[TowerTalk] Power dB w/o trig. A tutorial DE K0FF

[K0FF]

The .97716 solution by K0FF.

DeciBels are very confusing for most of us. If  you know the formula and how
to use it, read no further. I won't even mention the formula here, it's been
covered well elsewhere.
If you're not comfortable with Logarithms though, look at this chart, it may
help.
Below is a simplified method for figuring what the power might be at the
other end of a coax cable, or the gain of an amplifier.
                                           ***  I call it the .97716
solution.***
First, the unit of measurement is the Bel, named for Alexander Graham Bell.
Why didn't they call the unit the Bell with 2 L's? I don't know. We don't
call the unit named for Farad a Fara, or for Ampere and Amper. Makes no
sense. Lissajous or Coulomb or Kirchoff I can see misspelling, but Bell?
Anyway it's a man's name and therefore should always be capitalized.
Al Bell's main area of interest was helping hard of hearing people, and to
develop aids for them. The telephone came out of his research into human
hearing, and the measurement Bel refers to the smallest difference in sound
level that the human ear can detect. The idea of using ratios became very
popular in  the electronic age, but the Bel is such a large unit, we usually
divide it into tenths and call it a deciBel for 1/10 Bel. I have never ever
seen or heard 10 dB referred to as a Bel, or 20 dB as 2 Bels...another
oddity.

Anyway concerning dB ratios dealing with power, in Watts:

Let's take a look at the bigger ratios first. 10 dB is worth 10 times the
power as a gain measurement or 1/10 if a loss.  Easy to remember the big
ones. It's just a 10 followed by as many zeros as the first number of the
figure. 10 dB is 100, and that's ten with 1 extra zero. 20 dB is 1000, and
that's ten followed by 2 zeros, 30 dB is 10,000, or ten with 3 extra zeros
etc. Easy.
The tenths are a little harder, but each 1/10 of a dB is worth roughly 2.25
percent. The exact figure is 2.284, or looking at it this way, If you start
with 100 percent of something and have a 1/10 dB loss, there will be 97.716
percent left.

That's all there is to it, the rest is simple arithmetic and can be done on
a 4 function hand calculator in steps.
Say you have 100 Watts (or is it Wats), and a coax loss of .3 dB :
100 x .97716= 97.716    (loss in the first 1/10 dB)
97.716 x .97716 = 95.484 left after the second 1/10 dB.
95.484 x .97716 = 93.303 Watts left at the other end.

If you multiply all the way to 1 full dB, you'll see that there is 80
percent of the starting power left, and at 2 dB only 64 per cent and at 3 dB
there is 50 percent left.

Now if it's a gain and not a loss, figure it by finding the percent number
as above and then divide that as a decimal into 1.

e.g.. 3 dB= 50 percent   >< 1/.5=2  ><   there it is, a 2 times gain for 3
dB.

Or you can break it down into smaller pieces like this: Gain of linear
amplifier is 13 dB. 13 is same as 10 plus 3. You have 50 Watts of drive,
times 10 dB (10 times gain, remember) is equal to 500....500 times 2 (for
the extra 3dB) = 1000. 50Watts in gives 1000 Watts out.
You could also say that the 13 dB amplifier has a gain factor of : 10 (for
the 10dB part) x 2 (for the 3 dB part)= 20 times power gain. And again, 50 x
20 = 1000 Watts.


Some easily remembered key figures are listed in the table, but you can find
any and all of these just by remembering the .97716 number, and doing a
chain multiplication.

These are rounded off approximations to make it easy to mentally juggle
them:

1 dB   80 Percent left as a loss factor   x1.25   gain factor
2dB    64                                                  x1.56
3dB    50                                                  x2
5dB    32                                                  x 3.125
6dB    25                                                  x4
10       10                                                   x10
20dB   100                                                x1000

When you have series losses, just add the dB numbers together, and figure
from there.
e.g.. 100 Watts, two pieces of coax spliced together with 3 dB loss each=
6dB total loss.

You lose half in the first 3dB, and half OF WHATS LEFT in the second 3 dB,
so you wind up with only 1/4 of what you started with.

Let's don't hear any more comments like: "the gain of this antenna must be
10 or 20 deciBels!".

 Hope this helps, Geo>K0FF




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