May 1936 RadioCraft
[Table
of Contents]
Wax nostalgic about and learn from the history of early electronics.
See articles from RadioCraft,
published 1929  1953. All copyrights are hereby acknowledged.

Arithmophobia (a real word)
is likely the root cause of of decibelphobia
(that one's made up), a condition
that causes some otherwise rational people to curl in the fetal
position in an attempt to avoid the topic. As with most subjects,
the more often you engage in using a term, the more comfortable
you become with it. Technicians and engineers who deal in voltage
and power levels in terms of dividing quantities or transmitting
them from one location to another would find conversation and
writing without the use of decibels quite inconvenient. It is
tempting to point out that using decibel units to express ratios
or relative levels, thereby permitting use of simple addition
and subtraction rather than multiplication and division, respectively,
is no different than using logarithms to do the same with any
number in general. However, logarithms are lost on most people
as well. Historically, logarithms were so important in science
and mathematics that large volumes were created to facilitate
rapid multiplication and division of numbers.
Just as it is unreasonable to go to a foreign country and
expect the indigenous people to adapt their common language
to accommodate your lack of knowledge*, if you expect to live
in the realm of the RF and microwave world citizens, developing
fluency in decibels is essential to a successful, productive
existence. This article from a 1936 edition of RadioCraft
is as good a place to start as any.
* Except for the case of the hoardes crossing the U.S. southern
border illegally with the expectation that we'll happily accommodate
their native language and even provide all governmental communication
in that language while berating protesting, legal citizens who
are forced to pay for the policy. Oh, wait, that's what we do >:(
Decibel Level vs. Decibel Gain
Do not miss this lucid explanation!
S. L. Canterbury
Amplifiers are rated according to the number of watts output
they can handle without distortion. The output depends upon
the size and design of the amplifier. This output tells what
volume of sound will come from a system and the area that can
be covered with the installation.
Fig. 1. The factors involved in db. gain
and level.
The amplifier performs but one important function: to receive
the voice of the speaker or music and raise the volume to a
much higher level so that the sound energy may be heard by many
people over a fairly large area.
Basic Ratings
Before the gain (amplification) of an amplifier can be measured
it is necessary to select some unit of measurement. As the output
of the amplifier is rated in terms of watts it would be logical
to measure the input in terms of watts also. Now the effect
of sound energy on the ear is not a direct (arithmetic) function
but varies in an exponential way. Therefore, the gain of an
amplifier is expressed in the same way, by means of logarithms.
The expression is given by the formula:
where db. represents the unit of transmission or amplificationthe
decibel; W_{0} is the power output; and W_{i}
is the power input. The formula states that the "decibel gain"
is equal to ten (10) times the logarithm of the efficiency of
the amplifier. Efficiency is here used in connection with sound
energy and does not mean the electrical efficiency which is
usually very low. The above formula will hold at all times in
rating amplifiers.
Amplifiers can also be rated in terms of currents and impedances.
Referring to Fig. 1, the formula is
If the resistance of the input impedance equals the load
resistance, the 'last term becomes zero and the first term gives
the decibel gain. In some designs, however, the second term
may be considerable and must not be neglected in such cases.
The gain may also be rated in terms of input and output voltages,
provided the input and output reactances are equal to zero;
that is, when both impedances are resistance only. The formula
is:
Again the last term equals zero, if the input and output
resistances are equal.
The "Zero Level"
Sound and noise levels are usually expressed in decibels
and not in watts, therefore, a reference level of zero decibels
must be set. For convenience, engineers have arbitrarily taken
the output of a commonbattery telephone transmitter (when spoken
into with a loud voice) as zero level. This equals 0.01watt
or 10 milliwatts. The output of a standard transmitter, used
by telephone engineers is also 10 milliwatts. Thus in telephone
work zero level has been set at 10 milliwatts, but in radio
work it will be noticed that the articles in the past have always
mentioned the reference level and is not universally standard.
The tendency among radio engineers is to refer the system to
a zero level of 0.006watt or 6 milliwatts and throughout this
article all levels will be with respect to 6 milliwatts. It
's of very little importance whether the level is 10 or 6 milliwatts
as long as one or the other is taken. as standard!
By using 6 milliwatts as zero level, amplifiers may be rated
at an energy level of a certain. number of decibels. This is
desirable because the ear responds to sound in a logarithmic
manner. This can be illustrated by the following example. If
an amplifier delivers 6 watts output it has a level of:
.
Now, if the output is doubled, the ear will notice an increase
in volume but not twice as great as the 6 watts output because
the ear will respond as the increase in decibels and not as
the increase in watts output. Thus,
The ear did not detect the increased volume in a direct ratio,
but as the logarithm of the ratio. Therefore, if this zero reference
level were not used, the amplifier control set at 30 db. gain
would not give any indication of the volume of the output unless
the input were known. With the control marked in decibels above
zero level, the 30 db. setting would indicate an output of 12
watts.
A commercial amplifier rated at 26 watts output has an energy
level, at full output, expressed in decibels equal to:
Now 'it is stated in the catalog that this amplifier has
a gain of 96.4 db. Where do the extra 60 decibels come from?
The answer to this question will become evident after the microphone
output has been considered.
Allowance for Mike "Level"
Different types ·of microphones have different energy output
levels, but most commercialtype carbonbutton microphones give
an energy level of 50 to 80 db. When the speaker (source of
sound) is near the mike, a good average is the 60 db. level.
The mike, therefore, lowers the energy level that it receives
and it is the function of the amplifier to raise the voice level
from 60 db. back to zero level and still higher in order to
have appreciable output at the loudspeaker. After the sound
has passed through the mike, it is at a very low level and has
very little energy. The actual power impressed on the amplifier
input, after passing through the mike, can be found as follows:
60 = 10 log R; where R is the ratio of mike output to mike
input, and here it is assumed that zero level is impressed upon
the mike. 40.0000  100 = 10 log R or 4.0000  10 = log R or
.
Therefore W_{0} = 0.006microwatt.
Thus the input of zero level to the mike is lowered to 60
db. in passing through the mike and the power that the amplifier
begins with is very small. The entire gain is therefore 96.4
db. as the amplifier ends up with a 36.4 db. level. In amplification
work it is desirable to know what level above zero the amplifier
will raise the sound of the speaker's voice, and, therefore,
the maximum reading on the control should be 36.4 db. and not
96.4 db. A highgain amplifier when used with a very poor mike
may give but little amplification. For example, suppose the
mike had a loss of 76.4 db. This would leave a gain of 20 db.
above zero. The output would be far below the rated 26 watts
and would be equal to:
20 = 10 log R or 2.0000 = log R or
or the output W_{0} equals 0.6·watt. After all, the
decibel gain is not so important. It is the decibel level above
zero that counts. It is well to point out here that there is
a limit to the overall gain that an amplifier may have, as
explained in RadioCraft July 1935, page 10.
The energy required to operate the amplifier is 90 watts,
while the output is but 26 watts. The efficiency is therefore
This may be expressed in decibels as would be done if used
in connection with telephone work.
or
which represents a loss.
The accompanying, Table I lists the efficiency for certain
decibel gains or losses. The table's use can be demonstrated
by means of the following examples. It is well to point out
that the table may be used for any value of decibel gain. Suppose
the efficiency at 15 db. gain is to be found. Fifteen decibels
equal 10 db. plus 5 db. but the resulting efficiency is the
product of the efficiencies at 10 db. and 5 db. A 15 db. gain
gives an efficiency of 10 x 3.16 = 31.6 or 3,160 per cent.
Table 1
A Db. Gain in  Dollars!
Let us now use this 15 db. gain in a problem. A man starts
out with $2 and at the end of two weeks he has a 15 db. gain
which is an efficiency of 3,160 per cent. Therefore, at the
end of two weeks the man has $63.20. The man's son also has
a decibel gain of 15 at the end of two weeks but he started
with 50 cents. His efficiency is also 3,160 per cent but instead
of having $63.20, like his father, the boy has only $15.80.
Again it is seen that the db. gain is not as important as the
db. level above a certain reference point. Suppose the reference
point chosen by the two is $5.00, and this is zero db. level.
The man at the end of 2 weeks, has a level of:
The boy has a db. level of:
level which shall be called a 5 db. level.
With the level above, as the reference point, it is at once
evident that the father has more money than his son. Both still
have the same gain, however. In this case the man began with
a 5 db. level and finished with 10 db., a gain of 15. The boy
began with a 10 db. level and ended with a 5 db. level which
is also a 15 db. gain.
Posted April 24,2015