dB calculator - Explanation of dB and decibel

The use of dBs is illustrated by this example.  Read it slowly and try to understand it because if you get to understand this dB example the whole business will become much easier to understand.

dB calculation problem:  What is the output power level in the following situation and will the transmitter output amplifier be overloaded ?. For reference, note the information table on the right

Input signal power level = 1 milliwatt or -30 dBW (or 0 dBm)
Devices in series:
A two transistor amplifier:  Gain 16 dB   (forty times increase in level, x40)
An adjustable 20 dB range attenuator, initially set half way, by you, at the 10 dB setting:   10 dB attenuation (10 times reduction)
Long coax cable:   Loss 3 dB attenuation  (reduction to half the level)
High power 10 watt amplifier: Gain=30 dB (increase in signal level by a factor of 1000 times. Note the 3 zeros = 30 dB)

Calculation:   Output = -30 + 16 -10 - 3 + 30  = 3 dBW = 2 watts

Comment: This should work, but note that if the adjustable attenuator were to be turned to its minimum attenuation value ( 0 dB ) the system would attempt to output +13 dBW or 20 watts.  This is not acceptable with a 10 watt amplifier as it will distort the signal badly and may damage the amplifier.  It will also cause interference to other people on the adjacent frequencies.   In the above case I would add an extra 3 dB attenuator (also called a 3 dB pad) somewhere along or at an end of the cable.  This would mean that a 0 dB setting on the attenuator would cause a 10 watt output and thus just saturate the amplifier.  This avoids risk of accidental interference to other people and damage to the expensive power amplifier.

Formulas:

To convert a ratio to dB, do log and then times by 10.
Example:   ratio = 1234 times.   Log(1234) =  3.09.   Ten times 3.09 = 30.9 dB

To convert dB to ratio, divide by 10 and then do ten to the x, like 10^x
Example: dB = +12.5 dB.   Divide +12.5 by 10 = +1.25.    Do 10^1.25 = 17.8 ratio.