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Let us assume for a moment that electromagnetic waves propagate under ideal conditions, ie, without dispersion If high-frequency energy is emitted by an isotropic radiator, then the energy propagates uniformly in all directions Areas with the same power density therefore form spheres (A = 4p r ) around the radiator (see Figure 29) The same amount of energy spreads out on an incremented spherical surface at an incremented spherical radius That means that the power density on the surface of a sphere is inversely proportional to the radius of the sphere Since a spherical segment emits equal radiation in all direction (at constant transmit power), if the power radiated is redistributed to provide more radiation in one direction, it results in an increase of the power density in the direction of the radiation This effect is called antenna gain, and it is obtained by directional radiation of the power So, the formula to calculate the directional power flux density, S, is PT GT [W/m 2 ] 4 r 2





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magnetic waves is described by its reflection cross-section Objects that are in resonance with the wave front that hits them, as is the case for an antenna at the appropriate frequency, for example, have a particularly large reflection cross-section An electromagnetic field propagates outward from the interrogator s antenna, and a small proportion of that field (reduced by free-space attenuation) reaches the tag s antenna The power is supplied to the antenna connections as high-frequency voltage, and after rectification by diodes it can be used to power the tag or activate or deactivate the tag Some proportion of the incoming RF energy is reflected by the antenna and reradiated outward into free space The amount of energy reflected depends on how well the antenna couples to the electromagnetic wave RFID tags that use backscatter to reply to their interrogators have antennas that are designed to resonate well with the carrier signal emitted by the interrogator The reflection characteristics of the antenna, its effective cross-section, can be influenced by altering the load connected to the antenna To transmit data from the tag to the interrogator, a load resistor connected in parallel with the antenna is switched on and off in time with the data stream to be transmitted By changing resonant properties of its antenna, the tag makes itself a good or poor reflector This varies the strength of the signal reflected from the tag, creating a pattern that is detected at the interrogator as data This technique is referred to as modulated backscatter Before the backscattered signal arrives at the interrogator antenna, it goes through forward and backward path loss, many types of interferences in both the directions, and absorption by the tag to power it The reflected signal also travels into the antenna connection of the interrogator in the reverse direction from the original signal It is decoupled using a directional coupler and transferred to the receiver input of the interrogator The forward signal of the transmitter is to a large degree suppressed by the directional coupler Tags operating at UHF and microwave frequencies use far-field and couple with the interrogator using backscatter The amount of energy received at the receiver decreases as an inverse of the square of the distance (r) between the interrogator antenna and tag (1/r2) Figure 2-10 shows far-field coupling phenomenon.

where PT = transmitted power (W) GT = gain of the transmitting antenna r = radius of the sphere (meters)

When the range is large, the spherical surface of uniform power density appears flat to a receiving antenna, which is very small compared to the surface of the sphere This is why the far field wave front is considered planar and the rays approximately parallel Also, it is apparent that at some shorter range, the spherical surface no longer appears flat, even to a very small receiving antenna The distance where the planer, parallel ray approximation breaks down is known as the near field The crossover distance between a near and far field is taken to be where the phase error is 1/16 of a wavelength The result is a well-known formula for the beginning of the far field of an antenna with the largest dimension D in feet and wavelength l in feet: RFF = 2D2 [ft] (213)

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