Decibel Level

[gL.edu] Este artículo recoge contribuciones de Pablo Arrieta Natal, elaboradas en el contexto de la Clarificación conceptual en torno a los Sistemas de transmisión, bajo la supervisión de J.M. Díaz Nafría.

Definitions

Decibel level, or simply level, is a logarithmic relationship between two quantities, x and y, of the same type, where x is a reference value and y is the value of the quantity at a point. It is designated by the letter L and is defined as:

$L=k\cdot \log _{10}{\frac {y}{x}}$

where k = 10 for power ratios, and k = 20 for ratios of two field quantities.

We speak of absolute levels and relative levels, depending on whether the reference, x, is an absolute (normalised) value of the quantity being compared, or a measurement of the same quantity at some other point in the system. Depending on the unit of the absolute reference, different subscripts are used, while relative levels are usually identified by the subscript r.

Code

function L = level (k, x, y)
% function L = level (k, x, y)
% This function returns the decibel value of the ratio between
# the magnitude value in a point, and a reference value.
% INPUTS
%    k:   proportionality constant, 10 for power relations, 20 for field-value relations 
%    x:   reference value
%    y:   magnitude value in a point
% OUTPUT
%    L:   level value in dB
if k == 10
   warning('You have chosen k=10 which is valid for power relations.')
   else if k == 20
         warning('You have chosen k=20 which is valid for field-value relations')
      end;
   else
      error('k is neither 10 (for power relations) nor 20 (for field-value relations).')
   end;
L = k*log10(abs(y/x));
end