The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities.[1] A decibel is one tenth of a bel, a seldom-used unit named in honor of Alexander Graham Bell.

The decibel is used for a wide variety of measurements in science and engineering, most prominently in acoustics, electronics, and control theory. In electronics, the gains of amplifiers, attenuation of signals, and signal-to-noise ratios are often expressed in decibels. The decibel confers a number of advantages, such as the ability to conveniently represent very large or small numbers, and the ability to carry out multiplication of ratios by simple addition and subtraction.

A change in power ratio by a factor of 10 is a 10 dB change. A change in power ratio by a factor of two is approximately a 3 dB change.

The decibel symbol is often qualified with a suffix, that indicates which reference quantity or frequency weighting function has been used. For example, dBm indicates a reference level of one milliwatt, while dBu is referenced to approximately 0.775 volts RMS.[2]

The definitions of the decibel and bel use base 10 logarithms. The neper, an alternative logarithmic ratio unit sometimes used, uses the natural logarithm (base e).[3]

Some familiar representations of dB ?? ...

Don't worry everybody gets confused now and then when dealing with decibels.

Definition

Decibel:  A unit used to express relative difference in power or intensity, usually between two acoustic or electric signals, equal to ten times the common logarithm of the ratio of the two levels.

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).

Incidentally 1 dB increase in sound level represents approximately the smallest sound change that the human ear can discern.

It may appear to be confusing but by having units defined in terms of logarithms, multiplication and division can be done using addition and subtraction.

For example, a 10 times increase in power is 10 dB, so if you have 1 Watt of RF and you amplify it 10 times, you have 10 times more power.  If you attenuate it to 1/10^th the original power, you decrease by 10 dB.

Taking this idea a little farther amplification by 100 times (10 times 10) results in an increase of 20 dB (10 plus 10).

Important thing to remember is that dB usage ultimately relates to either power ratios or absolute powers.

Commonly dB as the above definition says is that it is used to refer to power ratios.

What does dBm Mean?

Similarly, when dealing in RF, dBm refers to a power level relative to 0 dBm or 1 mW into 50 ohms, corresponding to 0.2236 mV rms.

At higher power levels it's common to refer to 1 Watt into 50 ohms or 0 dBW.

Table of common values showing dBm, dBW, rms voltage and rms power

Signal purity and dBC or dB relative to a carrier

 Spectrum analyzer photos with a carrier and several harmonics

Note that spectragraphs and equipment displays often represent the signals with a vertical axis in dB.  The major divisions are usually programmable, and more often than not they are in 10 dB increments such as shown in the image on the right of the HP-8561 spectrum analyzer.

On the left, one can see many harmonics of the 21.75 MHz fundamental frequency being measured, as well as other signals.  The fundamental signal is usually the highest level displayed, and the signals to each side of the fundamental exhibit smaller levels (sometimes!), which are often indicated in terms of "dB down from the fundamental". 

One the right, the spectrum analyzer is showing a view of the fundamental frequency (14,00070 kHz) being transmitted by an SDR Cube transmitter through the RF PowerCube amplifier.  With a close-in view of the signal (resolution bandwidth = 100 Hz), we can see the opposite sideband level of the 1.25 kHz test tone showing as being -47 dB ... or "47 dB below the carrier".

Attenuators ... Essential in Test Bench Measurement Equipment 

Dynamic Range

Signal-to-Noise Ratio (SNR

S- units and dB

               (From NA5N ...  http://www.gqrp.com/s_units.pdf)

A Typical (?) Test Bench

See how many places dB's are used in these tests that N2CX and N2APB were making for some SDR Cube IMD measurements ...

[Answer: 10 log (3765499 / 376549.9)]

Okay ... Now let's take a look at how all these components connect together ... with dB's in mind!

Antennas – dB gain relative to what?

     DB gain statement is meaningless without an appropriate reference.

     dBi sometimes used to refer gain to an isotropic antenna and this is ok for comparison of antenna gains in modeling but is often misapplied in antenna advertising as in

http://www.w8ji.com/antennas.htm

Excerpt from W8JI work:

dBd vs dBi

 

The dipole is the basic building block of many antennas. A dipole does NOT have 2.2 dB gain over an isotropic radiator when the dipole is placed over earth. The dipole has about 8.5 dB gain over an isotropic radiator! Always remember this when you see antenna models over earth given in dBi. If the model over earth shows a "gain" of about 8.5 dBi, the model effectively has the same gain as a dipole.

 

Here is the pattern of a 145-foot high copper wire dipole over medium real earth on EZNEC:

 

                            

You can see the gain is 8.5 dBi, and it is just a simple dipole just over 1/2 wave high. Any antenna you model should always be compared to a standard like this!

The notion a dipole has around 2.15 dBi gain is only true for freespace.

Relative antenna test - hams set up impromptu antenna test ranges to compare antennas:

VHF/UHF antenna shootouts

          Refs for antenna testing www.qsl.net/n1bwt/chap9.pdf 

HFPack HF antenna shootouts ... http://hfpack.com/antennas/

The purpose of the HFpack Pedestrian Antenna Shootout is to try out a variety of pedestrian antennas, measure and document the antennas in a well-controlled manner, and report the results as a service to radio operators around the world interested in furthering the state - of - the - art for HF portable.

1. All antenna entries should be physically present to register at the HFpack Shootout site, Pacificon Convention, at 11am on Sunday, 20 October 2002.
2. The antenna shootout is for "Pedestrian Antennas". A pedestrian antenna is considered to be a lightweight antenna that can easily be carried to the shootout by one person in a backpack or bag. It is not necessary to walk around carrying the antenna while in operation. The shootout is not intended to include heavy antennas designed mainly for base station operation, thus, antennas exceeding 11 pounds are discouraged from entry.
3. The test transmitter has a feedline with a 1:1 balun/unun at the feedpoint. The test feedpoint (antenna mounting point) is elevated above ground level, and provides a BNC, SO-239, or 3/8-24
female threads, or terminal lug to connect the antenna to. The balun has at least 20dB of isolation at 14MHz.
4. During the RF measurement, the test transmitter delivers about 5 Watts CW into the entry antenna for about 30 seconds.
5. For vertical quarterwave whips, the feedpoint has a single quarterwave resonant "radial" counterpoise, sloping down at about a 45 degree angle in the direction of the test receiver site. No other
counterpoise will be used for quarterwave whips.
6. Since the objective is to remove any extraneous variables from the RF measurement, the standard antenna test fixture will be used for all antennas. So no other feedline will be used, and it is not necessary
of desirable for the entry antenna to include a support pole, since the support is provided by the test fixture.
7. Commercial antenna manufacturer personnel may not participate as part of the HFpack Shootout engineering measurement team, however they are invited to be present and help set up their antenna on the test fixture.
8. The only frequency of the shootout is 14.1MHz (+/-10kHz).
9. Antennas will be physically measured (inches), weighed (pounds), photographed (digital), and tested for radiated RF on the test range. The results of the tests, measurements, photographs, and description
of the antenna may appear on the HFpack website or other publications.
10. Antenna RF radiation will be measured by a calibrated test receiver using linearly polarized small antenna on an elevated support pole. The test receiver antenna will be operated first in vertical and
then in horizontal polarization. The entry may enter appropriately in either the horizontal or vertical polarization category.
11. Horizontally polarized antennas and vertical antennas not requiring a counterpoise will be elevated to 16 feet at the feedpoint or radiation center.
12. Antennas should self-match to 50 ohms nominal impedance.
13. Antenna owners who are not present may privately arrange for another person to enter their antenna.
14. A commercial antenna may be entered by anyone who owns it, however, multiple entries of the same type of commercial antenna by different owners is discouraged.
15. The general public, amateur radio operators, volunteer witnesses, and others will be present to view the shootout.
16. Other guidelines may be posted or verbally announced or personally advised at the shootout.
17. Requests to test an antenna using other than the standard test fixture and methods will probably be rejected unless there is a good and compelling technical reason to do so.
18. In the unlikely event of confusion or dispute, a panel of 3 HFpack members chosen by the HFpack members present at the shootout will attempt to resolve the issue in an amiable manner.

 

Mobile antenna shootouts:  http://www.k0bg.com/shootout.html

1. Treatise by NA5N ...  http://www.gqrp.com/s_units.pdf

2. Other S-unit vs dBm table ... http://www.astrosurf.com/luxorion/qsl-db-power-units.htm

3. Wikipedia ... http://en.wikipedia.org/wiki/Decibels

4. Mobile antenna shootouts:  http://www.k0bg.com/shootout.html

5. HFPack HF antenna shootouts ... http://hfpack.com/antennas/

6. Antenna testing www.qsl.net/n1bwt/chap9.pdf 

7. Decibel Measurements (R&S) ... PDF

8. An Excel spreadsheet that prints dBm, Power, Volts RMS, Volts Peak, and S units ... by Terry Fox, WB4JFI

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