## WHAT IS A “dB” AND WHY IS IT USED?

**WHAT IS A “dB” AND WHY IS IT USED?**

**By Frank McClatchie**

The term “dB” is used throughout the electronics and communications industries to specify operating levels and equipment specifications. A full understanding of this term and its relationship to levels will help you in your day to day operations.

First of all the “d” is for deci which means one-tenth and the “B” stands For Bell (the same man who invented the telephone), so-many dB means so-many tenths of a Bell. The inventor of the telephone was first and foremost involved with sound and particularly deafness, so he needed a way to characterize sound levels. Sound levels cover an extreme volume level ratio, so to ease the calculation of sound power levels he decided to use a logarithmic notation for the measurement of sound levels. He chose to call it the “Bell”. Other engineers later adopted the terminology for other types of logarithmic measurements.

When using logarithmic notation, all successive amplifications or reductions in sound level which would require successive multiplication (for amplification) and division (for reduction) become simple additions and subtractions instead. It is much simpler to add and subtract than it is to multiply and divide, that is just what using logarithms does for you.

Today we use the dB notation for any power or voltage level that we wish to use it for, but we still invoke the name of Bell. Usually one Bell of power or voltage level change is much too great to use, so we usually use the term deci-Bell, or one tenth of a Bell.

The dB is a very convenient notation, but it can also lead to confusion. For instance, doubling the ** power** level always results in a +3 dB increase, while doubling the

**level will result in a +6 dB increase. The reason for this is really quite simple. After all, if the voltage is doubled in any linear circuit, so is the current. So if we count the voltage increase for 3 dB and the current increase for another 3 dB, then the total of the two is really 6 dB!**

__voltage__In addition to using “dB” simply to indicate changes of powers, voltages, or currents, by adding letters to the dB notation, actual voltage or power levels can also be designated. The letters following the dB designate the parameter being measured. The most common parameters are designated in the next table. In each case a zero level indicates that the particular level is equal to the quantity ** one** of whatever is being measured.

__Designation__

dB indicating value change only

dBw Power level in Watts, where 0 dBw = 1.000 Watt

dBm Power level in milli-Watts, where 0 dBm = 0.001 Watts

dBv Voltage level in Volts, where 0 dBv = 1.000 Volt

dBmv Voltage level in milli-Volts, where 0 dBmv = 0.001 Volts

There are many dB relationships that are very useful to memorize for anyone in the communications field, particularly anyone that needs to interpret specification sheets and other such documents in which these dB designations occur. A few are shown below, which are quite useful.

__#dB__ __POWER__ __VOLTAGE__ __#dB__ __POWER__ __VOLTAGE__

0 1 X 1 X 0 1 X 1 X

+1 1.259 X 1.122 X – 1 .7943 X .8913 X

+2 1.585 X 1.259 X – 2 .6310 X .7943 X

+3 1.995 X 1.413 X – 3 .5012 X .7079 X

+4 2.512 X 1.585 X – 4 .3981 X .6310 X

+5 3.162 X 1.778 X – 5 .3162 X .5623 X

+6 3.981 X 1.995 X – 6 .2512 X .5012 X

+7 5.012 X 2.239 X – 7 .1995 X .4467 X

+8 6.310 X 2.512 X – 8 .1585 X .3981 X

+9 7.943 X 2.818 X – 9 .1259 X .3548 X

+10 10.000 X 3.162 X – 10 .1000 X .3162 X

+11 12.549 X 3.548 X – 11 .0794 X .2818 X

+12 15.849 X 3.981 X – 12 .0631 X .2512 X

+13 19.953 X 4.467 X – 13 .0501 X .2239 X

+14 25.119 X 5.012 X – 14 .03981 X .1995 X

+15 31.623 X 5.623 X – 15 .03162 X .1778 X

+16 39.811 X 6.310 X – 16 .02512 X .1585 X

+17 50.118 X 7.079 X – 17 .01995 X .1413 X

+18 63.096 X 7.943 X – 18 .01585 X .1259 X

+19 79.433 X 8.913 X – 19 .01259 X .1122 X

+20 100 X 10 X – 20 .01000 X .1000 X

+30 1,000 X 31.6 X – 30 .00100 X .0316 X

+40 10,000 X 100.0 X – 40 .00010 X .0100 X

+50 100,000 X 316.2 X – 50 .00001 X .00316 X

+60 1,000,000 X 1,000.0 X – 60 .000001 X .00100 X

+70 10,000,000 X 3,162.3 X – 70 .0000001 X .000316 X

Note that there are several dB relationships that are particularly useful.

0 dB indicates no change.

+3 dB indicates double the power, and -3 dB indicates one half the power.

+6 dB indicates double the voltage, and -6 dB indicates one half the voltage.

+10 dB is ten times the power and -10 dB is one tenth the power.

+20 dB is ten times the voltage, but one hundred times the power.

– 20 dB is one tenth the voltage, but one hundredth the power.

Also certain dB conversion factors are repeated in the power and voltage ratios. Note that the 1 dB power ratio is exactly equal to the __2__ dB voltage ratio and the 2 dB power ratio is exactly equal to the __4__ dB voltage ratio and the 3 dB power ratio is equal to the __6__ dB voltage ratio. In order to have the same voltage and power ratio, the dB value of the voltage reading must be double the dB value of the power reading. The same is true of negative dB readings that are less than one. Again the fractional voltage readings are always one half the number of -dB for power as for voltage.

Keeping these general relationships in mind will help a person to become proficient in the use of dB, dBm, and dBv notations.

At first glance, the table seems to be very elaborate and complex, but there is a system behind this notation process that enables those who choose to become familiar with it, to gain a great deal of information from data sheets and other sources that use the dB notation process.

Audio power levels can exceed 120 dB, but it can be seen from the table just how these higher levels can be designated, so I will stop the table at 70 dB. Signal-to-noise measurements in video often exceed 70 dB. All powers, voltages, and currents in an electrical system can be expressed in terms of their relative relationships to each other or to some standard levels.

When these relationships are expressed in logarithmic terms, it becomes much easier to see the result, because performing a succession of additions and subtractions (say in a communication system containing a large number of sections) is very much easier than performing the requisite number of multiplications and divisions that would be necessary if the dB notation did not exist.

A great deal can be learned from this table by someone that is willing to spend the time to examine it to see the relationships. First of all note that all numbers greater than one are positive and all numbers that are less than one are negative, and when the input and the output are equal, no matter what the level actually is, the dB relationship between them is zero. That is a condition of no gain and no loss, or in the case where we are describing a voltage or power level, a zero indicates that the level is equal to the indicated standard, For instance a reading of zero dBm, as an example means that the power level being measured is equal to one milli-Watt, and a reading of zero dBv would mean a voltage of one volt is present.

Next, note from the table that very large numbers can be expressed with a small number of digits. Most Power or voltage levels can usually be expressed with only two digits in front of the decimal point. Additional numbers behind the decimal point can be used to stipulate any exact value desired. It very rarely requires more than three or fourdigits to define any particular voltage or power level, whereas if the dB scale were not available, it could require eight or ten digits to stipulate a given power or voltage level.

Positive dB numbers are always greater than unity, and negative dB numbers are always less than unity, and zero dB __is unity__. This is true whether the dB expression refers to a relative level (such as between the input and output of a device like a pad or amplifier), or the power or voltage level at any point in the system.

It can be seen that a small change in the number of dB can indicate a very large numerical change. That is a great advantage, because in electronics we routinely deal with very large numerical differences on the order or millions or billions to one and we need some way to write these differences down without getting involved with a large number of zeroes.

Remember that if the dB number is positive, it will always be greater than one, and if it is negative the number will always be less than one. If it is zero dB the number ** is** one. Also notice that the “tens digit” of the dB scale will tell you how many decimal places there are in the actual number, this is because it is a deci-Bell. The second digit in the dB number will tell you what the actual number is. A few such relatively simple rules will enable you to decode the approximate size of the number being described by the dB magnitude.

Of course dB can indicate any desired power level by simply using decimal values of dB whose antilog is equal to the power level that you wish to stipulate. An engineering style of calculator can provide the logarithm of any number and the antilog of any number of dB, so the table is not necessary, but an engineering calculator certainly is. If you know the power ratio that you wish to convert to dB, then simply enter that power level (in milli-Watts) into the calculator and convert that into the logarithm of that number, and then multiply by 10, and there is the dBm value of the power level.

If you know the voltage that you wish to express in dBv, then enter that number into the calculator and find the logarithm of that number and multiply that by 20. If it is a power level, multiply the logarithm by 10, and if it is a voltage level, again find the logarithm and then multiply by 20. To find actual powers from the dBm designations, divide the logarithm by 10 and find the antilog button. If you wish to discover the voltage value of a dBv designation, divide the dBv number by 20 then find the antilogarithm of that number. It is actually quite simple, but you do need an engineering style of calculator for this purpose.

Remember that once you convert voltages or powers to dB, all subsequent calculations can be accomplished by simple addition of dB (for gain), and subtraction of dB (for loss). That is a much easier task than multiplying (for gain) and dividing (for attenuation) to discover what the output really is.