The Bel and Decibel (db)

**bel (B)**

A logarithmic measure of sound intensity, invented by engineers of the Bell telephone network in 1923 and named in honor of the inventor of the telephone, Alexander Graham Bell (1847-1922). If one sound is 1 bel louder than another, this means the louder sound is 10 times more intense than the fainter one. A difference of 2 bels corresponds to an increase of 10 x 10 or 100 times in intensity. The beginning of the scale, 0 bels, can be defined in various ways originally intended to represent the faintest sound that can be detected by a person who has good hearing. In practice, sound intensity is almost always stated in decibels. One bel is equal to approximately 1.151 293 nepers.

**decibel (dB)**

A customary logarithmic measure most commonly used (in various ways) for measuring sound. The human ear is capable of detecting an enormous range of sound intensities.
Furthermore, our perception is not linear. Experiment shows that when humans perceive one sound to be twice as loud as another, in fact the louder sound is about ten times as
intense as the fainter one. For this reason, sound is measured on logarithmic scales. Informally, if one sound is 1 bel (10 decibels) "louder" than another,
this means the louder sound is 10 times louder than the fainter one. A difference of 20 decibels corresponds to an increase of 10 x 10 or 100 times in intensity.
The beginning of the scale, 0 decibels, can be set in different ways, depending on exactly which aspect of sound is being measured. For sound intensity
(the power of the sound waves per unit of area) 0 decibels is equal 1 pico watt per square meter; this corresponds approximately to the faintest sound that can be detected by a
person who has good hearing. A quiet room has a normal sound intensity of around 40 decibels, ten thousand times louder than the faintest perceptible sound, and a thunderclap may
have an intensity of 120 decibels, a trillion times louder than the faintest sound. For sound pressure (the pressure exerted by the sound waves) 0 decibels equals 20 micropascals
(µPa) RMS, and for sound power 0 decibels sometimes equals 1 picowatt. In all cases, one decibel equals about 0.115 129 neper and *d* decibels equal *d*
(ln 10)/20 nepers.

**dB -**

A symbol indicating that a measurement is made using a logarithmic scale similar to that of the decibel (see below) in that a difference of 10 dB- corresponds to a factor of 10.
In each case, the actual measurement *a* is compared to a fixed reference level *r* and the "decibel" value is defined to be 10 log_{10}(*a*/*r*).
Many units of this kind have been used and only a few of the more common ones are mentioned in the next entries. In each case the dB symbol is followed by a second symbol
identifying the specific measurement.
Often the two symbols are not separated (as in "dBA"), but the Audio Engineering Society recommends that a space be used (as in "dB A").

**dB A, dB C**

units of sound intensity, exactly like the decibel except that before the measurement is made sounds of high and low frequencies, heard poorly or not at all by the human ear, have been filtered out. The letters A and C refer to two filtering methods.

**dB c**

A unit of signal strength used in electronics, especially in measuring noise levels. The signals are measured relative to the strength of the carrier signal, which is the
desired signal. A typical statement might be that a certain noise level is -50 dB c, meaning that the noise is 50 "decibels below carrier" or 10^{-5}
times the carrier signal strength.

**dB FS**

Abbreviation for "decibels full scale," a unit of power as measured by a digital device. A digital measurement has a maximum value M depending on the number of bits used.
If the actual power measurement is *p*, the dB FS value displayed is 20·log_{10}(*p*/M) dB FS. Since *p* cannot exceed M, this reading is always negative.

**dB i**

A unit measuring the gain of an antenna. The reference level is the strength of the signal that would be transmitted by an isotropic antenna: one radiating equally in all
directions. For example, an antenna rated 20 dB i transmits a signal in the desired direction 10^{2} = 100 times stronger than an isotropic antenna.

**dB m, dB W**

logarithmic units of power used in electronics. These units measure power in decibels above the reference level of 1 milliwatt in the case of dB m and 1 watt in the case of
dB W. A power of *n* watts equals 10 log *n* dB W; conversely, a power of *p* dB W equals 10^{(p/10)} watts. The same formulas link dB m to milliwatts.
An increase of 10 dB m or 10 dB W represents a 10-fold increase in power. Since 1 watt = 1000 milliwatts, 0 dB W = 30 dB m.

**dB rn**

A symbol for "decibels above reference noise," a unit measuring noise levels in telecommunications. The usual reference level is -90 dB m, which is equivalent to a power of 1 picowatt (1 pW). For example, 50 dB rn equals -40 dB m.

**dB spl**

A logarithmic unit of sound intensity as computed from the sound pressure level. The reference level is a pressure of 20 micro pascals.
If sound waves exert a pressure of P pascals, the sound intensity is 100 + 20·log_{10}(P/2) dB spl.

**dB u**

A logarithmic unit of power, similar to dB m but computed from voltage measurements. The reference level is 0.775 volts, the voltage which
generates a power of 1 milliwatt across a circuit having an impedance of 600 ohms. A voltage of V volts corresponds to a power of 20·log_{10}
(V/0.775) dB u.

**dB V**

A logarithmic unit of power, similar to dB m but computed from voltage measurements. The reference level is 1 volt.
A voltage of V volts corresponds to a power of 20·log_{10}(V) dB V.

**dB W**

See dB m above.

**dB Z**

A unit of radar reflectivity used in meteorology. The unit measures the amount of energy returned to a weather radar site as a function of the amount transmitted. The scale is logarithmic, a difference of 10 dB Z indicating a 10-fold increase in energy returned. For display purposes, dB Z values are grouped as follows:

(Level 1, 18-30 dBZ) - Light precipitation

(Level 2, 30-38 dBZ) - Light to moderate rain

(Level 3, 38-44 dBZ) - Moderate to heavy rain

(Level 4, 44-50 dBZ) - Heavy rain

(Level 5, 50-57 dBZ) - Very heavy rain; hail possible

(Level 6, >57 dBZ) - Very heavy rain and hail; large hail possible

The colorful "radar images" shown on television are actually plots of these levels

For practical use just remember that the typical power levels for various types of radio station (in E.R.P.) are as follows:

Here's another person's discription on this:

What is a Decibel?

This is a relative power unit. At audio frequencies a change of one decibel (abbreviated dB) is just detectable as a change in loudness
under ideal conditions.For a given power ratio the decibel change is calculated as:

dB = 10 log P2/P1

If we used voltage or current ratios instead then our formula becomes:

dB = 20 log V2/V1

Examples of using the Decibel

The decibel units add and subtract.
For example, if we had an amplifier stage with a voltage gain of 22 which from above is 26.85 dB gain, followed by a further amplifier stage
which has a voltage gain of 17 (24.6 dB) then the total overall voltage gain is 22 * 17 = 374 (51.46 dB).

Adding together the 26.85 dB plus the 24.6 dB = 51.45 dB, The minor difference was caused by my rounding to the nearesting second decimal place.
What is dBm for example

I received this email question:

"could you please explain me the difference between db, dbmV and dbmicroV?"

My reply:
I assume you understand decibels, if not:

see http://www.electronics-tutorials.com/basics/decibel.htm [this page]

dBm for example simply is referenced to milli-watts where one milli-watt = 0dBm.

A very common dBm figure is +7dBm where following the decibel rules and dividing +7 by 10 we get 0.7 and the anti-log of that is 5.0118 or
five as the nearest whole number.

So +7dBm is another way of saying 5 milli-watts.

The same applies to the other values you mentioned, just different reference levels.

Why use this system? Instead of saying +7dBm why not say 5 milli-watts? There are several reasons:

a) In systems with gains and losses it is far easier to add and subtract the dBm's.

b) With different impedance's throughout circuits, power levels in dBm's remain constant, only the rf voltages and impedance's change.

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