Title: 3.4 Radio Frequency Math and Measurement
Course: Information and Communication Technology: Module B > Section: Section 3 - Wireless Technology Basics

3.4.1 Radio Frequency Math and Measurement

The sender of a wireless signal is concerned with how much power it will take to get the signal to the end users and which direction the signal needs to travel. The end user in a wireless network is concerned with coverage and performance.

As a wireless network is designed, implemented, and maintained, it is important to understand RF power and to perform some simple RF math that will aid in providing the level of coverage and performance that end users demand. Some of the measurements will represent absolute power, while others will serve as a comparison relative to another known quantity. For example: A CD records at a base rate of 150bps. This is an absolute measure of the speed. Compare that to 56X CD recorder, which is a relative measure of the recorder speed.

Examples of where each may be used:

- Absolute power might be used to measure the amplitude of the transmitted and received signals.
- Relative measurements might be used to measure the loss or gain due to a component (cabling, connector, etc).
- Relative measurements are also used to examine the change in power from point to point.

There are many terms that will be discussed as absolute and relative power measurements are examined. The first is Wattage. A Watt is a basic unit of power named after 18th Century Scottish inventor James Watt. A Watt is equal to 1 amp of current flowing at 1 volt.

You might remember this formula from an earlier lesson on the wattage of a power supply.

Amp (Ω) x Volts (V) = Watts (W)

A milliWatt is 10-3 or 0.001 or 1/1000th of a watt. It is more common in wireless networks than the watt. Most 802.11 equipment transmits at power levels between 1 mW and 100 mW. Occasionally in outdoor, building-to-building links may require transmit power greater than 250 mW.

3.4.2 Radio Frequency Math and Measurement

A Decibel (dB) is a relative unit for comparison. It represents the difference between two values or measures a change in power. It is applied in wireless to compare the power of two transmitters or to compare the difference between EIRP at a transmitter’s antenna (gain) versus power at receiver’s antenna (loss).

The term Decibel was derived from the term Bel (Bell Labs). One Bel is defined as ratio of 10 to 1 between two sounds or powers. Bels are too big for measurements, so decibel (dB) which is one-tenth of a Bel is used (5 Bel = 50dB or 5 dB = .5 Bel)

Example:

- 100 mW signal decreases to 1 mW →   10^2 decrease to 10^0
- Exponent drops from 2 to 0; drop of 2 →   -2 bels or -20 decibels

Example:

- 100 mW signal decreases to 0.00001 mW →  10^2 decrease to 10^-5
- Exponent drops from 2 to -5; drop of 7 →   -7 bels or -70 decibels

Decibels isotropic (dBi) is the power gain or increase relative to an isotropic radiator. It can be thought of as antenna gain. It is measured at the strongest or focus point of an antenna and is always greater or equal to 0. A 2.4 GHz half-wave dipole antenna has a gain of 2.14 dBi.

Example:

- If the cable loss to the antenna is .5 dB and EIRP is 3.2 dBi, then the antenna has a gain of 2.7 dBi.

3.4.3 Radio Frequency Math and Measurement

Decibels to milliwatts (dBm) is a measurement of absolute power (0 Decibel = 1 milliwatt).

A 3 dB increase roughly doubles the power, which means that 3 dBm equals roughly 2 mW. For a 3 dB decrease, the power is reduced by about one half, making -3 dBm equal to about 0.5 milliwatt. It is used because -40 dBm easier to understand than 0.0001 mW (less chance of error). Typical 802.11 radio can interpret signals as low as -30 dBm to -100 dBm

Example:

- 0 dBm = 1 mW

- +20 dBm = 100 mW

Confused? Think about these four simple rules (this is an approximation):

1. For every 3 dB of gain, double the absolute power (mW)

2. For every 3 dB of loss, halve the power (mW)

3. For every 10 dB of gain, multiply the absolute power (dB) by a factor of 10

4. For every 10 dB of loss, divide the absolute power (mW) by a factor of 10

Combinations of 10s and 3s rules are also possible:

- How about +12 dB gain?
  - +3 +3 +3 +3

- How about a -11 dB loss?
  - -10 -10 +3 +3 +3

- How about -7 dB loss?
  - -10 -10 -10 -10 +3 +3 +3 +3 +3 +3 +3 +3 +3 +3 +3

Example:

- AP transmits at 100 mW
Antenna rated at 3 dBi passive gain (Every 3 dB doubles the mW)
Gives us 200 mW of power radiating out of antenna (EIRP)

- What if a cable introduces 3 dB loss?
       Answer: 50 mW (EIRP) (Every -3 dB halves the mW)

Example:

- AP transmits at 40mW
Antenna rated at 10 dBi passive gain (Every 10 dB multiplies mW by 10)
Gives us 400 mW of power radiating out of antenna (EIRP)

- What if a cable introduces 10 dB loss?
       Answer: 4 mW (EIRP) (Every -10 dB divides mW by 10)

You can also use these formulas to get the exact values:

Complete Lab 3.4.1

3.4.4 Access Point Positioning

The position of an access point can greatly affect the coverage area and signal strength. You should pay close attention to the kinds of materials it is near. Different materials will affect how the signal travels. Line-Of-Sight gives you the best coverage but that is not always possible. For example, placing an AP near a mirror or up against a metal wall will cause problems with the signal. Signals can travel through wood and dry wall easily, but metal will obstruct the signals.

Effects of interference:

- a decrease in data throughput
- a decrease in the range between devices
- an intermittent or complete loss of the connection

Sources of interference

- microwave ovens
- cordless telephones
- electrical sources (power lines, florescent lights, transformers, breaker boxes)
- other wireless devices operating on the same 2.4 GHz or 5 GHz frequency
- other wireless devices that use the same channel or overlapping channels
- buildings and other external sources

3.4.5 Radio Frequency Math and Measurement

Free-Space Path Loss (FSPL) is the loss in signal between the transmitter and receiver. It take into account any obstructions between them. You have to know the wavelength of the signal, the obstruction value, and the distance between the transmitter and receiver.

The equation to find the FSPL is:

The Link Loss Budget accounts for the gains and losses from the transmitter to the receiver considering the medium and obstacles between the two points. It accounts for the attenuation of the transmitted signal due to propagation, antenna gains, and miscellaneous losses.

The equation to find the Link Loss Budget is:

Propagation losses can be much higher indoors than outdoors because of physical items or obstructions such as walls, ceilings, and furniture.  This occurs because of a combination of attenuation by walls and ceilings, and blockage due to equipment, furniture, and even people. For example, a 2" x 4” wood stud wall with drywall on both sides results in about 6dB loss per wall. For a dense office, propagation losses can be up to 30 dB per 30 meters. Actual losses are hard to estimate because a building's construction behind the drywall is hard to determine.We will use the FSPL as the propagation loss.

Received Signal Strength Indicator (RSSI) is a relative metric used by wireless radios to measure the signal strength received by the receiver (P_R). It is the power level the wireless signal must maintain so that data can be successfully received by the receiver. The higher the RSSI, the lower the throughput. As the power drop, the radio will automatically drop the throughput of the signal. Typically, more power is required for higher data rates.

Some wireless radios allow you to set the transmitters gain (output) thereby effecting the received power. Adding passive gain antennas will also add strength to the wireless signal. By adding the transmitter and antenna gains together (EIRP) you can determine the power needed to cover a given area.

Signal-to-Noise Ratio (SNR) is the difference in decibels (0-120) between received signal strength and background noise. For example, if you have a received signal of -85 dBm and background noise of -100 dBm, the SNR is 15 dB. A very low SNR has the potential for a corrupted signal and retransmissions. A SNR of 25 dB is considered great and has good signal quality. A SNR of 10 dB or lower is considered poor signal quality.

The equation to find the Signal-to-Noise Ratio is:

Complete Lab 3.4.2

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