Decibels

A decibel is a unit for measuring ratios of one quantity to another. In the case of the technician class amateur radio exam, all the questions involve ratios of power levels. If you have two power levels, you can use decibels to say how much bigger or smaller one power level is compared to the other. The formula for decibels is:

$decibels = 10 \times log_{10} \bigg(\frac{P_1}{P_0}\bigg)$

Here’s an example of how to use the formula. Let’s compare two power levels, 5 watts and 10 watts. On the exam, all the answers in decibels will be positive, so always plug in the bigger number for P1 . We get:

$decibels = 10 \times log_{10} \bigg(\frac{10}{5}\bigg)$

$decibels = 10 \times log_{10} \bigg(2\bigg)$

Using a calculator, the log of 2 is about 0.3. Then,

$decibels = 10 \times 0.3$

$decibels = 3$

Rules of thumb if you don’t want to use a calculator

In the above example, the power level doubled from 5 to 10 watts and that wound up being 3 decibels, (abbreviated dB). It turns out that every time the ratio of the two values doubles, you just add another 3 dB. From 5 to 10 watts was an increase in power of 3 dB. What if the power levels being compared are 3 and 12 watts? There’s one doubling from 3 to 6 watts, (3 dB), and another from 6 to 12 watts, (another 3 dB), for a total of 6 dB.

If the power levels differ by a factor of 10, then the result will be 10 dB. For example, if the power levels to be compared are 20 and 200 watts, 200 divided by 20 is 10 and the answer is 10 dB.

What if you get a negative sign on the calculator?

In the example above, if you had divided 5 by 10 instead of 10 by 5, you would have come up with the same answer, but with a negative sign. That’s OK. All answers on the technician class exam are expressed terms of positive decibels, so just ignore the negative sign.

Questions

What is the approximate amount of change, measured in decibels (dB), of a power increase from 5 watts to 10 watts?

A. 2 dB

B. 3 dB

C. 5 dB

D. 10 dB

What is the approximate amount of change, measured in decibels (dB), of a power decrease from 12 watts to 3 watts?

A. 1 dB

B. 3 dB

C. 6 dB

D. 9 dB

What is the approximate amount of change, measured in decibels (dB), of a power increase from 20 watts to 200 watts?

A. 10 dB

B. 12 dB

C. 18 dB

D. 28 dB

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