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The Decibel
Why all the Confusion?
Mark Rogers, The Greenbusch Group
AES - The Decibel Revisited
© 2016 Mark Rogers
First, a little Quiz:
 What
is the decibel, really?
AES - The Decibel Revisited
© 2016 Mark Rogers
The decibel defined:
 The


Dictionary
Webster’s
American Heritage
 Wikipedia
 Manufacturer’s
 IEEE
Web Sites
Dictionary
AES - The Decibel Revisited
© 2016 Mark Rogers
History of the Decibel
 Once
upon a time----
 Telephone
companies had a need to
measure signal levels
 And to compute losses from the new
cables being strung around the nation
AES - The Decibel Revisited
© 2016 Mark Rogers
Origin of the Decibel
 Standard
to 1923



Cable Mile, used by Telcos prior
based on 19 gauge copper
resistance of 88 ohms per mile
capacitance of 0.054 microfarads per mile
AES - The Decibel Revisited
© 2016 Mark Rogers
Origin of the Decibel
 Meanwhile,
Harvey Fletcher was doing
hearing research


To measure the minimum perceptible change
of human hearing
He called it the SU, which turned out to be
close to the SCM
AES - The Decibel Revisited
© 2016 Mark Rogers
Origin of the Decibel
 1923
article by WH Martin of Bell Labs
defined the Transmission Unit (TU)

To replace both SCM and SU
 1929
article by Martin renamed the TU to
be the deci-Bel, named after the company
founder, Alexander Graham Bell
AES - The Decibel Revisited
© 2016 Mark Rogers
Uses of the decibel
 To




quantify the signal strength of
electricity
sound
light
radio waves
 For
many types of systems
AES - The Decibel Revisited
© 2016 Mark Rogers
Basic principles
 Based
on human hearing
 Logarithmic
 Intended to accommodate very large
ranges of levels, for which logarithms are
convenient
 And allows computing gain/loss by
addition/subtraction
AES - The Decibel Revisited
© 2016 Mark Rogers
Why are we confused?
 The
decibel is often:
 Misused and abused (especially by those
darn audio people)
 Even many manufacturers do not use it
correctly

Some apparently do not even know how!
AES - The Decibel Revisited
© 2016 Mark Rogers
What is a decibel, really?
A
decibel is 1/10 of a Bel
 Why?


To make it nearly equal to the old TU
And because the Bel is too large an increment
to be useful.
 But

what is a Bel??
10 decibels
AES - The Decibel Revisited
© 2016 Mark Rogers
It’s very simple!
The
decibel is a POWER RATIO,
expressed logarithmically.
It is defined as:
P1
n dB  10 log
P2
AES - The Decibel Revisited
© 2016 Mark Rogers
Wait a minute!
 My
book says its 20 log something… not
10 log…
 And I don’t want to measure power… I
have seen dBs based on voltages
AES - The Decibel Revisited
© 2016 Mark Rogers
The ANSI Standard
definition
 decibel
is 1/10 of a
Bel
 The ratio of two
amounts of power
being ten times the
log of this ratio.
 Abbreviated dB
 n = 10 log (P1/P2)
AES - The Decibel Revisited
 When
the ratios of
currents or voltages
(or other quantities)
are the square roots
of the power ratios,
then the decibel is
also
 n = 20 log (E1/E2)
© 2016 Mark Rogers
But, but, but
 How
do I get to the voltage form
 And what are its limitations?
 Let’s
do a little algebra...
AES - The Decibel Revisited
© 2016 Mark Rogers
Derivation of the voltage
form
P1
n dB  10 log
P2

but,
2
E
P
Z
AES - The Decibel Revisited

substituting...
© 2016 Mark Rogers
Derivation of the voltage
form

therefore,
n
 E12 


Z1 

dB  10 log
2
 E2 


 Z2 
 E12   Z 2 
 10 log  2  x 
 E 2   Z1 
AES - The Decibel Revisited
© 2016 Mark Rogers
Derivation of the voltage
form

and,
E1
Z2
 20 log
 10 log
E2
Z1
This last term is the one
most texts omit, many are
unaware of, and we all
forget!
AES - The Decibel Revisited
© 2016 Mark Rogers
Derivation of the voltage
form
E1
Z2
 20 log
 10 log
E2
Z1

Hmmmmm …. What if Z1 = Z2?
E1
 20 log
 10 log 1
E2
E1
 20 log
0
E2
AES - The Decibel Revisited
Aha!
© 2016 Mark Rogers
When is a voltage ratio OK?
 When
the impedance is the same for both
voltages!
AES - The Decibel Revisited
© 2016 Mark Rogers
Remember!
 dB
is always a POWER RATIO!
 If the impedance is the same for both
voltages, then a voltage ratio is merely a
convenient way to calculate the power
ratio to obtain the decibel value.
AES - The Decibel Revisited
© 2016 Mark Rogers
The decibel
 Being
a ratio, it has no units, is not a unit
of measure

dB is dimensionless
 But
it can be used as a unit of measure
 How?

By making P2 an absolute reference level of
power
 Written
as dBr, where r is the reference
AES - The Decibel Revisited
© 2016 Mark Rogers
Variations on the decibel
 Plain


Old dB
dBr
(generic ref to standard level)
Audio






dBm
dBu
dBV
dBW
dBk
dB FS
AES - The Decibel Revisited
 Acoustics



dB-SPL (Lp)
dB-PWL (Lw)
dB A, dB C
 Radio




dBmv
dBµv
dBi
dBz
© 2016 Mark Rogers
Handy things to remember:
0
dBu = 0.775 volts
 0 dBm = 1 milliwatt
 dBu = dBm if and only if z = 600 ohms

0 dBm = 0.775 volts if and only if z = 600
ohms
0
dBV = 1.0 volts
 0 dBV = 1.107 dBu
AES - The Decibel Revisited
© 2016 Mark Rogers
Ponder This
 The
difference between +4 inputs and -10
inputs is not 14 dB.
 It is approximately 12.8 dB
 “+4” usually means 4 dBu, which is
referred to 0.775 volt
 “-10” usually means -10 dBV, which is
referred to 1.0 volt
AES - The Decibel Revisited
© 2016 Mark Rogers
Sound Levels in dB
0
dB-SPL = 20 microPascals
 0 dB-PWL = 1 picowatt (10-12 watt)

Beware, if you enjoy old textbooks, that some
used a different reference

that older reference was 10-13 watt, which is a 10
dB difference
AES - The Decibel Revisited
© 2016 Mark Rogers
True or False?
A
signal added to itself (mixed on two
inputs at equal levels) will double the
power (increase the mixed level by
around 3 dB)
 3 dB is twice as much power
 10 dB is twice (or half) as loud
 10 dB is ten times as much power
AES - The Decibel Revisited
© 2016 Mark Rogers
True or False?
A
signal added to itself (mixed on two
inputs at equal levels) will double the
power (increase the mixed level by 3 dB)
 Usually false.

If the signals are identical (voltage and
phase) the voltage will double, giving a 6 dB
increase.
AES - The Decibel Revisited
© 2016 Mark Rogers
True or False?
3
dB is twice as much power
 False



Not exactly
Double power is 3.01029995664… dB
3.0 dB is 1.99526231497… times as much
power
AES - The Decibel Revisited
© 2016 Mark Rogers
True or False?
 10
dB is twice (or half) as loud
 Well... maybe... sometimes


For a standard average human, whatever that
may be...
Because it is subjective, it will vary from
person to person.
 And,
it’s FALSE at low frequencies,
remember Fletcher-Munson!
AES - The Decibel Revisited
© 2016 Mark Rogers
True or False?
 10
dB is ten times as much power
 True, exactly.
AES - The Decibel Revisited
© 2016 Mark Rogers
Correct or Incorrect Usage?
 The
signal to noise ratio is 50 dB
 This mixer clips at 21 dB
 It was loud! It must have been 140 dB!
 I really like my Fluke because it measures
dBm directly
 The power amp’s voltage gain is 26 dB
 The sound pressure level was -4 dB A
AES - The Decibel Revisited
© 2016 Mark Rogers
Correct or Incorrect Usage?
 The


signal to noise ratio is 50 dB
This use of dB is generally correct
(although it would be nice to know the
weighting factor and bandwidth)
AES - The Decibel Revisited
© 2016 Mark Rogers
Correct or Incorrect Usage?
 The
dB.



spec sheet says this mixer clips at 21
Incorrect!
The reference is missing…..
Is is dBu, dBV, dBm, or dBcooper?
AES - The Decibel Revisited
© 2016 Mark Rogers
Correct or Incorrect Usage?
 It


was loud! It must have been 140 dB!
Incorrect!
This says the sound was 1012 times more
powerful than.


Than what?
The reference and weighting are missing!
AES - The Decibel Revisited
© 2016 Mark Rogers
Correct or Incorrect Usage?
I
really like my Fluke because it measures
dBm directly.


Incorrect! It is a volt meter, not a watt
meter.
Therefore, it is measuring dBu, not dBm.


Regardless of how it is labeled on the meter
If the circuit impedance is exactly 600 ohms, they
will be equal, but…
AES - The Decibel Revisited
© 2016 Mark Rogers
Correct or Incorrect Usage?
 The
dB.

Incorrect! It is missing the notation that it is
not a power ratio as the impedances differ...


power amp has a voltage gain of 26
Even with such notation, per IEEE/ANSI: this
usage “should preferably be avoided”)
A voltage gain may be properly expressed in
decilogs.
AES - The Decibel Revisited
© 2016 Mark Rogers
Correct or Incorrect Usage?
 The
sound pressure level was -4 dB A
 Correct!

Yes, Virginia, you can have sound levels
below 0 dB SPL
AES - The Decibel Revisited
© 2016 Mark Rogers
Easily compute dBs in your
head
 Take
advantage of the power of
logarithms:
 As power ratios multiply (divide), dBs add
(or subtract)
 negation is inversion of the ratio
AES - The Decibel Revisited
© 2016 Mark Rogers
Handy things to remember
 double
power is 3 dB, half power is -3 dB
 double voltage is 6 dB, half voltage is -6
dB
 quadruple power is 6 dB, 1/4 the power is
-6 dB
 10 dB is ten times the power
 20 dB is 100 times the power (10 times
the voltage)
AES - The Decibel Revisited
© 2016 Mark Rogers
Consider that:
 The
ratio of 1 watt to 10 watts is the
same as from 100 watts to 1000 watts


Exactly 10 dB
Approximately twice as loud

Or so they say, stick around for the demo!
AES - The Decibel Revisited
© 2016 Mark Rogers
Intermission
 Any
questions?
 After


break
We will ponder the Fletcher-Munson curves
and listen to some sound!
AES - The Decibel Revisited
© 2016 Mark Rogers
Fletcher-Munson Curves
 Equal-
loudness
contours
 SPL vs.
Frequency
 Using
human
subjects
AES - The Decibel Revisited
© 2016 Mark Rogers
Demonstration
 How
much is 1 dB?
 Barely perceptible change, they say
 26% increase in power, 12% increase in
voltage
AES - The Decibel Revisited
© 2016 Mark Rogers
Demonstration
 How
much is 3 dB?
 Twice the power, 41% increase in voltage
(1.414 = square root of 2)
AES - The Decibel Revisited
© 2016 Mark Rogers
Demonstration
 How
much is 10 dB?
 Twice as loud, they say
 10 times as much power, 3.16 times as
much voltage (square root of 10)
AES - The Decibel Revisited
© 2016 Mark Rogers
Demonstration
 How

much is 20 dB?
Four times as loud?
 100
times as much power, 10 times as
much voltage
AES - The Decibel Revisited
© 2016 Mark Rogers
Demonstration
 How
loud is 0 dB-SPL?
 The threshold of hearing, they say
AES - The Decibel Revisited
© 2016 Mark Rogers
Response of The Ear
3 dB
Just Perceptible
10 dB
Doubling/Halving
Pink Noise
6 dB
Noticeable
20 dB
Much More/Less
AES - The Decibel Revisited
© 2016 Mark Rogers
What about weighting?
 A-weighting
is intended to approximate
the human hearing at 40 phons

Use for levels below 55 dB SPL or so
 B-weighting
is intended to approximate
the human hearing at 70 phons

Use for levels below 55-85 dB SPL
 C-weighting
is intended to approximate
the human hearing at high levels (flattest)
AES - The Decibel Revisited
© 2016 Mark Rogers
Listen to This
 Samples
from Bob Smith
 Both samples have the same level in dBA,
and similar spectral shapes
 Why do they sound so different?
Factory
AES - The Decibel Revisited
Restaurant
© 2016 Mark Rogers
Now see the spectra
AES - The Decibel Revisited
© 2016 Mark Rogers
Summary
 The
dB is always a POWER RATIO
 n dB = 10 log (P1/P2)

You can also use 20 log (E1/E2) if the
impedances are equal
 By
setting P2 to an absolute level, dB can
be used to create a unit of measure

An absolute voltage can also be used, if
impedances are equal.
AES - The Decibel Revisited
© 2016 Mark Rogers
For further study
 IEEE
Standard Dictionary of Electrical and
Electronics Terms (An ANSI Standard)
 Sound System Engineering, Davis,
Patronis, Brown; Chapter 7 (4th edition)
 Handbook for Sound Engineers

The New Audio Cyclopedia, 1.17, 36.9, 37.7
 Acoustics,
Leo Beranek, Chapter 1
 Effects of Noise on Man, Karl Kryter
AES - The Decibel Revisited
© 2016 Mark Rogers
Thanks for Attending!
 Any

more questions?
There are no stupid questions. There are only
stupid answers. If you ask a question, the onus
will be on me to not be stupid.
– Don Davis, SynAudCon
AES - The Decibel Revisited
© 2016 Mark Rogers
Contact me
Mark Rogers
Director of AV Dept
The Greenbusch Group
206.378.0569
[email protected]
AES - The Decibel Revisited
© 2016 Mark Rogers