Suppose your station has a transmitter that puts out 50 watts of power, a feed line that loses all but 40% of the power, a duplexer that loses half the power, and an antenna that produces enough gain to make the signal 4 times as strong as a dipole antenna.  To find the effective radiated power of your station you need to multiply 50 watts times .4 (feed line loss) times .5 (duplexer loss) times 4 (antenna gain) = 40 watts.

Rather than multiply all these factors together, someone decided it would be good to represent them in a way that allows us to add them.  An increase of a factor of 10 is defined to be a 10 decibel increase.  Decibels are abbreviated dB.  Two 10dB increases produces a 20dB increase, because we add decibel increases.

Two increases by a factor of 10 results in an increase of 10 X 10 = 100; therefore 20dB = 100.  Three 10dB increases is 30dB, which is 10 X 10 X 10 = 1000. 

Because we want to be able to add the dB increases, 0 dB is a factor of 1.  Multiplying something by 1 does not change it, just as adding 0 to something results in no change.

Decibels	0	10	20	30
Factor	1	10	100	1000

It’s easy to figure out the meaning of 10, 20, 30, 40... dB, but how about decibels less than 10?

Note that if we multiply 2 by itself 10 times, it generates the following: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.

2 times itself 10 times is 1024, which is slightly more than 1000, which is 30dB.  3 added to itself 10 times is 30, and 30dB is a factor of 1000.  Therefore, 3dB represents a factor of (approximately) 2.

Another way to derive that 3dB represents a factor of 2 is this:  If we add 3dB to itself 3 times we get 9dB, which is less than, but close to, 10dB.  If we multiply 2 times itself 3 times we get 2X2X2=8, which is close to, but less than 10.  This is good because 9dB should be less than 10 (since 10 dB is 10).  We have to multiply 8 by 5/4 to equal 10, and we have to add 1dB to 9dB to equal 10dB.  Having 3dB = 2  will work if 1dB = 5/4.  Does 1 dB represent a factor of 5/4?  If we apply 1dB 3 times, we’ll have 3dB, which = 2.  (5/4)X(5/4)X(5/4) = 125/64, which is close to 2.  Therefore, a 3dB increase represents a 2 times increase, and 1 dB represents an increase of 1.25.

6dB = 3dB + 3dB.  A 3dB increase is a factor of 2, so 6dB = 2 X 2 = 4.  Similarly, 9 dB = 2 X 2 X 2 = 8.

So far we have:

Decibels	0	1	2	3	4	5	6	7	8	9	10
Factor	1	1.25		2			4			8	10

Let’s consider negative decibels.  -1dB changes 10dB to 9dB, which changes 10 to 8.  Therefore, -1 dB is .8, because .8 times 10 = 8.

To find 8dB, think of 8dB as 9dB – 1dB = 8 X .8 = 6.4.  To find 5dB, think of 5dB as 6dB - 1dB = 4 times .8 = 3.2.  Note that 5dB + 5dB = 10dB = 10.  Using 5dB = 3.2:  3.2 X 3.2 = 10.24, which is about 10.  To find 2dB, use 2dB = 3dB – 1dB = 2 X .8 = 1.6

Decibels	0	1	2	3	4	5	6	7	8	9	10
Estimated Factor	1	1.25	1.6	2	2.5	3.2	4	5	6.4	8	10
Actual Value	1	1.26	1.58	1.99	2.51	3.16	3.985	5.01	6.31	7.94	10
% Error		.714	-.944	-.236	.475	-.178	-.473	.237	-1.41	-.708	0

You’ll notice from the chart that the results are all within 1.5%.

To summarize the system:

Realize that 3dB = 2, so 6dB = 4, and 9dB = 8.

You know the value for 3, 6, and 9dB (2, 4, 8).

To find 2, 5, or 8dB (1 less than 3dB, 6dB, or 9dB), use -1dB = .8.

If you want to know 4 or 7dB (1 more than 3dB or 6dB), use 1dB = 1.25.

To find fractions of 1dB, realize that 1dB represents a 25% increase, so .1dB is a 2.5% increase, .2dB is a 5% increase, .4dB is a 10% increase.  (This interpolation method isn’t exact, but it’s fairly close when dealing with such small values).

You can carry this further for hundredths of a decibel.  .01dB is one tenth of .1dB.  .1dB is 2.5%, so .01dB is .25%.  .04 dB is 1%.

An example:  Suppose an antenna has a gain of 17.68 dB.  How much increase is this?  Note that 17.68 = 10 + 7 + .68.  A 10 dB increase is a factor of 10.  A 7 dB increase is a factor of 5.  Therefore, a 17 dB increase is a factor of 10 X 5 = 50.  .6 dB is 15%, .08 dB is 2%, so .68 dB is about 17%.  50 X 1.17 = 58.5, so the antenna increases the signal strength by a factor of 58.5, the signal is 58.5 times as strong (the exact value is 58.61).

Another example:  An antenna’s signal is 25 times stronger than a dipole antenna.  How many decibels is this?  This is actually quite easy.  A 10 dB increase is a factor of 10.  Because 25 = 10 X 2.5, we still have an increase of 2.5 to account for.  An increase of 2.5 is 4 dB, so the total increase = 10 dB + 4 dB = 14 dB (the exact value is 13.98 dB).

Suppose we have an increase of a factor of 30.  How many decibels is this?  30 = 10 X 3.  To multiply by 10 requires 10dB.  But, we need to add the decibels needed to multiply by 3.   4dB is 2.5, but we need 20% more (3 is 20% more than 2.5).  20% is about .8dB, so 30 = 14.8dB (the exact value is 14.77).

Well, that’s my little system for decibels, and as promised, I didn’t mention logarithms!