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Posted on: February 20th, 2010; Filed under: Wireless No Comments »

My original title for this paper was “Quantum Electrodynamics, diffraction, the Huygens-Fresnel Principle, earth bulge and their effects on the Fresnel Zone,” but I thought that was a bit much. Plus I was afraid it might scare some people away. This paper does assume some RF competence on the part of the reader, and at least a basic understanding of algebra. As my original title indicates the actual scope of this article is much more refined than the revised title would lead one to believe. I will not be discussing the finer points of establishing long distance connections from start to finish. This paper’s main focus is on the Fresnel Zone (Pronounced Fra-nel btw).

The Fresnel Zone gets a lot of attention by today’s wireless network admins but the fact remains a lot of them do not truly understand just what it is, nor how it works. Many of the people whom refer to the Fresnel Zone do so incorrectly. The purpose, therefore, of this paper is to explain this interesting aspect of RF wave propagation in detail so that you too can enter the informed.

When one sets out to discuss so a vast topic as I have it becomes clear that finding a place to start is of paramount importance. One must weight the cost of starting both too early and too late. I do not want to bore the reader, nor do I wish to assume too much. I am not sure exactly where to make the plunge, so if you find it boring just skip ahead a little and if it is a little over your head maybe check out a couple other resources first then come back.

When an RF wave propagates through space it is prone to a number of disturbances. I am not just talking about various obstacles in the path of the wave. Specifically I am referring to the effect the different types of obstacles have on the wave. If the wave is absorbed by the medium that is called (get this) absorption. The other possibilities include reflection (bouncing off), refraction (kind of a combination between the two, some bounces off and some bends as it moves *through* a medium of a different density), scattering (bouncing off a bunch of sharp jagged points), and diffraction. This is the one that is the most important to this article so we will spend a bit more time discussing what exactly diffraction is.

So, what exactly *is* diffraction? Diffraction describes how a wave will bend around an obstacle. To continue in the tradition of over using a metaphor, imagine a pond. Now in this pond suppose you have a stick sticking up through the water. The last part of the metaphor involves you dropping a rock into the pond. You can think of the ripples from the rock as the RF wave, now when the waves reach the stick they will bend around it.

This is important. Why? The effect of diffraction is multidimensional, first it causes a change in direction of the wave, second it distorts the wavefront and third it slows the wave at the cause of impedance. Think about it, the wave can not possibly pick up more speed… it is traveling at the speed of light (ok… not technically… just bear with me here) but now it has to move around the object. This can result in a whole slew of problems.

Ok, so we know *what* diffraction is, now we need to tackle the why of it. What about a wave makes it bend around an obstacle like that? Logic would have us believe the wave would bounce off, refract, be absorbed, etc. Why does it bend? Sure, we call it a wave, but it is not fluid, you can not just bend a beam of light around a corner can you? I am not talking about universally here where you have got an object with massive gravity which can bend light… think flashlight.

Before we go any further I am going to be up front with you. What I am about to describe is not technically correct. It does describe the correct outcome but… the reasoning behind is not so much a reality. The reality has to do with Quantum Electrodynamics (QED). The problem is that getting into a full on discussion of QED is a bit beyond the scope of this paper and the model I am about to describe does a pretty good job of getting the point across.

If you know anything about quantum mechanics one of the first realities you must grapple with is the duality of light. For the uninitiated this is a simple concept to understand, but terribly difficult to grasp. If that does not make sense, good. The duality of light simply states that light is both a particle * and* a wave. Right now one of two reactions have occurred. One: The reader has said “Yes, that is great… so what?” or Two: “What the…?” The first can be attributed to either individuals whom have previously encountered this, or people who do not really grasp the significance of this. The latter are usually the people who take the time to try and understand things.

To be perfectly honest the significance of this aspect of light is again beyond the scope of this paper. However one needs to realize that this duality is not limited just to light. A photon for instance is not just the massless boson of light, but that of any electromagnetic wave. Like.. RF waves for example.

A long time ago (1678) there was this smart guy by the name of Christian Huygens. He was exceptionally smart as it turns out, way ahead of his time. He wrote a paper on the wave theory of light. This paper was very technical and requires a knowledge of advanced calculus to really get anything from it. I stipulated at the beginning of this paper however, that I would not require such a breadth of mathematical knowledge. Therefore I am going to lay out the “brass tacks” of the paper.

In a nutshell the paper basically says consider a source of RF wave propagation. To make things easier let us consider an isotropic radiator. The expanding wavefront can be consider as an infinite number of source points each emanating their own spherical wavefront and it is really the interactions of these so dubbed “wavelets” that produce the over all wavefront. How does one calculate an infinite number of points? Well, that is where the calculus comes into play, just know it is possible and not something crazy I made up.

The problem with Huygens’s equations is that they only account for some of those problems waves face like reflection and refraction but not diffraction. Enter Augustine Fresnel, another terribly intelligent individual. He went over Huygens’s work and kinda polished it up to account for the all important diffraction. Finally Gustav Kirchoff took this information and applied it to James Maxwell’s equations.

You see, what happens is that the wave technically does get blocked by the obstacle in the path of the wave. What happens then is that these little wavelets expand the wave back out making it look like it is bending around. They realign the wavefront making it seem like the obstruction is the source and not the actual IR.

When diffraction occurs it creates a number of “areas”. At the back of the obstruction you have the “umbra region” which is sometimes called the “diffraction zone”. This is the area where the coverage has “bent” around the object. If you picture a cube, you can think of connecting the four points on the far side of the cube into a pyramid. The area of the pyramid is called the “cone of silence” (Looks like those guys on Get Smart were not just making that term up…) which is technically a misnomer since in most situations multi-path will result in there being some coverage there, it will just tend to be noticeably less. Now if you were to think of the cube expanding backwards to cover the pyramid the are between the pyramid and the side of this extended cube (well now it is a three dimensional rectangle…) that would be the umbra region. Again, remember these concepts are generalizations and are meant to serve as a mental aid. There is not really this “cone” coming out of the back of the obstacle.

Another thing to take into account with diffraction is that it is most noticeable with objects around the size of the wavelength (approx. 12.5cm for 2.4Ghz) and once it gets to around 60 wavelengths (or approx. 7.5m) you really can not notice the effect. Think about it, the very definition of diffraction is the bending of the wave around the obstacle. If the obstacle gets to big it will just block the wavefront entirely.

If you ask wireless admins what the Fresnel Zone is they will probably tell you it is this thing you can not block. Several of them do not know much more than that. They might even be able to tell you how to calculate this zone (which may be wrong, watch out!) and some might be able to tell you it has something to do with phases. All of this information is (hopefully) correct, but very vague.

To explain what the Fresnel Zone is, first we are going to describe *why* the Fresnel Zone is. Here is the deal. You have an isotropic radiator, and it is producing this spherical wavefront expanding outward. Every point on this wavefront is in phase from the view point of the transmitter, this is not so much the case with the receiver though. Now generally speaking in the far field this is negated. What happens is that the sphere gets so big, that compared to the tiny little antenna it looks like a plane. Specifically it has to do with the phase being less than the Rayleigh phase angle of 22.5 degrees but that is not pertinent to this discussion.

What if you put something in the way of that wavefront? Problem. Now the wavefront is disrupted and can not form that plane. Let us think about the expanding wave front and at some random point we will pick out three points on the wavefront and label them p1, p2, and p3 such that p1 will be considered the 0 point, p2 has “fallen behind” by one wavelength/2 and p3 is one full wavelength out of phase. As you can see that would put p2 180 degrees out of phase with p1 which would cause them to cancel out. Therefore, from p1 to p2 the signal is within 1/2 a wavelength and additive. This constitutes one zone. You can keep going from there creating p4 and so on, each section being one zone where the wave is in phase with itself and out of phase with either zone which encloses it.

These zones are called Fresnel Zones. Each zone is indicated by the 180 degrees of phase separation. The first Fresnel Zone in my lovely picture would be the reddish area, and the blueish would be the second Fresnel Zone. As it happens the first Fresnel Zone is the most crucial to the viability of a link. It should also be pointed out that the Fresnel Zones are entirely dependent upon the line of sight between the receiver and transmitter. Generally speaking your transmitter will be stationary, but often times the receiver will be moving around. Every time the receiver moves the position of the Fresnel Zones move with it. You can think of the Fresnel Zones by picturing a target, the center of the bullseye would like if you had a string connecting the transmitter to the receiver, each alternating ring of the target would be a zone and it would look like two big cones sticking out of each side of the target connected to the two points of the link such that it looks something like this. Just… imagine someone who could draw doing it though. The “red zones” are all in phase while the “blue zones” would be out of phase.

The first Fresnel Zone is so important in fact, that if too much of it is blocked you will have poor reception at best. Some numbers were crunched and it turns out you need at least 60% of the first Fresnel Zone free of obstruction or your connection will be about as reliable as a wet paper bag. Now, in an indoor environment that is not entirely true. With all the scattering, reflection, etc creating multi-path you can pretty much discount the effects of the Fresnel Zone. I say pretty much because hey, it is not exactly disappearing, just that with all the objects around you tend to get decent coverage.

Now, in order to calculate the area of the first Fresnel Zone you need simply plug in a couple numbers to this equation…

So what we have here then is:

- R
_{n}is the Radius of the nth Fresnel Zone - M is a constant (17.3 for metric [radius in m, distance in Km] and 71.3 for US[radius in feet, distance in miles])
- F
_{Ghz}is the frequency of the signal in gigahertz - N is the Fresnel Zone number
- D
_{1}is the distance from the source to the obstacle - D
_{2}is the distance from the destination to the obstacle.

A lot of times what you will encounter is a simplified version of this equation. What this form of the equation does is determine the maximum radius. That is, the radius of the first Fresnel Zone at the very center of the link. This equation often looks like this:

Much simpler, you have your constant, the distance of the link, and 4 times the frequency in Ghz (approx. 9.6 for 2.4Ghz). Now remember we need to keep 60% of this clear so it is probably more common to see that equation with the value of 43.3 instead of 72.1 to compensate. Somewhere along the line though someone got the idea that 43.3 was the value for the radius of the **full** first Fresnel Zone. Do not ask me how, I have no clue. Probably someone copied it down half asleep and told someone and from there it spread. Please note that if you are using the 43.3 value and then taking 60% of that you are calculating a much smaller value so you might think you have a clear zone when you really do not. This can be very frustrating so it is extremely important to get this right.

When I first set out to write this paper I had high hopes of doing something that, while not original, I thought would be beneficial. However, given my lack of skills with creating equations (It does require around 25 steps… 30 if you count creating the constant) and the fact that it has indeed been done, I have decided against it. What I wanted to do was do what Fresnel himself did which would be to derive the equation used to calculate the first Fresnel Zone. It is really not difficult at all, applying basic algebraic principles to knowledge of triangles. If you want to see how to do it (and I hope you do!) I suggest you pick up a copy of the paper by Joseph Bardwell, a link to which is provided at the end of this article. This is a very well written paper and if you find this stuff interesting I highly recommend picking it up.

We know all about the Fresnel Zone now, we know what it is, and why it is important. We also realize it is dependent only upon the distance between the two ends of the link. That is to say you can not simply bypass the effects of the Fresnel Zone by using a highly directional antenna with high gain. Which can be hard to get used to at first, but we know the physics behind it, and we saw how only distance was involved. There was never any mention of the gain of the antenna so… not like it is rocket science (perhaps a future article?).

We also realize that this is particularly relevant in long distance communication. We are talking about distances of miles and a radius measured in feet after all. One thing that we have to remember regarding these long distance links is that eventually the Earth itself will encroach upon the Fresnel Zone. The Earth is spherical and at some point it will bend. It is that whole illusion of a planar surface because of how small we are compared to the size of the Earth.

The magic number is 7, after 7 miles you need to take what is know as “earth bulge” into account. In order to keep your antenna up high enough to make sure the Earth clears the Fresnel Zone you will want to know how much higher to place said antenna which is a simple equation:

H is height in feet and D is distance in miles, simple as that. If we combine the two equations we can find out the minimum height of an antenna in a long distance link (greater than 7 miles):

We have made it, the end is here. Hopefully now you can fully appreciate just what the Fresnel Zone is, why it is important, and how to work with it when building long distance 802.11 links. We have covered every aspect of the Fresnel Zone starting way back with diffraction to taking the very Earth into account when creating our links. As any 802.11 admin will tell you, RF waves are often unpredictable and a pain to work with… but… um… I forgot where I was going with this…

- CWNA Certified Wireless Network Administrator Official Study Guide 3rd Edition by Joshua Bardwell et al
- “I’m Going To Let My Chauffeur Answer That…” Math and Physics for the 802.11 wireless LAN engineer by Joseph Bardwell

Pick it up for free at: - Also Thanks to MathBin for the LaTeX images.