Diffraction effects are most noticeable when objects are close to one wavelength in size (roughly 12 cm for an 802.11 2.4 GHz transmitter). By the time an object gets to roughly 60 wavelengths in size (7.5 meters) diffraction becomes negligible. This means that typical objects in any buildingʼs interior space will introduce diffraction. A tall cubicle wall, high shelving unit, or free-standing kiosk in an auditorium will all fall under the 7.5 meter height guideline. Horizontally, wall segments (not separated by doors) will typically be narrower than 7.5 meters and will act like horizontal barriers, also introducing diffraction at their edges.

In essence, waves propagate around electrically small (close to 1-wavelength) objects without any crisp shadows. The umbra region has sufficient energy to often go unnoticed by the casual user of 802.11 equipment.

The bending effect observed when a wave is diffracted around an object is the result of interference between different parts of the electromagnetic field. This concept is very mysterious and a concise explanation of the field behavior can only be expressed through some very complicated equations. The effect can be understood, however, by considering the basic characteristics of field propagation as expressed in the Huygens-Fresnel principle.

How Interference Relates To Diffraction

The details of the mathematics underlying Huygens-Fresnel diffraction are beyond the scope of this paper, and beyond the scope of the reader without a background in advanced math. As such, youʼre going to be faced with a mystery that youʼll be able to fully appreciate from your reading, but it will remain mysterious nonetheless. We start by remembering that the spherical wavefront expands

outwards as a series of Huygensʼwavelets. The wavefront at some particular future time (t2) will be the result of the interaction between all the wavelets produced by the wavefront at a previous time (t1).

Figure 6.4 Wavelets Combining Out of Phase at the Receiver

There are three point sources shown at time t1 in the figure above and weʼll call them “top” “middle” and “bottom”. Each point source produces its own spherically expanding wavelet and those wavelets combine to produce the new wavefront at t2. In the overall picture the wavefront itself is expanding spherically with the transmitter as its center. The length of the radius (from transmitter to any point source on the wavefront at time t1) is always equal and the effects of interaction between the wavelets always produce a new, spherical wavefront at time t2. The view from the receiverʼs perspective is

Copyright 2003 - Joseph Bardwell

quite different. Notice in the figure that the path length from the top point source is shorter than the path length from the receiver to the middle or bottom point source. At t1 all points on the expanding wavefront are in phase. From the view of the receiver the phase of the wavelet from the top point source has fallen behind the phase of the wavelet from the bottom point source because of the longer distance traveled.

Now if you contemplate the description just offered you should be thinking to yourself “Wait a minute! The receiver isnʼt going to see wavelets from each t1 point source separately. The combined wavelets from t1 will produce a spherically expanding wavefront that will pass across the antenna of the receiver and all parts of that wavefront will be in phase.” Previously in this discussion we explained how the spherical wavefront was seen as a flat, planar wavefront as long as the phase

is less than the Rayleigh phase angle of 22.5º. The planar presentation was an illusion (like the “flat Earth”) due to the size of the receiving antenna compared to the curvature of the spherical wavefront. Hereʼs the key to the mystery: The expanding wavefront does retain its spherical (and planar) characteristics, and Huygensʼwavelets are a moot, theoretical aspect of propagation, until an obstruction blocks some of the point sources at t1. When some of the t1 wavelets canʼt propagate to t2 then the differing path lengths are not just theoretical (from the view of the receiver), they are descriptive of the reality in the electromagnetic field.

When the path length taken by one component is 1⁄2 wavelength longer than another then the phase of the two components is 1800 out of phase and they cancel each other out. As the path length becomes longer it eventually reaches a point where an entire additional wavelength has been added. At this point the signal is back in phase with the original, albeit one wavelength further along.

Figure 6.5 The Critical Angle at Which the Wave is 180O Out of Phase

All of the signal coming from the zone of wavelets between the bottom point source and the middle point source are within 1⁄2 wavelength of the original. In this zone they are adding together to produce the resultant signal. The entire signal in the zone between the middle point source and the top point source is more than 1800 out of phase with the original and this part of the signal is opposing the first zone. The first zone presents a field to the receiver, the second zone is opposing it. The third zone is, again, in phase with the original and the fourth is, again, opposing. As it turns out, the first zone is the most critical. Itʼs here that the field is within the Rayleigh phase angle. Of course, as has been pointed out, this entire line of reasoning doesnʼt apply unless thereʼs an obstruction. Without an obstruction the receiver doesnʼt see any difference in the wavelets, it just sees a spherical wavefront (or the planar presentation of a spherical wavefront). Now letʼs introduce an obstruction and see what happens. The obstruction is partially blocking the first zone. In this case there are two effects.

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First, the wavefront is diffracted downwards, around the edge of the obstruction. Secondly, and more importantly, the opposing phase relationship of the second zone has less “straight-on” signal from the first zone, and the signal power at the receiver is reduced.

Figure 6.6 The Effect of an Obstruction on the Received Wavelets

With an obstruction present not all of the wavelets from the point sources at t1 are participating in the construction of the wavefront at the receiver. If we consider a situation where the receiver is moving it can be seen that this effect is directly related to the relationship between the receiver, the obstacle, and the transmitter and not some sort of magical zones in space surrounding the transmitter.

Figure 6.7 The Receiver’s Location Determines the Obstructions Affect

When the receiver is at “A” there is no radius of the originally transmitted spherical wavefront that is obstructed. The construction of the top set of three propagation lines in the figure is theoretical, and has no significance to the practical world. As the receiver begins to move downwards in the figure it reaches a point where radial lines from the original transmitting antenna are blocked by the obstruction. At this point the first phase zone begins to be blocked and bad things happen to the signal strength at the receiver. Itʼs very important to realize that these phase zones are not fixed in space relative to the transmitter but, rather, are angular zones related to the direct line-of-sight between transmitter and receiver. As the receiver moves, the line-of-sight line moves as well. Itʼs

Copyright 2003 - Joseph Bardwell