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On logarithmic ratio quantities and their units

On logarithmic ratio quantities and their units
On logarithmic ratio quantities and their units
The use of special units for logarithmic ratio quantities is reviewed. The neper is used with a natural logarithm (logarithm to the base e) to express the logarithm of the amplitude ratio of two pure sinusoidal signals, particularly in the context of linear systems where it is desired to represent the gain or loss in amplitude of a single-frequency signal between the input and output. The bel, and its more commonly used submultiple, the decibel, are used with a decadic logarithm (logarithm to the base 10) to measure the ratio of two power-like quantities, such as a mean square signal or a mean square sound pressure in acoustics. Thus two distinctly different quantities are involved. In this review we define the quantities first, without reference to the units, as is standard practice in any system of quantities and units. We show that two different definitions of the quantity power level, or logarithmic power ratio, are possible. We show that this leads to two different interpretations for the meaning and numerical values of the units bel and decibel. We review the question of which of these alternative definitions is actually used, or is used by implication, by workers in the field. Finally, we discuss the relative advantages of the alternative definitions.
0026-1394
246-52
Mills, Ian
7c91c014-d4bb-4a3d-add2-46ffc8eaeb9a
Morfey, Christopher
4ee977af-f99c-4a2c-ae5a-d8875b829d5c
Mills, Ian
7c91c014-d4bb-4a3d-add2-46ffc8eaeb9a
Morfey, Christopher
4ee977af-f99c-4a2c-ae5a-d8875b829d5c

Mills, Ian and Morfey, Christopher (2005) On logarithmic ratio quantities and their units. Metrologia, 42 (4), 246-52. (doi:10.1088/0026-1394/42/4/008).

Record type: Article

Abstract

The use of special units for logarithmic ratio quantities is reviewed. The neper is used with a natural logarithm (logarithm to the base e) to express the logarithm of the amplitude ratio of two pure sinusoidal signals, particularly in the context of linear systems where it is desired to represent the gain or loss in amplitude of a single-frequency signal between the input and output. The bel, and its more commonly used submultiple, the decibel, are used with a decadic logarithm (logarithm to the base 10) to measure the ratio of two power-like quantities, such as a mean square signal or a mean square sound pressure in acoustics. Thus two distinctly different quantities are involved. In this review we define the quantities first, without reference to the units, as is standard practice in any system of quantities and units. We show that two different definitions of the quantity power level, or logarithmic power ratio, are possible. We show that this leads to two different interpretations for the meaning and numerical values of the units bel and decibel. We review the question of which of these alternative definitions is actually used, or is used by implication, by workers in the field. Finally, we discuss the relative advantages of the alternative definitions.

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Published date: 2005

Identifiers

Local EPrints ID: 28440
URI: https://eprints.soton.ac.uk/id/eprint/28440
ISSN: 0026-1394
PURE UUID: e60fd075-113e-41b5-b492-404e23e02ad8

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Date deposited: 28 Apr 2006
Last modified: 17 Jul 2017 16:01

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