## Antenna Field Calculations

There are several calculations regarding the antenna field that you may perform to understand the antenna performance based on power input and other variables. In this section, we discuss antenna gain and loss calculations, free space loss, effective radiated power, and field density calculations.

#### Antenna Gain and Loss

An *antenna gain* is achieved by focusing the radiated RF into narrower patterns to get more power coming from the antenna in the required direction, as illustrated in Figure 3.4.

Figure 3.4 Antenna gain.

Antenna gain is the relative increase in radiation at the maximum point expressed as a value in decibels (dB) above a reference—in this case, the basic antenna, a half-wavelength dipole by which all other antennas are measured. The reference is known as 0 dBD (zero decibels referenced to dipole):

Antenna gain in dBD = 10**log* (*Power output*/*Power input*)

An antenna with the effective radiated power of twice the input power would therefore have a gain of 10**log* (2/1) = 3dBD. Therefore, if you know the power output and input, you can find out the gain or "efficiency" of an antenna.

#### Effective Radiated Power (ERP)

There are several definitions of effective radiated power from an antenna. The most common definition of effective radiated power is the power supplied to an antenna multiplied by the antenna gain in a given direction, or as the product of the power supplied to the antenna and its gain relative to a half-wave dipole in a given direction:

ERP (dBm) = Power of transmitter (dBm) – loss in transmission line (dB) + antenna gain in dBd

Note that if the direction is not specified, the direction of maximum gain is assumed. The type of reference antenna also must be specified. A reference antenna can be real, virtual, or theoretical. Antenna examples are unit dipoles, half-wave dipoles, or isotropic, that is, omnidirectional antennas. If the cable loss is not specified, you should consider it zero.

The ERP value is frequently measured in watts.

#### Effective Isotropically Radiated Power (EIRP)

Effective isotropically radiated power is the arithmetic product of the power supplied to an antenna and its gain relative to an isotropic source:

EIRP (dBm) = Power of transmitter (dBm) – loss in transmission line (dB) + antenna gain in dBi

dBm = 10 *log(power out / 1mW)

**Example:** An antenna has a gain of 16 dBi, and the power delivered to the antenna is 100 milliwatts (0.1 watt). What is the effective isotropic radiated power?

100 mW equals to 20 dBm.

10 *log (100 mW/1 mW) = 10*2 = 20 dBm

EIRP = 20 + 16 = 36 dBm = 4 watts

To help you convert between watts and decibels, you can refer to Table 3.2.

#### Table 3.2. RF Power Conversion

dBm = 10*log (x mW/1mW) |
||

Power in Watts |
Power in mW |
Power in dBm |

4 |
4000 |
36 |

2 |
2000 |
33 |

1 |
1000 |
30 |

0.100 |
100 |
20 |

0.010 |
10 |
10 |

0.001 |
1 |
0 |

#### Beam Width

The generally accepted description of beam width is that it is the angle between two points on the same plane where the radiation falls to "half power," that is, 3dB below the point of maximum radiation.

#### Radiation Pattern

Radiation pattern is a graphical representation of the intensity of the radiation versus the angle from the perpendicular. The graph is usually circular, and the intensity is indicated by the distance from the center of the corresponding angle.

Component materials cannot create power; the only other alternative is to focus wasted energy using reflectors and bounce the radiated signal toward a more useful direction. The method by which an antenna is made to have "gain" is merely focusing the radiation (this is often compared to taking a doughnut and flattening it into a pancake), which makes the radiation more intensified toward one plane.

If a reflector is placed next to a dipole, all the energy that would have radiated in the direction of the reflector is now reflected back in the direction of the dipole. This makes all the energy appear in only one hemisphere and thus results in a doubling of radiated energy in this direction.

Further focusing can be achieved with the use of "directors," and again, by making the angle smaller and smaller (that is, packing all the radiation into one direction), higher gain is achieved. Achieving high gains may be practical in certain applications; however, the effective angle of such an antenna is therefore small.

#### Front-Back Ratio

In front-back ratio, the doughnut radiation pattern mentioned previously is achieved, and it is squeezed into a beam off the front of the antenna. The reflector used for focusing the beam does not stop all the radiated energy, and some is radiated toward the rear (or, in the case of reception, bypasses the reflector and is intercepted by the dipole). Even a solid sheet of metal as a reflector does not completely isolate the front from the rear because of *diffraction*. The tips of the metal cause some signal to "bend" on the edges of the reflector and toward the rear (or, in the case of reception, from the rear toward the dipole).

You need to be concerned not only about the antenna gain but also about the loss of signal in free space.

#### Free Space Loss

Free space loss is the power loss of a radio signal as it travels from the transmitter to the receiver through free space without other sources of loss such as reflections, cable, or connector loss. In the case of an RFID system, the free space loss would be the power loss of a radio signal as it travels from the interrogator's antenna to the tag. The gains from particular antennas are not taken into account.

The loss is caused by beam divergence, which is signal energy spreading over larger areas at increased distances from the source.

A free space loss can be expressed in dB as

FSL(dB) = 20 * *log*(*d*) + 20 * *log*(*f*) + *K*

where *d* is the distance, *f* is the frequency, *log* is to the base 10, and *K* is a constant that depends on the units used and details of the radio link.

**Example:** If *d* is measured in meters, *f* in Hz, and if the isotropic antennas are used, the expression becomes

FSL(dB) = 20 * *log*(*d*) + 20 * *log*(*f*) – 147.5

As an example, the FSL(dB) of a 1000 meter link operating at 1 gigahertz using isotropic antennas is 92.5 dB.

If *d* is measured in miles, *f* in MHz, and the isotropic antennas are used, the expression stays the same, except that the *K* equals 36.6. If the free space loss is based on nonisotropic antennas (dipole), the *K* equals 32.3.

A free space loss can be also calculated as

FSL (dB) = (4p*R*/l)2 = (4p*Rf*/*c*)2

where *R* is the radius or the distance from the source of the signal, l is signal wavelength, *f* is frequency. and *c* is the speed of light.

It is important to use consistent units; therefore, if the distance (*d*, *R*) is counted in meters, the speed of light (*c*) must be in meters per second.

#### Field Density

Field density or power density can be determined through a very complex mathematical calculation. The power density of an isotropic antenna is

where *P _{D}
* is power density,

*P*is transmitted power or power input to the antenna (either average or peak transmitted power depending on the approach), and

_{t}*R*is the distance to the center of radiation.

The power density of a directional antenna is

where *G _{t}
* is the antenna gain.

A typical RFID professional does not need to perform these calculations regularly. Instead, you need a clear understanding of what field density is and how it relates to your interrogation zones.

Figure 3.5 depicts an antenna and three measurement areas. The closer to the antenna the measurement is taken, the higher the collected power is, because the RF field is denser at that point. Therefore, at the first point, the radiation collected for the measurement is higher than that collected at points 2 or 3.

Figure 3.5 Field density.

If you think of this like a garden hose with a spray attachment on the end, 6 inches from the sprayer, the water is very close together, or dense. The farther you get from that sprayer, the wider the water disperses, leaving more and more room for air between the water, making the spray less dense. This is exactly the phenomena seen in RF field density.