[TowerTalk] Re: (corrected ver.1) Power dB w/o trig. A tutorial DE K0FF

[K0FF]

Here is a corrected version. Hope there are no more errors..Tnx to all, Geo
-----Original Message-----
From: K0FF <K0FF@arrl.net>
To: Tower Talk (mail list) <towertalk@contesting.com>; VHF reflector
<vhf@w6yx.stanford.edu>; W3EP <W3EP@ARRL.ORG>
Date: Wednesday, July 05, 2000 1:56 PM
Subject: (corrected ver.1) Power dB w/o trig. A tutorial DE 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 Faraday 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 1 followed by as many zeros as the first number of the
>figure. 10 dB is 10, and that's one with 1 extra zero. 20 dB is 100, and
>that's one followed by 2 zeros, 30 dB is 1,000, or one 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
>
>
>
>


--
FAQ on WWW:               http://www.contesting.com/FAQ/towertalk
Submissions:              towertalk@contesting.com
Administrative requests:  towertalk-REQUEST@contesting.com
Problems:                 owner-towertalk@contesting.com