1. Why all the Confusion? Mark Rogers, The Greenbusch Group
The Decibel
Why all the Confusion?
Mark Rogers, The Greenbusch Group

2. First, a little Quiz:
What is the decibel, really?

3. The decibel defined: The Dictionary Wikipedia Manufacturer’s Web Sites
Webster’s
American Heritage
Wikipedia
Manufacturer’s Web Sites
IEEE Dictionary

4. 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

5. Origin of the Decibel
Standard Cable Mile, used by Telcos prior to 1923
based on 19 gauge copper
resistance of 88 ohms per mile
capacitance of microfarads per mile

6. 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

7. 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

8. Uses of the decibel To quantify the signal strength of
electricity
sound
light
radio waves
For many types of systems

9. 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

10. 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!

11. 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

12. It’s very simple!
The decibel is a POWER RATIO, expressed logarithmically.
It is defined as:

13. 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

14. 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)
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)

15. But, but, but How do I get to the voltage form
And what are its limitations?
Let’s do a little algebra...

16. Derivation of the voltage form
but,
substituting...

17. Derivation of the voltage form
therefore,

18. Derivation of the voltage form
and,
This last term is the one most texts omit, many are unaware of, and we all forget!

19. Derivation of the voltage form
Hmmmmm …. What if Z1 = Z2?
Aha!

20. When is a voltage ratio OK?
When the impedance is the same for both voltages!

21. 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.

22. 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

23. Variations on the decibel
Plain Old dB
dBr (generic ref to standard level)
Audio
dBm
dBu
dBV
dBW
dBk
dB FS
Acoustics
dB-SPL (Lp)
dB-PWL (Lw)
dB A, dB C
Radio
dBmv
dBµv
dBi
dBz

24. Handy things to remember:
0 dBu = volts
0 dBm = 1 milliwatt
dBu = dBm if and only if z = 600 ohms
0 dBm = volts if and only if z = 600 ohms
0 dBV = 1.0 volts
0 dBV = dBu

25. 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 volt
“-10” usually means -10 dBV, which is referred to 1.0 volt

26. 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 watt, which is a 10 dB difference

27. 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

28. 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.

29. True or False? 3 dB is twice as much power False Not exactly
Double power is … dB
3.0 dB is … times as much power

30. 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!

31. True or False?
10 dB is ten times as much power
True, exactly.

32. 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

33. 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)

34. Correct or Incorrect Usage?
The spec sheet says this mixer clips at 21 dB.
Incorrect!
The reference is missing…..
Is is dBu, dBV, dBm, or dBcooper?

35. 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!

36. 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…

37. Correct or Incorrect Usage?
The power amp has a voltage gain of 26 dB.
Incorrect! It is missing the notation that it is not a power ratio as the impedances differ...
Even with such notation, per IEEE/ANSI: this usage “should preferably be avoided”)
A voltage gain may be properly expressed in decilogs.

38. Correct or Incorrect Usage?
The sound pressure level was -4 dB A
Correct!
Yes, Virginia, you can have sound levels below 0 dB SPL

39. 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

40. 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)

41. 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!

42. Intermission Any questions? After break
We will ponder the Fletcher-Munson curves
and listen to some sound!

43. Fletcher-Munson Curves
Equal-loudness contours
SPL vs. Frequency
Using human subjects

44. Demonstration How much is 1 dB? Barely perceptible change, they say
26% increase in power, 12% increase in voltage

45. Demonstration How much is 3 dB?
Twice the power, 41% increase in voltage (1.414 = square root of 2)

46. 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)

47. Demonstration How much is 20 dB?
Four times as loud?
100 times as much power, 10 times as much voltage

48. Demonstration
How loud is 0 dB-SPL?
The threshold of hearing, they say

49. Response of The Ear 3 dB 10 dB Pink Noise 6 dB 20 dB Just Perceptible
Doubling/Halving
Pink Noise
6 dB
Noticeable
20 dB
Much More/Less

50. 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 dB SPL
C-weighting is intended to approximate the human hearing at high levels (flattest)

51. 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
Restaurant

52. Now see the spectra

53. 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.

54. 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

55. 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

56. Contact me Mark Rogers Director of AV Dept The Greenbusch Group