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Decade (log scale)
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Decade (log scale)
One decade (symbol dec) is a unit for measuring ratios on a logarithmic scale, with one decade corresponding to a ratio of 10 between two numbers.
When a real number like 0.007 is denoted by 7.0×10−3, it is said that the number is represented in scientific notation. More generally, to write a number in the form a × 10b, where 1 ≤ a < 10 and b is an integer, is to express it in scientific notation, and a is called the significand or the mantissa, and b is its exponent. The numbers so expressible with an exponent equal to b span a single decade, from 10b to 10b+1.
Decades are especially useful when describing frequency response of electronic systems, such as audio amplifiers and filters.
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 (f1 and f2), use the logarithm of the ratio of the two values:
or, using natural logarithms:
To find out what frequency is a certain number of decades from the original frequency, multiply by appropriate powers of 10:
To find out the size of a step for a certain number of frequencies per decade, raise 10 to the power of the inverse of the number of steps:
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Decade (log scale)
One decade (symbol dec) is a unit for measuring ratios on a logarithmic scale, with one decade corresponding to a ratio of 10 between two numbers.
When a real number like 0.007 is denoted by 7.0×10−3, it is said that the number is represented in scientific notation. More generally, to write a number in the form a × 10b, where 1 ≤ a < 10 and b is an integer, is to express it in scientific notation, and a is called the significand or the mantissa, and b is its exponent. The numbers so expressible with an exponent equal to b span a single decade, from 10b to 10b+1.
Decades are especially useful when describing frequency response of electronic systems, such as audio amplifiers and filters.
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 (f1 and f2), use the logarithm of the ratio of the two values:
or, using natural logarithms:
To find out what frequency is a certain number of decades from the original frequency, multiply by appropriate powers of 10:
To find out the size of a step for a certain number of frequencies per decade, raise 10 to the power of the inverse of the number of steps:
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