AM Scott Dorsey spake thus:

> In article >, Randy Yates >
> wrote:
>
>>> No. There's an informal standard used in the film industry and in
>>> many broadcast applications of +4dBu = -20dBFS, but it's never
>>> been codified as an official standard. The informal standard,
>>> though, is (I believe) based on an rms scale -- in other words, a
>>> tone that would read 0 VU on a VU meter calibrated to +4dBu would
>>> be -20dBFS. Correct me if I'm wrong on that last bit, but that's
>>> what I think is the case.
>>
>> There seems to be no universal agreement, but you are close to what
>> this guy says (under "Here come the numbers..."):
>>
>> +22dBu = 0dBFS ==> +4dBu = -18dBFS.
>>
>> I'm still not sure if that's FS sine or FS square.
>
> That's assuming a sine wave.
>
> Unfortunately if you use that standard and you record a trumpet with peaks
> at 0 dBu, you'll clip the hell out of your converters.
>
> This is because trumpets aren't making sine waves.

Nor violins. (Make pretty close to a triangular wave, I believe.)

--
The fashion in killing has an insouciant, flirty style this spring,
with the flaunting of well-defined muscle, wrapped in flags.

- Comment from an article on Antiwar.com (http://antiwar.com)

Mike Rivers

November 19th 10, 10:34 PM

On 11/19/2010 10:09 AM, Randy Yates wrote:

> What I meant to ask is if
> there is a standard way to map the full-scale output of a DAC
> (or input of an ADC) to a specific voltage voltage level.

Nope.

>> There are a few conventions, however, but mostly there's things that
>> you choose for yourself, not a standard to which a manufacturer
>> adheres. Back when people had VU meters and digital recorders had
>> readable meter scales and an adjustable input level control, there was
>> often a mark typically somewhere between -16 and -20 dBFS on the
>> digital meter that was the recommended point corresponding to 0 VU.
>
> And 0 VU correspondings to +4dBu?

Another point of great confusion. 0 VU is whatever nominal
operating level is. On "pro" equipment, it's usually +4 dBu.
On "semi-pro" equipment, it's usually -10 dBV. On some phone
company, it's +8 dBm (a unit of power, not voltage, but
usually into 600 ohms, so you can calculate the voltage). On
a consumer tape deck, who the heck knows? Usually somewhere
around -20 dBu.

> That's the same translation Paul mentioned: +4dBu = -20 dBFS.

Yup, he's a smart feller.

> No one has yet answered the question about whether it's FS sine
> or FS square.

It doesn't really matter until you want to find the RMS
value of the waveform that got you to that digital level. If
0dBFS = +24 dBu, either a square wave or a sine wave with
the same peak value will get you there.

The RMS value of a sine wave is 0.707 (1/2 the square root
of 2) times the peak amplitude. The RMS value of a square
wave is the same as the peak amplitude.

--
"Today's production equipment is IT based and cannot be
operated without a passing knowledge of computing, although
it seems that it can be operated without a passing knowledge
of audio." - John Watkinson

http://mikeriversaudio.wordpress.com - useful and
interesting audio stuff

Mike Rivers

November 19th 10, 10:40 PM

On 11/19/2010 10:22 AM, Randy Yates wrote:
> Mike > writes:
>> dBFS is a peak level.
>
> That's not the way I understand it. Am I wrong? It's
> no different than dBu or dBV - just a different "reference"
> level. Thus it would be an RMS measure.

We're getting wrapped around the axle here since I don't
know what your real question is. What you're asking is kind
of abstract.

dBFS is dB referenced to full scale which is all the bits on
dBu is dB referenced to .775 volts
dBV is dB referenced to 1 volt

Any of those can be RMS or peak. Peak is significant when
dealing with digital levels, but the only level that's
really significant is the one beyond which you can't go
higher, and that's only one level, 0 dBFS

> So you're saying then it's FS sine.

If you say so. Please ask your REAL question if you have
one. Are you looking for a solution to a problem? Or trying
to interpret some marketing goof's data sheet or manual? If
you're just looking for definitions and conventions, then
you have them.

--
"Today's production equipment is IT based and cannot be
operated without a passing knowledge of computing, although
it seems that it can be operated without a passing knowledge
of audio." - John Watkinson

http://mikeriversaudio.wordpress.com - useful and
interesting audio stuff

Randy Yates

November 20th 10, 12:52 AM

Mike Rivers > writes:

> On 11/19/2010 10:22 AM, Randy Yates wrote:
>> Mike > writes:
>>> dBFS is a peak level.
>>
>> That's not the way I understand it. Am I wrong? It's
>> no different than dBu or dBV - just a different "reference"
>> level. Thus it would be an RMS measure.
>
> We're getting wrapped around the axle here since I don't know what
> your real question is. What you're asking is kind of abstract.

Is dBFS abstract? If so, then I guess I'm asking an abstract
question.

My question is this: What is the definition of dBFS?

> dBFS is dB referenced to full scale which is all the bits on
> dBu is dB referenced to .775 volts
> dBV is dB referenced to 1 volt
>
> Any of those can be RMS or peak.

> Peak is significant when dealing with digital levels, but the only
> level that's really significant is the one beyond which you can't go
> higher, and that's only one level, 0 dBFS

If dBFS is defined as

dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),

where XRMS is the RMS value of the digital data stream, and you're
generating a "digital square wave," then you are wrong. The digital
square wave can go to +3dBFS as defined above.

>> So you're saying then it's FS sine.
>
> If you say so. Please ask your REAL question if you have one. Are you
> looking for a solution to a problem? Or trying to interpret some
> marketing goof's data sheet or manual? If you're just looking for
> definitions and conventions, then you have them.

It seems that there really is no standard definition. That's the
problem. It's not a matter of abstractness, but rather of
well-definedness.
--
Randy Yates % "She's sweet on Wagner-I think she'd die for Beethoven.
Digital Signal Labs % She love the way Puccini lays down a tune, and
% Verdi's always creepin' from her room."
http://www.digitalsignallabs.com % "Rockaria", *A New World Record*, ELO

Bill Graham

November 20th 10, 01:18 AM

"Randy Yates" > wrote in message
...
> Hi Paul,
>
> Thank you for your answers. Comments below.
>
> PStamler > writes:
>
>> On Nov 18, 8:39 pm, Randy Yates > wrote:
>>> > 1. If you backtrack to 0 dB from this wikipedia article
>>> > http://en.wikipedia.org/wiki/Line_level
>>> > the reference levels for dBu and dBV are 0.775 VRMS and 1 VRMS,
>>> > respectively. Is this correct? Are the reference levels I've given
>>> > here exact?
>>
>> No and yes, respectively. The reference level for dBu is actually
>> 0.77459666924148337703585307995648V, according to my calculator --

Wow! You have a calculator that goes to 32 significant digits? My old HP15C
is only good for about 15. You can calculate the distance to Alpha Centauri
to the nearest tenth of an inch...:^)

Mike Rivers

November 20th 10, 01:25 AM

On 11/19/2010 7:52 PM, Randy Yates wrote:

> My question is this: What is the definition of dBFS?

Decibels relative to full scale. 0 dBFS is full scale,
everything else is down from there. -6 dBFS is half the
maximum number as with all the bits on.

> If dBFS is defined as
>
> dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),
>
> where XRMS is the RMS value of the digital data stream, and you're
> generating a "digital square wave," then you are wrong. The digital
> square wave can go to +3dBFS as defined above.

But it's not defined that way. In reality, you can't have
anything higher than 0 dBFS. That's where you run out of
numbers to express the amplitude. There's such a thing as
"intersample overload" where the input actually goes higher
than the 0 dBFS level between two adjacent samples, but
that's an anomaly.

> It seems that there really is no standard definition. That's the
> problem. It's not a matter of abstractness, but rather of
> well-definedness.

The thing is that what you're concerned with in digital
recording is how much headroom you have. You can choose your
own headroom amount simply by choosing the analog reference
level that gives your desired headroom. If you're
compressing the **** out of everything, you don't need as
much headroom as if you're recording an orchestra or
something where you're unsure of the input dynamic range,
and you can choose a higher reference level. For most music,
20 dB of headroom is pretty safe, which is why the -20 dBFS
reference is fairly common.

--
"Today's production equipment is IT based and cannot be
operated without a passing knowledge of computing, although
it seems that it can be operated without a passing knowledge
of audio." - John Watkinson

http://mikeriversaudio.wordpress.com - useful and
interesting audio stuff

Randy Yates

November 20th 10, 01:32 AM

Mike Rivers > writes:

> On 11/19/2010 7:52 PM, Randy Yates wrote:
>
>> My question is this: What is the definition of dBFS?
>
> Decibels relative to full scale.

Nonsense. All you've given is the meaning of the acronym, not an
engineering definition of the unit. This is similar to stating the
definition of RMS is "root mean square."

> [...]
> But it's not defined that way.

I'm not asking how it's not defined. I'm asking how it is defined (in a
sensible way).
--
Randy Yates % "And all that I can do
Digital Signal Labs % is say I'm sorry,
% that's the way it goes..."
http://www.digitalsignallabs.com % Getting To The Point', *Balance of Power*, ELO

hank alrich

November 20th 10, 01:50 AM

Randy Yates > wrote:

> Is dBFS abstract?

In the sense that it correlates to no specific power or voltage level in
the analog world, yes. When we include information about the converter's
input expectations then we can link these disparate measurements.

> If so, then I guess I'm asking an abstract
> question.

I don't think that's the case. There are concrete answers to your
question(s), even if they wrap an abstract concept.

> My question is this: What is the definition of dBFS?

Theorectically, when the last bit of dynamic range is utilized, that
will be shown by the metering as 0 dBFS. Any increase of input level
thereafter will result in clipping.

--
shut up and play your guitar * http://hankalrich.com/
http://armadillomusicproductions.com/who'slistening.html
http://www.sonicbids.com/HankandShaidriAlrichwithDougHarman

hank alrich

November 20th 10, 02:05 AM

Randy Yates > wrote:

> Mike Rivers > writes:
>
> > On 11/19/2010 7:52 PM, Randy Yates wrote:
> >
> >> My question is this: What is the definition of dBFS?
> >
> > Decibels relative to full scale.
>
> Nonsense. All you've given is the meaning of the acronym, not an
> engineering definition of the unit. This is similar to stating the
> definition of RMS is "root mean square."

Nope. It is exactly what Mike stated. It's the "that's all there is and
there ain't no more" point in the converter, assuming <heh> that the
metering and the conveter's actual performance are accurately linked.

--
shut up and play your guitar * http://hankalrich.com/
http://armadillomusicproductions.com/who'slistening.html
http://www.sonicbids.com/HankandShaidriAlrichwithDougHarman

Scott Dorsey

November 20th 10, 02:12 AM

In article >, Randy Yates > wrote:
>
>If dBFS is defined as
>
> dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),
>
>where XRMS is the RMS value of the digital data stream, and you're
>generating a "digital square wave," then you are wrong. The digital
>square wave can go to +3dBFS as defined above.

dBFS has not got a damn thing to do with sine waves or reference levels
or anything in the analogue world.

It has ONLY to do with how far a digital level is below the point at
which the digital value reaches full scale (all bits on).
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

Randy Yates

November 20th 10, 02:46 AM

(Scott Dorsey) writes:

> In article >, Randy Yates > wrote:
>>
>>If dBFS is defined as
>>
>> dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),
>>
>>where XRMS is the RMS value of the digital data stream, and you're
>>generating a "digital square wave," then you are wrong. The digital
>>square wave can go to +3dBFS as defined above.
>
> dBFS has not got a damn thing to do with sine waves or reference levels
> or anything in the analogue world.

Again, I'm not asking how it's not defined, I'm asking how it is
defined.

You guys have danced around this one all day. It's getting humorous.

> It has ONLY to do with how far a digital level is below the point at
> which the digital value reaches full scale (all bits on).

If you know what it means, and you're literate, then you should be able
to come up with a precise definition. I haven't seen one yet.
--
Randy Yates % "She has an IQ of 1001, she has a jumpsuit
Digital Signal Labs % on, and she's also a telephone."
%
http://www.digitalsignallabs.com % 'Yours Truly, 2095', *Time*, ELO

davew

November 20th 10, 03:16 AM

On Nov 20, 2:46*am, Randy Yates > wrote:
> (Scott Dorsey) writes:
> > In article >, Randy Yates > wrote:
>
> >>If dBFS is defined as
>
> >> *dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),
>
> >>where XRMS is the RMS value of the digital data stream, and you're
> >>generating a "digital square wave," then you are wrong. The digital
> >>square wave can go to +3dBFS as defined above.
>
> > dBFS has not got a damn thing to do with sine waves or reference levels
> > or anything in the analogue world.
>
> Again, I'm not asking how it's not defined, I'm asking how it is
> defined.
>
> You guys have danced around this one all day. It's getting humorous.
>
> > It has ONLY to do with how far a digital level is below the point at
> > which the digital value reaches full scale (all bits on).
>
> If you know what it means, and you're literate, then you should be able
> to come up with a precise definition. I haven't seen one yet.
> --
> Randy Yates * * * * * * * * * * *% "She has an IQ of 1001, she has a jumpsuit
> Digital Signal Labs * * * * * * *% * * * * * *on, and she's also a telephone."
> * * * * *%http://www.digitalsignallabs.com% * * * *'Yours Truly, 2095', *Time*, ELO *

ratio (dBFS) = 20log10 (magnitude / maximum possible or allowable
magnitude).

How you measure/define magnitude is the interesting question. i.e.
peak, rms, average, whatever

Eric Jacobsen

November 20th 10, 03:42 AM

On Fri, 19 Nov 2010 20:32:08 -0500, Randy Yates >
wrote:

>Mike Rivers > writes:
>
>> On 11/19/2010 7:52 PM, Randy Yates wrote:
>>
>>> My question is this: What is the definition of dBFS?
>>
>> Decibels relative to full scale.
>
>Nonsense. All you've given is the meaning of the acronym, not an
>engineering definition of the unit. This is similar to stating the
>definition of RMS is "root mean square."
>
>> [...]
>> But it's not defined that way.
>
>I'm not asking how it's not defined. I'm asking how it is defined (in a
>sensible way).

I think you're asking what color the sky is, and people are telling
you "blue", but you're expecting a wavelength or something, so you're
not accepting the answer.

As you know, dB measurements are always relative to some reference
level. With dBFS the reference level is Full Scale of the converter
or number system or whatever. The ratio of the level measured to the
Full Scale level provides the argument for the logarithm, and the
scaled result is dBFS.

If you can do dBm, or dBW, or dBC, you should be able to do dBFS.

The odd part is that you're not seeing this after being told correctly
what it is several times.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com

Randy Yates

November 20th 10, 04:01 AM

(Eric Jacobsen) writes:

> The ratio of the level measured to the Full Scale level provides the
> argument for the logarithm, and the scaled result is dBFS.

"the level measured"? I can immediately think of three different ways to
measure levels.

> The odd part is that you're not seeing this after being told correctly
> what it is several times.

You don't define it with any precision yourself, Eric.
--
Randy Yates % "Rollin' and riding and slippin' and
Digital Signal Labs % sliding, it's magic."
%
http://www.digitalsignallabs.com % 'Living' Thing', *A New World Record*, ELO

Les Cargill

November 20th 10, 04:08 AM

Randy Yates wrote:
> (Scott Dorsey) writes:
>
>> In >, Randy > wrote:
>>>
>>> If dBFS is defined as
>>>
>>> dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),
>>>
>>> where XRMS is the RMS value of the digital data stream, and you're
>>> generating a "digital square wave," then you are wrong. The digital
>>> square wave can go to +3dBFS as defined above.
>>
>> dBFS has not got a damn thing to do with sine waves or reference levels
>> or anything in the analogue world.
>
> Again, I'm not asking how it's not defined, I'm asking how it is
> defined.
>
> You guys have danced around this one all day. It's getting humorous.
>
>> It has ONLY to do with how far a digital level is below the point at
>> which the digital value reaches full scale (all bits on).
>
> If you know what it means, and you're literate, then you should be able
> to come up with a precise definition. I haven't seen one yet.

0dBFs is the upper limit for an instantaneous voltage measure for
the output of a system of digital to analog conversion.

--
Les Cargill

rickman

November 20th 10, 04:33 AM

On Nov 19, 10:42*pm, (Eric Jacobsen) wrote:
> On Fri, 19 Nov 2010 20:32:08 -0500, Randy Yates >
> wrote:
>
>
>
> >Mike Rivers > writes:
>
> >> On 11/19/2010 7:52 PM, Randy Yates wrote:
>
> >>> My question is this: What is the definition of dBFS?
>
> >> Decibels relative to full scale.
>
> >Nonsense. All you've given is the meaning of the acronym, not an
> >engineering definition of the unit. This is similar to stating the
> >definition of RMS is "root mean square."
>
> >> [...]
> >> But it's not defined that way.
>
> >I'm not asking how it's not defined. I'm asking how it is defined (in a
> >sensible way).
>
> I think you're asking what color the sky is, and people are telling
> you "blue", but you're expecting a wavelength or something, so you're
> not accepting the answer.
>
> As you know, dB measurements are always relative to some reference
> level. * With dBFS the reference level is Full Scale of the converter
> or number system or whatever. * The ratio of the level measured to the
> Full Scale level provides the argument for the logarithm, and the
> scaled result is dBFS.
>
> If you can do dBm, or dBW, or dBC, you should be able to do dBFS.
>
> The odd part is that you're not seeing this after being told correctly
> what it is several times.

I think you are using an inappropriate metaphor. It is more like
Randy is asking what is the elephant like and the blind men are all
telling him something different in these two threads. One person says
0 dBFS is a sample of all 1's and all 0's is -96 dBFS (I won't even go
into what is wrong with that one)! Another describes how a VU meter
works. Yet another tells him 0 dBFS is the peak clipping point (that
one alone actually says somethng).

None of the blind men are really right and none are wrong. In the
meantime no coherent picture of the dBFS elephant has emerged and more
disjointed statements are made on the topic.

Another metaphor is that this is a can of worms!

Rick

PStamler

November 20th 10, 04:42 AM

On Nov 19, 7:18*pm, "Bill Graham" > wrote:
> "Randy Yates" > wrote in message
>
> ...
>
> > Hi Paul,
>
> > Thank you for your answers. Comments below.
>
> > PStamler > writes:
>
> >> On Nov 18, 8:39 pm, Randy Yates > wrote:
> >>> > 1. If you backtrack to 0 dB from this wikipedia article
> >>> >http://en.wikipedia.org/wiki/Line_level
> >>> > the reference levels for dBu and dBV are 0.775 VRMS and 1 VRMS,
> >>> > respectively. Is this correct? Are the reference levels I've given
> >>> > here exact?
>
> >> No and yes, respectively. The reference level for dBu is actually
> >> 0.77459666924148337703585307995648V, according to my calculator --
>
> Wow! You have a calculator that goes to 32 significant digits? My old HP15C
> is only good for about 15. You can calculate the distance to Alpha Centauri
> to the nearest tenth of an inch...:^)

It was the calculator build into WinXP.

Peace,
Paul

PStamler

November 20th 10, 04:53 AM

I smell a troll.

When somebody asks a question and gets the precise answer from several
people at once, and keeps on arguing that nobody has given him the
answer, then a troll should be suspected.

0dBFS is the level at which one or the other extremes of a digital
waveform is at maximum codeable level. There are no established
standards relating that to any standards in the analog world, be they
dBu, dBV, dBm or any other. There are some informal standards in the
movie and broadcast world, but no standards body such as IEC or AES
has adopted an official standard.

And Randy, before you tell me "I don't want to know what isn't, I want
to know what is," what I've written above is what is (a definition of
dBFS), and there really ain't no more, and until a standards committee
gets together and votes out a standard, there won't be.

Peace,
Paul

glen herrmannsfeldt

November 20th 10, 09:21 AM

In comp.dsp Eric Jacobsen > wrote:
(snip, someone wrote)

>>Nonsense. All you've given is the meaning of the acronym, not an
>>engineering definition of the unit. This is similar to stating the
>>definition of RMS is "root mean square."
(snip)

> I think you're asking what color the sky is, and people are telling
> you "blue", but you're expecting a wavelength or something, so you're
> not accepting the answer.

> As you know, dB measurements are always relative to some reference
> level. With dBFS the reference level is Full Scale of the converter
> or number system or whatever. The ratio of the level measured to the
> Full Scale level provides the argument for the logarithm, and the
> scaled result is dBFS.

But there is more to it than just the reference. Well, if you
just measure one sample then that is all, but for a signal
of some duration, it is more complicated. I can, for example,
compute RMS for a whole CD track. I could also compute the
mean of the absolute value, the geometric mean of the absolute
value, or many other mathematical functions of the samples.

If I have a sine that reaches peak at exactly a sample point,
and reaches full scale at that point, then RMS is 5 log(2),
or about 1.5dB lower. For mean absolute value, 10 log(2/pi),
or about 1.96dB lower.

> If you can do dBm, or dBW, or dBC, you should be able to do dBFS.

> The odd part is that you're not seeing this after being told correctly
> what it is several times.

-- glen

Mr.T

November 20th 10, 10:26 AM

"rickman" > wrote in message
...
>None of the blind men are really right and none are wrong. In the
>meantime no coherent picture of the dBFS elephant has emerged and more
>disjointed statements are made on the topic.

It seems to me if you realise the Bell or dB is a RELATIVE LOG term of power
(and it's constituents) ratio's with no absolute UNLESS defined as a subset,
(eg dBv, dBu, dBm etc) then asking for a SINGLE absolute point of reference,
or single definition, is simply asking for the impossible.

dBFS is simply the *Full Scale* point of ANY system so defined. IF you want
it to mean anything specific, you must define it as such.

MrT.

Mr.T

November 20th 10, 10:31 AM

"Scott Dorsey" > wrote in message
...
> dBFS has not got a damn thing to do with sine waves or reference levels
> or anything in the analogue world.

Well actually *dB Full Scale*, by simple definition can be the *full scale
dB value* of any digital OR analog system. It's use now is more commonly
connected to digital systems of course.

MrT.

Mr.T

November 20th 10, 10:35 AM

"Randy Yates" > wrote in message
...
> You guys have danced around this one all day. It's getting humorous.

That you expect a simple answer without providing any real definition is
humorous. There is no answer except when defined.
The only simple answer has been given many times, dBFS is simply the Full
Scale point of any relative power measurement scale as defined.

MrT.

Mike Rivers

November 20th 10, 12:24 PM

On 11/19/2010 8:32 PM, Randy Yates wrote:

>>> My question is this: What is the definition of dBFS?
>>
>> Decibels relative to full scale.
>
> Nonsense. All you've given is the meaning of the acronym, not an
> engineering definition of the unit. This is similar to stating the
> definition of RMS is "root mean square."

Question asked and answered. You've also had plenty of
people explain to you the significance of "full scale."
Ferchrissake, what more do you want to know?

--
"Today's production equipment is IT based and cannot be
operated without a passing knowledge of computing, although
it seems that it can be operated without a passing knowledge
of audio." - John Watkinson

http://mikeriversaudio.wordpress.com - useful and
interesting audio stuff

Mike Rivers

November 20th 10, 12:32 PM

On 11/19/2010 11:08 PM, Les Cargill wrote:

> 0dBFs is the upper limit for an instantaneous voltage
> measure for
> the output of a system of digital to analog conversion.

I'm still having a difficult time understanding what he
wants to be defined. We're telling him what 0 dBFS means
because that's really the only significant point in a
sampling system. He's asking for some arbitrary conversion
to a sine wave of arbitrary amplitude, and as far as I know,
there's no way to calculate that from anything but an
infinite number of samples. I don't have time for that.

--
"Today's production equipment is IT based and cannot be
operated without a passing knowledge of computing, although
it seems that it can be operated without a passing knowledge
of audio." - John Watkinson

http://mikeriversaudio.wordpress.com - useful and
interesting audio stuff

Scott Dorsey

November 20th 10, 01:05 PM

Mr.T <MrT@home> wrote:
>"Scott Dorsey" > wrote in message
...
>> dBFS has not got a damn thing to do with sine waves or reference levels
>> or anything in the analogue world.
>
>Well actually *dB Full Scale*, by simple definition can be the *full scale
>dB value* of any digital OR analog system. It's use now is more commonly
>connected to digital systems of course.

What is the full scale of an analogue system? Is it where it starts to
get nonlinear, where it gets really nonlinear, or where it stops and won't
go any more at all?

dBFS isn't really useful on a system that does not clip abruptly and
simultaneously on all stages.
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

Eric Jacobsen

November 20th 10, 04:01 PM

On Fri, 19 Nov 2010 23:01:58 -0500, Randy Yates >
wrote:

(Eric Jacobsen) writes:
>
>> The ratio of the level measured to the Full Scale level provides the
>> argument for the logarithm, and the scaled result is dBFS.
>
>"the level measured"? I can immediately think of three different ways to
>measure levels.

And the point remains:

If you measure peak, then the peak is the value referenced to Full
Scale.

If you measure RMS, then the RMS level is the value reference to Full
Scale.

If you measure furriness, then the furriness is the value referneced
to Full Scale.

I really don't see the source of the confusion.

>> The odd part is that you're not seeing this after being told correctly
>> what it is several times.
>
>You don't define it with any precision yourself, Eric.

It's a very simple definition. dB is always pretty simple, scale the
log of the ratio of the value measured to the reference level.

The only possible complication is keeping the units compatible between
the reference and the measured value. In this case Full Scale can be
thought of as an amplitude or a power reference (and probably
interpreted otherwise as well).

You should know all this, and I suspect you do. It puzzles me why
this seems difficult.

>--
>Randy Yates % "Rollin' and riding and slippin' and
>Digital Signal Labs % sliding, it's magic."
%
>http://www.digitalsignallabs.com % 'Living' Thing', *A New World Record*, ELO

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com

Eric Jacobsen

November 20th 10, 04:03 PM

On Sat, 20 Nov 2010 21:26:21 +1100, "Mr.T" <MrT@home> wrote:

>
>"rickman" > wrote in message
...
>>None of the blind men are really right and none are wrong. In the
>>meantime no coherent picture of the dBFS elephant has emerged and more
>>disjointed statements are made on the topic.
>
>
>It seems to me if you realise the Bell or dB is a RELATIVE LOG term of power
>(and it's constituents) ratio's with no absolute UNLESS defined as a subset,
>(eg dBv, dBu, dBm etc) then asking for a SINGLE absolute point of reference,
>or single definition, is simply asking for the impossible.
>
>dBFS is simply the *Full Scale* point of ANY system so defined. IF you want
>it to mean anything specific, you must define it as such.
>
>MrT.

Pretty much. As long as the units of the reference and the measured
value are compatible it's just an equation to plug into.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com

Eric Jacobsen

November 20th 10, 04:05 PM

On Sat, 20 Nov 2010 09:21:25 +0000 (UTC), glen herrmannsfeldt
> wrote:

>In comp.dsp Eric Jacobsen > wrote:
>(snip, someone wrote)
>
>>>Nonsense. All you've given is the meaning of the acronym, not an
>>>engineering definition of the unit. This is similar to stating the
>>>definition of RMS is "root mean square."
>(snip)
>
>> I think you're asking what color the sky is, and people are telling
>> you "blue", but you're expecting a wavelength or something, so you're
>> not accepting the answer.
>
>> As you know, dB measurements are always relative to some reference
>> level. With dBFS the reference level is Full Scale of the converter
>> or number system or whatever. The ratio of the level measured to the
>> Full Scale level provides the argument for the logarithm, and the
>> scaled result is dBFS.
>
>But there is more to it than just the reference. Well, if you
>just measure one sample then that is all, but for a signal
>of some duration, it is more complicated. I can, for example,
>compute RMS for a whole CD track. I could also compute the
>mean of the absolute value, the geometric mean of the absolute
>value, or many other mathematical functions of the samples.
>
>If I have a sine that reaches peak at exactly a sample point,
>and reaches full scale at that point, then RMS is 5 log(2),
>or about 1.5dB lower. For mean absolute value, 10 log(2/pi),
>or about 1.96dB lower.

Yup. If you have a different measure, you'll get a different value.
Why is that confusing? People in our area don't normally confuse
amplitude and power, or even various ways to measure power. Why does
it become so difficult when you plug it into a simple equation?

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com

hank alrich

November 20th 10, 04:23 PM

Scott Dorsey > wrote:

> In article >, Randy Yates > wrote:
> >
> >If dBFS is defined as
> >
> > dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),
> >
> >where XRMS is the RMS value of the digital data stream, and you're
> >generating a "digital square wave," then you are wrong. The digital
> >square wave can go to +3dBFS as defined above.
>
> dBFS has not got a damn thing to do with sine waves or reference levels
> or anything in the analogue world.

When the input sensitivity of the convertor is considered we have a
basis upon which to spec the relationship between the analog and digital
levels.

This holds only for that make and model of converter set to that
particular sensitivity (is such is adjustable).

> It has ONLY to do with how far a digital level is below the point at
> which the digital value reaches full scale (all bits on).
> --scott

--
shut up and play your guitar * http://hankalrich.com/
http://armadillomusicproductions.com/who'slistening.html
http://www.sonicbids.com/HankandShaidriAlrichwithDougHarman

hank alrich

November 20th 10, 04:23 PM

Randy Yates > wrote:

> (Scott Dorsey) writes:
>
> > In article >, Randy Yates > wrote:
> >>
> >>If dBFS is defined as
> >>
> >> dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),
> >>
> >>where XRMS is the RMS value of the digital data stream, and you're
> >>generating a "digital square wave," then you are wrong. The digital
> >>square wave can go to +3dBFS as defined above.
> >
> > dBFS has not got a damn thing to do with sine waves or reference levels
> > or anything in the analogue world.
>
> Again, I'm not asking how it's not defined, I'm asking how it is
> defined.
>
> You guys have danced around this one all day. It's getting humorous.
>
> > It has ONLY to do with how far a digital level is below the point at
> > which the digital value reaches full scale (all bits on).
>
> If you know what it means, and you're literate, then you should be able
> to come up with a precise definition. I haven't seen one yet.

You have, but you aren't recognizing it, because it is not what you
expected it to be, Randy.

My Metric Halo converter has a wide range of available input
sensitivities. Set it to -10 and it can reach 0 dBFS. Set it to +4 and
it can reach 0 dBFS. For each of those conditions we can relate an
incoming analog signal level to a specific number of bits. Here's the
rub: in either case we can get 0 dBFS. In each case the corresponding
analog input level is quite different.

--
shut up and play your guitar * http://hankalrich.com/
http://armadillomusicproductions.com/who'slistening.html
http://www.sonicbids.com/HankandShaidriAlrichwithDougHarman

hank alrich

November 20th 10, 04:33 PM

PStamler > wrote:

> I smell a troll.

I think maybe not, based on Randy's previous postings. I think he's a
knowledgeable cat in the digital domain, has a basic understanding of
analog audio concepts, but isn't getting his head around this particular
question, now answered for him many times.

I think the answer is one he was not expecting, and like many engineers
who are appreciably rational, the irrational aspect of an audio metering
system in which the measured level increments need bear no specific
relationship to the corresponding analog signal levels is disturbing to
him.

> When somebody asks a question and gets the precise answer from several
> people at once, and keeps on arguing that nobody has given him the
> answer, then a troll should be suspected.

I do understand that part of it, but unless someone has hijacked his
account I think he's just not getting it, and he might think we're
screwing around with him. All responses I have seen here have been well
intentioned.

> 0dBFS is the level at which one or the other extremes of a digital
> waveform is at maximum codeable level.

Therefrom, the answer to his question can only be stated in absolute
terms when we know how many bits a given converter uses to convert an
analog signal of a particular level.

> There are no established
> standards relating that to any standards in the analog world, be they
> dBu, dBV, dBm or any other. There are some informal standards in the
> movie and broadcast world, but no standards body such as IEC or AES
> has adopted an official standard.
>
> And Randy, before you tell me "I don't want to know what isn't, I want
> to know what is," what I've written above is what is (a definition of
> dBFS), and there really ain't no more, and until a standards committee
> gets together and votes out a standard, there won't be.
>
> Peace,
> Paul

--
shut up and play your guitar * http://hankalrich.com/
http://armadillomusicproductions.com/who'slistening.html
http://www.sonicbids.com/HankandShaidriAlrichwithDougHarman

Steve King

November 20th 10, 04:35 PM

"Mike Rivers" > wrote in message
...
| On 11/19/2010 11:08 PM, Les Cargill wrote:
|
| > 0dBFs is the upper limit for an instantaneous voltage
| > measure for
| > the output of a system of digital to analog conversion.
|
| I'm still having a difficult time understanding what he
| wants to be defined. We're telling him what 0 dBFS means
| because that's really the only significant point in a
| sampling system. He's asking for some arbitrary conversion
| to a sine wave of arbitrary amplitude, and as far as I know,
| there's no way to calculate that from anything but an
| infinite number of samples. I don't have time for that.

Mike, he's just yanking your chain. He gets off on it. It has nothing to
do with anything but that.

Steve King

John O'Flaherty

November 20th 10, 05:00 PM

On Fri, 19 Nov 2010 21:46:25 -0500, Randy Yates >
wrote:

(Scott Dorsey) writes:
>
>> In article >, Randy Yates > wrote:
>>>
>>>If dBFS is defined as
>>>
>>> dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),
>>>
>>>where XRMS is the RMS value of the digital data stream, and you're
>>>generating a "digital square wave," then you are wrong. The digital
>>>square wave can go to +3dBFS as defined above.
>>
>> dBFS has not got a damn thing to do with sine waves or reference levels
>> or anything in the analogue world.
>
>Again, I'm not asking how it's not defined, I'm asking how it is
>defined.
>
>You guys have danced around this one all day. It's getting humorous.
>
>> It has ONLY to do with how far a digital level is below the point at
>> which the digital value reaches full scale (all bits on).
>
>If you know what it means, and you're literate, then you should be able
>to come up with a precise definition. I haven't seen one yet.

The problem is that dB is defined as a unit of power, usually applied
to signals with some time duration. Obviously, a square wave at full
scale of a converter has more power than, say, a sine wave or a 1%
duty cycle signal at full scale. So, how can one define dBFS so it
represents how the figure is actually used? How about "a signal at 0
dBFS is one whose instantaneous power reaches but never exceeds the
instantaneous power associated with full scale of the converter"?
Modifying your formula above,
dBFS = 20 * log_10(peak signal voltage / converter maximum voltage)

--
John

Scott Dorsey

November 20th 10, 06:47 PM

hank alrich > wrote:
>
>I think the answer is one he was not expecting, and like many engineers
>who are appreciably rational, the irrational aspect of an audio metering
>system in which the measured level increments need bear no specific
>relationship to the corresponding analog signal levels is disturbing to
>him.

I don't see what's irrational about that, because the way we think about
analogue and digital levels are so totally different. They really are
different things.
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

Al Clark

November 20th 10, 08:03 PM

rickman > wrote in news:27189e84-f6c3-4f34-8d1d-
:

> On Nov 19, 10:42*pm, (Eric Jacobsen) wrote:
>> On Fri, 19 Nov 2010 20:32:08 -0500, Randy Yates >
>> wrote:
>>
>>
>>
>> >Mike Rivers > writes:
>>
>> >> On 11/19/2010 7:52 PM, Randy Yates wrote:
>>
>> >>> My question is this: What is the definition of dBFS?
>>
>> >> Decibels relative to full scale.
>>
>> >Nonsense. All you've given is the meaning of the acronym, not an
>> >engineering definition of the unit. This is similar to stating the
>> >definition of RMS is "root mean square."
>>
>> >> [...]
>> >> But it's not defined that way.
>>
>> >I'm not asking how it's not defined. I'm asking how it is defined (in a
>> >sensible way).
>>
>> I think you're asking what color the sky is, and people are telling
>> you "blue", but you're expecting a wavelength or something, so you're
>> not accepting the answer.
>>
>> As you know, dB measurements are always relative to some reference
>> level. * With dBFS the reference level is Full Scale of the converter
>> or number system or whatever. * The ratio of the level measured to the
>> Full Scale level provides the argument for the logarithm, and the
>> scaled result is dBFS.
>>
>> If you can do dBm, or dBW, or dBC, you should be able to do dBFS.
>>
>> The odd part is that you're not seeing this after being told correctly
>> what it is several times.
>
> I think you are using an inappropriate metaphor. It is more like
> Randy is asking what is the elephant like and the blind men are all
> telling him something different in these two threads. One person says
> 0 dBFS is a sample of all 1's and all 0's is -96 dBFS (I won't even go
> into what is wrong with that one)! Another describes how a VU meter
> works. Yet another tells him 0 dBFS is the peak clipping point (that
> one alone actually says somethng).

I'm not sure I want to jump in again at all, but here are a couple of
points:

1. I think I concur with Erik Jacobsen on definitions.

2. 0 dBFS does not mean the level of all 1s as someone suggested. It is the
value of the full scale range of the converter which is virtually always
expressed as twos complement in the audio world. This is either
0x7FFFFF...etc depending or word length for positive peaks or 0x80000...
for negative peaks. If we really wanted to nitpik, I suppose it should be
the positive value which is 1 bit less than the absolue value of full scale
negative. This distinction is meaningless in dB when the bit depth is
large.

3. dBFS does not by itself refer to rms levels at all. In a practical
system, there will be a relationship to the rms level of a sine wave to
dBFS. This is because the crest factor of a sine wave is fixed at 3dB. A
square wave has a crest factor of 0dB, music and voice has a crest factor >
3dB in almost all cases. We can relate a the rms level of a +4dBu sinusoid
to an equivalent dBFS value only when we know the conversion. This may be
18 or 20 dB (or something else) and simply establishes the balance between
headroom and low level noise.

4. RMS measurements will also vary. In most cases, we will be using
exponential averaging with some arbitrary time constant. It really doesn't
matter whether we a considering signals in either the digital domain or
analog domain. With exponential averaging, the most recent signals
(samples) have more weight than earlier signals (samples). A long time
constant will yield a measurement that reflects the overall long term
level. A shorter time constant will accent more current events. A sinusoid
would measure the same assuming that the averaging filter has settled to a
steady state value. VU meters are similar where averaging is at least
partially the result of meter balistics. Like a typical low cost
multimeter, they may not be TRMS either.

Al Clark
www.danvillesignal.com

>
> None of the blind men are really right and none are wrong. In the
> meantime no coherent picture of the dBFS elephant has emerged and more
> disjointed statements are made on the topic.
>
> Another metaphor is that this is a can of worms!
>
> Rick

Randy Yates

November 20th 10, 08:09 PM

John O'Flaherty > writes:

> On Fri, 19 Nov 2010 21:46:25 -0500, Randy Yates >
> wrote:
>
(Scott Dorsey) writes:
>>
>>> In article >, Randy Yates > wrote:
>>>>
>>>>If dBFS is defined as
>>>>
>>>> dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),
>>>>
>>>>where XRMS is the RMS value of the digital data stream, and you're
>>>>generating a "digital square wave," then you are wrong. The digital
>>>>square wave can go to +3dBFS as defined above.
>>>
>>> dBFS has not got a damn thing to do with sine waves or reference levels
>>> or anything in the analogue world.
>>
>>Again, I'm not asking how it's not defined, I'm asking how it is
>>defined.
>>
>>You guys have danced around this one all day. It's getting humorous.
>>
>>> It has ONLY to do with how far a digital level is below the point at
>>> which the digital value reaches full scale (all bits on).
>>
>>If you know what it means, and you're literate, then you should be able
>>to come up with a precise definition. I haven't seen one yet.
>
> The problem is that dB is defined as a unit of power, usually applied
> to signals with some time duration.

YES!!! Thank you, John!

> Obviously, a square wave at full scale of a converter has more power
> than, say, a sine wave or a 1% duty cycle signal at full scale. So,
> how can one define dBFS so it represents how the figure is actually
> used?

Not a bad question, but I was hoping there was _THE_ definition.
Apparently there is not. And this is really the crux of the issue (for
dBFS). Some people say it's a peak (instantaneous) measurement, yet I
see meters that use it for RMS measurements. I'm afraid the truth is
that there is no universal meaning for it like there is for dBm, dBV,
and several other dB units.

> How about "a signal at 0 dBFS is one whose instantaneous power

I'm not comfortable with the concept of "instantaneous power." Rather, I
think we have to just concede that the "dB" sometimes breaks tradition
and works with instantanous quantities rather than power.

> reaches but never exceeds the instantaneous power associated with full
> scale of the converter"? Modifying your formula above, dBFS = 20 *
> log_10(peak signal voltage / converter maximum voltage)

That is essentially what I wrote last night. Thanks for your input, John.
--
Randy Yates % "Maybe one day I'll feel her cold embrace,
Digital Signal Labs % and kiss her interface,
% til then, I'll leave her alone."
http://www.digitalsignallabs.com % 'Yours Truly, 2095', *Time*, ELO

Don Pearce[_3_]

November 20th 10, 08:28 PM

On Sat, 20 Nov 2010 15:09:19 -0500, Randy Yates >
wrote:

>John O'Flaherty > writes:
>
>> On Fri, 19 Nov 2010 21:46:25 -0500, Randy Yates >
>> wrote:
>>
(Scott Dorsey) writes:
>>>
>>>> In article >, Randy Yates > wrote:
>>>>>
>>>>>If dBFS is defined as
>>>>>
>>>>> dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),
>>>>>
>>>>>where XRMS is the RMS value of the digital data stream, and you're
>>>>>generating a "digital square wave," then you are wrong. The digital
>>>>>square wave can go to +3dBFS as defined above.
>>>>
>>>> dBFS has not got a damn thing to do with sine waves or reference levels
>>>> or anything in the analogue world.
>>>
>>>Again, I'm not asking how it's not defined, I'm asking how it is
>>>defined.
>>>
>>>You guys have danced around this one all day. It's getting humorous.
>>>
>>>> It has ONLY to do with how far a digital level is below the point at
>>>> which the digital value reaches full scale (all bits on).
>>>
>>>If you know what it means, and you're literate, then you should be able
>>>to come up with a precise definition. I haven't seen one yet.
>>
>> The problem is that dB is defined as a unit of power, usually applied
>> to signals with some time duration.
>
>YES!!! Thank you, John!
>
FFS. The dB is NOT a unit of anything. It is a ratio expressed in log
form for convenience (to avoid huge numbers). Nothing more and nothing
less.

>> Obviously, a square wave at full scale of a converter has more power
>> than, say, a sine wave or a 1% duty cycle signal at full scale. So,
>> how can one define dBFS so it represents how the figure is actually
>> used?
>
>Not a bad question, but I was hoping there was _THE_ definition.
>Apparently there is not. And this is really the crux of the issue (for
>dBFS). Some people say it's a peak (instantaneous) measurement, yet I
>see meters that use it for RMS measurements. I'm afraid the truth is
>that there is no universal meaning for it like there is for dBm, dBV,
>and several other dB units.
>

This is getting increasingly ridiculous. FS is simply the point at
which you hit the ceiling. There is no more. You have limited. dBFS is
the ratio of the present signal to that ceiling. The relevant
measurement is instantaneous - this very next sample is the one you
have to care about. Normal good practice would suggest that you keep
between 10 and 20dB below to allow for the unexpected. If you do that,
you won't be troubled by either overload or noise.

>> How about "a signal at 0 dBFS is one whose instantaneous power
>
>I'm not comfortable with the concept of "instantaneous power." Rather, I
>think we have to just concede that the "dB" sometimes breaks tradition
>and works with instantanous quantities rather than power.
>
There is no problem with instantaneous power. Instantaneous energy is
the one you can't be doing with. That final sentence of yours is
simply gibberish.

>> reaches but never exceeds the instantaneous power associated with full
>> scale of the converter"? Modifying your formula above, dBFS = 20 *
>> log_10(peak signal voltage / converter maximum voltage)
>
>That is essentially what I wrote last night. Thanks for your input, John.

How many people have slightest idea what power their converters will
handle? Everybody thinks in terms of voltage, which is the fixed term
in non-matched systems such as audio gear.

d

Eric Jacobsen

November 20th 10, 08:44 PM

On Sat, 20 Nov 2010 15:09:19 -0500, Randy Yates >
wrote:

>John O'Flaherty > writes:
>
>> On Fri, 19 Nov 2010 21:46:25 -0500, Randy Yates >
>> wrote:
>>
(Scott Dorsey) writes:
>>>
>>>> In article >, Randy Yates > wrote:
>>>>>
>>>>>If dBFS is defined as
>>>>>
>>>>> dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),
>>>>>
>>>>>where XRMS is the RMS value of the digital data stream, and you're
>>>>>generating a "digital square wave," then you are wrong. The digital
>>>>>square wave can go to +3dBFS as defined above.
>>>>
>>>> dBFS has not got a damn thing to do with sine waves or reference levels
>>>> or anything in the analogue world.
>>>
>>>Again, I'm not asking how it's not defined, I'm asking how it is
>>>defined.
>>>
>>>You guys have danced around this one all day. It's getting humorous.
>>>
>>>> It has ONLY to do with how far a digital level is below the point at
>>>> which the digital value reaches full scale (all bits on).
>>>
>>>If you know what it means, and you're literate, then you should be able
>>>to come up with a precise definition. I haven't seen one yet.
>>
>> The problem is that dB is defined as a unit of power, usually applied
>> to signals with some time duration.
>
>YES!!! Thank you, John!

Except he's wrong.

As others have said, dB is a way of rescaling and is independent of
the units involved or the characteristics of the measurement. It is
simply the scaled log of a ratio, where one of the terms in the ratio
is a reference level. If the reference level and the measurement
have units of power, then the resulting dB value will have units of
power, and will usually reflect that, e.g., dBm, dBW, etc. If the
reference level and measurement have units of amplitude, then the
output will generally reflect that as well, e.g., dBV.

Perhaps the confusion is that FS is unitless and can be anything;
power, amplitude, time, price, whatever. Since it is just a
reference to a number within a number system, the output will then
have the units of whatever that number represents. Meanwhile, since
it is just a number within a particular dynamic range indicated by FS,
dBFS is still a useful expression for evaluating a system.

But it is not inherently power or amplitude or anything. It takes on
the units (or unitlessness) of whatever the number system represents.

>> Obviously, a square wave at full scale of a converter has more power
>> than, say, a sine wave or a 1% duty cycle signal at full scale. So,
>> how can one define dBFS so it represents how the figure is actually
>> used?
>
>Not a bad question, but I was hoping there was _THE_ definition.
>Apparently there is not. And this is really the crux of the issue (for
>dBFS). Some people say it's a peak (instantaneous) measurement, yet I
>see meters that use it for RMS measurements. I'm afraid the truth is
>that there is no universal meaning for it like there is for dBm, dBV,
>and several other dB units.

dBx always takes on the units of the input values. The reference and
the measurement have to have the same units for the result to be
meaningful.

>> How about "a signal at 0 dBFS is one whose instantaneous power
>
>I'm not comfortable with the concept of "instantaneous power." Rather, I
>think we have to just concede that the "dB" sometimes breaks tradition
>and works with instantanous quantities rather than power.

It can be anything. Instantaneous, averaged, glacial, whatever.
Time may not be involved at all, or it might be.

>> reaches but never exceeds the instantaneous power associated with full
>> scale of the converter"? Modifying your formula above, dBFS = 20 *
>> log_10(peak signal voltage / converter maximum voltage)
>
>That is essentially what I wrote last night. Thanks for your input, John.
>--
>Randy Yates % "Maybe one day I'll feel her cold embrace,
>Digital Signal Labs % and kiss her interface,
% til then, I'll leave her alone."
>http://www.digitalsignallabs.com % 'Yours Truly, 2095', *Time*, ELO

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com

Randy Yates

November 20th 10, 08:57 PM

(Don Pearce) writes:
> [...]
> FFS. The dB is NOT a unit of anything. It is a ratio expressed in log
> form for convenience (to avoid huge numbers). Nothing more and nothing
> less.

"dB" is a ratio of powers.

http://www.digitalsignallabs.com/db.pdf

"dBm", "dBV", etc., are units.
--
Randy Yates % "...the answer lies within your soul
Digital Signal Labs % 'cause no one knows which side
% the coin will fall."
http://www.digitalsignallabs.com % 'Big Wheels', *Out of the Blue*, ELO

Randy Yates

November 20th 10, 09:04 PM

(Eric Jacobsen) writes:
> [...]
> It can be anything.

Thanks for your input, Eric. I realize this is honestly what you
believe, but I'm not sure I agree with it.
--
Randy Yates % "How's life on earth?
Digital Signal Labs % ... What is it worth?"
% 'Mission (A World Record)',
http://www.digitalsignallabs.com % *A New World Record*, ELO

Don Pearce[_3_]

November 20th 10, 09:22 PM

On Sat, 20 Nov 2010 15:57:15 -0500, Randy Yates >
wrote:

(Don Pearce) writes:
>> [...]
>> FFS. The dB is NOT a unit of anything. It is a ratio expressed in log
>> form for convenience (to avoid huge numbers). Nothing more and nothing
>> less.
>
>"dB" is a ratio of powers.
>

Quite, but provided you don't change the impedances in the meantime it
is also a ratio of voltages or currents.

> http://www.digitalsignallabs.com/db.pdf
>
>"dBm", "dBV", etc., are units.

The "m" and the "V" are the units, not the "dB" part.

d

John O'Flaherty

November 20th 10, 11:19 PM

On Sat, 20 Nov 2010 20:44:55 GMT, (Eric
Jacobsen) wrote:

>On Sat, 20 Nov 2010 15:09:19 -0500, Randy Yates >
>wrote:
>
>>John O'Flaherty > writes:
>>
>>> On Fri, 19 Nov 2010 21:46:25 -0500, Randy Yates >
>>> wrote:
>>>
(Scott Dorsey) writes:
>>>>
>>>>> In article >, Randy Yates > wrote:
>>>>>>
>>>>>>If dBFS is defined as
>>>>>>
>>>>>> dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),
>>>>>>
>>>>>>where XRMS is the RMS value of the digital data stream, and you're
>>>>>>generating a "digital square wave," then you are wrong. The digital
>>>>>>square wave can go to +3dBFS as defined above.
>>>>>
>>>>> dBFS has not got a damn thing to do with sine waves or reference levels
>>>>> or anything in the analogue world.
>>>>
>>>>Again, I'm not asking how it's not defined, I'm asking how it is
>>>>defined.
>>>>
>>>>You guys have danced around this one all day. It's getting humorous.
>>>>
>>>>> It has ONLY to do with how far a digital level is below the point at
>>>>> which the digital value reaches full scale (all bits on).
>>>>
>>>>If you know what it means, and you're literate, then you should be able
>>>>to come up with a precise definition. I haven't seen one yet.
>>>
>>> The problem is that dB is defined as a unit of power, usually applied
>>> to signals with some time duration.
>>
>>YES!!! Thank you, John!
>
>Except he's wrong.
>
>As others have said, dB is a way of rescaling and is independent of
>the units involved or the characteristics of the measurement. It is
>simply the scaled log of a ratio, where one of the terms in the ratio
>is a reference level. If the reference level and the measurement
>have units of power, then the resulting dB value will have units of
>power, and will usually reflect that, e.g., dBm, dBW, etc. If the
>reference level and measurement have units of amplitude, then the
>output will generally reflect that as well, e.g., dBV.

But it isn't an independent way of rescaling a measurement. If it
were, then the formula for dB as a ratio of voltages would have the
same form as that for a ratio of powers: 10 * log(v2/v1). The fact
that it has 20 means that it is squaring the voltage ratio to make it
a power ratio (implicitly assuming constant impedance). It's a hybrid
system of units when it is dBV, but it still represents a power ratio.
Wikipedia offers this definition for "decibel":
"A ratio in decibels is ten times the logarithm to base 10 of the
ratio of two power quantities.", citing this:
" IEEE Standard 100 Dictionary of IEEE Standards Terms, Seventh
Edition, The Institute of Electrical and Electronics Engineering, New
York, 2000; ISBN 0-7381-2601-2; page 288"

This isn't to say that it's not used otherwise, but that's the
definition.

>Perhaps the confusion is that FS is unitless and can be anything;
>power, amplitude, time, price, whatever. Since it is just a
>reference to a number within a number system, the output will then
>have the units of whatever that number represents. Meanwhile, since
>it is just a number within a particular dynamic range indicated by FS,
>dBFS is still a useful expression for evaluating a system.
>
>But it is not inherently power or amplitude or anything. It takes on
>the units (or unitlessness) of whatever the number system represents.
>
>>> Obviously, a square wave at full scale of a converter has more power
>>> than, say, a sine wave or a 1% duty cycle signal at full scale. So,
>>> how can one define dBFS so it represents how the figure is actually
>>> used?
>>
>>Not a bad question, but I was hoping there was _THE_ definition.
>>Apparently there is not. And this is really the crux of the issue (for
>>dBFS). Some people say it's a peak (instantaneous) measurement, yet I
>>see meters that use it for RMS measurements. I'm afraid the truth is
>>that there is no universal meaning for it like there is for dBm, dBV,
>>and several other dB units.
>
>dBx always takes on the units of the input values. The reference and
>the measurement have to have the same units for the result to be
>meaningful.

It's true that the input units must be the same, but dB is actually
unitless, since it's a ratio of two like units.
Again, from Wikipedia:
"Being a ratio of two measurements of a physical quantity in the same
units, it is a dimensionless unit."

>
>>> How about "a signal at 0 dBFS is one whose instantaneous power
>>
>>I'm not comfortable with the concept of "instantaneous power." Rather, I
>>think we have to just concede that the "dB" sometimes breaks tradition
>>and works with instantanous quantities rather than power.
>
>It can be anything. Instantaneous, averaged, glacial, whatever.
>Time may not be involved at all, or it might be.
>
>>> reaches but never exceeds the instantaneous power associated with full
>>> scale of the converter"? Modifying your formula above, dBFS = 20 *
>>> log_10(peak signal voltage / converter maximum voltage)
>>
>>That is essentially what I wrote last night. Thanks for your input, John.

--
John

Ala

November 21st 10, 12:12 AM

Scott Dorsey

November 21st 10, 12:59 AM

In article >, Randy Yates > wrote:
(Don Pearce) writes:
>> [...]
>> FFS. The dB is NOT a unit of anything. It is a ratio expressed in log
>> form for convenience (to avoid huge numbers). Nothing more and nothing
>> less.
>
>"dB" is a ratio of powers.

dB is a ratio.

dBft and dBlb to talk about decibels with respect to a foot or a pound
are perfectly reasonable.

Probably the most common measurement, dBSPL, is actually referenced to a
pressure.
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

rickman

November 21st 10, 01:08 AM

On Nov 20, 4:04*pm, Randy Yates > wrote:
> (Eric Jacobsen) writes:
> > [...]
> > It can be anything.
>
> Thanks for your input, Eric. I realize this is honestly what you
> believe, but I'm not sure I agree with it.
> --
> Randy Yates * * * * * * * * * * *% "How's life on earth?
> Digital Signal Labs * * * * * * *% *... What is it worth?"
> * * * * *% 'Mission (A World Record)',http://www.digitalsignallabs.com% *A New World Record*, ELO

Why do you have a problem with instantaneous power? Power is a rate,
just like speed. Energy per unit time / distance per unit time. Of
course no measurement of any kind can be done instantaneously, but
that is more an issue of quantum mechanics than a theoretical issue.
If you can perform measurements at a point in time that allow power to
be calculated such as voltage/current/resistance, you can calculate
instantaneous power. RMS is just a way to calculating an average
power of a varying signal. But it is found by using an integral of an
infinite number of power points or in the discrete domain, a sum of
many discrete powers. If the instantaneous or discrete powers don't
exist, how can the integral or sum exist?

Rick

Mr.T

November 21st 10, 01:36 AM

"Scott Dorsey" > wrote in message
...
> >> dBFS has not got a damn thing to do with sine waves or reference levels
> >> or anything in the analogue world.
> >
> >Well actually *dB Full Scale*, by simple definition can be the *full
scale
> >dB value* of any digital OR analog system. It's use now is more commonly
> >connected to digital systems of course.
>
> What is the full scale of an analogue system? Is it where it starts to
> get nonlinear, where it gets really nonlinear, or where it stops and won't
> go any more at all?

Right. With an analog meter it's full scale point is obvious. But power
supply limitations mean there is always a maximum point that cannot be
exceeded in any system. It gets a bit harder to define when you consider
power supply regulation etc. But as I said, it's the *definition* that
counts. not necessarily the real world practical implementations.

MrT.

Les Cargill

November 21st 10, 02:07 AM

Randy Yates wrote:
> (Don Pearce) writes:
>> [...]
>> FFS. The dB is NOT a unit of anything. It is a ratio expressed in log
>> form for convenience (to avoid huge numbers). Nothing more and nothing
>> less.
>
> "dB" is a ratio of powers.
>

.... into a fixed 600 ohm impedance, so they
have a mathematical dual in swings in voltage
(which is much more convenient to measure ).

> http://www.digitalsignallabs.com/db.pdf
>
> "dBm", "dBV", etc., are units.

They're still unitless. The specializations just let you know
some measure of detail about how many dimensions are represented
for cases like power vs. voltage...

--
Les Cargill

Eric Jacobsen

November 21st 10, 05:23 AM

On Sat, 20 Nov 2010 17:19:53 -0600, John O'Flaherty
> wrote:

>On Sat, 20 Nov 2010 20:44:55 GMT, (Eric
>Jacobsen) wrote:
>
>>On Sat, 20 Nov 2010 15:09:19 -0500, Randy Yates >
>>wrote:
>>
>>>John O'Flaherty > writes:
>>>
>>>> On Fri, 19 Nov 2010 21:46:25 -0500, Randy Yates >
>>>> wrote:
>>>>
(Scott Dorsey) writes:
>>>>>
>>>>>> In article >, Randy Yates > wrote:
>>>>>>>
>>>>>>>If dBFS is defined as
>>>>>>>
>>>>>>> dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),
>>>>>>>
>>>>>>>where XRMS is the RMS value of the digital data stream, and you're
>>>>>>>generating a "digital square wave," then you are wrong. The digital
>>>>>>>square wave can go to +3dBFS as defined above.
>>>>>>
>>>>>> dBFS has not got a damn thing to do with sine waves or reference levels
>>>>>> or anything in the analogue world.
>>>>>
>>>>>Again, I'm not asking how it's not defined, I'm asking how it is
>>>>>defined.
>>>>>
>>>>>You guys have danced around this one all day. It's getting humorous.
>>>>>
>>>>>> It has ONLY to do with how far a digital level is below the point at
>>>>>> which the digital value reaches full scale (all bits on).
>>>>>
>>>>>If you know what it means, and you're literate, then you should be able
>>>>>to come up with a precise definition. I haven't seen one yet.
>>>>
>>>> The problem is that dB is defined as a unit of power, usually applied
>>>> to signals with some time duration.
>>>
>>>YES!!! Thank you, John!
>>
>>Except he's wrong.
>>
>>As others have said, dB is a way of rescaling and is independent of
>>the units involved or the characteristics of the measurement. It is
>>simply the scaled log of a ratio, where one of the terms in the ratio
>>is a reference level. If the reference level and the measurement
>>have units of power, then the resulting dB value will have units of
>>power, and will usually reflect that, e.g., dBm, dBW, etc. If the
>>reference level and measurement have units of amplitude, then the
>>output will generally reflect that as well, e.g., dBV.
>
>But it isn't an independent way of rescaling a measurement. If it
>were, then the formula for dB as a ratio of voltages would have the
>same form as that for a ratio of powers: 10 * log(v2/v1). The fact
>that it has 20 means that it is squaring the voltage ratio to make it
>a power ratio (implicitly assuming constant impedance). It's a hybrid
>system of units when it is dBV, but it still represents a power ratio.
> Wikipedia offers this definition for "decibel":
>"A ratio in decibels is ten times the logarithm to base 10 of the
>ratio of two power quantities.", citing this:
>" IEEE Standard 100 Dictionary of IEEE Standards Terms, Seventh
>Edition, The Institute of Electrical and Electronics Engineering, New
>York, 2000; ISBN 0-7381-2601-2; page 288"
>
>This isn't to say that it's not used otherwise, but that's the
>definition.

The issue is that it's muddy and not consistently used and hasn't been
nearly since inception. Antenna gains, e.g., dBi, Sound pressures,
e.g., dBSPL, radar cross sectional area, dBsm, bandwidth, e.g., dBHz,
and the current topic, dBFS, are often used with or implemented with
power measurements, but they aren't really power, and sometimes don't
have anything to do with power.

The point is that it's just an equation to plug numbers into, and the
meaning is only relevant to the interpretation of what got plugged in.

Things like dBFS, or even dBC or other common applications of
deciBels, are very often ambiguous and have to have additional context
or explanation if one really wants to remove all ambiguity.

Get a group of comm engineers in a room and see if anybody agrees on
the definition of SNR. Hint: don't get people started. There is no
single definition. deciBels are a similar animal. e.g., what is
power? What kind of power? RMS? Peak? Which is appropriate for
dB?

There are common uses that usually apply, but there are enough
inconsistencies that one has to be very careful. When writing, if in
doubt, spell it out. When reading, if in doubt, don't assume
anything, because it could be anything.

>>Perhaps the confusion is that FS is unitless and can be anything;
>>power, amplitude, time, price, whatever. Since it is just a
>>reference to a number within a number system, the output will then
>>have the units of whatever that number represents. Meanwhile, since
>>it is just a number within a particular dynamic range indicated by FS,
>>dBFS is still a useful expression for evaluating a system.
>>
>>But it is not inherently power or amplitude or anything. It takes on
>>the units (or unitlessness) of whatever the number system represents.
>>
>>>> Obviously, a square wave at full scale of a converter has more power
>>>> than, say, a sine wave or a 1% duty cycle signal at full scale. So,
>>>> how can one define dBFS so it represents how the figure is actually
>>>> used?
>>>
>>>Not a bad question, but I was hoping there was _THE_ definition.
>>>Apparently there is not. And this is really the crux of the issue (for
>>>dBFS). Some people say it's a peak (instantaneous) measurement, yet I
>>>see meters that use it for RMS measurements. I'm afraid the truth is
>>>that there is no universal meaning for it like there is for dBm, dBV,
>>>and several other dB units.
>>
>>dBx always takes on the units of the input values. The reference and
>>the measurement have to have the same units for the result to be
>>meaningful.
>
>It's true that the input units must be the same, but dB is actually
>unitless, since it's a ratio of two like units.
>Again, from Wikipedia:
>"Being a ratio of two measurements of a physical quantity in the same
>units, it is a dimensionless unit."

It is a dimensionless unit, but it can preserve the dimensions of the
input value. Or reflect them, whatever you want to call it.
Provide any quantity in dBm, or dBW, and without any other information
you also know the power level dimensions without ambiguity. That's
an odd thing to be able to do with a dimensionless number or a
dimensionles unit, whatever you wish to call it.

So one has to keep track of what's going on, regardless of what
Wikipedia says. Experienced people still get tripped up on it all
the time.

>>
>>>> How about "a signal at 0 dBFS is one whose instantaneous power
>>>
>>>I'm not comfortable with the concept of "instantaneous power." Rather, I
>>>think we have to just concede that the "dB" sometimes breaks tradition
>>>and works with instantanous quantities rather than power.
>>
>>It can be anything. Instantaneous, averaged, glacial, whatever.
>>Time may not be involved at all, or it might be.
>>
>>>> reaches but never exceeds the instantaneous power associated with full
>>>> scale of the converter"? Modifying your formula above, dBFS = 20 *
>>>> log_10(peak signal voltage / converter maximum voltage)
>>>
>>>That is essentially what I wrote last night. Thanks for your input, John.
>
>--
>John

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com

Eric Jacobsen

November 21st 10, 05:31 AM

On Sat, 20 Nov 2010 15:57:15 -0500, Randy Yates >
wrote:

(Don Pearce) writes:
>> [...]
>> FFS. The dB is NOT a unit of anything. It is a ratio expressed in log
>> form for convenience (to avoid huge numbers). Nothing more and nothing
>> less.
>
>"dB" is a ratio of powers.
>
> http://www.digitalsignallabs.com/db.pdf
>
>"dBm", "dBV", etc., are units.

Except it's not always. See my note to John O'Flaherty. Not all dBs
are created equal.

>--
>Randy Yates % "...the answer lies within your soul
>Digital Signal Labs % 'cause no one knows which side
% the coin will fall."
>http://www.digitalsignallabs.com % 'Big Wheels', *Out of the Blue*, ELO

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com

davew

November 21st 10, 10:10 AM

On Nov 21, 5:31*am, (Eric Jacobsen) wrote:
> On Sat, 20 Nov 2010 15:57:15 -0500, Randy Yates >
> wrote:
>
> (Don Pearce) writes:
> >> [...]
> >> FFS. The dB is NOT a unit of anything. It is a ratio expressed in log
> >> form for convenience (to avoid huge numbers). Nothing more and nothing
> >> less.
>
> >"dB" is a ratio of powers.
>
> > *http://www.digitalsignallabs.com/db.pdf
>
> >"dBm", "dBV", etc., are units.
>
> Except it's not always. * See my note to John O'Flaherty. *Not all dBs
> are created equal.
>
> >--
> >Randy Yates * * * * * * * * * * *% "...the answer lies within your soul
> >Digital Signal Labs * * * * * * *% * * * 'cause no one knows which side
> * * * * *% * * * * * * * * * the coin will fall."
> >http://www.digitalsignallabs.com% *'Big Wheels', *Out of the Blue*, ELO
>
> Eric Jacobsen
> Minister of Algorithms
> Abineau Communicationshttp://www.abineau.com

I don't know why there is so much confusion in this thread.
0 dBV = 1V. It is unambiguously 1V i.e. one volt, not just "one"
That's why it has a "V" slapped on the end.
0dB = 1 - just "one"
Dave.

Mike Rivers

November 21st 10, 01:46 PM

On 11/20/2010 3:09 PM, Randy Yates wrote:

> (for
> dBFS). Some people say it's a peak (instantaneous) measurement, yet I
> see meters that use it for RMS measurements. I'm afraid the truth is
> that there is no universal meaning for it like there is for dBm, dBV,
> and several other dB units.

You're still not getting it, Randy. 0 dBFS has a precise
definition. What it doesn't have (and you seem to object to
"not definitions") is a magnitude, either voltage or power,
that relates the maximum digital number that a system
component can deal with to a physical property that can be
measured. You don't MEASURE dBFS, you look at the number
represented by the bits at some time and that's it.

If you were to take a bunch of samples of program material
over time, represent them as dB relative to digital full
scale, and plug them into the general RMS formula, you could
indeed come up with an RMS value for that set of numbers.
But what would be the value of that information? It will
always be below zero, but you can't just crank up the level
until your "RMS dBFS" is closer to zero unless you don't
care about clipping or you're working with a known,
continuous waveform.

So you're getting engineering answers. We tend to be
practical folk, and use concepts that are physically
meaningful, not purely theoretical.

> I'm not comfortable with the concept of "instantaneous power." Rather, I
> think we have to just concede that the "dB" sometimes breaks tradition
> and works with instantanous quantities rather than power.

Initially dB referred to power because the Bel was a measure
of acoustic energy (which becomes power when related by
time). But it's always been a ratio to a given reference.
The Telephone Company (tm) defined a Transmission Unit as
the amount of attenuation in a mile of cable that could just
be detected by an average listener. This was important in
the days when you had to talk louder when making a long
distance call. It turned out that 1/10 of a Bel was about
equivalent to a Transmission Unit, so the deciBEL became a
useful measure.

As commonly used today, dB without any modifiers is usually
understood to be sound pressure level referenced to a
specific pressure in Pascals. We have "units" like dBA,
which means sound pressure measured through a bandpass
filter of a known transfer function. We have the "20"
formula for dB as a ratio since power is the product of two
physical quantities (voltage and current) where voltage is
only one, so we make then numbers work by compensating for
the "squared" term in the power equation.

If you have a dollar and I have fifty cents, you can say you
have 6 dB more money than I have (or maybe 3 dB more
spending power). If a TV station increases its power from
50,000 watts to 100,000 watts, that's a 3 dB increase. If
the digitized value of a sample is 1 bit smaller than
another sample, that's half the value, so we say that its
amplitude is 6 dB lower. If 1111111111111111 (that's 15 bits
plus the first bit representing the sign) is full scale,
then 111111111111111 is -6 dBFS.

--
"Today's production equipment is IT based and cannot be
operated without a passing knowledge of computing, although
it seems that it can be operated without a passing knowledge
of audio." - John Watkinson

http://mikeriversaudio.wordpress.com - useful and
interesting audio stuff

Eric Jacobsen

November 21st 10, 04:01 PM

On Sun, 21 Nov 2010 08:46:10 -0500, Mike Rivers >
wrote:

>On 11/20/2010 3:09 PM, Randy Yates wrote:
>
>> (for
>> dBFS). Some people say it's a peak (instantaneous) measurement, yet I
>> see meters that use it for RMS measurements. I'm afraid the truth is
>> that there is no universal meaning for it like there is for dBm, dBV,
>> and several other dB units.
>
>You're still not getting it, Randy. 0 dBFS has a precise
>definition. What it doesn't have (and you seem to object to
>"not definitions") is a magnitude, either voltage or power,
>that relates the maximum digital number that a system
>component can deal with to a physical property that can be
>measured. You don't MEASURE dBFS, you look at the number
>represented by the bits at some time and that's it.
>
>If you were to take a bunch of samples of program material
>over time, represent them as dB relative to digital full
>scale, and plug them into the general RMS formula, you could
>indeed come up with an RMS value for that set of numbers.
>But what would be the value of that information? It will
>always be below zero, but you can't just crank up the level
>until your "RMS dBFS" is closer to zero unless you don't
>care about clipping or you're working with a known,
>continuous waveform.
>
>So you're getting engineering answers. We tend to be
>practical folk, and use concepts that are physically
>meaningful, not purely theoretical.
>
>> I'm not comfortable with the concept of "instantaneous power." Rather, I
>> think we have to just concede that the "dB" sometimes breaks tradition
>> and works with instantanous quantities rather than power.
>
>Initially dB referred to power because the Bel was a measure
>of acoustic energy (which becomes power when related by
>time). But it's always been a ratio to a given reference.
>The Telephone Company (tm) defined a Transmission Unit as
>the amount of attenuation in a mile of cable that could just
>be detected by an average listener. This was important in
>the days when you had to talk louder when making a long
>distance call. It turned out that 1/10 of a Bel was about
>equivalent to a Transmission Unit, so the deciBEL became a
>useful measure.
>
>As commonly used today, dB without any modifiers is usually
>understood to be sound pressure level referenced to a
>specific pressure in Pascals.

I think this is exemplary of one issue. This may be true in your
area of work, that dB without a modifier has to do with sound
pressure, but in communications dB without a modifier is generally
representative of a unitless scale factor in a system. e.g., an
amplifier that increases the signal power by a factor or ten has 10dB
of gain. If 0dBW goes in, 10dBW comes out, if 0dBm goes in, 10dBm
comes out.

Since logarithms convert multiplication to addition, any application
of a scale factor in a signal chain, due to gain (e.g., amplifier) or
attenuation, (e.g., cable loss), can be represented in dB (without a
modifier). Antenna gain has this characteristic, but then it gets a
modifier (usually dBi) to indicate which sort of antenna provides the
reference gain.

So dB without a modifier is usually representative of a dimensionless
scale factor in the signal chain.

But not always. ;)

>We have "units" like dBA,
>which means sound pressure measured through a bandpass
>filter of a known transfer function. We have the "20"
>formula for dB as a ratio since power is the product of two
>physical quantities (voltage and current) where voltage is
>only one, so we make then numbers work by compensating for
>the "squared" term in the power equation.
>
>If you have a dollar and I have fifty cents, you can say you
>have 6 dB more money than I have (or maybe 3 dB more
>spending power). If a TV station increases its power from
>50,000 watts to 100,000 watts, that's a 3 dB increase. If
>the digitized value of a sample is 1 bit smaller than
>another sample, that's half the value, so we say that its
>amplitude is 6 dB lower. If 1111111111111111 (that's 15 bits
>plus the first bit representing the sign) is full scale,
>then 111111111111111 is -6 dBFS.
>
>
>--
>"Today's production equipment is IT based and cannot be
>operated without a passing knowledge of computing, although
>it seems that it can be operated without a passing knowledge
>of audio." - John Watkinson
>
>http://mikeriversaudio.wordpress.com - useful and
>interesting audio stuff

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com

Scott Dorsey

November 21st 10, 06:16 PM

Eric Jacobsen > wrote:
>On Sun, 21 Nov 2010 08:46:10 -0500, Mike Rivers >
>wrote:
>>
>>As commonly used today, dB without any modifiers is usually
>>understood to be sound pressure level referenced to a
>>specific pressure in Pascals.
>
>I think this is exemplary of one issue. This may be true in your
>area of work, that dB without a modifier has to do with sound
>pressure, but in communications dB without a modifier is generally
>representative of a unitless scale factor in a system. e.g., an
>amplifier that increases the signal power by a factor or ten has 10dB
>of gain. If 0dBW goes in, 10dBW comes out, if 0dBm goes in, 10dBm
>comes out.

I believe that Mike is incorrect in this. Some people DO use "dB" to
mean "dBSPL." However, those people are wrong.
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

Mike Rivers

November 21st 10, 07:02 PM

On 11/21/2010 11:01 AM, Eric Jacobsen wrote:

> in communications dB without a modifier is generally
> representative of a unitless scale factor in a system.

You mean they actually get it right? Really, audio people
for the most part understand this as well, and they know
that gain or signal-to-noise ratio is expressed simply as
"dB." However then you see spec sheets that read: "Noise:
-86 dB" and you don't know what they're talking about. If
it's electronics, it's surely not SPL. It's probably dBu but
only your hairdresser knows for sure.

> amplifier that increases the signal power by a factor or ten has 10dB
> of gain. If 0dBW goes in, 10dBW comes out, if 0dBm goes in, 10dBm
> comes out.

In the RF world, you put power into an amplifier and get
more power out. You have to. It goes with the territory. At
the frequencies where you're working, it's important to
provide the proper load impedance for the feedline in order
to avoid loss from standing waves. But this tread initiated
(at least for me) in rec.audio.pro and had audio
connotations, so let's stick to audio.

In audio you put voltage into a signal processor (like an
equalizer, compressor, or even a mic preamp) and you get
voltage out. You can make sense of a gain specification or
measurement in dB. You put voltage into a power amplifier
and you (intend to) get power out, so dB of gain doesn't
make much sense. Nor does it when you put in voltage and get
a digital word out.

> So dB without a modifier is usually representative of a dimensionless
> scale factor in the signal chain.
> But not always. ;)

My statement that it CONVENTIONALLY represented sound
pressure level doesn't mean that it's correct. It's a
reasonably well understood mistake, or bad shorthand. Take
your pick.

--
"Today's production equipment is IT based and cannot be
operated without a passing knowledge of computing, although
it seems that it can be operated without a passing knowledge
of audio." - John Watkinson

http://mikeriversaudio.wordpress.com - useful and
interesting audio stuff

Fred Marshall[_2_]

November 21st 10, 07:55 PM

On 11/21/2010 10:16 AM, Scott Dorsey wrote:
> Eric > wrote:
>> On Sun, 21 Nov 2010 08:46:10 -0500, Mike >
>> wrote:
>>>
>>> As commonly used today, dB without any modifiers is usually
>>> understood to be sound pressure level referenced to a
>>> specific pressure in Pascals.
>>
>> I think this is exemplary of one issue. This may be true in your
>> area of work, that dB without a modifier has to do with sound
>> pressure, but in communications dB without a modifier is generally
>> representative of a unitless scale factor in a system. e.g., an
>> amplifier that increases the signal power by a factor or ten has 10dB
>> of gain. If 0dBW goes in, 10dBW comes out, if 0dBm goes in, 10dBm
>> comes out.
>
> I believe that Mike is incorrect in this. Some people DO use "dB" to
> mean "dBSPL." However, those people are wrong.
> --scott
>
>

In decades of working with sound, I have always heard coloquially "dB"
but it was always understood to mean "dB" relative to 1 micropascal for
underwater applications (up to 1970 it had been the microbar so we had
to add 100dB to absolute levels thereafter) and relative to 20
micropascals for airborne sound.
You can Google enough references to the need for knowing the particular
reference system you're using....

When you're in a system or physical context then it's shorthand to say
"dB" for absolute levels - but everyone who has thought about it even
just a little bit understands what they really mean. It was one of the
*first* things I learned out of school in the real world of acoustics.

Then, as one switches from underwater to air and vice versa, we
understand that the SPL absolute reference changes as above.

I don't think that Mike is wrong - he did say "referenced to a specific
pressure". In communications had been pretty typical to talk about "dB"
in reference to *particular* voltage levels.

That said, I won't argue against it being a unitless measure in a system
- as it is, after all, all about ratios.

It depends on your context. The amplifier example is a good one. But,
in that case we're talking in the context of out/in ratio. In system
examples we often talk about *absolute* levels and need a reference
level to do so. In other cases we do talk about out/in ratios: e.g.
transmission loss and the absolute level issue isn't included.

Here's a system example - it could be sonar or space communications or
.......:

We start with a transmitter with output of "150 dB". Well, that means
relative to something - it's a statement of absolute level.
Then, we run the transmitter output through a channel that attenuates
the signal by 100 dB. This statement of "dB" is purely a ratio with no
reference level involved as it is the ratio of in/out .
Then, we receive the signal and we're interested in the absolute level
being received because we have a transducer conversion to deal with and
environmental noise to overcome and system noise to overcome.
The absolute level received in this case is:
150 - 100 = 50 dB relative to our original reference.

Notice that here we mix references to fixed absolute levels with
references to pure ratios in order to get what we need. So, both uses
are appropriate.

The logs just make it easier to compute and to comprehend when one is
used to it. This is no different than saying:

200upa/10^5 = 0.002upa
or
7w/m^2/10^10 = 0.007uW/m^2

which both use a ratio equivalent to 100dB.

Fred

John O'Flaherty

November 21st 10, 09:39 PM

On Sun, 21 Nov 2010 05:23:37 GMT, (Eric
Jacobsen) wrote:

>On Sat, 20 Nov 2010 17:19:53 -0600, John O'Flaherty
> wrote:
>
>>On Sat, 20 Nov 2010 20:44:55 GMT, (Eric
>>Jacobsen) wrote:
>>
>>>On Sat, 20 Nov 2010 15:09:19 -0500, Randy Yates >
>>>wrote:
>>>
>>>>John O'Flaherty > writes:
>>>>
>>>>> On Fri, 19 Nov 2010 21:46:25 -0500, Randy Yates >
>>>>> wrote:
>>>>>
(Scott Dorsey) writes:
>>>>>>
>>>>>>> In article >, Randy Yates > wrote:
>>>>>>>>
>>>>>>>>If dBFS is defined as
>>>>>>>>
>>>>>>>> dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),
>>>>>>>>
>>>>>>>>where XRMS is the RMS value of the digital data stream, and you're
>>>>>>>>generating a "digital square wave," then you are wrong. The digital
>>>>>>>>square wave can go to +3dBFS as defined above.
>>>>>>>
>>>>>>> dBFS has not got a damn thing to do with sine waves or reference levels
>>>>>>> or anything in the analogue world.
>>>>>>
>>>>>>Again, I'm not asking how it's not defined, I'm asking how it is
>>>>>>defined.
>>>>>>
>>>>>>You guys have danced around this one all day. It's getting humorous.
>>>>>>
>>>>>>> It has ONLY to do with how far a digital level is below the point at
>>>>>>> which the digital value reaches full scale (all bits on).
>>>>>>
>>>>>>If you know what it means, and you're literate, then you should be able
>>>>>>to come up with a precise definition. I haven't seen one yet.
>>>>>
>>>>> The problem is that dB is defined as a unit of power, usually applied
>>>>> to signals with some time duration.
>>>>
>>>>YES!!! Thank you, John!
>>>
>>>Except he's wrong.
>>>
>>>As others have said, dB is a way of rescaling and is independent of
>>>the units involved or the characteristics of the measurement. It is
>>>simply the scaled log of a ratio, where one of the terms in the ratio
>>>is a reference level. If the reference level and the measurement
>>>have units of power, then the resulting dB value will have units of
>>>power, and will usually reflect that, e.g., dBm, dBW, etc. If the
>>>reference level and measurement have units of amplitude, then the
>>>output will generally reflect that as well, e.g., dBV.
>>
>>But it isn't an independent way of rescaling a measurement. If it
>>were, then the formula for dB as a ratio of voltages would have the
>>same form as that for a ratio of powers: 10 * log(v2/v1). The fact
>>that it has 20 means that it is squaring the voltage ratio to make it
>>a power ratio (implicitly assuming constant impedance). It's a hybrid
>>system of units when it is dBV, but it still represents a power ratio.
>> Wikipedia offers this definition for "decibel":
>>"A ratio in decibels is ten times the logarithm to base 10 of the
>>ratio of two power quantities.", citing this:
>>" IEEE Standard 100 Dictionary of IEEE Standards Terms, Seventh
>>Edition, The Institute of Electrical and Electronics Engineering, New
>>York, 2000; ISBN 0-7381-2601-2; page 288"
>>
>>This isn't to say that it's not used otherwise, but that's the
>>definition.
>
>The issue is that it's muddy and not consistently used and hasn't been
>nearly since inception. Antenna gains, e.g., dBi, Sound pressures,
>e.g., dBSPL, radar cross sectional area, dBsm, bandwidth, e.g., dBHz,
>and the current topic, dBFS, are often used with or implemented with
>power measurements, but they aren't really power, and sometimes don't
>have anything to do with power.

But antenna gains are compared to the power provided by an isotropic
antenna, aren't they? For dBSPL, it's a power measurement too. Though
it's called a pressure level, the defining formula involves pressure
squared, so it should be interpreted as the pressure corresponding to
a particular power level. What criterion do you use to decide whether
to include a factor of 10 or a factor of 20 in your formula?

>The point is that it's just an equation to plug numbers into, and the
>meaning is only relevant to the interpretation of what got plugged in.
>
>Things like dBFS, or even dBC or other common applications of
>deciBels, are very often ambiguous and have to have additional context
>or explanation if one really wants to remove all ambiguity.
>
>Get a group of comm engineers in a room and see if anybody agrees on
>the definition of SNR. Hint: don't get people started. There is no
>single definition. deciBels are a similar animal. e.g., what is
>power? What kind of power? RMS? Peak? Which is appropriate for
>dB?

Power is rate of transfer of energy, and its time distribution, its
form, and its location of measurement require further specification,
but I don't see why dB shouldn't be applicable to all cases.

>There are common uses that usually apply, but there are enough
>inconsistencies that one has to be very careful. When writing, if in
>doubt, spell it out. When reading, if in doubt, don't assume
>anything, because it could be anything.
>
>>>Perhaps the confusion is that FS is unitless and can be anything;
>>>power, amplitude, time, price, whatever. Since it is just a
>>>reference to a number within a number system, the output will then
>>>have the units of whatever that number represents. Meanwhile, since
>>>it is just a number within a particular dynamic range indicated by FS,
>>>dBFS is still a useful expression for evaluating a system.
>>>
>>>But it is not inherently power or amplitude or anything. It takes on
>>>the units (or unitlessness) of whatever the number system represents.

Why then is a factor of 20 used for voltages rather than a factor of
10? Are there any actual examples of the use of dBFS that don't relate
to a full-scale voltage or current? Of course, the FS has to be
defined- voltage current, pressure. But I bet that anyone who was
using a full scale defined in terms of power would use a formula with
a factor of 10, not 20.

>>>>> Obviously, a square wave at full scale of a converter has more power
>>>>> than, say, a sine wave or a 1% duty cycle signal at full scale. So,
>>>>> how can one define dBFS so it represents how the figure is actually
>>>>> used?
>>>>
>>>>Not a bad question, but I was hoping there was _THE_ definition.
>>>>Apparently there is not. And this is really the crux of the issue (for
>>>>dBFS). Some people say it's a peak (instantaneous) measurement, yet I
>>>>see meters that use it for RMS measurements. I'm afraid the truth is
>>>>that there is no universal meaning for it like there is for dBm, dBV,
>>>>and several other dB units.
>>>
>>>dBx always takes on the units of the input values. The reference and
>>>the measurement have to have the same units for the result to be
>>>meaningful.
>>
>>It's true that the input units must be the same, but dB is actually
>>unitless, since it's a ratio of two like units.
>>Again, from Wikipedia:
>>"Being a ratio of two measurements of a physical quantity in the same
>>units, it is a dimensionless unit."
>
>It is a dimensionless unit, but it can preserve the dimensions of the
>input value. Or reflect them, whatever you want to call it.
>Provide any quantity in dBm, or dBW, and without any other information
>you also know the power level dimensions without ambiguity. That's
>an odd thing to be able to do with a dimensionless number or a
>dimensionles unit, whatever you wish to call it.
>
>So one has to keep track of what's going on, regardless of what
>Wikipedia says. Experienced people still get tripped up on it all
>the time.

Yes, dB per se is unitless but dBm and dBW aren't. +20 dB has no
units, but +20 dBm means 100 milliwatts. If you append RMS to dB,
that's a procedural specification, and you can have +10 dBVRMS, where
a unit is specified as well as the measurement procedure.
I agree that everything should be specified; nevertheless, if dB is
used for something that is not power, or not directly relatable to
power, I think it's being misused.

>>>
>>>>> How about "a signal at 0 dBFS is one whose instantaneous power
>>>>
>>>>I'm not comfortable with the concept of "instantaneous power." Rather, I
>>>>think we have to just concede that the "dB" sometimes breaks tradition
>>>>and works with instantanous quantities rather than power.
>>>
>>>It can be anything. Instantaneous, averaged, glacial, whatever.
>>>Time may not be involved at all, or it might be.
>>>
>>>>> reaches but never exceeds the instantaneous power associated with full
>>>>> scale of the converter"? Modifying your formula above, dBFS = 20 *
>>>>> log_10(peak signal voltage / converter maximum voltage)
>>>>
>>>>That is essentially what I wrote last night. Thanks for your input, John.

--
John

PStamler

November 21st 10, 11:18 PM

On Nov 21, 12:16*pm, (Scott Dorsey) wrote:

> I believe that Mike is incorrect in this. *Some people DO use "dB" to
> mean "dBSPL." *However, those people are wrong.

Scott, we had this debate here a couple of years ago, and what it came
down to was a discussion between what would in the world of
lexicography be called prescriptivists and descriptivists. A
prescriptivist writes a dictionary to tell people what words mean and
how they should be used. A descriptivist writes a dictionary to tell
what people mean by words and how they use them. It's a philosophical
and practical division.

So a descriptivist would say that one meaning for dB is as a shorthand
for dBSPL, which is how a lot of audio engineers use it. A
prescriptivist would say, as you did, that's wrong, because it doesn't
correspond with the officially-defined meaning of dB.

More to the point, someone who uses "dB" to mean the voltage gain of
something, ignoring the power aspects, is violating the official
definition. But that usage is near-universal among audio circuit
designers, who talk about opanp circuits with "20dB of gain", and mean
a voltage gain of 10x, with no reference to impedance or power. They
may even refer to dB of gain in a transformer, which can never have
any power gain, being a passive device.

Whether you accept that this is the usage of the population, or
condemn it as wrong, is a choice, just as a dictionary-maker must
choose whether to be prescriptivist or descriptivist. The fact is that
the speech of the community has taken a turn which deviates
significantly from the official standards.

Parenthetically, we invented dBu as a standard when people stopped
using dBm; perhaps it's time to invent dBG for voltage gain
situations.

Peace,
Paul

John O'Flaherty

November 22nd 10, 04:41 AM

On Sun, 21 Nov 2010 15:18:08 -0800 (PST), PStamler
> wrote:

>On Nov 21, 12:16*pm, (Scott Dorsey) wrote:
>
>> I believe that Mike is incorrect in this. *Some people DO use "dB" to
>> mean "dBSPL." *However, those people are wrong.
>
>Scott, we had this debate here a couple of years ago, and what it came
>down to was a discussion between what would in the world of
>lexicography be called prescriptivists and descriptivists. A
>prescriptivist writes a dictionary to tell people what words mean and
>how they should be used. A descriptivist writes a dictionary to tell
>what people mean by words and how they use them. It's a philosophical
>and practical division.
>
>So a descriptivist would say that one meaning for dB is as a shorthand
>for dBSPL, which is how a lot of audio engineers use it. A
>prescriptivist would say, as you did, that's wrong, because it doesn't
>correspond with the officially-defined meaning of dB.
>
>More to the point, someone who uses "dB" to mean the voltage gain of
>something, ignoring the power aspects, is violating the official
>definition. But that usage is near-universal among audio circuit
>designers, who talk about opanp circuits with "20dB of gain", and mean
>a voltage gain of 10x, with no reference to impedance or power. They
>may even refer to dB of gain in a transformer, which can never have
>any power gain, being a passive device.
>
>Whether you accept that this is the usage of the population, or
>condemn it as wrong, is a choice, just as a dictionary-maker must
>choose whether to be prescriptivist or descriptivist. The fact is that
>the speech of the community has taken a turn which deviates
>significantly from the official standards.
>
>Parenthetically, we invented dBu as a standard when people stopped
>using dBm; perhaps it's time to invent dBG for voltage gain
>situations.

There is a sense in which calling a voltage gain of 10 a gain of 20 dB
does refer to power. In a circuit in which nothing is changed but that
gain (including output loading and input signal level), if that gain
is reduced to 0 dB, the output power level will be reduced by a factor
of 100.
Similarly, suppose a converter is fed a signal that runs it at a level
of -6 dBFS. Halving the input power (f.e., by decreasing a voltage
input by a factor of 1.414) will shift the converter to -9 dBFS.
Quadrupling the input power by doubling the input level will move the
converter to 0 dBFS. The output powers will show the same dB changes
(assuming linearity and no tricks).
I believe these examples show the power nature of dB measurements.

--
John

John O'Flaherty

November 22nd 10, 04:57 AM

On Sun, 21 Nov 2010 22:41:07 -0600, John O'Flaherty
> wrote:

>On Sun, 21 Nov 2010 15:18:08 -0800 (PST), PStamler
> wrote:
>
>>On Nov 21, 12:16*pm, (Scott Dorsey) wrote:
>>
>>> I believe that Mike is incorrect in this. *Some people DO use "dB" to
>>> mean "dBSPL." *However, those people are wrong.
>>
>>Scott, we had this debate here a couple of years ago, and what it came
>>down to was a discussion between what would in the world of
>>lexicography be called prescriptivists and descriptivists. A
>>prescriptivist writes a dictionary to tell people what words mean and
>>how they should be used. A descriptivist writes a dictionary to tell
>>what people mean by words and how they use them. It's a philosophical
>>and practical division.
>>
>>So a descriptivist would say that one meaning for dB is as a shorthand
>>for dBSPL, which is how a lot of audio engineers use it. A
>>prescriptivist would say, as you did, that's wrong, because it doesn't
>>correspond with the officially-defined meaning of dB.
>>
>>More to the point, someone who uses "dB" to mean the voltage gain of
>>something, ignoring the power aspects, is violating the official
>>definition. But that usage is near-universal among audio circuit
>>designers, who talk about opanp circuits with "20dB of gain", and mean
>>a voltage gain of 10x, with no reference to impedance or power. They
>>may even refer to dB of gain in a transformer, which can never have
>>any power gain, being a passive device.
>>
>>Whether you accept that this is the usage of the population, or
>>condemn it as wrong, is a choice, just as a dictionary-maker must
>>choose whether to be prescriptivist or descriptivist. The fact is that
>>the speech of the community has taken a turn which deviates
>>significantly from the official standards.
>>
>>Parenthetically, we invented dBu as a standard when people stopped
>>using dBm; perhaps it's time to invent dBG for voltage gain
>>situations.
>
>There is a sense in which calling a voltage gain of 10 a gain of 20 dB
>does refer to power. In a circuit in which nothing is changed but that
>gain (including output loading and input signal level), if that gain
>is reduced to 0 dB, the output power level will be reduced by a factor
>of 100.
>Similarly, suppose a converter is fed a signal that runs it at a level
>of -6 dBFS. Halving the input power (f.e., by decreasing a voltage
>input by a factor of 1.414) will shift the converter to -9 dBFS.
>Quadrupling the input power by doubling the input level will move the
>converter to 0 dBFS. The output powers will show the same dB changes
>(assuming linearity and no tricks).

I misspoke on that last sentence; there is no physical power
associated with the numbers from a converter. But if and when the
output is converted to analog again, the system output will reflect
the power changes.

>I believe these examples show the power nature of dB measurements.

--
John

Eric Jacobsen

November 22nd 10, 06:53 AM

On Sun, 21 Nov 2010 15:39:11 -0600, John O'Flaherty
> wrote:

>On Sun, 21 Nov 2010 05:23:37 GMT, (Eric
>Jacobsen) wrote:
>
>>On Sat, 20 Nov 2010 17:19:53 -0600, John O'Flaherty
> wrote:
>>
>>>On Sat, 20 Nov 2010 20:44:55 GMT, (Eric
>>>Jacobsen) wrote:
>>>
>>>>On Sat, 20 Nov 2010 15:09:19 -0500, Randy Yates >
>>>>wrote:
>>>>
>>>>>John O'Flaherty > writes:
>>>>>
>>>>>> On Fri, 19 Nov 2010 21:46:25 -0500, Randy Yates >
>>>>>> wrote:
>>>>>>
(Scott Dorsey) writes:
>>>>>>>
>>>>>>>> In article >, Randy Yates > wrote:
>>>>>>>>>
>>>>>>>>>If dBFS is defined as
>>>>>>>>>
>>>>>>>>> dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),
>>>>>>>>>
>>>>>>>>>where XRMS is the RMS value of the digital data stream, and you're
>>>>>>>>>generating a "digital square wave," then you are wrong. The digital
>>>>>>>>>square wave can go to +3dBFS as defined above.
>>>>>>>>
>>>>>>>> dBFS has not got a damn thing to do with sine waves or reference levels
>>>>>>>> or anything in the analogue world.
>>>>>>>
>>>>>>>Again, I'm not asking how it's not defined, I'm asking how it is
>>>>>>>defined.
>>>>>>>
>>>>>>>You guys have danced around this one all day. It's getting humorous.
>>>>>>>
>>>>>>>> It has ONLY to do with how far a digital level is below the point at
>>>>>>>> which the digital value reaches full scale (all bits on).
>>>>>>>
>>>>>>>If you know what it means, and you're literate, then you should be able
>>>>>>>to come up with a precise definition. I haven't seen one yet.
>>>>>>
>>>>>> The problem is that dB is defined as a unit of power, usually applied
>>>>>> to signals with some time duration.
>>>>>
>>>>>YES!!! Thank you, John!
>>>>
>>>>Except he's wrong.
>>>>
>>>>As others have said, dB is a way of rescaling and is independent of
>>>>the units involved or the characteristics of the measurement. It is
>>>>simply the scaled log of a ratio, where one of the terms in the ratio
>>>>is a reference level. If the reference level and the measurement
>>>>have units of power, then the resulting dB value will have units of
>>>>power, and will usually reflect that, e.g., dBm, dBW, etc. If the
>>>>reference level and measurement have units of amplitude, then the
>>>>output will generally reflect that as well, e.g., dBV.
>>>
>>>But it isn't an independent way of rescaling a measurement. If it
>>>were, then the formula for dB as a ratio of voltages would have the
>>>same form as that for a ratio of powers: 10 * log(v2/v1). The fact
>>>that it has 20 means that it is squaring the voltage ratio to make it
>>>a power ratio (implicitly assuming constant impedance). It's a hybrid
>>>system of units when it is dBV, but it still represents a power ratio.
>>> Wikipedia offers this definition for "decibel":
>>>"A ratio in decibels is ten times the logarithm to base 10 of the
>>>ratio of two power quantities.", citing this:
>>>" IEEE Standard 100 Dictionary of IEEE Standards Terms, Seventh
>>>Edition, The Institute of Electrical and Electronics Engineering, New
>>>York, 2000; ISBN 0-7381-2601-2; page 288"
>>>
>>>This isn't to say that it's not used otherwise, but that's the
>>>definition.
>>
>>The issue is that it's muddy and not consistently used and hasn't been
>>nearly since inception. Antenna gains, e.g., dBi, Sound pressures,
>>e.g., dBSPL, radar cross sectional area, dBsm, bandwidth, e.g., dBHz,
>>and the current topic, dBFS, are often used with or implemented with
>>power measurements, but they aren't really power, and sometimes don't
>>have anything to do with power.
>
>But antenna gains are compared to the power provided by an isotropic
>antenna, aren't they? For dBSPL, it's a power measurement too. Though
>it's called a pressure level, the defining formula involves pressure
>squared, so it should be interpreted as the pressure corresponding to
>a particular power level. What criterion do you use to decide whether
>to include a factor of 10 or a factor of 20 in your formula?

Like any computation, dimensional analysis suggests one uses whatever
makes the computation consistent so that the result is useful.

Consider an amplifer (which is pretty much the same as an antenna for
this purpose, gain is gain). If one were comparing voltage gain,
then one has to be consistent with that. If one is comparing (or
computing) power gain, then one has to be consistent with that.
Power is the most convenient partly because it removes the ambiguity
associated with impedance. So that gets used most often, hence the
additional factor of two when using voltages for most cases.

The "10" is pretty much an arbitrary scale factor, and it turns into
"20" so that people can mix power and voltage measures (with careful
assumptions).

>>The point is that it's just an equation to plug numbers into, and the
>>meaning is only relevant to the interpretation of what got plugged in.
>>
>>Things like dBFS, or even dBC or other common applications of
>>deciBels, are very often ambiguous and have to have additional context
>>or explanation if one really wants to remove all ambiguity.
>>
>>Get a group of comm engineers in a room and see if anybody agrees on
>>the definition of SNR. Hint: don't get people started. There is no
>>single definition. deciBels are a similar animal. e.g., what is
>>power? What kind of power? RMS? Peak? Which is appropriate for
>>dB?
>
>Power is rate of transfer of energy, and its time distribution, its
>form, and its location of measurement require further specification,
>but I don't see why dB shouldn't be applicable to all cases.

It is applicable, but it's not as clearly defined as some think or are
at least expressing here. Power measurement, as you just said,
requires integration over time. How much time? It is often
(usually) not specified, so there's already ambiguity in the
"definition" or "standard". "Instantaneous power" is a hand-wavy way
around that, but you can't measure that practically, so time
integration is required. How much is up to the implementer. ;)

>>There are common uses that usually apply, but there are enough
>>inconsistencies that one has to be very careful. When writing, if in
>>doubt, spell it out. When reading, if in doubt, don't assume
>>anything, because it could be anything.
>>
>>>>Perhaps the confusion is that FS is unitless and can be anything;
>>>>power, amplitude, time, price, whatever. Since it is just a
>>>>reference to a number within a number system, the output will then
>>>>have the units of whatever that number represents. Meanwhile, since
>>>>it is just a number within a particular dynamic range indicated by FS,
>>>>dBFS is still a useful expression for evaluating a system.
>>>>
>>>>But it is not inherently power or amplitude or anything. It takes on
>>>>the units (or unitlessness) of whatever the number system represents.
>
>Why then is a factor of 20 used for voltages rather than a factor of
>10?

To make voltage and power measurements compatible.

>Are there any actual examples of the use of dBFS that don't relate
>to a full-scale voltage or current? Of course, the FS has to be
>defined- voltage current, pressure. But I bet that anyone who was
>using a full scale defined in terms of power would use a formula with
>a factor of 10, not 20.

Actually, dBFS implies a digital number scale system, so the
traditional notions of voltage or current or power don't really even
apply any more. The analysis is performed on a numeric sequence,
which could represent anything. A single sample can be taken from
the numeric sequence, say X, and dBFS could be computed as either

ans = 10*log(X/FS) if one were interested in interpreting X as an
instantaneous power measurement (and ADCs often have internal
integration over some fraction of the sample period so that can be
argued). This follows the definition of RMS for a numeric sequence
when n = 1, as long as X is positive.

or

ans = 10*log(X/FS) if one were interested in interpreting X as a
voltage.

I'd suggest, though, that one use whatever is consistent with the rest
of the analysis being performed.

There's nothing magical about the factor of 10 or 20. As always, one
just has to keep track of what one is doing and be consistent to get a
useful result.

>>>>>> Obviously, a square wave at full scale of a converter has more power
>>>>>> than, say, a sine wave or a 1% duty cycle signal at full scale. So,
>>>>>> how can one define dBFS so it represents how the figure is actually
>>>>>> used?
>>>>>
>>>>>Not a bad question, but I was hoping there was _THE_ definition.
>>>>>Apparently there is not. And this is really the crux of the issue (for
>>>>>dBFS). Some people say it's a peak (instantaneous) measurement, yet I
>>>>>see meters that use it for RMS measurements. I'm afraid the truth is
>>>>>that there is no universal meaning for it like there is for dBm, dBV,
>>>>>and several other dB units.
>>>>
>>>>dBx always takes on the units of the input values. The reference and
>>>>the measurement have to have the same units for the result to be
>>>>meaningful.
>>>
>>>It's true that the input units must be the same, but dB is actually
>>>unitless, since it's a ratio of two like units.
>>>Again, from Wikipedia:
>>>"Being a ratio of two measurements of a physical quantity in the same
>>>units, it is a dimensionless unit."
>>
>>It is a dimensionless unit, but it can preserve the dimensions of the
>>input value. Or reflect them, whatever you want to call it.
>>Provide any quantity in dBm, or dBW, and without any other information
>>you also know the power level dimensions without ambiguity. That's
>>an odd thing to be able to do with a dimensionless number or a
>>dimensionles unit, whatever you wish to call it.
>>
>>So one has to keep track of what's going on, regardless of what
>>Wikipedia says. Experienced people still get tripped up on it all
>>the time.
>
>Yes, dB per se is unitless but dBm and dBW aren't. +20 dB has no
>units, but +20 dBm means 100 milliwatts. If you append RMS to dB,
>that's a procedural specification, and you can have +10 dBVRMS, where
>a unit is specified as well as the measurement procedure.
>I agree that everything should be specified; nevertheless, if dB is
>used for something that is not power, or not directly relatable to
>power, I think it's being misused.

dBm and dBW are, actually, strictly speaking, still unitless or
dimensionless. The units cancel in the ratio of the reference and the
measurement, which HAVE to have the same units to get a meaningful
result. dBm and dBW (and others, but definitely not all) have the
odd property that they completely define a dimension, despite being
dimensionless. They still carry or reflect (or whatever) the
indicated dimensional unit with the quantity conveyed. Sort of.
IMHO, that's actually a hint that one has to pay attention to what one
is doing to get usable results.

>
>>>>
>>>>>> How about "a signal at 0 dBFS is one whose instantaneous power
>>>>>
>>>>>I'm not comfortable with the concept of "instantaneous power." Rather, I
>>>>>think we have to just concede that the "dB" sometimes breaks tradition
>>>>>and works with instantanous quantities rather than power.
>>>>
>>>>It can be anything. Instantaneous, averaged, glacial, whatever.
>>>>Time may not be involved at all, or it might be.
>>>>
>>>>>> reaches but never exceeds the instantaneous power associated with full
>>>>>> scale of the converter"? Modifying your formula above, dBFS = 20 *
>>>>>> log_10(peak signal voltage / converter maximum voltage)
>>>>>
>>>>>That is essentially what I wrote last night. Thanks for your input, John.
>
>--
>John

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com

PStamler

November 22nd 10, 07:14 AM

On Nov 21, 10:41*pm, John O'Flaherty > wrote:

> There is a sense in which calling a voltage gain of 10 a gain of 20 dB
> does refer to power. In a circuit in which nothing is changed but that
> gain (including output loading and input signal level), if that gain
> is reduced to 0 dB, the output power level will be reduced by a factor
> of 100.

Huh-uh. We had this discussion years ago.

Given a non-inverting opamp with high input impedance and negligible
output impedance, a 1k resistor from the + input to ground, and a 100k
resistor from the output to ground (in other words a 100k load).
Assume the feedback resistance network is high enough that it draws
negligible current.

1V into 1k, at the input, means 1mA, so the power is 1mW. 10V into
100k at the output means 0.1mA, so the power is 1mW again. There's 0dB
power gain, but there's voltage gain of 10x, which is coded +20dB in
the voltage-gain realm of decibel calculation. This deviates from the
"real" standard of what decibels are, by divorcing the voltage and
power gains, but using the same unit for them, dB. The usage, however,
is nearly universal, so speaking as a descriptivist who believes that
dictionaries should reflect how people actually use the language,
perhaps the official definition needs revision to take into account
the dual usage of the term. I've suggested "dBG" as an indicator that
voltage gain is being discussed rather than power gain, and perhaps
that's the way to go.

Peace,
Paul

[other things snipped[

> I believe these examples show the power nature of dB measurements.

davew

November 22nd 10, 11:18 AM

On Nov 22, 7:14*am, PStamler > wrote:
> On Nov 21, 10:41*pm, John O'Flaherty > wrote:
>
> > There is a sense in which calling a voltage gain of 10 a gain of 20 dB
> > does refer to power. In a circuit in which nothing is changed but that
> > gain (including output loading and input signal level), if that gain
> > is reduced to 0 dB, the output power level will be reduced by a factor
> > of 100.
>
> Huh-uh. We had this discussion years ago.
>
> Given a non-inverting opamp with high input impedance and negligible
> output impedance, a 1k resistor from the + input to ground, and a 100k
> resistor from the output to ground (in other words a 100k load).
> Assume the feedback resistance network is high enough that it draws
> negligible current.
>
> 1V into 1k, at the input, means 1mA, so the power is 1mW. 10V into
> 100k at the output means 0.1mA, so the power is 1mW again. There's 0dB
> power gain, but there's voltage gain of 10x, which is coded +20dB in
> the voltage-gain realm of decibel calculation. This deviates from the
> "real" standard of what decibels are, by divorcing the voltage and
> power gains, but using the same unit for them, dB.
But, if I were to double the input voltage I would see a 6dB increase
in power output would I not? In context, the use of dB for voltage
gain is entirely correct and acceptable.

The usage, however,
> is nearly universal, so speaking as a descriptivist who believes that
> dictionaries should reflect how people actually use the language,
> perhaps the official definition needs revision to take into account
> the dual usage of the term. I've suggested "dBG" as an indicator that
> voltage gain is being discussed rather than power gain, and perhaps
> that's the way to go.
I think the world has already decided, so it's a bit late for a new
definition an in any case everyone would think that dBG was dB
referred to 1G. What's that? Gravity?

Adrian Tuddenham[_2_]

November 22nd 10, 12:41 PM

davew > wrote:

> On Nov 22, 7:14*am, PStamler > wrote:
[...]
> > 1V into 1k, at the input, means 1mA, so the power is 1mW. 10V into
> > 100k at the output means 0.1mA, so the power is 1mW again. There's 0dB
> > power gain, but there's voltage gain of 10x, which is coded +20dB in
> > the voltage-gain realm of decibel calculation. This deviates from the
> > "real" standard of what decibels are, by divorcing the voltage and
> > power gains, but using the same unit for them, dB.
> But, if I were to double the input voltage I would see a 6dB increase
> in power output would I not? In context, the use of dB for voltage
> gain is entirely correct and acceptable.

It can be used that way as long as the two voltages being compared are
across the same impedance and both relate to the power in the same way.
This was the case in your example.

You can compare voltages at two different places as long as the
impedances at those places are the same. So an amplifier working with
600-ohm input and output terminations could have its power gain
expressed in dB by just measuring the voltage gain.

What you must not do (which is all-too frequently done) is to use the
same calculation to compare voltages in different impedances. For that,
you must use the voltages to calculate the power at each point and then
compare the powers to get a result in dB. If you want to use a
logarithmic scale to compare voltages, call it something different (dBu,
dBV) because it is not "dB".

The convenient shortcut dB formula relating voltages is often taught
with insufficient emphasis being placed on the conditions for which it
is valid. After a while, people begin to believe that the voltage
formula is the true representation of dB until a situation arises where
it generates nonsense results - then they get confused and sometimes
adamant. At least one well-known textbook has got it wrong.

--
~ Adrian Tuddenham ~
(Remove the ".invalid"s and add ".co.uk" to reply)
www.poppyrecords.co.uk

Don Pearce[_3_]

November 22nd 10, 12:52 PM

On Mon, 22 Nov 2010 12:41:10 +0000,
(Adrian Tuddenham) wrote:

>davew > wrote:
>
>> On Nov 22, 7:14*am, PStamler > wrote:
>[...]
>> > 1V into 1k, at the input, means 1mA, so the power is 1mW. 10V into
>> > 100k at the output means 0.1mA, so the power is 1mW again. There's 0dB
>> > power gain, but there's voltage gain of 10x, which is coded +20dB in
>> > the voltage-gain realm of decibel calculation. This deviates from the
>> > "real" standard of what decibels are, by divorcing the voltage and
>> > power gains, but using the same unit for them, dB.
>> But, if I were to double the input voltage I would see a 6dB increase
>> in power output would I not? In context, the use of dB for voltage
>> gain is entirely correct and acceptable.
>
>It can be used that way as long as the two voltages being compared are
>across the same impedance and both relate to the power in the same way.
>This was the case in your example.
>
>You can compare voltages at two different places as long as the
>impedances at those places are the same. So an amplifier working with
>600-ohm input and output terminations could have its power gain
>expressed in dB by just measuring the voltage gain.
>
>What you must not do (which is all-too frequently done) is to use the
>same calculation to compare voltages in different impedances. For that,
>you must use the voltages to calculate the power at each point and then
>compare the powers to get a result in dB. If you want to use a
>logarithmic scale to compare voltages, call it something different (dBu,
>dBV) because it is not "dB".
>
>The convenient shortcut dB formula relating voltages is often taught
>with insufficient emphasis being placed on the conditions for which it
>is valid. After a while, people begin to believe that the voltage
>formula is the true representation of dB until a situation arises where
>it generates nonsense results - then they get confused and sometimes
>adamant. At least one well-known textbook has got it wrong.

The full equation is

20 log(v2/v1 *sqrt(z1/z2))

That gets the power gain right for any impedance. (V1 is across
impedance z1, and v2 is across z2).

d

davew

November 22nd 10, 01:52 PM

On Nov 22, 12:41*pm, (Adrian
Tuddenham) wrote:
> davew > wrote:
> > On Nov 22, 7:14*am, PStamler > wrote:
> [...]
> > > 1V into 1k, at the input, means 1mA, so the power is 1mW. 10V into
> > > 100k at the output means 0.1mA, so the power is 1mW again. There's 0dB
> > > power gain, but there's voltage gain of 10x, which is coded +20dB in
> > > the voltage-gain realm of decibel calculation. This deviates from the
> > > "real" standard of what decibels are, by divorcing the voltage and
> > > power gains, but using the same unit for them, dB.
> > But, if I were to double the input voltage I would see a 6dB increase
> > in power output would I not? *In context, the use of dB for voltage
> > gain is entirely correct and acceptable.
>
> It can be used that way as long as the two voltages being compared are
> across the same impedance and both relate to the power in the same way.
> This was the case in your example.
>
> You can compare voltages at two different places as long as the
> impedances at those places are the same. *So an amplifier working with
> 600-ohm input and output terminations could have its power gain
> expressed in dB by just measuring the voltage gain.
>
> What you must not do (which is all-too frequently done) is to use the
> same calculation to compare voltages in different impedances. *For that,
> you must use the voltages to calculate the power at each point and then
> compare the powers to get a result in dB. *If you want to use a
> logarithmic scale to compare voltages, call it something different (dBu,
> dBV) because it is not "dB".
>
> The convenient shortcut dB formula relating voltages is often taught
> with insufficient emphasis being placed on the conditions for which it
> is valid. *After a while, people begin to believe that the voltage
> formula is the true representation of dB until a situation arises where
> it generates nonsense results - then they get confused and sometimes
> adamant. *At least one well-known textbook has got it wrong.
>
> --
> ~ Adrian Tuddenham ~
> (Remove the ".invalid"s and add ".co.uk" to reply)www.poppyrecords.co.uk

This is all well and good, but in a lot of small signal territory and
in DSP, we don't care about power or impedances. We may worry about
output impedance and power drain of a small signal stage, for example,
but we would usually say that a given stage has a voltage gain, not a
power gain i.e. where voltage gain, not power gain, is the object.
So, a gain of 10 in the signal chain would result in an end output
power increase (assuming we were feeding some form of power amplifier)
of 20dB.

Consider a FET source follower as an example. Tremendous gain i.e.
power gain in dB but voltage gain of a little under unity or 0dB. Now
you ask a hundred analogue electronics engineers what the gain is in
dB and (yes it's a trick question) 99/100 will say a bit less than
0dB.

Mike Rivers

November 22nd 10, 02:24 PM

On 11/22/2010 7:41 AM, Adrian Tuddenham wrote:

> The convenient shortcut dB formula relating voltages is often taught
> with insufficient emphasis being placed on the conditions for which it
> is valid.

This is why it's only been used over the last 30 or maybe 40
years, while the "power dB" goes back 80 years or so. It's
only been since the adoption of the nearly universal
voltage-not-power scheme of interfacing. This is primarily a
result of the use of solid state electronics which
characteristically have nearly zero output (source)
impedance but without the ability to supply any significant
amount of current. It's just how things work now.

> After a while, people begin to believe that the voltage
> formula is the true representation of dB until a situation arises where
> it generates nonsense results

Not a lot of confusion, because, in general, audio people
TODAY work with dB of gain or voltage levels, and absolute
(not relative) watts when dealing with power levels. Someone
will understand a 100W or 200W amplifier, but won't think of
one having 3 dB more (power) gain than the other.

--
"Today's production equipment is IT based and cannot be
operated without a passing knowledge of computing, although
it seems that it can be operated without a passing knowledge
of audio." - John Watkinson

http://mikeriversaudio.wordpress.com - useful and
interesting audio stuff

Arny Krueger

November 22nd 10, 02:34 PM

"Mike Rivers" > wrote in message

> Someone will understand a 100W or 200W amplifier, but
> won't think of one having 3 dB more (power) gain than the
> other.

That would be their loss. If you compare amp power in dBs, and remember that
it takes about 10 dB to create the perception of "twice as loud", then a lot
of things in the real world that may seem mysterious become understandable.

Adrian Tuddenham[_2_]

November 22nd 10, 03:03 PM

davew > wrote:

> On Nov 22, 12:41*pm, (Adrian
> Tuddenham) wrote:
> > davew > wrote:
> > > On Nov 22, 7:14*am, PStamler > wrote:
> > [...]
> > > > 1V into 1k, at the input, means 1mA, so the power is 1mW. 10V into
> > > > 100k at the output means 0.1mA, so the power is 1mW again. There's 0dB
> > > > power gain, but there's voltage gain of 10x, which is coded +20dB in
> > > > the voltage-gain realm of decibel calculation. This deviates from the
> > > > "real" standard of what decibels are, by divorcing the voltage and
> > > > power gains, but using the same unit for them, dB.
> > > But, if I were to double the input voltage I would see a 6dB increase
> > > in power output would I not? *In context, the use of dB for voltage
> > > gain is entirely correct and acceptable.
> >
> > It can be used that way as long as the two voltages being compared are
> > across the same impedance and both relate to the power in the same way.
> > This was the case in your example.
> >
> > You can compare voltages at two different places as long as the
> > impedances at those places are the same. *So an amplifier working with
> > 600-ohm input and output terminations could have its power gain
> > expressed in dB by just measuring the voltage gain.
> >
> > What you must not do (which is all-too frequently done) is to use the
> > same calculation to compare voltages in different impedances. *For that,
> > you must use the voltages to calculate the power at each point and then
> > compare the powers to get a result in dB. *If you want to use a
> > logarithmic scale to compare voltages, call it something different (dBu,
> > dBV) because it is not "dB".
> >
> > The convenient shortcut dB formula relating voltages is often taught
> > with insufficient emphasis being placed on the conditions for which it
> > is valid. *After a while, people begin to believe that the voltage
> > formula is the true representation of dB until a situation arises where
> > it generates nonsense results - then they get confused and sometimes
> > adamant. *At least one well-known textbook has got it wrong.

> This is all well and good, but in a lot of small signal territory and
> in DSP, we don't care about power or impedances.

There is nothing wrong with that approach, but you must not then express
the ratios as 'dB'.

You may include the letters 'dB' to suggest a logarithmic scale as long
as they also have some sort of qualifier prefix or suffix to warn the
student or the pedant (or anyone in between) that you are not comparing
powers and these measurements do not follow the correct definition of a
decibel.

Much confusion has been caused over the years by the omission of that
qualifier. Try explaining to a student who is used to thinking of dB in
terms of voltage alone where the gain occurs in the following example:

http://www.poppyrecords.co.uk/other/images/Gain.gif

--
~ Adrian Tuddenham ~
(Remove the ".invalid"s and add ".co.uk" to reply)
www.poppyrecords.co.uk

November 22nd 10, 03:14 PM

In article >, "Arny Krueger" > wrote:
>"Mike Rivers" > wrote in message

>
>> Someone will understand a 100W or 200W amplifier, but
>> won't think of one having 3 dB more (power) gain than the
>> other.
>
>That would be their loss. If you compare amp power in dBs, and remember that
>it takes about 10 dB to create the perception of "twice as loud", then a lot
>of things in the real world that may seem mysterious become understandable.

You got to consider that.
But, for understanding basics, knowing 6 dB is twice the voltage is what
people should know and use, and talk about. The only thing power
dB is good for is speaker dissapation and cost of amplifiers, and
indirectly, mains power. Forget volume levels.

greg

Adrian Tuddenham[_2_]

November 22nd 10, 04:36 PM

GS > wrote:

> In article >,
> "Arny Krueger" > wrote:
> >"Mike Rivers" > wrote in message
>
> >
> >> Someone will understand a 100W or 200W amplifier, but
> >> won't think of one having 3 dB more (power) gain than the
> >> other.
> >
> >That would be their loss. If you compare amp power in dBs, and remember that
> >it takes about 10 dB to create the perception of "twice as loud", then a lot
> >of things in the real world that may seem mysterious become understandable.
>
> You got to consider that.
> But, for understanding basics, knowing 6 dB is twice the voltage is what
> people should know....

They should first know that dB is a power measurement, this is the
fundamental fact on which the rest is based. When they have grasped the
basics, then they can be shown that the voltage is a handy way of
comparing two power levels in the right circumstances (and they can
remember some handy voltage ratios if appropriate).

--
~ Adrian Tuddenham ~
(Remove the ".invalid"s and add ".co.uk" to reply)
www.poppyrecords.co.uk

John O'Flaherty

November 22nd 10, 04:46 PM

On Sun, 21 Nov 2010 23:14:27 -0800 (PST), PStamler
> wrote:

>On Nov 21, 10:41*pm, John O'Flaherty > wrote:
>
>> There is a sense in which calling a voltage gain of 10 a gain of 20 dB
>> does refer to power. In a circuit in which nothing is changed but that
>> gain (including output loading and input signal level), if that gain
>> is reduced to 0 dB, the output power level will be reduced by a factor
>> of 100.
>
>Huh-uh. We had this discussion years ago.
>
>Given a non-inverting opamp with high input impedance and negligible
>output impedance, a 1k resistor from the + input to ground, and a 100k
>resistor from the output to ground (in other words a 100k load).
>Assume the feedback resistance network is high enough that it draws
>negligible current.
>
>1V into 1k, at the input, means 1mA, so the power is 1mW. 10V into
>100k at the output means 0.1mA, so the power is 1mW again. There's 0dB
>power gain, but there's voltage gain of 10x, which is coded +20dB in
>the voltage-gain realm of decibel calculation. This deviates from the
>"real" standard of what decibels are, by divorcing the voltage and
>power gains, but using the same unit for them, dB. The usage, however,
>is nearly universal, so speaking as a descriptivist who believes that
>dictionaries should reflect how people actually use the language,
>perhaps the official definition needs revision to take into account
>the dual usage of the term. I've suggested "dBG" as an indicator that
>voltage gain is being discussed rather than power gain, and perhaps
>that's the way to go.

My point, though, was that it's not a comparison of input to output
power, but of the difference in output power that holds between an
amplifier with 20 dB gain vs. one with 19 dB or 0 dB, all else being
equal. If it ever gets to, say, a loudspeaker, there will be that
difference. I incline to descriptivism too, but it just seems to me
that this actual usage of "dB" does refer to power, in the sense I
meant.
--
John

John O'Flaherty

November 22nd 10, 05:18 PM

On Mon, 22 Nov 2010 06:53:48 GMT, (Eric
Jacobsen) wrote:

>On Sun, 21 Nov 2010 15:39:11 -0600, John O'Flaherty
> wrote:

{trimmed}

>>>Get a group of comm engineers in a room and see if anybody agrees on
>>>the definition of SNR. Hint: don't get people started. There is no
>>>single definition. deciBels are a similar animal. e.g., what is
>>>power? What kind of power? RMS? Peak? Which is appropriate for
>>>dB?
>>
>>Power is rate of transfer of energy, and its time distribution, its
>>form, and its location of measurement require further specification,
>>but I don't see why dB shouldn't be applicable to all cases.
>
>It is applicable, but it's not as clearly defined as some think or are
>at least expressing here. Power measurement, as you just said,
>requires integration over time. How much time? It is often
>(usually) not specified, so there's already ambiguity in the
>"definition" or "standard". "Instantaneous power" is a hand-wavy way
>around that, but you can't measure that practically, so time
>integration is required. How much is up to the implementer. ;)

But the measurement procedure is a separate question from what power
is and what dB means.

{trimmed again}

>>Are there any actual examples of the use of dBFS that don't relate
>>to a full-scale voltage or current? Of course, the FS has to be
>>defined- voltage current, pressure. But I bet that anyone who was
>>using a full scale defined in terms of power would use a formula with
>>a factor of 10, not 20.
>
>Actually, dBFS implies a digital number scale system, so the
>traditional notions of voltage or current or power don't really even
>apply any more. The analysis is performed on a numeric sequence,
>which could represent anything. A single sample can be taken from
>the numeric sequence, say X, and dBFS could be computed as either
>
>ans = 10*log(X/FS) if one were interested in interpreting X as an
>instantaneous power measurement (and ADCs often have internal
>integration over some fraction of the sample period so that can be
>argued). This follows the definition of RMS for a numeric sequence
>when n = 1, as long as X is positive.
>
>or
>
>ans = 10*log(X/FS) if one were interested in interpreting X as a
>voltage.

I'm assuming you meant 20 in that sentence. If so, I don't think we
disagree much. As you point out, when it's numeric, the use depends on
the interpretation. But if X _is_ being interpreted as a voltage, and
it is squared, then "ans" will be indistinguishable from a power
ratio.

>I'd suggest, though, that one use whatever is consistent with the rest
>of the analysis being performed.
>
>There's nothing magical about the factor of 10 or 20. As always, one
>just has to keep track of what one is doing and be consistent to get a
>useful result.

Hard to argue with that!

{trimmed yet again}

>>Yes, dB per se is unitless but dBm and dBW aren't. +20 dB has no
>>units, but +20 dBm means 100 milliwatts. If you append RMS to dB,
>>that's a procedural specification, and you can have +10 dBVRMS, where
>>a unit is specified as well as the measurement procedure.
>>I agree that everything should be specified; nevertheless, if dB is
>>used for something that is not power, or not directly relatable to
>>power, I think it's being misused.
>
>dBm and dBW are, actually, strictly speaking, still unitless or
>dimensionless. The units cancel in the ratio of the reference and the
>measurement, which HAVE to have the same units to get a meaningful
>result. dBm and dBW (and others, but definitely not all) have the
>odd property that they completely define a dimension, despite being
>dimensionless. They still carry or reflect (or whatever) the
>indicated dimensional unit with the quantity conveyed. Sort of.
>IMHO, that's actually a hint that one has to pay attention to what one
>is doing to get usable results.

Well, good point. You can't plug dBm into an ordinary equation and
have the units cancel correctly, so they just carry the information
about the unit.

--
John