Everything about Decade Log Scale totally explained
» For other uses of this term, see decade (disambiguation).
One
decade is a factor of 10 difference between two numbers. It is a useful concept in
logarithmic scale graphical representations, especially of frequencies; and when describing
frequency response of
electronic systems, such as
audio amplifiers and
filters.
Calculations
The factor-of-ten in a decade can be in either direction: so one decade up from 100 Hz is 1000 Hz, and one decade down is 10 Hz. The factor-of-ten is what is important, not the unit used, so 3.14 rad/s is one decade down from 31.4 rad/s.
To determine the number of decades between two frequencies, use the
logarithm of the ratio of the two values:
» How many decades is it from 15 rad/s to 150,000 rad/s?
:
- or each step is 7.9775% larger than the last.
Graphical representation and analysis
Decades on a
logarithmic scale, rather than unit steps (steps of 1) or other
linear scale, are commonly used on the horizontal axis when representing the frequency response of electronic circuits in graphical form, such as in
Bode plots, since depicting large frequency ranges on a linear scale is often not practical. For example, an
audio amplifier will usually have a frequency band ranging from 20 Hz to 20 kHz and representing the entire band using a decade log scale is very convenient. Typically the graph for such a representation would begin at 1 Hz (10
0) and go up to perhaps 100 kHz (10
5), to comfortably include the full audio band in a standard-sized graph paper, as shown below. Whereas in the same distance on a linear scale, with 10 as the major step-size, you might only get from 0 to 50.
Electronic frequency responses are often described in terms of "per decade". The example Bode plot shows a slope of -20
dB/decade in the stopband, which means that for every factor-of-ten increase in frequency (going from 10 rad/s to 100 rad/s in the figure), the gain decreases by 20 dB.
Further Information
Get more info on 'Decade Log Scale'.
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