RF Power Values

Radio frequency (RF) power levels and the most common measure, the decibel (dB).

Power Level

The dB measures the power of a signal as a function of its ratio to another standardized value. The abbreviation dB is often combined with other abbreviations in order to represent the values that are compared.

Here are two examples:

• dBm The dB value is compared to 1 mW.
• dBw The dB value is compared to 1 W.

We can calculate the power in dBs from this formula:

Power (in dB) = 10 * log10 (Signal/Reference)

This list defines the terms in the formula:

• log10 is logarithm base 10.
• Signal is the power of the signal (for example, 50 mW).
• Reference is the reference power (for example, 1 mW).

Here is an example. If we want to calculate the power in dB of 50 mW, apply the formula in order to get:

Power (in dB) = 10 * log10 (50/1) = 10 * log10 (50) = 10 * 1.7 = 17 dBm

Because decibels are ratios that compare two power levels, we can use simple math in order to manipulate the ratios for the design and assembly of networks. For example, we can apply this basic rule in order to calculate logarithms of large numbers:

log10 (A*B) = log10(A) + log10(B)

If we use the formula above, we can calculate the power of 50 mW in dBs in this way:

Power (in dB) = 10 * log10 (50) = 10 * log10 (5 * 10) = (10 * log10 (5)) +

(10 * log10(10)) = 7 + 10 = 17 dBm

These are commonly used general rules:

Increase Of	Decrease Of	Produces
3dB		Double Transmit Power
	3dB	Half Transmit Power
10dB		10 times the Transmit Power
	10dB	Divide Transmit Power by 10 times
30dB		1000 times the Transmit Power
	30dB	Divide Transmit Power by 1000 times

This table provides approximate dBm to mW values:

dBm	mW
0	1
1	1.25
2	1.56
3	2
4	2.5
5	3.12
6	4
7	5
8	6.25
9	8
10	10
11	12.5
12	16
13	20
14	25
15	32
16	40
17	50
18	64
19	80
20	100
21	128
22	160
23	200
24	256
25	320
26	400
27	512
28	640
29	800
30	1000 or 1W

Here is an example:

1. If 0 dB = 1 mW, then 14 dB = 25 mW.

2. If 0 dB = 1 mW, then 10 dB = 10 mW, and 20 dB = 100 mW.

Subtract 3 dB from 100 mW in order to drop the power by half (17 dB = 50 mW). Then, subtract 3 dB again in order to drop the power by 50 percent again (14 dB = 25 mW).

3. We can find all values with a little addition or subtraction if we use the basic rules of algorithms.

Antennas

We can also use the dB abbreviation in order to describe the power level rating of antennas:

• dBi_For use with isotropic antennas.

Isotropic antennas are theoretical antennas that transmit equal power density in all directions. They are used only as theoretical (mathematical) references. They do not exist in the real world.

• dBd_With reference to dipole antennas.

Isotropic antenna power is the ideal measurement to which antennas are compared. All FCC  calculations use this measurement (dBi). Dipole antennas are more real−world antennas. While some antennas are rated in dBd, the majority use dBi.

The power rating difference between dBd and dBi is approximately 2.2_that is, 0 dBd = 2.2 dBi. Therefore, an antenna that is rated at 3 dBd is rated by the FCC (and Cisco) as 5.2 dBi.

Effective Isotropic Radiated Power

The radiated (transmitted) power is rated in either dBm or W. Power that comes off an antenna is measured as effective isotropic radiated power (EIRP). EIRP is the value that regulatory agencies, such as the FCC or European Telecommunications Standards Institute (ETSI), use to determine and measure power limits in applications such as 2.4−GHz or 5−GHz wireless equipment. In order to calculate EIRP, add the transmitter power (in dBm) to the antenna gain (in dBi) and subtract any cable losses (in dB).

Path Loss

The distance that a signal can be transmitted depends on several factors. The primary hardware factors that are involved:

• Transmitter power
• Cable losses between the transmitter and its antenna
• Antenna gain of the transmitter
• Localization of the two antennas

This refers to how far apart the antennas are and if there are obstacles between them. Antennas that can see each other without any obstacles between them are in line of sight.

• Receiving antenna gain
• Cable losses between the receiver and its antenna
• Receiver sensitivity

Receiver sensitivity is defined as the minimum signal power level (in dBm or mW) that is necessary for the receiver to accurately decode a given signal. Because dBm is compared to 0 mW, 0 dBm is a relative point; much like 0 degrees is in temperature measurement. This table shows example values of receiver sensitivity:

dBm	mW10
10	10
3	2
0	1
-3	.5
-10	.1
-20	.01
-30	.001
-40	.0001
-50	.00001
-60	.000001
-70	.0000001

The receiver sensitivity of the radios in Aironet products is −84 dBm or 0.000000004 mW.

Estimate Outdoor Ranges

Cisco has an Outdoor Bridge Range Calculation Utility to help determine what to expect from an outdoor wireless link. Because the outputs of the calculation utility are theoretical, it is helpful to have some guidelines on how to help counteract outside factors.

• For every increase of 6 dB, the coverage distance doubles.
• For every decrease of 6 dB, the coverage distance is cut in half.

In order to make these adjustments, choose antennas with higher (or lower) gain. Or use longer (or shorter) antenna cables.

• If we change to 100−foot cables instead of 50−foot (which adds 3 dB of loss on each end), the range drops to 9 miles.
• If we change the antenna to 13.5−dBi yagis instead of the dishes (which reduces gain by 14 dBi overall), the range drops to less than 4 miles.

Estimate Indoor Ranges

There is no antenna calculation utility for indoor links. Indoor RF propagation is different than outdoor propagation. However, there are some quick calculations that we can do in order to estimate performance.

• For every increase of 9 dB, the coverage area doubles.
• For every decrease of 9 dB, the coverage area is cut in half.

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RF Principle in Wireless Network

RF Principle in Wireless Network

• Wireless network use RF signals
• RF is electromagnetic waves
• Spectrum defines wave’s size, grouped by categories
• Wireless N/W radio range is in the microwave segment

 Wavelength

• The signal generated in the transmitter is sent to the antenna
• The elections movement generates an electric field which is a wave
• The size of the cycle pattern is called wavelength

Radio waves repeat their pattern over time (at a given point in space), but also over space. The physical distance from one point of the cycle to the same point in the next cycle is called a wavelength, which is usually represented by the Greek symbol λ (lambda). The wavelength is the physical distance covered by the wave in one cycle.

Frequency

• The frequency determines how often a signal is seen
• 1 cycle per second in 1 Hertz
• Low frequency travel farther in the air than higher frequencies

 Antenna

• Amplitude is the vertical distance, or height, between crests
• For the same wavelength and frequency, different amplitude can exists
• It represents the quality of energy injected in the signal
• This value is usually regulated as it can affect the receiver

Free Path Loss

• As the wave spreads away from the emitter, it gets weaker
• The quantity of energy declines as the distance increases: the available quantity of energy available on each point of the circle is less as the circle is larger; the receiver catches only part of this energy
• Determining a range is determining the energy loss depending on the distance

Absorption

 

• Absorption takes energy from the wave
• This energy is dissipated in heat in the obstacle
• When 100% of the energy is taken, the wave stops
• The effect of absorption is to reduce amplitude
• The signal is therefore less powerful, but keeps the same wavelength and frequency

Reflection

• Part of the energy is reflected
• Part may be transmitted
• The angle of reflection is the same as the initial angle
• Reflection depends on the material roughness relative to the wavelength and the angle
• Amplitude has no impact

Multipath

• Occurs when the signal reflects on surface and arrives to the receiver at different times
• Delayed multiple copies of the same signal hit the receiver
• Depends on the wavelength and the position of the receiver

Multipath: Phase

• 2 signals are in phase when their cycle crests coincide
• Being out of phase weakens both signal or cancels them if amplitude and wavelength are the same

Scattering

• Occurs when micro particle deviate the wave in multiple directions
• Affects shorter wavelengths more than longer ones
• Can weaken the signal or block it

Refraction

 

• Occurs when the wave passes from one medium to another: direction change
• Minor effects on indoor networks
• Can have high impacts on outdoor long range links

RF Calculation:

RSSI and SNR

• RSSI is the signal strength indicator
• dBm value transformed from a vendor dependant grading coefficient
• Usually negative value, the closer to 0 is better
• SNR is signal strength relative to noise level
• The higher the better

The dB scale is also used to compare the relative power (called gain) of antennas.

dBi is the most common scale for antenna gains, but some wireless professionals prefer to use an existing antenna as the reference.

The antenna chosen is the simplest possible antenna, called a dipole antenna. This comparison is expressed in dBd.

 

dBi = dBd + 2.14

dBd = dBi – 2.14

Covert mW to dBm

EIRP

With the multiple possible combinations of AP transmitter power level, cables and antenna, you need a way to determine how much energy is actually radiated from the antenna toward the main beam. This measure is called the Effective Isotropic Radiated Power (EIRP). In simple terms, the EIRP, expressed in dBm, is simply the amount of power emitted by the transmitter plus the gain (in dBi) of the antenna (and any amplifier on the path). We also must remove the power lost in cable or attenuators:

EIRP = Tx power (dBm) + antenna gain (dBi) – cable loss (dB)

The EIRP is very important. Most countries allow a maximum Tx power of the transmitter and a final maximum EIRP value. When designing networks with specific antennas, you must know your system EIRP and make sure it complies with local regulations.