# Logarithmic relationship between db and dbm

### dB vs. dBm - ISA

To be exact, decibel dB is expressed in this term: dB = 10 log (P1/P2). dBm is considered as an absolute unit '“ a unit to measure power. Decibel (dB) and dB relative to a milliwatt (dBm) represent two different but absolute power "P" (in watts) to dBm, use the formula dBm = 10*log (P/1 mW). of Automation (ISA) is a nonprofit professional association serving. dB.. Decibels Power-ratio.. P2/P1 (P2 is the power being measured, and P1 is the reference) Voltage-ratio.. V2/V1 (V2 is the voltage being measured, and V1 is the reference) dBm.. dB for reference 1 Decibels are logarithmic, not linear.

Photographers typically use an alternative base-2 log unit, the stopto describe light intensity ratios or dynamic range.

Suffixes and reference values[ edit ] Suffixes are commonly attached to the basic dB unit in order to indicate the reference value by which the ratio is calculated. For example, dBm indicates power measurement relative to 1 milliwatt. In cases where the unit value of the reference is stated, the decibel value is known as "absolute".

If the unit value of the reference is not explicitly stated, as in the dB gain of an amplifier, then the decibel value is considered relative.

The SI does not permit attaching qualifiers to units, whether as suffix or prefix, other than standard SI prefixes. Therefore, even though the decibel is accepted for use alongside SI unitsthe practice of attaching a suffix to the basic dB unit, forming compound units such as dBm, dBu, dBA, etc.

Outside of documents adhering to SI units, the practice is very common as illustrated by the following examples.

Measurements made on this scale are expressed as dB C. There is also a rarely used B weighting scale, intermediate between A and C. The figure below shows the response of the A filter left and C filter, with gains in dB given with respect to 1 kHz. For an introduction to filters, see RC filters, integrators and differentiators. On the music acoustics and speech acoustics sites, we plot the sound spectra in dB.

The reason for this common practice is that the range of measured sound pressures is large. It thus gives large values for sounds and infrasounds that cannot readily be heard. To convert from dB to phons, you need a graph of such results. Such a graph depends on sound level: This graph, courtesy of Lindoslandshows the data from the International Standards Organisation for curves of equal loudness determined experimentally.

Plots of equal loudness as a function of frequency are often generically called Fletcher-Munson curves after the original work by Fletcher, H. You can make your own curves using our hearing response site.

The sone is derived from psychophysical measurements which involved volunteers adjusting sounds until they judge them to be twice as loud. This allows one to relate perceived loudness to phons. So that approximation is used in the definition of the phon: This relation implies that loudness and intensity are related by a power law: Wouldn't it be great to be able to convert from dB which can be measured by an instrument to sones which approximate loudness as perceived by people? This is usually done using tables that you can find in acoustics handbooks.

However, if you don't mind a rather crude approximation, you can say that the A weighting curve approximates the human frequency response at low to moderate sound levels, so dB A is very roughly the same as phons.

### Decibel Tutorial: dB and dBm vs. Gain and Milliwatts - RF Cafe

Then one can use the logarithmic relation between sones and phons described above. Recording level and decibels Meters measuring recording or output level on audio electronic gear mixing consoles etc are almost always recording the AC rms voltage see links to find out about AC and rms. So what is the reference voltage? The obvious level to choose is one volt rms, and in this case the level is written as dBV.

This is rational, and also convenient with modern analog-digital cards whose maximum range is often about one volt rms. So one has to remember to the keep the level in negative dBV less than one volt to avoid clipping the peaks of the signal, but not too negative so your signal is still much bigger than the background noise.

Sometimes you will see dBm. This used to mean decibels of electrical power, with respect to one milliwatt, and sometimes it still does. However, it's complicated for historical reasons. When I was a boy, calculators were expensive so I used dad's old slide rule, which had the factor 0. How to convert dBV or dBm into dB of sound level?

There is no simple way. It depends on how you convert the electrical power into sound power. Even if your electrical signal is connected directly to a loudspeaker, the conversion will depend on the efficiency and impedance of your loudspeaker.

And of course there may be a power amplifier, and various acoustic complications between where you measure the dBV on the mixing desk and where your ears are in the sound field. Intensity, radiation and dB How does sound level or radio signal level, etc depend on distance from the source?

A source that emits radiation equally in all directions is called isotropic. Consider an isolated source of sound, far from any reflecting surfaces — perhaps a bird singing high in the air.

Imagine a sphere with radius r, centred on the source. The source outputs a total power P, continuously. This sound power spreads out and is passing through the surface of the sphere. If the source is isotropic, the intensity I is the same everywhere on this surface, by definition.

The intensity I is defined as the power per unit area. So we see that, for an isotropic source, intensity is inversely proportional to the square of the distance away from the source: But intensity is proportional to the square of the sound pressure, so we could equally write: So, if we double the distance, we reduce the sound pressure by a factor of 2 and the intensity by a factor of 4: If we increase r by a factor of 10, we decrease the level by 20 dB, etc. Be warned, however, that many sources are not isotropic, especially if the wavelength is smaller than, or of a size comparable with the source.

Further, reflections are often quite important, especially if the ground is nearby, or if you are indoors.

What's The Difference Between dB and dBm? - WilsonPro

In Acoustic impedance, intensity and powerwe show how to relate RMS acoustic pressure p and intensity I: For fresh water, the specific acoustic impedance for water is 1. So a sound wave in water with the same pressure has a much lower intensity than one in air. For many cases in communication, isotropic radiation is wasteful: Remember that logarithms were developed before automatic mechanical or electronic computers were available.

A slide rule exploits the properties of logarithms for calculation, but that is a separate major topic. Those are simple examples, but hold for any base or exponent. In the absence of a calculator, in order to be useful for general application you need a table of numbers and their equivalent logarithms.

Early log tables filled volumes, depending on the spacing between numbers 1. The good news for creators of logarithm tables is that only a single 'decade' of numbers e.

I use base 10 in this discussion since that is the base of our common number system - hence the term 'common logarithm' for base 10 logs.

You might have heard of natural logarithmswhich uses the base of ebut e is not used very often when calculating scalar electrical power, voltage, and current quantities although it is used when phase angles are included, i. Natural logarithms are written as ln x without the 'e' subscript, whereas usually base 10 logarithms are written simply as log x without the 10 subscript; i.

That is so because there is no power to which you can raise any number and obtain 0 zero. You can asymptotically approach zero, but you cannot get to zero.

## Difference Between dB and dBm

There will never be the number zero displayed on a log scale; they usually run from some power of 10 to some other power of ten. An example of log graph paper is shown on the right. It has 5 'cycles' or 'decades' of range. Note there is no zero on the y-axis.

The base common logarithm of a number, then, is the exponent that 10 must be raised to in order to obtain that number.