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RF Workbench  (shareware) # A Decibel NomographSeptember 1945 Radio-Craft

 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 usefulness.

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 (Line A).

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 B).

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 / Nomograms Available on RF Cafe:

Posted July 13/2021
(updated from original post on 7/24/2014)    