NOTE 

 Decibel Tables 



By K. S. JOHNSON 



ABOUT twenty years ago, Bell System communication engineers felt 

 the need for, and adopted, a new "Transmission Unit," initially ab- 

 breviated "TU" but some five years later given the name "Decibel," or db. 

 This unit is now universally used throughout the communication world and 

 is fundamentally a measure of the ratio of any two powers. Quantitatively, 

 the number of decibels corresponding to the ratio of any two powers is 10 

 times the common logarithm of that ratio.* If the ratio of the first power 

 to the second power is greater than unity, the first power is said to represent 

 a transmission "gain" with respect to the second power, or the latter is said 

 to represent a "loss" with respect to the first power. 



Since currents flowing through, or voltages impressed across, the same or 

 equal impedances will result in powers that are proportional to the squares 

 of these currents or voltages, it is possible, under these specific conditions, 

 to state that the number of decibels corresponding to the ratio of any two 

 such currents or voltages is 20 times the common logarithm of the absolute 

 magnitude of the ratio of these currents or voltages. 



Another unit that is frequently employed in theoretical transmission prob- 

 lems is the "Neper." The use of this unit often results in the simplification 

 of such problems and, hence, its relationship to the decibel and to exponential 

 and hyperbolic functions is frequently of interest to communication en- 

 gineers. 



Although the relations between these various values are obviously not 

 complicated ones, it has been found by experience that tables of numerical 

 values are often very useful to communication engineers. As a result, rather 

 extended tables (21 pages) have been computed under the direction of the 

 writer and P. H. Richardson, in which the entering arguments are: (1) 

 decibels, with the tabular values giving the corresponding current, voltage, 

 or power ratios — and their reciprocals; (2) current or voltage ratios, with 

 the tabular values being the corresponding decibels. Tables (16 pages) 

 have also been computed in which the entering arguments are decibels and 

 the corresponding tabular values are nepers (A), e , e~^ ^ sinh A, cosh A 

 and tanh A. These latter tables are, among other things, useful in the 

 design of attenuators or pads, etc. 



Photo offset copies of any of the above tables may be obtained gratis 

 from the Director of Publication of the Bell Telephone Laboratories, Inc., 

 463 West Street, New York 14, N. Y. 



* See "Decibel — The Name for the Transmission Unit", by W. H. Martin, Bell Sys. 

 Tech. Jour., January 1929. 



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