February 1968 RadioElectronics
[Table of Contents]
Wax nostalgic about and learn from the history of early electronics.
See articles from RadioElectronics,
published 19301988. All copyrights hereby acknowledged.

You can tell by the number of articles in electronics magazines (see list at
the bottom) that a lot of
people struggled with the concept of decibels (dB). Probably the issue was more
converting between linear units and decibel units, since exponents and
logarithms are involved. Teaching someone to add and subtract decibels, or to
multiply and divide, respectively, linear units is relatively simple, and is not
confusing. For some people, converting power levels from watts (or milliwatts)
to decibels can become a rote operation; no real understanding of the concepts
is required, but throw in a factor of two for voltage to power (and vice versa), and the eyeballs are
likely to roll back in the head ;) Mr. Eric Leslie did his part to try to
ease the pain in this "The Useful Decibel" article in the February 1968 issue of
RadioElectronics magazine.
The Useful Decibel
Fig. 1  Functional diagram of typical MATV system, with signal
levels in volts. Boxed figures are absolute values.
Everywhere in electronics you find dB's  now learn them the painless way  without
logarithms!
By Eric Leslie
Much nonsense, and worse  a lot of incomprehensible sense  has been written
about the decibel, probably the most useful unit of measurement in electronics.
Yet in spite of that usefulness, too many technicians don't understand it. Why?
Because most articles on the how and why of the decibel do more talking about logarithms
than about decibels. That's fine, if you know logs. But if you don't, you have to
learn logarithms and decibels, both at the same time.
Nonlinear measurement
How did the decibel come about? It was devised to measure nonlinear quantities.
Did you know your ear does not have linear response to changes in sound volume?
This is the reason you can hear a whisper across a quiet room, and also tolerate
the blare of auto horns or the roar of a subway express train.
Suppose you're listening to an amplifier with a wattmeter across the output.
First you hear a 1watt sound; then you crank up the gain to 2 watts. Does the speaker
output sound twice as loud? No  it just sounds a little bit louder. You have to
turn up the gain until you increase power output 10 times  to 10 watts  before
you hear twice as much audio as you did at the 1watt level. That, briefly, is the
way your ear works.
Fig. 2  Same system, using dB's. Again, signal levels are shown
in boxes; gains and losses are not. See text for details.
To describe this interesting system, the 10to1 power relationship was described
mathematically and called a bel (in honor of Alexander Graham Bell). For more precise
measurements, a tenthofabel unit  the decibel  was put in service.
The decibel, then, is a measure of power ratio. It doesn't matter whether you
increase or decrease the power  dB's work both way. Double the power, and you've
increased it by 3 dB. Cut the power in half, and you've decreased it by 3 dB. Check
this with the table. In column B find the ratio of power increase  2.0. Opposite
this point in column E you'll find 3  the number of dB's of change.
Decibels can also be used to measure the ratio between two voltages or between
two currents. Since power equals voltage times current, though, voltage dB's come
out differently than power dB's. Look at the chart again. Increase voltage by ratio
of 2 (2.0 in column B) How many dB's of voltage increase? In column A you'll find
6.
Here's why: Put 1 volt across a 1ohm resistor. Since P = E^{2}/Ror
1^{2}/1, power is 1 watt. Now increase voltage 3 dB. The chart says that
a 3dB voltage increase is a ratio of 1.4 to 1. So now what's the power? P = E^{2}/Ror
(1.4)^{2}/1 or about 2 watts. Power has doubled  and according to the chart,
that is 3 dB of power gain. (The same figures work for current, by the way.)
How to use dB's
Using dB's to measure changes in power, voltage or current makes difficult jobs
easy. As an example, suppose you want to install a master antenna system in a large
40unit apartment building. You make a diagram  like Fig. 1  of the equipment.
Then you figure how to get enough signal to each TV to furnish an acceptable picture.
Assume you've got a 1mV signal at the rooftop antenna, and you want no less
than 1 mV at each receiver. From the antenna, the signal goes through coaxial cable.
dropping to half the voltage (1/2 of 1 mV is 0.5 mV) by the time it arrives at the
amplifier, where it's stepped up 300 times (300 times 0.5 mV is 150 mV). From the
amplifier, the signal divides at a fourway splitter, and each output has half the
voltage of the input (1/2 of 150 mV is 75 mV).
Next there's more coax, dropping signal voltage to 1/4 (1/4 of 75 mV is 18.75
mV). The 10 receiver tapoffs in series cut the signal in half again (1/2 of 18.75
mV is 9.375 mV).
The last receiver is isolated from the line by the tapoff, and this isolation
drops the signal again  to perhaps 15% of the line signal (15% of 9.375 mV is about
1.4 MV). That's what the last receiver gets.
If you like to multiply, as we've done, you're welcome to the method. There is
an easier system, though  using decibels.
Decibel Table
But first we've got to have a reference point. A dB figure is only a measure
of the ratio between two power or voltage levels. It does not refer to an absolute
value. In TV antenna work, 1 mV (or 1,000 μV) has become the reference point,
because it is often the lowest signal that should be delivered to a receiver. Therefore,
1 mV is called "0 dBmV."
Now look at Fig. 2, where 0 dBmV is beside the antenna, to show that's the signal
available there. Coax drops the signal in half, and from the table you'll find that's
a 6dB loss, so write that down and subtract it from 0 dBmV, getting 6 dBmV. (The
minus sign here indicates the signal is 6 dB below 0 dBmV.)
Next convert the 300times gain of the amplifier to the nearest value in the
table, or 50 dB. Add +50 dB to 6 dBmV, getting +44 dBmV. (You can also do it by
subtracting 6 dBmV from +50 dB; the result is the same. The plus sign here shows
the signal is 44 dB above 0 dBmV.)
Continue through the diagram, using the table to convert voltage increases or
decreases to dB gain or loss. Eventually you'll find you have about +3 dBmV at the
last receiver. From the chart, you see that's about 1.4 m V.
Sure, you've had to do a lot of converting and using the table to work with dB's
in this exampleand it has been a nuisance. But you don't have to do it in practice.
If manufacturers of amplifiers, splitters, tapoffs and cable told you only that
their equipment would amplify a signal "300 times" or attenuate it "by 15%" you'd
have to multiply and divide to layout a master antenna system. They don't do that,
however. They give you dB gain or loss figures, and all you have to do is add and
subtract them.
Assume you've made a plan of the apartment
building. From equipment catalogs, you obtain the following figures  all the losses
in your system:
You determine the signal at the antenna is 0 dBmV. Since you also want 0 dBm
V at the last receiver. It's obvious you need at least 47 dB of gain from the amplifier.
You buy the nearest thing  a 50dB unit. See how simple it is?
Other dB uses
Decibels aren't used solely in antenna work. Various reference levels are used
in other areas of electronics. In broadcasting and recording studios, "0 dBm" is
defined as 1 mW in 600 ohms of impedance. Years ago telephone companies and some
radio stations used a 0dBm reference point of 6 mW in 500 ohms. For higherpower
applications, such things as "0 dBW" (1 watt) and "0 dBk" (1 kW) are used. There
is even "0 dBV" (1 volt).
Notice that 0 dBm means 1 mW only in 600 ohms. Impedance is defined because radio,
television and recording studios have standardized on 600ohm inputs, outputs and
lines. A similar situation exists in masterantenna computations involving voltage.
Hence, 0 dBm V means 1 mV (or 1,000 μV) across 75 ohms of impedance, since that's
the common type of coax used.
You can't use dB's to compare voltage differences unless the two voltages are
across the same value of impedance.
So you see, the dB is really not too difficult to work with. As a stranger, it's
an unknown, perhaps incomprehensible element. Once you get to know it, the decibel
will become a valuable tool in your electronics work. RE
Posted May 8, 2023
