Fresnel zone

The primary wave will travel in a relative straight line from the transmitter to the receiver.

Aberrant transmitted radio, sound, or light waves which are transmitted at the same time can follow slightly different paths before reaching a receiver, especially if there are obstructions or deflecting objects between the two.

The size of the calculated Fresnel zone at any particular distance from the transmitter and receiver can help to predict whether obstructions or discontinuities along the path will cause significant interference.

The n-th Fresnel zone is defined as the locus of points in 3D space such that a 2-segment path from the transmitter to the receiver that deflects off a point on that surface will be between n-1 and n half-wavelengths out of phase with the straight-line path.

In order to ensure limited interference, such transmission paths are designed with a certain clearance distance determined by a Fresnel-zone analysis.

The dependence on the interference on clearance is the cause of the picket-fencing effect when either the radio transmitter or receiver is moving, and the high and low signal strength zones are above and below the receiver's cut-off threshold.

Although intuitively, clear line-of-sight between transmitter and receiver may seem to be all that is required for a strong antenna system, but because of the complex nature of radio waves, obstructions within the first Fresnel zone can cause significant weakness, even if those obstructions are not blocking the apparent line-of-sight signal path.

For this reason, it is valuable to do a calculation of the size of the 1st, or primary, Fresnel zone for a given antenna system.

Doing this will enable the antenna installer to decide if an obstacle, such as a tree, is going to make a significant impact on signal strength.

The first region includes the ellipsoidal space which the direct line-of-sight signal passes through.

If a stray component of the transmitted signal bounces off an object within this region and then arrives at the receiving antenna, the phase shift will be something less than a quarter-length wave, or less than a 90º shift (path ACB on the diagram).

However, the positive attributes of this deflection also depends on the polarization of the signal relative to the object.

If a reflective object is located in the second region, the stray sine-wave which has bounced from this object and has been captured by the receiver will be shifted more than 90º but less than 270º because of the increased path length, and will potentially be received out-of-phase.

Use of same circular polarization (e.g. right) in both ends, will eliminate odd number of reflections (including one).

If unobstructed and in a perfect environment, radio waves will travel in a relatively straight line from the transmitter to the receiver.

But if there are reflective surfaces that interact with a stray transmitted wave, such as bodies of water, smooth terrain, roof tops, sides of buildings, etc., the radio waves deflecting off those surfaces may arrive either out-of-phase or in-phase with the signals that travel directly to the receiver.

Sometimes this results in the counter-intuitive finding that reducing the height of an antenna increases the signal-to-noise ratio at the receiver.

Although radio waves generally travel in a relative straight line, fog and even humidity can cause some of the signal in certain frequencies to scatter or bend before reaching the receiver.

This means objects which are clear of the line of sight path will still potentially block parts of the signal.

To maximize signal strength, one needs to minimize the effect of obstruction loss by removing obstacles from both the direct radio frequency line of sight (RF LoS) line and also the area around it within the primary Fresnel zone.

The strongest signals are on the direct line between transmitter and receiver and always lie in the first Fresnel zone.

In the early 19th century, French scientist Augustin-Jean Fresnel created a method to calculate where the zones are — that is, whether a given obstacle will cause mostly in-phase or mostly out-of-phase deflections between the transmitter and the receiver.

The concept of Fresnel zone clearance may be used to analyze interference by obstacles near the path of a radio beam.

The first zone must be kept largely free from obstructions to avoid interfering with the radio reception.

[2] The cross sectional radius of each Fresnel zone is the longest at the midpoint of the RF LoS, shrinking to a point at each vertex, behind the antennas.

, note that the volume of the zone is delimited by all points for which the difference in distances, between the reflected wave (

are much larger than the radius and applying the binomial approximation for the square root,

, and applying the binomial approximation only at the right-hand antenna, we find: The quadratic polynomial roots are: Applying the binomial approximation one last time, we finally find: So, there should be at least half a wavelength of clearance at the antenna in the direction perpendicular to the line of sight.

The vertical clearance at the antenna in a slant direction inclined at an altitude angle a would be: For practical applications, it is often useful to know the maximum radius of the first Fresnel zone.

followed by a unit conversion results in an easy way to calculate the radius of the first Fresnel zone