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Amateur Radio Education

The Decibel

The decibel (dB) is one of the most useful parameters in radio communications. It allows one to simply add all of the losses and gains together in order to calculate how much power is actually leaving the antenna and to calculate the effective radiated power.

The decibel itself is a ratio, it has no unit and is meaningless unless you state the value or unit that it is related to.

Transmitter output power can be quoted in decibel watts (dBW). This value is calculated from the equation 10 log P, where P is the power in watts.

Coaxial cable loss is normally quoted as dB loss per 10m or 100m. If a particular cable has a loss of 3dB per 100m and you require a 20m run of cable, the loss on your cable will be 3 x (20/100) = 0.6dB. Note however that all coax cable losses vary with frequency and tend to increase as the frequency increases.

Antenna gains are usually quoted as either dBd - decibel gain relative to a dipole antenna or dBi - decibel gain relative to a theoretical omidirectional antenna.

The effective radiated power can therefore be calculated by taking power output of the transmitter in dBW, subtracting all of the losses due to coax, VSWR, filters etc. and then adding the antenna gain.

To convert back into watts, use 10(or ten to the power d over ten), where d is the power in dBW.

The History of the Decibel

The decibel originates from methods used to quantify reductions in audio levels in telephone circuits. These losses were originally measured in units of Miles of Standard Cable (MSC), where 1 MSC corresponded to the loss of power over a 1 mile (approximately 1.6 km) length of standard telephone cable at a frequency of 5000 radians per second (795.8 Hz), and roughly matched the smallest attenuation detectable to an average listener. Standard telephone cable was defined as "a cable having uniformly distributed resistances of 88 ohms per loop mile and uniformly distributed shunt capacitance of .054 microfarad per mile" (approximately 19 gauge).

The transmission unit (TU) was devised by engineers of the Bell Telephone Laboratories in the 1920s to replace the MSC. 1 TU was defined as ten times the base-10 logarithm of the ratio of measured power to a reference power level. The definitions were conveniently chosen such that 1 TU approximately equaled 1 MSC (specifically, 1.056 TU = 1 MSC). Eventually, international standards bodies adopted the base-10 logarithm of the power ratio as a standard unit, named the bel in honor of the Bell System's founder and telecommunications pioneer Alexander Graham Bell. The bel was larger by a factor of ten than the TU, such that 1 TU equaled 1 decibel. For many measurements, the bel proved inconveniently large, giving way to the decibel becoming the common unit of choice.

In April 2003, the International Committee for Weights and Measures (CIPM) considered a recommendation for the decibel's inclusion in the SI system, but decided not to adopt the decibel as an SI unit. However, the decibel is recognized by other international bodies such as the International Electrotechnical Commission (IEC). The IEC permits the use of the decibel with field quantities as well as power and this recommendation is followed by many national standards bodies, such as NIST, which justifies the use of the decibel for voltage ratios.

Absolute and relative decibel measurements

Although decibel measurements are always relative to a reference level, if the numerical value of that reference is explicitly and exactly stated, then the decibel measurement is called an "absolute" measurement, in the sense that the exact value of the measured quantity can be recovered using the formula given earlier. For example, since dBm indicates power measurement relative to 1 milliwatt,

0 dBm means no change from 1 mW. Thus, 0 dBm is the power level corresponding to a power of exactly 1 mW.

3 dBm means 3 dB greater than 0 dBm. Thus, 3 dBm is the power level corresponding to 10 × 1 mW, or approximately 2 mW.

−6 dBm means 6 dB less than 0 dBm. Thus, −6 dBm is the power level corresponding to 10 × 1 mW, or approximately 250 μW (0.25 mW).

Uses of the Decibel

Acoustics (Sound Pressure)

The decibel is commonly used in acoustics to quantify sound levels relative to a 0 dB reference which has been defined as a sound pressure level of .0002 microbar. The reference level is set at the typical threshold of perception of an average human and there are common comparisons used to illustrate different levels of sound pressure. As with other decibel figures, normally the ratio expressed is a power ratio (rather than a pressure ratio).

The human ear has a large dynamic range in audio perception. The ratio of the sound intensity that causes permanent damage during short exposure to the quietest sound that the ear can hear is greater than or equal to 1 trillion. Such large measurement ranges are conveniently expressed in logarithmic units: the base-10 logarithm of one trillion (10) is 12, which is expressed as an audio level of 120 dB. Since the human ear is not equally sensitive to all sound frequencies, noise levels at maximum human sensitivity—somewhere between 2 and 4 kHz—are factored more heavily into some measurements using frequency weighting.

(See also Stevens' power law.)

Electronics

In electronics, the decibel is often used to express power or amplitude ratios (gains), in preference to arithmetic ratios or percentages. One advantage is that the total decibel gain of a series of components (such as amplifiers and attenuators) can be calculated simply by summing the decibel gains of the individual components. Similarly, in telecommunications, decibels are used to account for the gains and losses of a signal from a transmitter to a receiver through some medium (free space, wave guides, coax, fiber optics, etc.) using a link budget.

The decibel unit can also be combined with a suffix to create an absolute unit of electric power. For example, it can be combined with "m" for "milliwatt" to produce the "dBm". Zero dBm is the power level corresponding to a power of one milliwatt, and 1 dBm is one decibel greater (about 1.259 mW).

In professional audio, a popular unit is the dBu (see below for all the units). The "u" stands for "unloaded", and was probably chosen to be similar to lowercase "v", as dBv was the older name for the same thing. It was changed to avoid confusion with dBV. This unit (dBu) is an RMS measurement of voltage which uses as its reference 0.775 V. Chosen for historical reasons, it is the voltage level which delivers 1 mW of power in a 600 ohm resistor, which used to be the standard reference impedance in telephone audio circuits.

The bel is used to represent noise power levels in hard drive specifications. It shares the same symbol (B) as the byte.

Electric power

dBm dB(1 mW) – power measurement relative to 1 milliwatt

dBW dB(1 W) – similar to dBm, except the reference level is 1 watt.

Voltage

Since the decibel is defined with respect to power, not amplitude, conversions of voltage ratios to decibels must square the amplitude, as discussed above.

A schematic showing the relationship between dBu (the voltage source) and dBm (the power dissipated as heat by the 600 Ω resistor)

dBV dB(1 V) – voltage relative to 1 volt, regardless of impedance.

dBu or dBv

In pro audio most equipment for processing signals will operate at +4 dBu. Consumer equipment will typically operate at -10 dBu. Therefore, many devices offer dual voltage operation for interoperability reasons, typically with a switch for +4/-10 dBu.

dBmV

dBμV or dBuV

Optics

Video and Digital Imaging

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