Skip to content Skip to navigation

Connexions

You are here: Home » Content » Decibels

Navigation

Content Actions
  • Download module PDF
  • Add to ...
    Add the module to:
    • My Favorites
    • A lens
    • An external social bookmarking service
    • My Favorites (What is 'My Favorites'?)
      'My Favorites' is a special kind of lens which you can use to bookmark modules and collections directly in Connexions. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need a Connexions account to use 'My Favorites'.
    • A lens (What is a lens?)

      Definition of a lens

      Lenses

      A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

      What is in a lens?

      Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

      Who can create a lens?

      Any individual Connexions member, a community, or a respected organization.

      What are tags? tag icon

      Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

    • External bookmarks
  • E-mail the author
  • Rate this module (How does the rating system work?)

    Rating system

    Ratings

    Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

    How to rate a module

    Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

    		(0 ratings)

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Rice DSS - Braille display tagshide tags

    This module is included inLens: Rice University Disability Support Services's Lens
    By: Rice University Disability Support ServicesAs a part of collection:"Fundamentals of Electrical Engineering I"

    Comments:

    "Electrical Engineering Digital Processing Systems in Braille."

    Click the "Rice DSS - Braille" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

  • Featured Content display tagshide tags

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection:"Fundamentals of Electrical Engineering I"

    Comments:

    "The course focuses on the creation, manipulation, transmission, and reception of information by electronic means. It covers elementary signal theory, time- and frequency-domain analysis, the […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Decibels

Module by: Don Johnson

Summary: Working with amplitude and the decibel scale.

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

The decibel scale expresses amplitudes and power values logarithmically. The definitions for these differ, but are consistent with each other.

powers in decibels=10log10powerspower s 0 power s in decibels 10 10 power s power s 0 (1)
amplitudes in decibels=20log10amplitudesamplitude s 0 amplitude s in decibels 20 10 amplitude s amplitude s 0

Here power s 0 power s 0 and amplitude s 0 amplitude s 0 represent a reference power and amplitude, respectively. Quantifying power or amplitude in decibels essentially means that we are comparing quantities to a standard or that we want to express how they changed. You will hear statements like "The signal went down by 3 dB" and "The filter's gain in the stopband is -60-60" (Decibels is abbreviated dB.).

Exercise 1

The prefix "deci" implies a tenth; a decibel is a tenth of a Bel. Who is this measure named for?

Solution

Alexander Graham Bell. He developed it because we seem to perceive physical quantities like loudness and brightness logarithmically. In other words, percentage, not absolute differences, matter to us. We use decibels today because common values are small integers. If we used Bels, they would be decimal fractions, which aren't as elegant.

The consistency of these two definitions arises because power is proportional to the square of amplitude:

powers∝amplitude2s ∝ power s amplitude s 2 (2)
Plugging this expression into the definition for decibels, we find that
10log10powerspower s 0 =10log10amplitude2samplitude2 s 0 =20log10amplitudesamplitude s 0 10 10 power s power s 0 10 10 amplitude s 2 amplitude s 0 2 20 10 amplitude s amplitude s 0 (3)
Because of this consistency, stating relative change in terms of decibels is unambiguous. A factor of 10 increase in amplitude corresponds to a 20 dB increase in both amplitude and power!

Figure 1: Common values for the decibel. The decibel values for all but the powers of ten are approximate, but are accurate to a decimal place.
Decibel table
Power Ratio dB
11 00
2 2 1.51.5
22 33
10 10 55
44 66
55 77
88 99
1010 1010
0.10.1 -10-10

The accompanying table provides "nice" decibel values. Converting decibel values back and forth is fun, and tests your ability to think of decibel values as sums and/or differences of the well-known values and of ratios as products and/or quotients. This conversion rests on the logarithmic nature of the decibel scale. For example, to find the decibel value for 2 2, we halve the decibel value for 2 2; 26 26 dB equals 10+10+6 10 10 6 dB that corresponds to a ratio of 10×10×4= 400 10 10 4 400 . Decibel quantities add; ratio values multiply.

One reason decibels are used so much is the frequency-domain input-output relation for linear systems: Yf=XfHf Y f X f H f . Because the transfer function multiplies the input signal's spectrum, to find the output amplitude at a given frequency we simply add the filter's gain in decibels (relative to a reference of one) to the input amplitude at that frequency. This calculation is one reason that we plot transfer function magnitude on a logarithmic vertical scale expressed in decibels.

Comments, questions, feedback, criticisms?

Send feedback