Are you afraid of Decibel conversion?

What is db, dbm?

%, dB, dBm and dB(μV/m) are important concepts that every engineer

should understand in his (or her) sleep. Because if he doesn’t, he is bound

to be at a disadvantage in his work. When these terms come up in

discussions with customers or colleagues, he will have trouble focusing on

the real issue if he is busy wondering whether 3 dB means a factor of 2 or 4

(or something else). It is well worth the effort to review these concepts from

time to time and keep familiar with them.

While this Application Note is not intended as a textbook, it will help to

refresh your knowledge of this topic if you studied it before or provide a

decent introduction if it is new to you.

When it comes to writing formulas and units, we have followed the

international standards specified in ISO 31 and IEC 27 (or else we have

indicated where it is common practice to deviate from the standard).

Why use decibels in our calculations?

Engineers have to deal with numbers on an everyday basis, and some of
these numbers can be very large or very small. In most cases, what is
most important is the ratio of two quantities. For example, a mobile radio
base station might transmit approx. 80 W of power (antenna gain included).
The mobile phone receives only about 0.000 000 002 W, which is
0.000 000 002 5% of the transmitted power.
Whenever we must deal with large numerical ranges, it is convenient to use
the logarithm of the numbers. For example, the base station in our example
transmits at +49 dBm while the mobile phone receives -57 dBm, producing
a power difference of +49 dBm - (-57 dBm) = 106 dB.
Another example: If we cascade two amplifiers with power gains of 12 and
16, respectively, we obtain a total gain of 12 times 16 = 192 (which you can
hopefully calculate in your head – do you?). In logarithmic terms, the two
amplifiers have gains of 10.8 dB and 12 dB, respectively, producing a total
gain of 22.8 dB, which is definitely easier to calculate.
When expressed in decibels, we can see that the values are a lot easier to
manipulate. It is a lot easier to add and subtract decibel values in your head
than it is to multiply or divide linear values. This is the main reason we like
to make our computations in decibels.

Definition of dB

Although the base 10 logarithm of the ratio of two power levels is a
dimensionless quantity, it has units of “Bel” in honor of the inventor of the
telephone (Alexander Graham Bell). In order to obtain more manageable
numbers, we use the dB (decibel, where “deci” stands for one tenth)
instead of the Bel for computation purposes. We have to multiply the Bel
values by 10 (just as we need to multiply a distance by 1000 if we want to
use millimeters instead of meters).

Conversion from decibels to percentage and vice versa

The term “percent” comes from the Latin and literally means “per hundred”.
1% means one hundredth of a value.

1% of x = 0,01. x

When using percentages, we need to ask two questions:

•  Are we calculating voltage quantities or power quantities?
• Are we interested in x% of a quantity or x% more or less of a quantity?

As mentioned above, voltage quantities are voltage, current, field strength
and reflection coefficient, for example.
Power quantities include power, resistance, noise figure and power flux
density.