Explanation of Calculation Basis

Theoretical calculations of exposure levels estimates should always be designed so that the calculation leads to fields being overestimated. When considering exposures, the fields of various transmitters and hence various frequencies occurring at the location need to be taken into account. To achieve this, the factor for the limit value needs to be determined relative to each transmitter frequency and then totalled across all transmitters. The following relationship can therefore be derived from DIN VDE 0848 (Chap., equation 2) or from the “Guidelines for Limiting Exposure to Time-varying Electric, Magnetic, and Electromagnetic Fields – ICNIRP Guidelines” (equations 6 and 9):

This must be fulfilled so that the limit value is observed regardless of the frequency.
Here SiLimit is the limit value for power density for transmitter number i, for example, 9 W/m² for a 1800 MHz transmitter and Sixy is the power density due to transmitter number i at location x,y.

Due to the far field relation between distance and power density.

where rX is the distance from the transmitter, it follows therefore that:

Here riLimit is the safety distance for the transmitter relative to the public exposure limit. For example, according to the location certified in RegTP (German Regulatory Authority for Telecommunications and Post). In the present case, i = 1,…,4. For simplification, it is assumed that the antenna properties and hence the safety distance for antennas 1 and 2 and for antennas 3 and 4 are the same, which in practice is generally the case.

Due to the radiation (directivity) pattern of the antennas riLimit depends on the angle. We can therefore conclude the following:

The term riLimit(0) is the safety distance in the boresight (antenna main beam) direction. R reflects the radiation pattern of the antenna. φ is the vertical and θ the horizontal angle dependence. For horizontal angle dependence, it is assumed that the person is always located in direction of boresight. This too leads to the fields being overestimated. In the diagram below.

The vertical radiation pattern is represented as a function of the angle. The side lobes show deep recesses as a rule. If these were to be taken into account in the calculation, even small deviations in angle would result in large differences in levels. For this reason, an envelope has been placed across the side lobes. This approach leads to the fields being overestimated too.
The following function was chosen as the envelope:

Here parameters A and σ describe the boresight, parameters B and μ the side lobes and C the backward (φ = 180∞) envelope. Examples of this are shown in Figures 1 and 2.

The theoretical curve is shown in red, the antenna radiation pattern stated by the manufacturer is shown in blue. For antennas without electrical tilt, A+B+C = 1 always applies.

For antennas with electrical tilt, the sum also may initially be greater than 1. For values great than 1, the function is subsequently limited to 1. The reason for this is that the electrical downtilt enables the antennas to be lowered across an angular range. Therefore, the location certification has to be applied for across the possible range of angles. The radiation pattern is changed in such a way that the boresight is widened by the range of angular adjustment (see Figure 2). With some antennas, there is no need, when adjusting the theoretical curve in the angle range from –120° to –30° (pointing skywards), for the theoretical curve to be greater than the actual curve in order to obtain greater accuracy in the relevant 0°-120° angle range.

Signals reflected once are taken into account such that 50 % (3 dB) is assumed as a reflected signal in the power.

Diffraction (bending) is only considered in the case of central masts on corners of houses. A linear transition from the area without diffraction to the area 90° beneath the antenna is calculated using 6 dB.


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