Conference napalm::commusic_v1

>	Would anyone care to offer a primer in sound terms and applications
>to a frustrated PA Manual Reader?
No
>	I have been reading the manual recently supplied me (thanks, Brian)
>of my mixing board, and have held conversations with knowledgable people about
Don't listen to what people say (or write) off the cuff; it's always wrong.
>thinks like 'db' levels, voltages, impedances, etc.  All I can say is that I'm
>obviously missing something.
No, i won't, it's just too easy a feed line...  8-)
>	So let me ask you folks to answer me in the simplest terms you can
>contrive (that leaves Tom Janzen and sometimes Ron Ross out of the discussion)
>the following:
>
>	1)  What is db (other than a popular COMMUSIC tape compiler and 
>neighboring conference moderator)?  I've been told it is a relative measurement
>of sound level.  Relative to what?  Can an output from a mixer be measured for
relative to whatever.
dB decibel is a ratio between two powers.  If you know the voltages or currents,
you can skip power and get the dB directly from them.
if you know the two voltages:
dB=20*log_10(Voltage(1)/Voltage(2))
if you know the two currents:
dB=20*log_10(Current(1)/Current(2))
if you know the two powers:
dB=10*log_10(Power(1)/Power(2))

Let's say an amplifier has a 35V supply, peak; that's about 20 rms.
p=e**2/r, the speakers are 8ohms (this is my hi-fi, btw), so
p=20*20/8= 400/8= how do you spawn from here? 50 watts rms one channel.
Maybe the SNR ~ 80dB I forgot my slide rule, 
but that's like  the enp (equivalent noise power) ~ 50/1E8=50*10E-8=.5E-6 W.
Often the dB output of something is given above the threshhold of hearing
some distance away.  I don't know how far away.

>db using a volt/ohm meter?  How is this measurement useful to me?  When people
No man.  You need a network analyzer, a signal generator, a sampling 
oscilloscope, and a few years in school.
>measure noise, they often use the term 'db'.  What does that mean?  And when
usu. the signal-to-noise ratio, i.e., a reference signal at -0dB, relative to
a recommended highest magnetization of audio tape or other reference, such as the
maximum allowed modulation of a transmitter, is compare to the noise
power below it.  So if noise is -60dB(pretty cruddy now, what my equipment
specs give) then the peak levels, certainly for music (speech is often 
overmodulated at the peaks), can be 60dB above the noise of the equipment,
say the audio tape on playback, or through a mixer, or whatever.
>dynamic range is represented on a piece of equipment, it may say something like
>20hz to 20khz *at + or - 1 db*.  What does that mean?
>
>	2)  I also see voltages thrown around a lot in terms of input and
>output levels.  These, it seems to me, are a little more comprehensible.  But,
>he asks, in applying the voltage level, is the purpose to match adjacent 
>components?  For example, my mixer can send an output level of up to 5 volts.
>Should I have an acceptable input to my EQ of approximately the same voltage?
national standards should make these work together but you may have to adjust
it anyway.  Most audio inputs are high impedance, >5Kohm and much higher.
Most audio outputs are low impedance , say <100ohms.  Adjust your levels;
calibrate you equipment every day to a standard EIA test tape and test
tone generator.  Adjust head azimuth daily.  Wear matching socks.
>Incidently, my Tapco EQ only speaks of input level in terms of +20dbm.  Here
>we go again...
Like how?  What does it say completely?
>
>	3)  Along the same lines as the voltage question, I also see the use of
>impedance.  Now I think I have conquered the idea of impedance in previous
Impedance is a complete form for opposition to current flow; it is a complex
phasor.  Resistance, for example, is just the real part of this phasor.
Actually, in most audio applications, Impedance is mostly real anyway,
so it would be OK to talk about resistance, source resistance and input
resistance.  Source resistance is usu. low for line levesl (0dB = 1V peak)
and input resistance is usu. low.
>discussions.  But my question here is - Do I need to match output impedance of
>the mixer to the input impedance of the EQ, etc?  My Mixer is rated for 10K
Forget it.  They're all op amps and similar anyway.  High Z in, Low Z out.
Ignore it, unless your splitting a signal into lots of inputs.  Fan out 
lowers the impedance, and increases the load seen by the source.
>load ohms impedance.  The EQ says 50K for unbalanced cable.
>
>	Thanks to any and all that care to enter this web of confusion and help
>to pry me loose.
>
No problem at all.
Tom

    
    	Dan,
    
    	db is a ratio or fraction, but maybe it will halp if you envision
    it as a mapping:
    
    -db values...0db...+db values	=>	
    
    Fractions less than "1"..."1"...Fractions greater than "1".
    
    Example: -3db is a fraction <1; 0.707. 0db *is* the value "1". +3db
    is a fraction >1; 1.414. Tom's formulas can be used to calculate...
    
    So, if a audio type says "bring me 3 db down" he means make the
    level, er, about 3/4 of what it was...
    
    0 db on a tape deck is "1" or "*all* the signal you can handle".
    
    	Joe Jas
    

    
    	(Wish I could scroll the base note as I reply)
    
    So, +20dbm is how many volts? Well, if I happened to know how many
    volts 0dbm was I could tell you! A 10:1 ratio is +20 db, so if 0dbm
    was 0.5 volts, +20 dbm would be 5 volts.
    
    The generic rule for impedance matching is that the driving device's
    impedance should be less than the recieving device's impedance.
    So, if you're driving with 10K ohms and recieving with 50K ohms,
    it should be "OK". Not so if the situation were reversed.
    
    The generic "order" of voltages produced by various devices follows:
    
    Microphone, Electric Guitar, Phono Cartridge - 10's of millivolts
    Graphic EQ, Tape Deck line out, "aux" level  - 100's of millivolts
    Speaker output, Headphone output, etc	 - 1000's of millivolts
    
    ...where 1 millivolt is 1/1000 of 1 volt, or, -60 db. The above
    values are for "unbalanced" lines, like a guitar cord...
    
    Balanced, or "Low Z", "Low impedance" lines work in the single
    millivolt range. You generally cannot drive a balanced input with
    an unbalanced output, or the vice-versa. A impedance matching
    transformer is needed, which arranges the voltage, impedance and
    connection style suitably.
    
    	Joe Jas
    

    Eventually, you should be able to cope with this.
    
    First, a historical note.  dB stands for deci-Bell, but it has been
    truncated to decibel.  Where one bel (named after Alexander Graham,
    actually) is log10(power2/power1).
    
    Why use this logrithmic stuff?  Because people's ears respond
    logarithmically.  That is, sounds appear to increase smoothly
    (linearly) in volume when the actually power being poured into the
    sound is being increased exponentially.  So logs provide a number
    which measures this.  10dB is (generally) twice as loud as 5db.
    (don't mention 0dB).
    
    In spite of all this talk about dB being a relative term, with respect
    to the electrical portion of sound reproduction, there is a ``magic''
    value.
    
    The magic value is 0dB = .779 volts RMS.
    
    Assuming that you wouldn't know an RMS volt from the more garden
    variety volt, I'll explain.  Without going too deeply, a (normal) volt
    is a measure of a static (DC) value.  Every wire in a circuit has a DC
    voltage associated with it at each instant in time.  If you have an
    oscillatory (AC) signal (which you always do in sound production, I
    hope), a volt RMS is a measure of the size of this signal. (Its
    amplitude).
    
    So, if you have a wire with a +4dB signal on it, that means that
    that (without showing you the math) it has a signal of 1.23 volts
    RMS.  You can measure this with an AC volt meter.  Assuming that
    it doesn't have a logarithmic scale, which most of them do, you
    measure the AC voltage (in volts RMS) on a wire, and you divide
    that value by .779 volts RMS, and take the log10 and multiply by
    20:
    
    	(1.23/.779) = 1.579
        log10(1.579) = .198
        20 * .198 = 3.97 dB  (well, we lost a little in the rounding)
    
    Most of the aforementioned is basically useless unless you design
    stuff, but can be interesting, at least.
    
    Things to think about are maximum output levels of various devices:
    
    	Keyboards -> ~0dB = 779 milli-VRMS
    
    	Guitars -> ~ -50db = 2.46 milli-VRMS.
    
    Once you get into the domain of mixers and (studio) effects, the
    maximum levels are all around -10dB (for semi-pro) or +4dB (for
    pro), so you don't have to worry.
    
    Now impedance.  Not much to say about this (unless you want to design).
    
    As Tom said, most (really all) studio equipment (everything after the
    actual instruments themselves) except stomp boxes (which I certainly
    wouldn't call studio equipment) and some devices which connect to
    microphones, have high impedance inputs (this means that they measure
    the input signal without disturbing it) and low impedance outputs
    (which means that it can force its signal on the output even if there
    is a heavy load on the wire). Basically, there is nothing to worry
    about here. 
    
    Steph
    

    
    There are a lot of very good books on the subject, so you can search
    your local library for a good primer. Even some of the older 50's
    and 60's books are great for just starting out.
    
    Re: db
    
    The reason the db scale is used so much in the audio field is that
    the normal range of sound pressure levels, voltages, currents, power
    etc. is too great to be measured in a linear fashion, the log scale
    makes it much easier to represent. Thus the db. 0db is any reference
    level picked by you or the manufacturer. For example, your tape
    deck may need to be calibrated for 0 db at 400 nanowebers/second,
    a measurement of magnetic flux, or energy. Your board may read 0db
    on the output meters at 1 volt. It's all relative to the reference
    standard.
    
    There are no iondustry standards, but there are several defacto
    standards. For example, .775 volts output=0db is one of them.
    Outboard effects devices, like your eq, are grouped into two
    catagories. The semiprofessional market uses -20dbm as a reference
    level for measurement, the pro market uses +4dbm. If your Tapco
    has an output spec of +20dbm, then that means that its outputs will
    clip (start to seriously distort) at a voltage equal to 20db above
    0 db, whatever that is speced at. If you're still with me, let me
    use an example. My Rane GE27's are referenced 0db at .775 volts
    output, .775 volts=0db. The maximum output is +28dbm. The noise
    floor is at -96db, which means a voltage 96db below .775 volts.
    The frequency response is 20Hz-50Khz +/- 1db; in other words the
    response is flat over the specified range of frequencies to within
    2db.
    
    You can measure your equipment in terms of db's, without network
    analyzers and the like. What you need is a calibrated signal generator
    and a voltmeter that reads in db scale (or a calculator, YUK). One
    of the nicest little all-in-one test sets is the Loft TS-1?. It's
    just that, a calibrated signal generator and db reading DVM in one
    package for $199. You set the output level at 0 db for any frequency
    (1 KHz is another defacto standard) and step through your equipment
    setting input and output levels to all read 0db, thus you have just
    normalized your signal chain to unity gain (no gain). This will
    maximize the dynamic range and headroom of your electronics. That's
    just one of the many things you can do with this little gem.
    
    Re: impedances
    
    Tom hit it all on the head. You really only have to worry about
    matching high impedances properly with low impedances and vice-versa.
    Actual values don't mean too much except for the real discriminating
    studio owner. 50K ohms input impedance is still another defacto
    standard for unbalanced inputs.
    
    Now I know you're going to ask what's the difference between balanced
    and unbalanced signal lines. Unbalanced means that the send and
    the return line are of unequal impedance, like mike cable that is
    single conductor with shield. Balanced means they're the same
    impedance, like 2 conductor cable. Now, the inputs and outputs of
    the devices must be designed to accept either one of these types
    of connections. On the back of your Peavey you may find two sets
    of outputs, one balanced and one unbalanced, especially if the balanced
    set is XLR connectors. Balanced is better because the inputs are
    built differentially, which has the ability to cancel common mode
    signals (noise) by nature. They can be built with transformers
    or electronics, both ways have their good and bad points.
    
    But by no means assume that:
    
    1) Because an input or output uses XLR connectors it is a balanced
       connection. Read the panel ID or the manual for details. An XLR
       can be wired unbalanced on purpose or by mistake (crossing the
       return with the signal ground)
    
    2) A 1/4" connection is always unbalanced. 3 conductor TRS plugs
       can be wired as balanced connections just as easy as XLR's.
    
    Enough for now.
    
    CdH
    

1 ! tom janzen 9-22-87 for commusic conference use VAX BASIC
2 ! digital equipment corporation for internal use only
10 print "do you know the powers (2), the voltages/currents(1) or the dB(3)?"
20 input which
30 if which=2 goto powers
   end if
40 if which=3 goto db
   end if
45 print "OK, you know 2 voltages or 2 currents"
50 print "enter the first one: ";
60 input v1
70 print "enter the second one: ";
80 input v2
90 print "the power ratio in dB is: ",20*log10(v1/v2)
100 goto 570
200 powers:
210 print "OK, you know 2 powers in watts."
220 print "enter the first power: ";
230 input p1
240 print "enter the second power: ";
250 input p2
260 print "fine.  the power ratio in dB is: ",10*log10(p1/p2)
270 goto 570
300 db:
310 print "OK fine.  Enter the db: ";
320 input decibel
330 print "fabulous.  the power ratio is: ";10**(decibel/10)
340 print "wonderful.  the voltage or current ratio is: ";10**(decibel/20)
570 !stop
580 end

RE < Note 956.3 by FLOWER::JASNIEWSKI >

	Can you show me how you arive at .707 from the formulas?  Tom's reply
was as predictably complex as I had asked replies *not* to be, so the formulas
he listed and the answers you derived have yet to 'wave' to each other in my
pea-brain.

RE < Note 956.4 by FLOWER::JASNIEWSKI >

	O.K., I can see a little better that what I may be looking for at *this*
time is more of the general rules of thumb than lists, charts and formulas.  The
part here about impedance matching is useful to me.  Thank you.

	You see, I have thrown together a wild assortment of equipment mostly 
based on *immediate* need (well, maybe not all of it was immediately needed...)
and bargain prices.  This means that while I have just about all the COMPONENTS
I felt I needed, the task of maximising their effectiveness according to my
needs has yet to be done.  It all boils down to the following:

	1)  How can I make best use of the equipment I have now?  How can I
		insure getting the best signal quality, the lowest noise and
		distortion, the most 'true to the instruments they come from' 
		sound possible with what equipment I've been able to snarf up.

	2)  How can I insure, apart from obvious care and sensitivity, that I	
		am not inflicting damage upon my equipment (thus subverting the 
		upgrade process always in motion) by mismatching voltages,
		impedances and the whole host of other factors that fly by my	
		eyes every time I glance upon an equipments spec sheet?

	3)  How can I know what is a 'good' piece of equipment from a 'bad' one?
		Or perhaps; How can I identify an 'appropriate' piece of 
		equipment (for my setup) from an inappropriate one?  Now, before
		you all say 'only you know what is appropriate for you', let
		me qualify that by saying I mean 'appropriate' in terms of
		quality factors and specifications, not style and preference.  
		I have done this, by and large, with all of my musical 
		instruments, principly through the help aquired in this 
		conference.  Now I would like to expand this onto the field of 
		sound reinforcement.

	So to make a long story even longer, the motivation for the opening 
questions of this topic were not so much to aquire the 'theory of operation'
but to for the building up of basic guidelines for the use of my equipment.  In
other words, I can most benefit by 'application'-type answers rather than 
'theory'.  I have found that I assimlilate theory quite well in the long haul 
when involved in the application.

	Does that make sense?

	Dan

	I can see that many of you crept your replies in while I was going 
through my long spiel in .9.  I just wanted to say to Joe, please don't construe
my remarks in .9 as saying I don't appreciate your explanations.  Far from it,
I have already weaned a good deal from them and expect to find more as I wade 
on...  The key issue for me is narrowing the wide gap between common terminology
amoung sound enthusiasts and the limited knowledge I've been able to obtain 
since I have entered the whole world of electronic music.

	To the other repliers, I will respond to them after I've had a chance
to look through them.  If I do not understand the content of these replies, I 
will ask further questions, based on the motives I have listed in .9.

	Thanks all (even you, Tom 8^)

	Dan

    
    Some simple rules of thumb:
    
    Most audio equipment that uses phone jacks operates at a -10 dBm
    line level.  Most equipment that uses XLR connectors  operates at
    a +4 dBm line level.
                                     
    Impedances:  In general, the driving impedance should be lower than
    the receiving impedance;  i.e. if your board is say 5 Kohms out,
    the power amp input should be 5K ohms or greater.  Technically,
    any mismatch of impedance causes distortions.  For all but super
    hi-fi applications a mismatch of a higher input impedance is OK.
    
    

	RE Steph

	O.k., I'm going to test some of this out.  My PV 600S manual says it is
capable of 5VRMS in its output (unbalanced).
    
    	(5/.779) = 6.42
        log10(6.42) = .81
        20 * .81 = 16.2 dB  

	Does 16 db sound right?  
    
>    Once you get into the domain of mixers and (studio) effects, the
>    maximum levels are all around -10dB (for semi-pro) or +4dB (for
>    pro), so you don't have to worry.

	So where does that put my mixer with 16 db?

	O.K., I can put the impedance problem to bed. 8^)

	RE Chris

>    There are no iondustry standards, but there are several defacto
>    standards. For example, .775 volts output=0db is one of them.
>    Outboard effects devices, like your eq, are grouped into two
>    catagories. The semiprofessional market uses -20dbm as a reference
>    level for measurement, the pro market uses +4dbm. 

	There is a slight discrepancy here betwixt Steph and you.  does this
further illustrate the lack of industry standard?

>    If your Tapco
>    has an output spec of +20dbm, then that means that its outputs will
>    clip (start to seriously distort) at a voltage equal to 20db above
>    0 db, whatever that is speced at. 

	How do I know what 0db is?  I looked at the specs, but found nothing
familiar.  For that matter, is it important to know?

    
    	So, is the 0.775 VRMS value the ellusive 0dbm?
    
    Equipment topologies for the best sound can be quite an exercize.
    Check out the audio folks sometimes and look what they go thru
    to capture "the absolute sound". There are rules and generalities;
    most boil down to a "common sense" feel that is aquired in long
    experience with the field. Let's see if I can think of some general
    ground rules -
    
    (I'll assume were talking about a "chain" of devices; like "preamp,
    reverb, eq, compressor, enhancer, mixer, recorder, poweramp, monitor")
    
    	1. Common Ground. Feed all 3 wire plugs from the same outlet
   	strip. If you're line monitoring an amp plugged in across the
    	room, you'll know it.
    
    	2. Get the signal to line level ASAP. I know, *most* stomp boxes
    	are set up for microphone level signals. Try not to use too
    	many of them before you bring up the signal level.
    
    	3. Put your compressor up front in the chain. This will allow
    	the latter devices to process a less dynamic signal and will
    	prevent you inadvertantly blasting out one of them with the
    	source dynamics.
    
    	4. Put the noisyest devices toward the end of the chain. You
    	dont want to be boosting or enhancing noise. Also, the signal
    	level is highest (typically) at the end of the chain.
    
    	5. Put the filters and EQ at the end. Not all recordings and
    	reproductions need full bandwidth, so you can "shut down"
    	frequency bands - and the noise therein - that you dont need.
    
    	6. Use balanced signal lines wherever possible, especially for
    	the mikes. For every mike that goes from unbalanced to balanced,
    	a perceptable change for the better happens too.
    
    	7. When monitoring an amp with a line out, shut off the speaker
    	if mikes are being used for vocals and drums. This avoids strange
    	phase cancellations of two signals - the amp line out and the
    	residual picked up by the various mikes.
    
    	8. Take a device completely out of the chain if not needed.
    
    	Got to run!
    
    	Joe Jas
       

    > Does 16 dB sound right?
    
    Yep.
    
    > How come it's not 0dB.
    
    That when talking about signal strengths, the ``0dB is a reference for
    the maximum a device can deal with'' idea is really only true for tape
    decks.  The VU meters are (supposedly) calibrated so that you know when
    you are approaching saturation on the tape.  As was mentioned by Mr.
    Dehan, what goes onto tape is Webers (a measure of magnetic flux), not
    volts. 
    
    In ``voltage domain equipment'' (equipment where the information
    manipulated is represented as voltages) the 0dB = .775 VRMS (I
    experienced a ``slip of the mind'' on the value) rule holds.
    Therefore, unless otherwise specified, when they talk about voltage,
    0dB =.775 VRMS
    
    The +4dB and -10dB ratings are historical values with which devices
    (mixers and effects, etc.) feel comfortable.  They are great enough
    that signals may be manipulated without introducing much noise,
    but small enough that exotic high-voltage devices are needed to
    manipulate them.
    
    For most devices, the values with which they can comfortably operate,
    and the maximum values are different.  Therefore, devices have a
    maximum input or output rating which is greater than that of the
    nominal value (+4dB and -10dB for ``line level'' signals, and -60dB
    for ``low level'' signals).  Operating at values near the rated
    maximum usually result in distortion, so the max values are,
    understandably, a few dB greater than the nominal value.
    
    Note that there are several other uses of the dB unit which are
    essentially unrelated to the ``signal-strength'' (level) one discussed
    here--signal to noise ratios, dynamic ranges and amplifier gains
    are examples.
    
    Steph
    
                 

RE < Note 956.14 by MAY14::BAILEY "Steph Bailey" >

>    Note that there are several other uses of the dB unit which are
>    essentially unrelated to the ``signal-strength'' (level) one discussed
>    here--signal to noise ratios, dynamic ranges and amplifier gains
>    are examples.

	I think the 'multi-usage' of the term db causes me much confusion.
Would you care to go into these?  Also, why the many usages?
    
	Dan (the_asker_of_many_questions)

    
    	How about this: Since db is a logrithmic based expression, you
    can cover a lot more ground with fewer numbers (i.e. 120db=1 million
    to 1 change). As mentioned before the ear hears volume level changes
    in this way, so the equipment designed to handle these changes better
    had accomodate them likewise. When something says "I have a 60 db
    dynamic range" that means it can handle a 1000:1 signal amplitude
    range.
    
    	Why 3 db? Well, this is the majic value. It holds two properties
    that I know of. First, supposedly it is the smallest change most
    untrained people can hear. Second, it is the "Half Power" point.
    Everyone knows power is a squared function, P=V(esquared)/R. In
    going from 1.0 to .7071, or -3 db, the power follows the square or
    goes from 1.0 to 0.49999. In going from 1.0 to 1.414, or +3db, the
    power goes to 1.999. Did you know you must *double* your amplifier
    power to be just perceptably louder than what you are now? No wonder
    the sound reinforcement people have all thos huge amps!
    
    	db is convienent when talking about huge differences, like the
    million to one sound level perception range of the human ear. If
    a piece of equipment says "noise 100db down", it waaaayyy down there
    at 1/100,000th of the signal at 0db.
    
    	Joe Jas
    

    
    	I'll talk on impedance a little bit (Oh Noooooooo!!!) Let me
    make the following analogys:
    
    	Voltage = Velocity (angular RPM's)
    
    	Current = Torque   (foot - lbs)
    
    	Transformer = Gearbox (N to 1 ratio)
    
    	Now we have the equation for impedance Z=voltage/current or
    Z=velocity/torque. 
    
    Commercial power lines, those big towers, are high impedance; lotsa
    voltage, low currents. Those big transformers you see are bringing
    the voltage down toward 110 and at the same time bringing the current
    up, to handle your toaster. They're really making an impedance match.
    A big PA system, say, in a church, is set up like a power distribution 
    grid. They run high impedance lines around the building, and at
    each speaker, a transformer swaps voltage loss for current gain,
    to drive the speaker. It's done this way because high current values
    drop voltage across the resistance of long wires.
    
    An automobile engine is a high impedance device (at least the ones
    on new cars are), that is, it spins pretty fast (thousands of RPM)
    and provides some torque. Your transmission, in first gear, is high
    impedance looking into the engine side and low impedance looking
    into the "rear wheels" end. It takes the 2000 rpm engine speed and
    matches it to the speed of the wheels, maybe 33 rpm when you're
    first taking off. The torque is increased, at the expense of RPMs,
    to the value needed to move the car forward. The impedance of the
    transmission decreases as you shift to higher gears. Taking off
    from a dead stop in 5th is like trying to drive eight 8 ohm spkrs
    in parallel with the 16 ohm amplifier output.
    
    	A microphone transformer, from hiZ to lowZ balanced, offers
    a "light load" to the microphone element; the voltage can be fairly
    high, with hardly any current. The balanced output, however, has
    hardly any voltage but more current, enough to drive long cables
    and be impervious to noise, etc. Since there is no power being
    transmitted, the current is so low that the voltage drop due to
    the wire resistance is negligable.
    
    	Joe Jas
    

aside from getting all the relationship backwards, that's a pretty bad analogy.
Tom

    RE: .16, .17, .18.  Sigh.
    
    Before going any further, you should note that a dB is a unitless
    quantity.  Since you divide apples by apples inside the log10
    operation, the result is unitless.  However, it is convenient to know
    what the units were before you converted them to dB.  Therefore, if I
    had 10 apples, and I let 1 apple = 0dB, then people would often say
    that 10 apples = 20dBapples. 
    
    Ok, here is a terse description of some of the uses, and motivations
    for the uses of the decibel unit in the audio world.
    
    
    1) dB SPL.  Stands for decibel, Sound Pressure Level.
    
    This is the dB referred to in my favorite Edd Cote personal name (I
    still haven't understood the Kawai one)--a measure of the effective
    pressure at a point in a fluid medium (esp. air).  It is calculated by
    dividing the pressure at a point by a reference pressure (analogous to
    the V0 = .775 volts) and then doing the 20*log10 thing.
    
    So why use dB for this application?  Because the ear responds
    roughly logarithmically to sound pressure.  Therefore, 70dB will
    sound roughly twice as loud as 35dB (but will require a squaring
    of the actual sound pressure).
    
    
    2) Dynamic range.  The maximum variation of a particular quantity.
    In the audio world, this quantity is sound pressure (volume).
    
    If a sound stays always at the same volume, its dynamic range is
    0.  If it varies a great deal, the dynamic range is large.  I'm
    assuming that you understand dynamic range.  It can be calculated
    by subtracting the amplitude (in dBwhatever) of the quietest
    passage from that of the loudest passage (also in dBwhatever).
    
    Why use dB for dynamic range?  Again, the ear is sensitive in a
    logarithmic way.  It can detect small absolute changes in sound
    pressure at low volumes, but only large ones at high volume. A passage
    with a dynamic range of 40dB will seem to have twice the volume
    variation of one with a dynamic range of 20dB even though the actual
    variation in sound pressure is the square.
    
    
    3) Signal to noise ratio.  A measure of how much non-signal information
    has been introduced from a chain of devices (including cables, etc.)
    
    To measure this, you can imagine taking the input signal and
    subtracting it from the output signal (at each point in time) and that
    will leave you with the ``noise-signal'' that was introduced by the
    chain Now calcuate the amplitude of that signal in dB, and subtract
    that from the amplitude of the input signal, in dB, and that will give
    you the signal to noise ratio. 
    
    Why use dB?  Again, you are hearing it, and you respond to the noise
    logarithmically.  So, even though you double the amount of noise
    superposed on a signal, that doesn't necessarily double the amount of
    noise that you will perceive.
    
    As a counter example to the human system of perception, digital
    systems do not respond logarithmically to noise. (Most don't respond
    linearly, either, but that's not the point).
    
    
    4) Amplifier gains and attenuations (hereafter all called
    ``amplifiers'' even though they aren't really).
    
    The gains of amplifiers are converted to dB to allow easy comprehension
    of several devices in series.  Most amplifiers produce as an output
    quantity the same as that which is their input quantity (eg, voltage
    input -> voltage output, or current input -> current output, or
    kinetic energy input -> kinetic energy output) if not, the gain
    of the amplifier is an ambiguous quantity, since it depends upon
    the units with which you, arbitrarily decide to measure the input
    and output quantities.
    
    A gain of unity (1) is defined to be the zero dB level.
    
    The gain of a number of amplifiers in series is equal to the product
    of the individual gains.  So if you have a voltage amp with a gain
    of two (2) , followed by an amp with a gain of .25, the net
    gain of the chain is 2 * .25 = .5, so the output signal is half
    that of the input.
    
    With a logarithmic scale, multiplication becomes addition.  That
    is, the same amplifier with a gain of 2, has a gain of 6 dB, and
    the other amp has a gain of -12 dB, so the net gain is the sum of
    the two -6 dB (which you notice=.5.)
    
    Makes it easy to figure out, and makes it even easier to calculate
    signal levels if they are both in dB.  Just add the gain value to
    the signal value.  If you have an amp with a
    30 dB gain, and a signal of -30 dBV, the output signal is going
    to be 0dB.
    
    
    
    So, in summary, ears respond logarithmically, and decibel units
    allow addition to take the place of multiplication.  These are the
    primary motivations for the use of the dB unit.
    
    
    Are we there yet?
    
    Steph
    

	I can't say that I'm getting all of it, but I know as I read and 
re-read, it will sink in (if ever so slowly).  Much thanks to Steph and all
for the intriguing lessons.  If you have more, please don't hesitate to write.
I'll try to come back with my own feedback when I've digested some of this.

	Dan

    
    
    	Take the following test, to see how much you've learned -
    
    	1. Using 0 db = 0.775 VRMS, what voltage do you expect at
    	the amplifier output for the following chain: CZ101-mixer-
    	EQ-amp with the respective signal gains -12db - +20db -
    	-3db - +10 db? (Take CZ101 output to be -12db from .775)
    
    	2. A compressor is set for a 1.2:1 compression ratio. The
    	input signal has a 90 db dynamic range. Find the dynamic
    	range of the output. (assume linear compression)
    
    	3. Eight 8 ohm spkrs reside in a single enclosure, all connected
    	in parallel. What turns ratio would be required for a matching
    	transformer to match this to a 8 ohm amplifier output?
    
    	4. A set of spkr cables is spec'd at a loss of 3 db/1000 ft,
    	when driving a 4 ohm load. Assuming you have to make the 1000
    	ft run, how much power will you save by going to high impedance
    	cables/matching transformer which has a negligable power loss?
    
    	5. 50 watts of amplifier power is not enough for your PA system.
    	You wish to purchase amplifiers that will go somewhat louder,
    	but you've also heard the cliche' "3 db headroom" and you want
    	that too. What amplifier power do you buy?
    
    	6. 100 watts of power is dissapated by a single 8 ohm speaker.
    	Whats the db voltage at the spkrs terminals? (Ref 0db=.775)
    
    	7. Seven devices, each having a 10K ohm input impedance and
    	a 3K ohm output impedance are connected in a chain. Assuming
    	each is set to unity gain, what is the db loss for the chain?
    	Also, assume no losses due to loading for the chain input and
    	output.
    
    	8. The smallest signal seen from a guitar pickup is 1mV. The
    	instrument is known to have a 60db dynamic range. What's the
    	largest input signal an amplifier would have to deal with,
    	to not distort the sound of the guitar?
    
    	Joe Jas
    

RE < Note 956.21 by FLOWER::JASNIEWSKI >

	You're gonna have to give me some time for this, ya know...

	Dan (feels_like_I'm_back_in_high_school)

    Although I have been absent for a while, Dan, I would
    heartily appreciate you clarifying that in note .0, 
    there was no "guilt-by-association" intended from your 
    gracious remark which failed to distinguish the perverse
    complexity of cranial constructs profferd as educational
    dogma from either Mr. Jantzen, or myself.
    
    Furthermore, please understand that it is extremely difficult
    for those who have achieved such a level of communication, either
    through written or musical idiom, at such a young age (circa 14),
    to recant those endowed gifts and communicate with low-life such
    as yourself. 
    
    I will now read the other replies. Have a nice day.
    
    toodles.
    
    .
    

    
    FOR THOSE OF YOU THAT DONT *KNOW* ME...
    
    		THAT WAS *HUMOR* in .-1
    
    I forgot my smiley face>>>>>>>>>>>>>> &*}
    
    ok?
    

RE < Note 956.24 by JON::ROSS "Micro-11: The VAX RISC" >

	And, for those of you who may not have understood .0, my mention of
Tom and Ron was simply an attempt to say that some people's knowledge is so
far over my head that I often cannot begin to approach their answers.  It was, 
by no means, an attempt to make a personal statement about either of them.

	Dan

	Answers to .21: 

    	1. Using 0 db = 0.775 VRMS, what voltage do you expect at
    	the amplifier output for the following chain: CZ101-mixer-
    	EQ-amp with the respective signal gains -12db - +20db -
    	-3db - +10 db? (Take CZ101 output to be -12db from .775)

	12 db down is about 1:4, so the value "0.775" becomes
	0.19375. 20 db up from this is 10:1, so we have 1.9375.
	3 db down is 1:1.414, so we have about 1.37. 10 db up
	from this is 3.162:1, so there should be a little
	more than 4 VRMS at the end of the chain. Or, adding all
	the gains, we have +15db from 0.775 or 4.36...

    
    	2. A compressor is set for a 1.2:1 compression ratio. The
    	input signal has a 90 db dynamic range. Find the dynamic
    	range of the output. (assume linear compression)

	Well, "linear decibel compression" means for a 2:1 compression 
	ratio, the dynamic range is cut in half. That is, 90db/2 = 45db, 
	or for this problem, 90/1.2 = 75db.

    
    	3. Eight 8 ohm spkrs reside in a single enclosure, all connected
    	in parallel. What turns ratio would be required for a matching
    	transformer to match this to a 8 ohm amplifier output?

	Let's see...8/8 = 1 ohm for the speaker enclosure impedance.
	So you're increasing the loading by a factor of 8. Therefore,
	the current needed to drive the system must increase by the same 
	factor. Just like output torque doubles through a set of gears of 
	2:1 ratio, (at the expense of angular velocity) so does current 
	through a 2:1 transformer (at the expense of voltage). The ratio 
	needed is 8:1. Just like down-shifting in a car!
    
    	4. A set of spkr cables is spec'd at a loss of 3 db/1000 ft,
    	when driving a 4 ohm load. Assuming you have to make the 1000
    	ft run, how much power will you save by going to high impedance
    	cables/matching transformer which has a negligable power loss?

	Since -3db is the half power point, you'd save half your power.

    
    	5. 50 watts of amplifier power is not enough for your PA system.
    	You wish to purchase amplifiers that will go somewhat louder,
    	but you've also heard the cliche' "3 db headroom" and you want
    	that too. What amplifier power do you buy?
    
	Recall you need +3db to go perceptably louder; 3 db more brings
	the total to 6. A 6 db voltage gain is appx 2:1, however the
	power is 2(squared):1 or 4X. 4X50 = 200 watt amplifiers.


    	6. 100 watts of power is dissapated by a single 8 ohm speaker.
    	Whats the db voltage at the spkrs terminals? (Ref 0db=.775)

	Use V(squared)/R = 100 watts. V = 28.3  28.3/.775 = 36.5
	36.5:1 is about +31.2 db.

    
    	7. Seven devices, each having a 10K ohm input impedance and
    	a 3K ohm output impedance are connected in a chain. Assuming
    	each is set to unity gain, what is the db loss for the chain?
    	Also, assume no losses due to loading for the chain input and
    	output.

	10K will load 3K; circuit wise it turns out 10K/(3K+10K)=0.77.
	0.77:1 is a -2.27db loss; there are 6 such losses in the chain,
	so the total is -13.62db.
	 
    
    	8. The smallest signal seen from a guitar pickup is 1mV. The
    	instrument is known to have a 60db dynamic range. What's the
    	largest input signal an amplifier would have to deal with,
    	to not distort the sound of the guitar?

	+60db is a 1000:1 increase, so the amp would have to handle
	1V without distorting.
    
    	Joe Jas
    

    I was reading in the Feynman lectures on physics last night that
    the acoustic reference is 200pico bar ~ 0dB.  
    	
    	acoustic dB = 20* log_10(P1/Pref)
    	Pref=200 pico bar.  One bar is ~= one atmosphere, actually 
    I think about 10 newtons/cm**2.  This is difference from ambient.
    So a 60dB signal has a pressure difference from ambient of
    	a 1000 times 200 pico bar, or 200 nano bar.  Tiny tiny difference.
    The thresshold of pain is like 120dB, so that's 1000000*200pico
    bar, or 200 micro bar, or a fifth of a thousandth of one atmosphere.
    dBdBdBdoo.
    Tom

    Right, but just to quell the obvious wonderment out there (you all
    WERE wondering, weren't you?) that pressure is an AC pressure. 
    You can stand much greater steady-state pressures on your ears.
    
    Steph
    

	This seemed the best place to ask this...

	In my search for a keyboard mixer, I happened upon the Korg KMX-62.
Neat little unit...  But anyway, it says the input level IS -35dBm.  Isn't that
awfully low for keyboards?  Is there any harm to it?

	Dan

    
    -35 dBm for what output level? -20dBm?? -10dBm? 0dBm? +4dBm?
    
    It sounds like that's the minimum input threshold. More important
    to you is, what is the *maximum* input level before clipping?
    
    Looks like a nice little mixer, BTW.
    
    What's your price?
    
    CdH
    

re < Note 956.31 by MPGS::DEHAHN >
    
>    -35 dBm for what output level? -20dBm?? -10dBm? 0dBm? +4dBm?

	Output = -10dB
    
>    It sounds like that's the minimum input threshold. More important
>    to you is, what is the *maximum* input level before clipping?

	doesn't say...
    
>    What's your price?

	Best (and only) so far is $215 - but that was only Union's price.  They
don't usually quote a very competitive price.
    
	Dan    

    I agree that the -35 dBm is probably a minimum.
    
    Can you post the unit's specs (controls, # of channels, etc.) in
    another note?
    
    Thanks
     Steph