# Antenna Field 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. Use of directors makes angle smaller and gain higher. By using a reflector all the energy appears in only one hemisphere and that results in a doubling of radiated energy in this direction or 3dB 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.

Another reference used in antenna gain figures helps to give an antenna an appearance of higher gain than what the antenna is truly rated. It is known as dBi and represents a gain of an antenna over the value rate of an isotropic antenna. An isotropic antenna radiates equally in a spherical pattern, or equally radiated in all directions. It gives an antenna a 2.14 dB boost: Antenna gain in dBi = antenna gain in dBd + 2.14.

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.

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.

This book excerpt is provided courtesy of OTA Training, from the book, CompTIA RFID+ Exam Cram, by OTA Training and published by Que Publishing.