September 1969 Electronics World
Table of Contents
Wax nostalgic about and learn from the history of early electronics. See articles
from
Electronics World, published May 1959
 December 1971. All copyrights hereby acknowledged.

Experienced RF engineers,
technicians, and hobbyists employ decibels in their writings and speech with the
fluidity and familiarity of chemists discussing pH levels, geneticists recommending
DNA sequencing enzymes, astrophysicists calculating gravitational lensing constants
for massive galaxies, or vintage car motorheads calling out ignition timing in reference
to TDC (topdeadcenter). This 1969 Electronics World magazine article by William Miller takes yet another shot
at helping those uninitiated in the realm of decibels to be effectively functional
until an eventual  and necessary  firm grasp of the concept is obtained. The
real solution, of course, is to just hunker down and learn the basics of
logarithms. They are not as scary as some believe them to be.
Decibels Without Logs
By William G. Miller / Industrial Electronics Corp.
A simple method of solving decibel problems
in seconds mentally without using charts, tables, or slide rules.
Decibel problems can be solved easily without the use of algebraic expressions,
log tables, slide rules, or nomograms. As a matter of fact, with a little practice,
you should be able to make accurate mental calculations.
To begin with, it is necessary to memorize two key numbers and their associated
dB figures. The key number will tell you what to do to the power value when its
related dB figure is used.
1. For 10 dB, the key number is 10.
2. For 3 dB, the key number is 2.
This means that for an increase or a +10dB change, our power level would be
multiplied by 10 and for a decrease or 10dB change, we would divide by 10.
Similarly, a +3dB change would then indicate that we multiply the power level
by 2 and a 3dB change would mean that we must divide by 2.
While it is quite easy to see how an amplifier with a 3dB gain will double the
input power, it may be more difficult to realize that an amplifier with a 57dB
gain will have double the power output of an amplifier with a 54dB gain (both referred
to the same 0dB level).
The power is doubled for every 3dB gain and halved for every 3dB loss. This
means that we had to double the power 18 times to get to 54 dB and once more to
get to 57 dB.
By way of another example, an antenna with a 30dB gain can deliver only one
tenth the signal power of an antenna with a 40dB gain. Note that the power is multiplied
by 10 for every 10dB gain and divided by 10 for every ladB loss.
The antenna reference level was multiplied by 10 four times to get to 40 dB and
then divided by 10 (10 dB) to get back down to 30 dB.
Up to this point, we have been using the 10dB and 3dB figures separately, but
they can be used together to form many combinations.
Problem 1: Increase 4 watts by 13 dB.
Solution: First increase the level by 10 of the 13 dB (to 40 watts). Now increase
it by the remaining 3 dB (double the 40 watts).
Answer: 80 watts.
Problem 2: Increase 4 watts by 7 dB.
Solution: First increase the level by 10 dB (40 watts), then subtract 3 dB by
dividing by 2.
Answer: 20 watts.
Many combinations of 3 and 10 can be used to arrive at the decibel figure you
want and different combinations can be used to achieve the same answer.
Technicians who are familiar with powers of ten can pick up even more speed when
it is considered that each 10dB change means that the decimal point is moved one
place.
Problem 3: Attenuate 6 watts by 33 dB.
Solution: Move the decimal point 3 places to the left and halve the result.
Answer: 0.003 watt.
Voltage and current ratios can also be expressed in decibels but the decibel
figure associated with the key number is doubled. 1. For 20 dB the key number is
10. 2. For 6dB the key number is 2. The same method as described above can then
be used for voltage and current ratios.
Posted August 8, 2024 (updated from original post
on 9/12/2017)
