September 1945 Radio-Craft
[Table of Contents]
Wax nostalgic about and learn from the history of early electronics.
See articles from Radio-Craft,
published 1929 - 1953. All copyrights are hereby acknowledged.
Yes, it's another nomograph. This one is for calculating the
number of decibels required to amplify or attenuate a voltage
level. The chart came from a 1945 edition of Hugo Gernsback's
Radio-Craft magazine, but decibels are still defined
today the way they were nearly 70 years ago. A hard copy of
a nomograph residing in a notebook or on the wall is still a
handy tool when you need to do a quick calculation. Unless you
have a voice-commanded app where Siri will instantly respond
with a conversion for you, printing out one of these nomographs
might be a really handy aid for the lab or office (cubicle).
As far as I know, there is no official name for Android OS
voice personalities, but there is an aftermarket version called
Skyvi (Siri for Android). That sounds a little to close
to Southern pronunciation of "scabie"
or even "skivvy"
for comfort, so let us prefer the voice go unnamed.
A Decibel Nomograph
This "equivalent to an infinite number of charts" calculates
gains or losses in decibels from the voltage input-output ratios
By Nathaniel Rhita
Many problems may be solved by graphical means. An advantage
of such representations is the bird's-eye view which results.
To connect two variables it is common to plot a chart which
is a line or curve, every point of which indicates one variable
in terms of the other. Charts may be designed to correlate frequency
vs. dial setting, antenna length vs. reactance, plate voltage
vs. plate. current, etc.
Decibel Nomograph (black on white).
Another type of graph is the nomograph which is useful in
certain types of problems. This is usually designed to contain
three lines or curves, each calibrated in terms of a variable.
The nomograph differs from the ordinary chart in that the reader
supplies his own indication by the use of a straight-edge, preferably
a celluloid ruler or other transparent straight-edge.
Suppose we wish to show the variation of three quantities:
Two may be shown on a chart, but there is no way of showing
the third, which will have to be assumed constant: We would
need an infinite number of curves on our chart, each corresponding
to some value of the third variable. A nomograph is therefore
equal to an infinite number of graphs. This is the key to its
Decibel Nomograph (white on black).
A useful nomograph is that relating DB gain or loss to voltage
or power ratio. The three variables are input, output and decibels.
In the figure, the left-hand scale is calibrated in values from
1 microvolt to 100 volts in two sections, A and B. The right-hand
scale indicates from one-half volt to 500 volts. The center
scale shows decibels in two sections, C corresponding to A and
D corresponding to B.
As the nomograph stands it indicates voltage gain or loss, but
since current varies directly with voltage in any constant impedance
circuit, amperes may be substituted for volts and microamperes
for microvolts. To extend to power values the center scale must
be divided by two for all readings.
To work out a problem, connect the larger of the two voltages,
currents or powers at scale E with the smaller at either A or
B by means of the ruler. If the output is larger there is a
gain, otherwise a loss. The answer is read off at C or D.
Five lines are shown on the figure as examples.
1 - We wish to find the voltage gain of an audio amplifier.
Making measurements with a V.T.V.M. we find the output is 55
volts when the input is .15 volts. There is a gain of 51.3 DB
2 - We have an R.F. tuner and after repairing and aligning
we wish to find its amplification. Applying a signal generator
to an artificial antenna we find an output of 3 volts when 1600
microvolts is measured at the input. The gain is 6.5 DB (Line
3 - How much attenuation must we use to obtain an output
of .51 volts when 20 volts is applied to the attenuator? All
impedances are assumed matched. We must design an attenuator
to have a 31.9 DB loss (Line C). The same line may be used to
show the output when the input and the attenuation are known.
4 - As mentioned before, power calculations are the same
except that the DB scale is read off as one-half its value.
The catalog lists a particular amplifier as having 10 watts
output. What is its power gain (above 6 milliwatts)? Connect
10 at E with 6000 at A. The gain is 64.2 divided by 2, equals
32.1 DB (Line D).
5 - Another useful transformation is that of percentage to
decibel loss. Amplifiers are sometimes rated in percentage distortion
or noise and sometimes in DB down from the rated output. Only
two variables are concerned, percentage and decibels. To operate,
the ruler is kept fixed against the bottom indication of the
left-hand scale at all times. Percentage is read at E, while
DB down is read at D. A particular amplifier is known to have
2% distortion. How many DB is this below rated output? The answer
is 17 DB below (Line E).
The nomograph below is suitable for most practical purposes.
For greater accuracy, a photostatic enlargement of any convenient
size may be employed.
Nomographs Available on RF Cafe:
Voltage and Power Level Nomograph
- Voltage, Current, Resistance,
and Power Nomograph
- Earth Curvature Nomograph
- Coil Design Nomograph
Coil Inductance Nomograph
- Antenna Gain Nomograph
Posted July 24, 2014