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Fresnel zone calculation

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This program is an applet for calculating the Fresnel zone.

A particularly common problem with radio systems is communication errors. The occurrence of communication errors changes significantly depending on the method of placement of the radio equipment. With radio communication, it is important to ensure "line of sight" between the transceivers.
When we can see the receiving antenna we use the expression "line of sight" without much thought, but with radio waves, it can be said that "line of sight" is only achieved when the Fresnel zone indicated below is established.
With radio systems used at about 1.5 m above ground, if a Fresnel zone is not established, multipath interference will occur, so that the true electric field intensity cannot be obtained. If operation of the equipment is unstable, it is necessary to consider whether the fixed station can be set up in a higher place.

Radio system errors
Radio system errors occur when the bit strings of 0's and 1's that make up the data cannot be identified by the electronic circuits inside the receiver, due to corruption of the transmission data.

Viewed on a temporal basis, assessment of the receive data is performed in the middle position of the receive bit width, and in terms of level, the bit is determined to be 1 or 0 by whether the received voltage of the median value (threshold value) is bigger or smaller. This identified signal is the signal after FSK demodulation. Because the signal and noise are a composite waveform to begin with, if the difference between the signal level and noise level (inside the receiver) is low, with certain sampling timing, since the decision is made with a waveform in which the threshold value is exceeded due to noise, an error results. Therefore in general, the signal level is required to be about 20 dB (100 times the voltage ratio) greater than the level of noise.

FSK radio equipment is immune to the influence of amplitude noise, but if there is an obstruction between the antennas (the ground, buildings, natural objects and so on), the radio waves will be reflected resulting in multipath interference. At the receiving point, the composite wave incorporating the delayed radio waves is distorted in amplitude, resulting in an error. In addition, the ratio of the noise component of signals that enter the demodulation circuit in a location with weak electric field intensity is high in relation to the signal, and this causes errors. Of course, signals generated by the antenna due to external noise will also have an impact on amplitude and frequency.

Fresnel zone
In order for radio waves emitted from the transmitter to reach the receiver without attenuation of power, a certain amount of space is required. The energy cannot reach the receiver via one straight line in space. It is easy to understand for example that the waves will not get there through a hole the size of a needle in a concrete wall.
The space required is a spheroid with its center along the shortest distance between antennas, and this is called the Fresnel zone. In fact this space expands indefinitely, but the part that principally contributes to communicating the energy is called the 1st Fresnel zone.
If there are obstacles inside the Fresnel zone, insufficient energy is transmitted so that received field intensity becomes weak. If the received field intensity is weak, the probability that errors will occur becomes gradually higher. The receive sensitivity of the receiver is absolute, and propagation loss which depends on the distance traveled by the radio waves cannot be avoided. Therefore in order to prevent errors from occurring, it is important to ensure that the received radio waves are as close as possible to the theoretical value.

The 1st Fresnel zone is a spheroid space formed within the trajectory of the path when the path difference when radio wave energy reaches the receiver by the shortest distance, and when it gets there by another route, is within λ/2. In this case, λ is the wave length of the radio wave (wave length = speed of light / frequency) which at 400 MHz is 0.75 m.

When positioning radio systems
The distance between the Fresnel zone boundary and a straight line running the shortest distance between the antennas is called the Fresnel radius, and if there are no obstacles in the space forming 60% of this distance, propagation characteristics are said to be the same as in free space.

< Click to move to the calculation window >

Fresnel zone formula

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1. Click the "Figure / Graph" button to display the calculation screen.
2. Enter the required items in the yellow input fields for entering parameters. To calculate the Fresnel zone, after setting the parameters in the input fields, push the Enter key on your PC, or click the "Calculate" button.
3. Set the distance d in the pink input field.
4. To find the Fresnel radius, decide the position to find (distance on the X axis), and left-click with your mouse on the graph.

* Right panel
The values shown in the panel on the right are the Fresnel radius and diameter at the midpoint.


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