Convert dbm to mw. Methodology for calculating effective distance

Now many people are buying 802.11n access points, but good speeds Not everyone can achieve it. In this post we’ll talk about not very obvious small nuances that can significantly improve (or worsen) Wi-Fi work. Everything described below applies to both home Wi-Fi routers with standard and advanced (DD-WRT & Co.) firmware, and to corporate hardware and networks. Therefore, as an example, let’s take the “home” theme, as it is more native and closer to the body. Because even the most administrative of admins and the most technical of engineers live in apartment buildings (or villages with a sufficient density of neighbors), and everyone wants fast and reliable Wi-Fi.
[Attention!]:After comments regarding publication, the article was posted in full. This article is left as an example of how not to publish. Sorry for the confusion :)

1. How to live well yourself and not disturb your neighbors.

It would seem - what is there? Turn the point to full power, get the maximum possible coverage - and rejoice. Now let's think: not only the access point signal must reach the client, but the client signal must also reach the point. The TD transmitter power is usually up to 100 mW (20 dBm). Now look at the datasheet for your laptop/phone/tablet and find the power of its Wi-Fi transmitter there. Found it? You are very lucky! Often it is not indicated at all (you can search by FCC ID). However, it can be confidently stated that the power of typical mobile clients is in the range of 30-50 mW. Thus, if the AP broadcasts at 100 mW, and the client broadcasts only at 50 mW, there will be places in the coverage area where the client will hear the point well, but the client’s AP will hear poorly (or will not hear at all) - asymmetry. There is a signal, but there is no connection. Or downlink is fast and uplink is slow. This is true if you use Wi-Fi for online games or Skype; for regular Internet access this is not so important (only if you are not at the edge of the coverage). And we will complain about a wretched provider, a buggy point, crooked drivers, but not about illiterate network planning.

Conclusion: it may turn out that in order to obtain a more stable connection, the power of the point will have to be reduced. Which, you see, is not entirely obvious :)

Rationale (for those interested in details):
Our task is to provide the most symmetrical communication channel between the client (STA) and the point (AP) in order to equalize the speeds of uplink and downlink. To do this, we will rely on SNR (signal-to-noise ratio).
SNR(STA) = Rx(AP) - RxSens(STA); SNR (AP) - Rx(STA) - RxSens(AP)
where Rx(AP/STA) - power received signal from point/client, RxSens(AP/STA) - reception sensitivity of point/client. To simplify, we assume that the threshold background noise below the sensitivity threshold of the AP/STA receiver. Such a simplification is quite acceptable, because if the background noise level for AP and STA is the same, it does not affect the channel symmetry in any way.
Further,
Rx(AP) = Tx(AP)[point transmitter power at antenna port] + TxGain(AP)[transmission gain of a point antenna taking into account all losses, gains and directivity] -PathLoss[signal loss on the way from point to client] + RxGain(STA)[reception gain of the client's antenna, taking into account all losses, gains and directivity].
Likewise, Rx(STA) = Tx(STA) + TxGain(STA) - PathLoss + RxGain(AP).
It is worth noting the following:

• PathLoss is the same in both directions
• TxGain and RxGain antennas in case conventional antennas is the same (true for both AP and STA). Cases with MIMO, MRC, TxBF and other tricks are not considered here. So you can accept: TxGain(AP) === RxGain(AP) = Gain(AP), similar for STA.
• Rx/Tx Gain of the client antenna is rarely known. Client devices are usually equipped with non-replaceable antennas, which allows you to specify the transmitter power and receiver sensitivity immediately taking into account the antenna. We will note this in our calculations below.

In total we get:
SNR(AP) = Tx*(STA) [including antenna] - PathLoss + Gain(AP) - RxSens(AP)
SNR(STA)=Tx(AP) + Gain(AP) - PathLoss -RxSens*(STA) [including antenna]

The difference between the SNR at both ends will be the channel asymmetry, we apply arithmetic: D = SNR(STA)-SNR(AP) = Tx*(STA) - Tx(AP) - (RxSens*(STA) - (RxSens(AP)).

Thus, the channel asymmetry does not depend on the type of antenna at the point and at the client (again, it depends if you use MIMO, MRC, etc., but it will be quite difficult to calculate anything here), but depends on the difference in power and sensitivity of the receivers. At D<0 точка будет слышать клиента лучше, чем клиент точку. В зависимости от расстояния это будет значить либо, что поток данных от клиента к точке будет медленнее, чем от точки к клиенту, либо клиент до точки достучаться не сможет вовсе.
For the power of the point (100mW=20dBm) and the client (30-50mW ~= 15-17dBm) we took, the power difference will be 3-5dB. As long as the point's receiver is more sensitive than the client's receiver by this same 3-5dB, problems will not arise. Unfortunately, this is not always the case. Let's carry out calculations for an HP 8440p laptop and a D-Link point DIR-615 for 802.11g@54Mbps:

• 8440p : Tx*(STA) = 17dBm, RxSens*(STA) = -76dBm@54Mbps
• DIR-615: Tx(AP) = 20dBm, RxSens(AP) = -65dBm@54Mbps.
• D = (17 - 20) - (-76 +65) = 3 - 11 = -7dB.

Thus, problems may occur in the work, moreover, due to the fault of the point.

Also, a far from well-known fact that adds to the asymmetry is that most client devices have reduced transmitter power on the “extreme” channels (1 and 11/13 for 2.4 GHz). Here's an iPhone example from the FCC documentation (power at the antenna port).


As you can see, on the extreme channels the transmitter power is ~2.3 times lower than on the middle ones. The reason is that Wi-Fi is a broadband connection; it will not be possible to keep the signal clearly within the channel frame. So you have to reduce the power in “borderline” cases so as not to affect the bands adjacent to the ISM. Conclusion: if your tablet does not work well in the toilet, try moving to channel 6.

Since we're talking about channels, next time we'll talk about them in more detail.

UPD: I have already been told that the note is too short. I already understood everything. But if I add the rest of the text here, many will no longer see it. In the next post I will post everything in its entirety (I will remove the first part under the cut). Additional comments are welcome if they expand on the topic of “competent” posting on Habré. For emotions there is this hub. Thanks for understanding.

Many people go to the store and buy the cheapest devices, but immediately encounter a lot of troubles that they didn’t even think about, for example, the router slows down the speed, constantly freezes, gets very hot, the connection constantly breaks, or in general, the provider refuses to connect this device. We will try to help you choose the right router for your home, we will tell you what characteristics you need to pay attention to.

Connection speed

The first thing the buyer pays attention to, although this is a very deceptive parameter. The theoretical maximum speed of even the most inexpensive budget routers is 150 Mbit/s (megabits per second), at the same time, not all providers can provide real at least 50 Mbit/s, so it becomes clear that tempting phrases like “up to 300 Mbit /s” or even “up to 1300 Mbit/s” in practical conditions means that when working on the Internet there will be almost no difference in speed between expensive and cheap Wi-Fi routers.

Radius of action

It would seem that everything is simple, because they usually indicate the distance outside and inside the premises, everything is clear and understandable. But these values ​​are very relative, especially indoors, since a couple of good reinforced concrete walls will nullify the signal of even the most powerful router, so the following three characteristics are truly important.

Transmitter power

Here the name speaks for itself and this is really very important. Many budget routers have a transmitter power of about 17 dBm or even less, which is usually enough to more or less reliably “break through” only 2 walls. The maximum power allowed by the legislation of most countries for the 2.4 GHz band is 20 dBm - they are recommended for purchase. It is worth keeping in mind that some Wi-Fi routers have the technical ability to operate at much higher power (usually up to 27 dBm), so they artificially reduce their power in accordance with local legislation.

Receiver sensitivity

Unfortunately, most manufacturers do not indicate this parameter in the characteristics of their devices, and buyers rarely even pay attention to the transmitter power, not to mention the sensitivity of the receiver. Without going into details, we can say that the most important thing is sensitivity at the minimum speed, since in places with very low signal levels it allows you to maintain communication between the router and the device without interruption. Most mainstream Wi-Fi routers have a sensitivity value of -90 dBm at 1 Mbps at 8% PER, but lower values ​​are preferable (-92, -94, -98)

Antenna gain

The antenna gain misleads many users, since in reality the antennas themselves are passive devices and do not amplify anything themselves, they can only more narrowly direct and receive the signal. For example, the higher the gain of an omnidirectional antenna, the more transmitter energy goes to sides perpendicular to the antenna axis, and the less transmitter energy goes up and down. Thus, a more powerful antenna is not a universal solution, since it makes it possible to “punch” the signal much further to the sides, but at the same time “taking” it from above and below.

Number and type of antennas

When using several antennas, their energy does not add up, as many buyers believe, so three antennas will not be able to “break through” three times as many walls; they will only make the connection more stable and the coverage more uniform. Usually, the difference in the quality of coverage between routers with one antenna and two antennas is significant, but the difference between two- and three-antenna devices is often almost absent, although a lot depends on the chip used. It is worth noting that it is not recommended to buy cheap multi-antenna routers from an unknown manufacturer, since their stable operation period is unknown, and very often even a single-antenna router with a good chip at the same price works much better.

Built-in antennas have low gain, so they distribute the signal almost evenly in all directions and can be useful only in small rooms or for accessing the network from adjacent floors. For a stable signal in a one-story house or apartment, it is recommended to buy Wi-Fi routers with 2-3 antennas with a gain of at least 5 dBi. To cover as much space as possible in a one-story house or apartment, it is necessary to install the antennas vertically or at a slight angle to one another.

Stability and firmware

Programmers are ordinary people and can make mistakes, and all their errors can only be identified by users during their work. Therefore, software updates (firmware, firmware) are constantly released for each router, which usually correct bugs and sometimes expand functionality. To avoid ending up with unstable “raw” firmware, it is recommended not to buy the newest, very rare or exclusive router models. The likelihood that a mass model that has been in production for several years contains fatal errors tends to zero.

Design

The last thing you need to pay attention to when choosing a Wi-Fi router for your home, since very often models that are beautiful in appearance have built-in omnidirectional antennas, which, in principle, cannot be very good.

Optimal location of a Wi-Fi router

The correct location of the router is of utmost importance, sometimes even more important than the transmitter power and antenna gain combined. The wrong choice of installation location can negate all the advantages of even the best router and cause resentment over why such an expensive device works so poorly.

Signal propagation

The main thing you need to know is that the Wi-Fi signal is weakly reflected and mainly propagates in a straight line, allowing you to work without obstacles at distances of 200-300 meters and even further, but it is very much lost when passing through walls, especially solid and reinforced concrete ones. Therefore, when choosing a location for installing a Wi-Fi router, it is necessary to imagine direct lines to those places in the apartment or house where clients will most often be located:

• laptop table in the room;
• SmartTV in the living room;
• a kitchen table, where many people like to sit with a tablet, etc.

It is important that there are as few walls and other large objects in the path of these straight lines as possible, or that they intersect at as right an angle as possible. In addition, it is worth considering that large metal or metal-containing objects (refrigerators, washing machines, mirrors in now fashionable wardrobes, etc.) are completely opaque to radio waves, so the signal will pass behind them only due to reflection from the side walls, i.e. .e. much weaker and of poor quality. It is also recommended to place the router at a distance of at least 20 cm from the walls.

The optimal location of the Wi-Fi router is in the center

Other Features

Naturally, routers, adapters in clients, and walls can be very different, but the general observation is that most laptops begin to receive signals unstably through 3 walls, and tablets and phones begin to receive signals through 2 walls. This rule is often observed, but still not an axiom, since there are cases when, even through 5 walls, by turning the laptop a little, it was possible to use the Internet relatively stably. In addition, in dense urban environments, the density of closely located active devices is often so high that even the best antennas and powerful Wi-Fi routers cannot always significantly improve the situation. In this case, it is recommended to scan the network (for example, with a very simple program for Android WiFi Analyzer) and occupy a channel where the signal from other routers will be as low as possible. Most often, channels 12 and 13 are the most free; only some client devices (laptops, tablets, phones) will not be able to connect to the access point on these frequencies.

To make calculations convenient, a special unit of measurement is used, called dBm (decibel milliwatt).

This is a very simple unit of measurement, it shows how many times the measured power is greater or less than 1 milliwatt. Let's show this in tables:

Power expressed in dBm	Power expressed in mW
	1 milliwatt	Power is 1 milliwatt
	2 milliwatts	Power is 2 times more than 1 milliwatt
	5 milliwatts	Power is 5 times more than 1 milliwatt
	10 milliwatts	Power is 10 times more than 1 milliwatt
	50 milliwatts	Power 50 times more than 1 milliwatt
	100 milliwatts	Power is 100 times greater than 1 milliwatt
	500 milliwatts	Power 500 times more than 1 milliwatt
	1000 milliwatts	Power 1000 times more than 1 milliwatt

As you have seen, there is nothing wrong with this unit of measurement, everything is simple. The beauty of the decibel compared to milliwatts is that it replaces multiplication and division with addition and subtraction (in cases where you need to multiply or divide). There are many such cases, so measuring in decibels is often convenient. For example, if a 10 dBm signal was attenuated by 4 dB, then its power would be 6 dBm.

However, there are calculations in which the energy levels must be added and not multiplied. For example, to calculate the total power of a group signal at the output of a multiplexer, you need to add the levels of incoming signals, expressed in milliwatts.

In the case when the signal power is less than 1 milliwatt, the value in decibels will be negative:

Power expressed in dBm	Power expressed in mW
	1 milliwatt	Power is 1 milliwatt
	0.5 milliwatt	Power is 2 times less than 1 milliwatt
	0.2 milliwatts	Power is 5 times less than 1 milliwatt
	0.1 milliwatt	Power is 10 times less than 1 milliwatt
	0.02 milliwatts (20 microwatts)	Power is 50 times less than 1 milliwatt
	0.01 milliwatt (10 microwatt)	Power is 100 times less than 1 milliwatt
	0.002 milliwatts (2 microwatts)	Power is 500 times less than 1 milliwatt
	0.001 milliwatt (1 microwatt)	Power is 1000 times less than 1 milliwatt

Please note that a negative decibel power value does not mean that the power itself is negative. Negative decibels mean that the measured signal is less than the reference signal.

To show how convenient it is to use decibel-milliwatt, we will solve a simple problem in dBm and in times.

Conditions: An optical signal with a power of 7.4 dBm is fed into a line, which introduces an attenuation of 4.8 dB. Determine whether a communication line with a receiver sensitivity of 1.4 dBm can operate reliably?	Conditions: An optical signal with a power of 5.5 mW is fed into a line, which introduces a 3-fold attenuation. Determine whether a communication line with a receiver sensitivity of 1.5 mW can operate reliably?
7.4 (power) - 4.8 (attenuation) = 2.6 (output power) Since the output power of 2.6 dBm is greater than the sensitivity of 1.4 dBm, it will work.	5.5 / 3 = ........ I don’t want to go get a calculator, it was easier to calculate it in my head with dBm.

As you can see, calculating power in decibel-milliwatts is easier and more convenient; in most cases, simple problems can be solved in your head. In complex problems, the convenience lies in the fact that addition and subtraction operations do not give a large number of decimal places, but in division operations they appear constantly, this is inconvenient.

In the field of optical communication lines, all powers are indicated in dBm. Now we are ready to tell you what the optical budget of the module is.

The optical budget is the amount of attenuation in the line at which the signal is still strong enough for the module receiver to receive it without errors.

Optical module budget = transmitter power - receiver sensitivity.

Both of these values ​​can be easily found in equipment specifications. For example, on the page of the MT-PP-55192-ZR module there is a detailed specification. Here are clippings from it.

As you can see, the transmitter power of this module can vary from 0 to +4 dBm. Any MT-PP-55192-ZR module is considered acceptable at the factory if the measurement result is within these limits.

If the module power is lower, for example -1 or -2 dBm, then such a ModulTech module is rejected, and the ModulTech label is not affixed to such a module. We really hope that such a module does not enter the Russian market under any other brand, although in our practice there have been cases that suggest such thoughts.

The sensitivity of the receiver is also indicated in the specification. For this module it is -24 dBm. As a result:

Guaranteed module budget = 0 (transmitter power) - (-24) (receiver sensitivity) = 24 dB.

If your optical line has a total attenuation of less than 24 dB, then the MT-PP-55192-ZR module will work on such a line. If the line attenuation has an attenuation of more than 24 dB, then this module on such a line may not work or work with errors.

As in our previous article, we will provide a table of budgets for different transceivers so that the reader can get a general idea of ​​this parameter.

Transceiver 1G	Transceiver budget in dB	Maximum signal attenuation (times)

Such a translation is required after measuring the cellular signal level - for proper calculation of the GSM or 3G amplification system and selection of the appropriate: cellular signal repeater, antennas and connecting cables.

To quickly convert dBm to mW - use the table below.

It shows the levels output power popular and most commonly used cellular signal repeater models.

dBm	mW
0	1
1	1,3
2	1,6
3	2
4	2,5
5	3,2
6	4
7	5
8	6
9	8
10	10
11	13
12	16
13	20
14	25
15	32
16	40
17	50
18	63
19	79
20	100
21	126
22	158
23	200
24	250
25	316
26	398
27	500
28	630
29	800
30	1000
31	1260
32	1580
33	2000

2. Detailed description of units of measurement - dBm and mW

dBm and mW- the most commonly used units of measurement in antenna technology and high-frequency radio engineering.

dB(dB) — decibel. In general, a logarithmic unit of the ratio of something. Replaces the concept of “times”. Those. This is not an absolute value, such as Volts or Watts, but a relative value, such as percentages.

N p (dB) = 10 log (P 1 / P 2)

Example No. 1: if the cellular signal level has increased 1000 times in power, then this corresponds to +30 dB (they say the signal has increased by 30 dB). The use of such a unit of measurement of ratios allows you to replace multiplication/division with addition/subtraction when calculating gain/attenuation.

Example No. 2: the signal in the cable was weakened by 4 times, and the amplifier increased it by 220 times. Then in the feeder-amplifier system, the signal was amplified 220 / 4 = 55 times. In decibels the calculation will be much simpler: 23 - 6 = 17 dB.

dBm - decibel per milliwatt. Sometimes it is convenient to take some value as a standard (zero level) and measure the level relative to it in decibels. So, if we take 1 mW as the zero level and measure it relative to it, then the unit of measurement appears as dBm (1 mW = 0 dBm). It already has a very significant physical meaning, in contrast to impersonal decibels, dBm is a measure of power. It measures the cellular signal level (for example, in a GSM/3G phone or 3G/LTE modem), receiver sensitivity, transmitter power, etc.

Example No. 3: a level of 50 μV at the 50-ohm input of the receiver corresponds to a power level of 5·10 -8 mW or -73 dBm.

Measuring sensitivity in power units is more convenient than in voltage units, since we have to deal with signals of different shapes, including noise. Plus, we get rid of the need to specify each time what the input impedance of the receiver is.

Example No. 4: the threshold power of most 3G/LTE modems, at which they can still connect to a cellular network base station, is about -110 dBm.

The power of a transmitter or cellular signal amplifier can also be measured in dBm.

Example No. 5: the output power of a standard GSM repeater of 100 mW is equal to 20 dBm.

1. dBi (dBi). A unit of measurement for antenna gain relative to a “reference” antenna. The so-called isotropic emitter is taken as such a reference antenna - an ideal antenna, the radiation pattern of which is a sphere, the gain of which is equal to unity and the efficiency of which is 100%. The signal is emitted by such an emitter with uniform intensity in all directions. Such an antenna does not exist in nature; it is a virtual object, however, it is very convenient as a standard for measuring the parameters of real antennas. dBi is a relative unit, essentially indistinguishable from a simple decibel, except for defining the standard against which it is measured.
2. Antenna gain determines how many decibels the energy flux density emitted by an antenna in a particular direction is greater than the energy flux density that would be recorded using an isotropic antenna. Antenna gain is measured in so-called isotropic decibels (dBi or dBi).

   Example No. 6: if the antenna gain in a given direction is 5 dBi, then this means that in this direction the radiation power is 5 dB (3.16 times) greater than the radiation power of an ideal isotropic antenna.

   Naturally, an increase in signal power in one direction entails a decrease in power in other directions. Of course, when they say that the antenna gain is 5 dBi, they mean the direction in which the maximum radiation power is achieved (the main lobe of the radiation pattern).

3. Cellular Signal Booster System Gain
   When calculating, all these dB, dBi, dBm are essentially all decibels, i.e. are summed (if gain) or subtracted (if attenuated), but dBm takes precedence as a measure of signal strength.

   Receiver input level(dBm) = Transmitter power(dBm) + Antenna gain(dBi) - Signal attenuation(dB)

   Knowing the antenna gain and the output power of the cellular signal repeater, you can easily calculate the signal power in the direction of the main lobe of the GSM or 3G antenna radiation pattern.

   Example No. 7: when using a cellular signal repeater with a transmitter output power of 20 dBm (100 mW) and a directional antenna with a gain of 10 dBi, the signal power in the direction of maximum gain will be 20 dBm + 10 dBi = 30 dBm (1000 mW), that is 10 times more than when using an isotropic antenna.