before I try to answer your question directly
and
this goes to the fact that I haven't read the question properly
cos there is reference to floating point and bit depths and RMS etc
which are not directly dB issues

" So question 2 is what are those dB's referring to? dBu? "

never assume
if they don't say u or FS or A or V then it could be anything

dB is a relative scale ... a ratio of one to another
one signal is 3dB greater that another
there are mathematical laws that cover this

+3dbu is an absolute and has a definition
1dbu is 1 mW into a 600 ohm load

BUT

a. Dynamic range is loudest to softest so 110dB is correct
maths will give you this figure as a multiplier

b. Gain control ... max of 60dB more ... again maths can give this a multiplier

c. Voltage gain ... interesting why this figure is 80 while the above is 60

these are all good questions and worth discussing
but ask them one at a time
...
and this could turn into an interesting thread

errr yes
bit depths of 16 and 24 do lead to a difference in dynamic range

dB is used in many places and it is important not to mix and match you different " relatives "

got to go
no more net time today
back soon

apstrong wrote: .....I usually record at 24 bit using a Mackie Onyx 1640 interface. I have two questions: (1) if 24 bits allows 144dB of dynamic range, what is that 144dB? I mean: what kind of dB’s are these? Not dBFS. dBu? dBm? According to Wikipedia, there are about 25 different kinds of dB. So what does that 144dB actually mean? And (2) My Onyx manual says the following things:

a. Dynamic Range: >110 dB (mic in to main out)
b. Input gain control range: 0dB to +60dB
c. Maximum voltage gain: mic in to main output: 80dB

So question 2 is what are those dB's referring to? dBu?

It seems to me that you have a good understanding of deciBels and the way they work, but are not sure how to interpret manufacturers' data.

Firstly, when we use the level of 0dBFS, it is a figure that applies to a particular piece of equipment only, and can map to different absolute levels for different equipment. For example, a Yamaha 01V96 mixer has an 0dBFS of +24dBu, which gives a headroom of 20dB above the nominal level of +4dBu. An Alesis HD24 hard disc recorder has an 0dBFS of +19dBu, only a headroom of 15dB above the nominal +4dBu. Both are 24-bit units having a nominal level of +4dBu, but if you were to use an analog connection from an 01V96 output to the HD24 input, you could overdrive the HD24 by 5dB.

So I have already used three different dB measures: dBu, dBFS and plain dB. Plain dB is always a measure of ratio, which translates to a difference when using a logarithmic scale such as deciBels. When we say "the headroom is 20dB", we mean that the ratio of nominal input level to maximum input level is a voltage ratio of 10 (=20dB).

dBu is an absolute level, derived from dBm, which corresponded to the voltage required to dissipate 1mW in a 600 Ohm resistor. This voltage is .775 V r.m.s., and this level is carried over into the dBu (u = unterminated) usage, so 0dBu = 0.775V.

dBFS is relative to the equipment, as we have said, and we need the equipment manufacturer to state what this is, either as an absolute level in dBu, or as headroom above a +4dBu nominal level.

Your Q1: The figures of 96dB for a 16-bit system and 144dB for a 24-bit system are not very meaningful, as they cannot be achieved in practice. They are simply an application of the ratio formula to the ratio of the maximum number to minimum number that can be represented by those number of bits. Since each additional bit allows an extra factor of two to be represented, each bit corresponds to approximately 6dB.

We can, however, apply the ratio formula to the maximum and minimum amplitudes of sounds that can be handled by a particular piece of equipment before it either clips, or the signal or is lost in the noise. This ratio is the dynamic range, and can be expressed in dB. An amplifier that has an input noise level of -120dBu and clips with an input of -10dBu could be said to have a dynamic range of 110dB, although this is a bit of an over-simplification.

A gain control range specifies the ratio of the maximum gain to the minimum gain. If the maximum gain is x10,000 (80dB) and the minimum gain is x10 (20dB), the gain control range is 10,000/10 = 1000 (=60dB). This can clearly also be found from 80dB - 20dB = 60dB.

The answer to your Q2 is that these these are ratios and not absolute levels, so they are plain dB.

I hope this explanation has made things clearer and not more confusing!

Thanks for your replies. Very busy today, so I will take some time to process this info and then respond. Partly I am just trying to get a half-decent theoretical understanding of what's going on (without doing too much math; some math is ok though!), but there is a practical motivation for my questions that I'll get to later on once I've got the basics down...

apstrong wrote: ....(without doing too much math; some math is ok though!), ....

Understanding basic high school logarithms and exponentials is, in fact, the easy way to learn this stuff. People make a huge amount of work for themselves trying to avoid the basic math. Fortunately, not only does learning logs make learning decibels easier, learning decibels makes it easier to learn logs and exponentials. Unless you were the type of high school kid who thinks abstract mathematical problems are about as much fun as any activity not involving unfastening bra straps, the high school approach to learning this stuff was probably hard and boring. It's much easier to learn if you have a concrete and important application.

Embrace the math!

Unless you were the type of high school kid who thinks abstract mathematical problems are about as much fun as any activity not involving unfastening bra straps, the high school approach to learning this stuff was probably hard and boring.

If you had seen my HS calc teacher you'd understand why my thoughts were on bra straps! I got an A but I don't know how since I'm pretty sure my eyes had disconnected my ears from my brain housing group....... :roll:

apstrong wrote: Partly I am just trying to get a half-decent theoretical understanding of what's going on (without doing too much math; some math is ok though!), but there is a practical motivation for my questions that I'll get to later on once I've got the basics down...

I think I can help
or at least want to try a new/different way of explaining things
both Boswell and Bob have brought up very relevant things but I can see that the points assume a level of understanding .... however I have some issues with some of the statements ... more on that later as there is too many points being fired at once

and this seems to be the problem with many areas of technical audio thingys

may plan is to narrow the discussion and bring some simple concepts which will lead to a better starting point

a little knowledge is good
but it can also be dangerous

anyone interested ?

Sure, I think we are all interested, but the aim of the responses in this thread were an attempt to answer the original poster's question. Maybe a general explanation of deciBels and/or relevance of a mathematical education to the audio industry should be a separate topic.

yes there were some questions in the original post
but the use of various " dB�s " ... that is a cut and paste from the original post
does make finding a specific question difficult

AND

the very clear question
So question 2 is what are those dB's referring to? dBu?

is why I left this little bomb in my reply

Kev wrote: " So question 2 is what are those dB's referring to? dBu? "
never assume
if they don't say u or FS or A or V then it could be anything

1dbu is 1 mW into a 600 ohm load

so even though I answered I also left the incorrect bit
BUT no-one picked up on it

0dBm is 1mW into 600ohm

pleases refer to
http://www.analog.com/Analog_Root/static/techSupport/designTools/interactiveTools/dbconvert/dbconvert.html

Firstly, when we use the level of 0dBFS, it is a figure that applies to a particular piece of equipment only, and can map to different absolute levels for different equipment. For example, a Yamaha 01V96 mixer has an 0dBFS of +24dBu, which gives a headroom of 20dB above the nominal level of +4dBu. An Alesis HD24 hard disc recorder has an 0dBFS of +19dBu, only a headroom of 15dB above the nominal +4dBu. Both are 24-bit units having a nominal level of +4dBu, but if you were to use an analog connection from an 01V96 output to the HD24 input, you could overdrive the HD24 by 5dB.

So I have already used three different dB measures: dBu, dBFS and plain dB. Plain dB is always a measure of ratio, which translates to a difference when using a logarithmic scale such as deciBels. When we say "the headroom is 20dB", we mean that the ratio of nominal input level to maximum input level is a voltage ratio of 10 (=20dB).

dBu is an absolute level, derived from dBm, which corresponded to the voltage required to dissipate 1mW in a 600 Ohm resistor. This voltage is .775 V r.m.s., and this level is carried over into the dBu (u = unterminated) usage, so 0dBu = 0.775V.

dBFS is relative to the equipment, as we have said, and we need the equipment manufacturer to state what this is, either as an absolute level in dBu, or as headroom above a +4dBu nominal level.

I get it! Well this is interesting. I think in a roundabout way, this is what I'm trying to figure out in the end: what does 0dBFS mean in absolute terms on my particular equipment? Ultimately, I'm also trying to figure out what the main stereo out fader in Cubase represents, given my hardware set up, when it's at unity. So I was starting with the Mackie for the most part and then was going to try to figure out what happens when the A/D converter then passes the data to Cubase. So just so you know, that's the ultimate goal for me here. But I don't want to deal with the Cubase part of the equation yet, I just want to make sure I've got this part down first.

So based on what you've said, I need to find out what 0dBFS is for my particular mixer/interface. Sadly, I've been searching the web for half an hour and looking at the Mackie manual over and over but can't find the info or figure it out based on what I can find - anyone know the dBu value for 0dBFS on the Mackie 1640? And can/do the analog preamps clip at a different point than the A/D converter clips (i.e. when the red channel led lights up, that's analog clipping; does that happen before, at the same time as, or after digital clipping occurs)?

The manual is here: http://www.mackie.com/pdf/onyx1640_om.pdf if that helps.

Kev, if you want to start a separate thread to deal with more general issues, please feel free! I think a thread dedicated to clearing up the mysteries of dBs in general would be very valuable to a lot of people. I know I'd find it useful.

apstrong wrote: So based on what you've said, I need to find out what 0dBFS is for my particular mixer/interface. Sadly, I've been searching the web for half an hour and looking at the Mackie manual over and over but can't find the info or figure it out based on what I can find - anyone know the dBu value for 0dBFS on the Mackie 1640? And can/do the analog preamps clip at a different point than the A/D converter clips (i.e. when the red channel led lights up, that's analog clipping; does that happen before, at the same time as, or after digital clipping occurs)?

Yes, Mackie are not very helpful when it comes to finding such things out, but there are some clues. The maximum rated output of the 1640 is +21dBu, and the LED metering is scaled such that the 0 LED is 0dBu, and the +20 LED represents clipping. So you would think that the analog clip level is +20 or +21dBu. In the void between what is covered in the mixer manual and the FIreWire interface manual is the information that the ADC for each channel also clips at this level, so you just have to assume that the digital 0dBFS is +20dBu.

It's relatively easy to check this by generating a constant 1KHz tone and feeding it through the mixer, adjusting the trims so that the LEDs read (say) +10. Record this in your DAW and see how many dB is needed to normalize the waveform. Add that to 10 and you have the digital 0dBFS.

However, although it's interesting to know the 0dBFS for the digital end of this mixer, you have to take it in context. Assuming you are monitoring on the computer while recording, you adjust the mixer gain trims to give you the correct digital recording level on each channel. It doesn't actually matter what absolute level corresponds internally to 0dBFS. What does matter is that the analog circuits in the mixer can drive the channel ADCs to at least their 0dBFS before they clip in an analog sense. I trust Mackie to have got that right, and all the Onyx mixers I have used have not shown a problem in this area.

Boswell gives some good pointers. Mackie designs their gear to have "unity" markings and it is at these settings your 1k tone should be checked.

Ok, I'm following along pretty well I think. I will run this test for interest's sake:

It's relatively easy to check this by generating a constant 1KHz tone and feeding it through the mixer, adjusting the trims so that the LEDs read (say) +10. Record this in your DAW and see how many dB is needed to normalize the waveform. Add that to 10 and you have the digital 0dBFS.

But can you clarify what you mean by "normalize the waveform"? Do you just mean increase the peak amplitude until it clips in my DAW?

It doesn't actually matter what absolute level corresponds internally to 0dBFS.

I had a feeling that was the case, but I'm a curious George lately. I understand though that the important thing is that the analog preamps can exceed the ADC's 0dBFS before they clip, otherwise you'd never be able to take full advantage of all the bits available. And even if you were pushing it close to the 24 bit limit (not that this is the goal), once it gets into the DAW it's processed at 32bit FP anyway so there's still some room for in-the-box processing. It's all coming together...

Incidentally, at my high school the degree to which you found math problems fun was inversely related to the number of opportunities you had to remove bra straps. ;)

I might leave things with Boswell and stay out as it seems you are getting what you want.

I still have issues with statements like,
" Firstly, when we use the level of 0dBFS, it is a figure that applies to a particular piece of equipment only, and can map to different absolute levels for different equipment."
however the following sentences do go on to help clarify the reasoning for presently the point in such a way.

0dBFS is a specific absolute and defined ... and should be the same for all equipment that uses PCM audio.
EVEN this statement needs discussion as there is some interesting issues that can develop when trying to use a data point at 0dbFS
this can lead to people using terms like +0dBFS , 0dBFS and -0dbFS while explaining what some error corrections algorithms and D to A chips can output.

When making a recording with a microphone,
" It doesn't actually matter what absolute level corresponds internally to 0dBFS. "
if you have a good understanding of your equipment and what you are trying to achieve.
However doing a transfer in an analog domain or digital domain at a technical unity for the purposed of copy or ingest may need a little more knowledge of the internals of the gear used.

Side note
The Tascam TD1000 (or was it the 4000) has a control panel in the software for adjusting the 0dbFS internally !! they shouldn'd say it like this and then the additional control for analog input and output trims via dip switches (I think)
You can also set what db digital will bring on the RED clip lights and for how many samples

So as Boswell describes, " It's relatively easy to check this by generating a constant 1KHz tone ... "
or grab a quality wave file from Bob Katz etc and insert it into the timeline of your audio editor.

while you are there check out the pan law being used in your editor.

Once that 0dBFS is coming out 1640, " The maximum rated output of the 1640 is +21dBu, ... "
you can now check with a VU meter or a multimeter that you have the signal
but try it with the load attached and see if there is any changes with load.

experiment and learn your gear
things are not always what they seem ... or what is said in the spec sheets

apstrong wrote: But can you clarify what you mean by "normalize the waveform"? Do you just mean increase the peak amplitude until it clips in my DAW?

Yes, pretty much. Most DAWS have a normalise function with a pre-pass that reports how much it would have to amplify the waveform so that the peaks would be 1 bit below a maximum level. Usually you can set the maximum level in the preferences, if not when normalising. The level could be for example -0.1dBFS, or even +0.5dBFS (i.e. deliberately clipped).

Kev wrote: I still have issues with statements like,
" Firstly, when we use the level of 0dBFS, it is a figure that applies to a particular piece of equipment only, and can map to different absolute levels for different equipment."
however the following sentences do go on to help clarify the reasoning for presently the point in such a way.

I see where the opportunity to take issue has come in. 0dBFS is an internal level that every piece of gear has, analog or digital, although the analog variety tend to be softer than the digital. What I was referring to in that sentence was the absolute input or output level in dBu that corresponds to a piece of gear's internal 0dBFS.

yep
I know you know
that's why I said that you had clarified things with the next sentence

it's all good

aligning the analog inputs and output of digital gear with other ... both analog and digital ... is a fascinating and interesting subject.

as an example
Sony DVW tape decks have software setting for -18 or -20 dbFS
does 2db really matter and why did Sony provide those 2 choices

Bob Katz has info on setting levels and so do many other Mastering Engineers and Equipment makers
BUT
as the years go by and people are doing analog transfers less and less
the knowledge and reasoning and history will fade

this is not the thread for this

apstrong has enough info for now

for anyone doing analog transfers
OR
for those that have shelled out big money for analog gear like LA2s and Neve Preamps ... it is worth getting advice on the best way to interface this stuff with their new DAW interface
get your levels and loading sorted out

it is worth the efforts