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From dB to S-point : Learn to play with power units

A Sommer beam XP804. This is a 7-bander log-periodic, offering 10 dBd or 12.14 dBi gain on 20m.

dB, dBm, dBW, dBi and dBd

Everybody uses the decibel (dB) and other power units, including manufacturers in their advertisements. It is thus necessary to well understand what they represent. See also the pages about Basics of antennas for other definitions.

There is a fundamental difference between dB and dBm, two units that we usually find when a technician reviews an antenna, the receive module of a transciever (dynamic range, 3d-order IMD, etc) or check propagation charts for a specific circuit. 

As it suggests, the decibel is a tenth of Bel (after Graham Bell). Where does it come from ? We use this unit because by nature the human ear shows a logarithm response to power variations (sound). For example, if you increase the power of your speaker by a 10 factor, you will only feel a doubling of the sound power.

The wave pressure that the human ear is able to detect or tolerate is ranging between 2x10-5 mbar (weakest) and 2 mbar (louder), and forget the other units like dynes, psi or Pa. The ratio between both signals reaches 10 millions or a factor of 7 equals to... 7 Bel. This is thus a large unit and in radioelectricity we usually work with values ten times lower, hence the use of decibel.

The dB always expresses the logarithmic measurement of a power, current or voltage ratio. It has thus a meaning only if one specifies a starting level. For example, "a signal is 20 dB over S9". In this example, the starting power is indicated by S9, which is the power transferred by a 50 mV signal to a 50W load. "20 dB over S9" thus means a power that is 100 times greater than the starting power, because 20 dB means a power ratio of 100 (see below).

dB :  back to school !

The decibel is :

A power ratio :  dB = 10 Log P2/P1

A voltage ratio : dB = 20 Log V2/V1

If a stage offers a voltage gain of 30, followed with another stage having a voltage gain of 10, the system will have a total voltage gain of 30 x 10 = 300.

or, expressed in decibels (2d formula) : 29.5 + 20 = 49.5 dB

dB and S-point

What represents 1 S-point in dB ? Each S-point corresponds to a current or voltage ratio of 2 and a power ratio of 4. 1 S-point or S-unit represents thus a power ratio of  6 dB (and rather 4 dB in average in some Japanese RTX in the lower part of the meter).

From S1 to S2 there is a 10 dB change. As you win 3 dB each time you double your power, a 100 W signal at S1 will require 400 W to reach S2.

In the same way a signal strength dropping of 6 dB is equivalent to a power loss of 75% (2x 3 dB or 2x 50% less in this case). 6 dB is also a power ratio of 4 times knowing that 3 dB = 2x, 6 dB = 4x, 9 dB = 8x, 10 dB = 10x, 20 dB = 100x.

NB. "Log" with an uppercase "L" uses here means in base 10, to not confuse with "log", in lowercases, that uses the natural logarithm, in base "e" (~2.72).

See alo Wikipedia on Decibel.

Decibel over milliwatt, dBm

Contrarily to dB, dBm is a measurement of the absolute power, not a power ratio. For convenience, the "m" in "dBm" refers to milliwatt, and by convention, 0 dBm equals the power dissipated by a power of 1 mW into a 50W load. This reference is important because 0 dBm into 50W is not equivalent to 0 dBm into 75W. The dBm relation is next, P being the power :

dBm(mW) = 10 Log P    and    P(mW) = 10 (dBm/10)

For example 100 W is 50 dBm into 50W, 40 dBm = 10 W.

A value of 10 dBm thus means 10 times that power, +20 dBm means 100 times that power, etc. 

The dBm is very interesting because we can calculate the output power of a transceiver in dBm after removing losses and add the antenna gain to estimate for example the signal strength at a target location like do propagation programs. For example, a 12 dBm signal amplified by a system offering a 20 dB gain, becomes a signal that is +32 dBm stronger or a little more than 1 watt. Of course we could also use directly the S-meter but the signal strength expressed in power is more accurate because it is also equivalent to a voltage developing at the load (antenna). 

S-meter standard readings as defined by IARU. One S-point is equals to a signal difference of 6 dB. The value in microvolt is given into 50W. On frequencies below 30 MHz, a S-9 signal is equivalent to a power of -73 dBm (continuous wave on receive).

A signal level of +12 dBm for example is 12 dB greater than a milliwatt, or about 13 mW. In this case the gain does not indicate the "own power" of an antenna but rather the increase in power compared to another antenna. An antenna does not amplify signals by re-distributing the energy or improving the modulation ! Excepting active antennas, all aerials radiate passively like does a radiator more or less directed. 

Calculations of gains and losses must always be expressed in dB instead of dBm. The dBm is used in all circuits offering different impedances; the calculation of the power expressed in dBm remains constant while RF voltages and impedances change.

IARU Region 1 Technical Recommendation R.1-Brighton 1981, Torremolinos 1990 defined that on frequencies below 30 MHz, a S-9 signal is equivalent to a power of -73 dBm (continuous wave on receive). Note that on frequencies higher than 30 MHz a S-9 signal is equivalent to a power of -93 dBm (continuous wave on receive). The 20 dB difference between HF and VHF is due to the less noise temperature as frequencies increase and the use of  transverters in front of HF transceivers calibrated  for S9 = - 73 dBm showing usually a gain over 20 dB.

We will also see below that there is of course a relation between the antenna voltage (dBm) and the field strength (dB>mV).

The correct interpretation on these measurements is another thing that we must tackle now.

Power and field strength, dBW and dB>mV

Among the other scales often used, there is the signal strength or noise level estimation, also known as the "dB below W" (dBW or SDBW). It uses the same principle as dBm excepted that the power is expressed over the watt. The dBW relation is next, P being the power :

dBW(W) = 10 Log P    and    P(W) = 10 (dBW/10)

For example, 100 W is 20 dBW into 50W.

Knowing the power in dBm (see above), it is easy to get its equivalence in dBW, knowing that 30 dB is a power ratio of 1000. For example a signal at -73 dB or S9 is also -103 dBW.

At last the power can also qualify the field strength, using the "dB over microvolt" better known as "dB over mV/m" (dB > mV). As a given field strength generates different voltage in the antenna at different frequencies, we generally use approximations between common values set by IARU and what you might read on an S-meter, knowing that each S-point is 6 dB  :

At left the equivalence between S-points and signal power at receiver (SDBW or dBW) as defined by IARU. At right the field strength scale or "dB over mV/m", often displayed using the abbrevation "dB>mV", valid below 30 MHz. It displays the field strength generated by your signal if greater than 1 mV into 50 ohms. For example +32 dB>mV is S9 below 30 MHz or 50 mV, or equivalent to -103 dBW. These units are also commonly used in propagation programs.

These values are often used in amateur propagation programs to provide an easier reading of signal or field strength displayed in prediction charts and other map predicting ionospheric conditions.

There is thus some relations between the antenna voltage (dBm), the field strength (dB>mV) and the wavelength (l) to name :

- The antenna voltage

Uant = 0.132 El Grx

- The receive antenna gain

Grx = U2ant / (0.132 El)2

- The power density

S = EH = E2/Zo with Zo= 377W

- The receiving antenna's area

A = 1.64 (l2/4p) Grx

You will find more explanations in the next document dealing with EM radiations and RF safety available on this site.

Last but not least, one of the most used unit is the antenna voltage Uant converted in dBm :

- The Uant/dBm =  45 - 20 log f(Hz) + E/(dB>mV)

This relation is a function of the frequency and the related S-unit and field strength (dB>mV) change thus consequently as follows :

S-Unit

1

3

5

7

9

dBm

-121.0

-109.0

-97.0

-85.0

-73.0

3.5 MHz

-35.1

-23.1

-11.1

0.9

+12.9

7 MHz

-29.1

-17.1

-5.1

6.9

18.9

14 MHz

-23.1

-11.1

0.9

12.9

24.9

21 MHz

-20.6

-8.6

4.4

16.4

28.4

28 MHz

-17.1

-5.1

6.9

18.9

30.9

In addition, the field strength expressed in dB>mV for a receive antenna that yields 0 dBd gain = 2.14 dBi. This infers that on low bands, noise plays an important role in propagation forecasts. For exmaple, if a field strength reaches S9 on 7 MHz, it is 18.9 dB>mV. But if we use an isotropic antenna (gain 0 dBi), this value must be increased by 2.14 dB.

As we just introduced dBi and dBd units, let's see how they are applyied to define the gain of antennas.

dBi vs. dBd

To get comparable numbers is measuring the gain of antennas, one decided to define an isotropic radiator as offering a zero gain, that we write 0 dBi. The radiation pattern of this antenna is circular and even like a sphere centered on the antenna viewed in space. But such a pattern does not exist on earth as there are numerous objects and obstacles that alter this theoretical pattern. In practice the comparison is made in measuring the field strength produced by a half-wave dipole placed at the same height and used in the same polarization as the antenna under test.

Evolution with frequency of the radiation patterns of a dipole. Each time we double the frequency, new lobes appear, modifying the way the antenna spreads power into space. This pattern is also affected by the proximity of ground and its properties. Document EEF Group.

With this comparison model we can accurately measure the gain of any antenna. Let's begin with the simplest case of a dipole. What is its gain ? From various measurements we can estimate it at 2.14 dB over an isotropic antenna (we note 2.14 dBi).  In fact  we should say 2.14 dBd, thus comparing the dipole to itself instead of speaking in dBi what is never met, excepting in simulation programs. In this context it is not impossible to find a dipole offering a 6 dBd gain placed over saltwater (or 8.14 dBi)... Each frame of reference is thus valid, as long as it is used consistently and clearly, what is far to be the case.

Some people, including manufacturers, will say that their aerial has a 5 dB gain... Compared to what ? This is meaningless. This second answer is false because not accurate enough. He should have say that his antenna offers a 5 dB gain over an isotropic for example. In this case you can tell him his antenna has also a (5-2.1) 2.9 dB gain over a dipole (2.9 dBd). You are both on the same wavelength now !

Practically below a 3 dB gain, the improvement is not very appreciable but in the field even a 0.5 dB can mean hearing or not a far station... So we have to put this value in context and translate in the field what advertisers write... Some will say that their antenna offers a 10 dBi gain. Well, fine ! But what does it mean ? In the field this aerial has really a 7.9 dBd (10-2.1) compared to the dipole. This is not a high gain, especially if the new antenna is expensive ! Worst, all manufacturers do not compare their aerial to the same reference antenna; usually it is over a dipole (in dBd) but some advertise over an isotropic (dBi). Both figures are completely differents. 

So instead of using gain figures from advertisers be more smart and work with decibels. Knowing than when doubling your output power you improve your signal of 3 dB, it is easy to understand that a fine tuned system can sometimes exceed the theoretical performances of a so-called high-gain antenna.

But even if you transmit with an emitter twice as powerful as the previous, although your emitting power has increased much, your receive range will stay unchanged as long as you use the same antenna ! In other words now DX stations can hear you but you can always not hear them ! So do you really need a high-gain antenna ? What for if you can't hear your "most wanted DX" ? 

So for short, to notice a difference in what you hear you must make un big jump in increasing the performances of your installation. Begin by improving the sensitivity of your antenna in installing a more directional one. On the contrary, for anyone to hear any difference in your signal begin by doubling your emitting power in place of replacing your antenna as that can already improve your signal strength of 3 dB ! This being said, it is obvious that concentrating 100 W in a high-gain beam directed toward your correspondent is by far preferable than dissipating 1 kW in an omnidirectional antenna... !

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