October 1931 QST
Table of Contents
Wax nostalgic about and learn from the history of early electronics. See articles
from
QST, published December 1915  present (visit ARRL
for info). All copyrights hereby acknowledged.

In 1931, QST reader John H.
Miller, Electrical Engineer, of the Jewell Electrical Instrument Company, wrote
to the editor regarding the story "What
Is This Thing Called Decibel?," by James L McLaughlin and James J. Lamb, which
appeared in the August issue of that year. Mr. Miller wished to inform (or remind)
readers that the American Wire Gauge system for assigning sizes to wire crosssection
ratios closely follows a decibel (i.e., logarithmic) relationship. Applying his
information: A 28 AWG solid wire has a crosssection of 160 circular mils, so at
3 sizes larger, 25 AWG should be 320 circular mils. In fact, it is 320 circular
mils (see table on the Copper
Wire Properties & Gauge Conversions page). A 12 AWG solid wire has a crosssection
of 5,630 circular mils, so at 3 sizes larger, 9 AWG should be 13,060 circular mils,
and it is 13,090 circular mils. That verifies the 3 dB per three differences
in gauge for two cases using small and large wire sizes. What about, say, 5 dB
for 5 wires sizes in difference? Using 28 AWG again as a reference, a 5 dB
increase in size for 285=23 AWG wire should be about 160 * 10^(5/10) = 506
circular mils. The table gives 510 circular mils, which is within cumulative rounding
errors in the calculations, so the rule of thumb works for decibel values other
than 3.
The Decibel: AWG Wire Size Rule of Thumb
Editor, QST:
I have read with much interest the article in the August issue of QST entitled,
"What Is This Thing Called Decibel?"
The writer's picture of the decibel may be of some interest, and is based on
wire table ratios.
The B & S gauge, which is universally used for copper wire, very closely
approaches the decibel ratio as regards area or cross section and consequent resistance.
A change of ten decibels either multiplies or divides the power by ten, depending
whether it is up or down; a decrease of ten sizes in the wire table multiplies the
cross section or divides the resistance by ten. An increase of ten sizes does the
reverse.
A threedecibel change doubles or halves the power, and a change in three sizes
of wire doubles or halves the cross section and the resistance changes also by a
factor of two.
Engineers who are accustomed to working with copper wire have these ratios well
in mind, and the fact that the decibel ratio is the same as the wire table crosssection
ratio allows a mental picture to be had directly from past experience, and does
not require a complete new set of ratios to be memorized.
It should be noted that the wire table ratios are not exactly those given, the
error being of the order of 3/4 of 1%, which may be entirely neglected when ratios
in multiples of unity are considered.
 John H. Miller, Electrical Engineer, Jewell Electrical Instrument Co.
Posted August 2, 2016
