Figure 5.3 The Far Field Transformation of the Field Strength

The terms of the field strength equation that quickly become very small define characteristics of whatʼs termed the near field or sometimes referred to as the reactive near field. The terms that are left after removing these quickly shrinking aspects define characteristics of whatʼs termed the far field or sometimes referred to as the propagating far field. All of the effects that weʼre interested in with regard to practical assessment of an RF environment are in the far field and are embodied in the last term of the equation. An antenna designer, or a student of basic antenna design, will encounter the near field when considering the direct interaction of antennae in a coupled array or coupled antennae components to modify their combined transmission characteristics. Coupling refers to multiple radiating elements that are within each otherʼs near field.

The classic Inverse Square Law states that “power varies inversely as the square of the distance”. This “law” is a description of the expanding nature of the spherical wavefront, and relates to the density of the electric charge. If a sphere doubles in size its surface area increases by a factor of 4. The surface area of a sphere varies with the square of the radius. Therefore, if the distance from a field doubles the field density will decrease by a factor of four, varying inversely as the square of the distance. This is the essence of the classic Inverse Square Law.

Signal Acquisition from the Spherical Wavefront

There is a significant difference in the way a receiver is electrically and magnetically affected in the near field as opposed to the far field. One aspect of this difference comes from the fact that a spherically propagating wavefront presents out-of-phase portions of the wavefront to a receiving antenna. When the signal is received itʼs possible for the antenna to acquire portions of the original signal that are out of phase with each other and hence may decrease the receivable power. Diagram 5.4 (below) shows a transmitting antenna and for the purposes of this present discussion the wavefront will be considered spherical. In the real world the 3-dimensional signal space will be more “flattened” (even with a standard, typical 802.11 omnidirectional dipole antenna as would be found on an access point). Even with a “flattened” propagation area there is still a curved wavefront moving perpendicularly outward from the antenna. Notice, in the diagram (5.4) that the wavefront

Copyright 2003 - Joseph Bardwell

is made up of the points that lie at the same phase angle in the propagated signal. That is, there is a 3-dimensional surface, the “flattened” sphere, the surface of which is defined as the place where the phase angle of the transmitted signal is the same. You can see this in the diagram.

Figure 5.4 The Spherical Presentation of the Wavefront

In Figure 5.4 (above) you see the curve on the right representing the spherical wavefront. Itʼs moving to the right, away from the antenna. Notice that the sine wave in the diagram has just returned to zero from its negative half-cycle at the point where the diagram shows the wavefront. Since the wavefront is expanding in 3-dimensions, the inverse square law tells us that if the radius of the wavefront sphere were to double then the area on the sphere defined in degrees for some particular vertical and horizontal width would have four times the area. The overall surface area of a sphere is given by 4πr2 hence if r is doubled for any part of the sphere then the resulting surface area will increase by a factor of 4. It is this physical property of spherical surface area that is the basis for any inverse square relationships in the electromagnetic world.

Now letʼs examine an implausible diagram. Itʼs implausible because itʼs grossly disproportionate to anything that would be encountered in the real world. Nonetheless, weʼll start with this implausible scenario and then explain exactly what the implausibility is and how this impacts the realm of RF signal analysis. Figure 5.5 (below) shows a very long vertical antenna in the signal propagation area of the field.

Figure 5.5 An Impossible Antenna of Unreasonable Length

Copyright 2003 - Joseph Bardwell