Free space is a perfect vacuum space (ideal environment) for the spreading of electromagnetic wave. It is completely homogeneous and its material parameters are constant in the entire volume and independent of the electromagnetic field of propagating wave, therefore it does not absorb the wave.

Electromagnetic wave spreading in free space shows no losses due to reflection, refraction, bending or absorption. The total energy of the wave is not altered, but the electric field intensity decreases inversely proportional to the distance. It is therefore a diffuse loss of electromagnetic wave due to “dilution” of energy in a space in the spread of the spherical wave. These so-called free space losses (FSL – Free Space Loss) are used in many areas for signal strength prediction required for establish a reliable radio connection.

Free space loss:

where: **L _{FSL}** free space loss

**d**the distance between the source and receiving point

**λ**the wavelength of the electromagnetic wave

where: **c** speed of light

**f** frequency of electromagnetic wave

It is evident from the equation [1] that the free space loss is proportional to the square of the distance between transmitter and receiver.

Free space loss in dB:

Figure 1: Distribution of signal strength in free space

For an ideal radio connection the wave spread from the transmitter to the receiver only. However, in the real world we have to consider other losses caused by delays caused by the finite speed of signal propagation. Depending on the terrain the reflection, diffraction, bending or dispersion (usually neglected) on the outside can still take effect to the electromagnetic wave attenuation.

Because modelling of the waves is very large topic which has a goal to find the balance between the demands of calculation challenging and usability in practice, there is various models for different types of problems. In our case, it was used the MWMF (Multi Wall Multi Floor Model) method, which is suitable for approximate estimation of the theoretical range of the RFID tag with respect to the frequency and environment.

## Multi Wall Multi Floor Model (MWMF)

This method considers a non-linear relation between cumulative losses by passing a number of outdated walls and floors. It is used as a alternative method of “ray tracing” for closed environments simulation. Attenuation on the path is therefore calculated according to the relation:

Where: ** L_{0} **gradient coefficient

** d** the distance between transmitter and receiver

** L_{wik}** attenuation of the

*i*wall type by its

*k*-th passage

**L _{fjk}** attenuation of the

*j*floor type by its

*k*-th passage

** I** the number of wall types

** J** the number of floor types

** K_{wi}** the number of

*i*category walls

** K_{fj}** the number of

*j*category floors

For our purpose (change of the environment type) we use one barrier (wall) only with given properties and the one pass through the barrier only. Thus we get a simplified relation:

For the L_{0} losses, it can be used losses by the open space for the 1 m distance. Here the exponent _{n} is essential, it indicates the losses increase rate with the distance. It is obtained by measured values approximation based on statistically significant number of measurements in the given environment. An example of a gradient coefficient for different environments in given in the Table 1 below.

Tab. 1: Gradient coefficient n

Environment |
(gradient coefficient) |

Free space | 2 |

Grocery store | 1.8 |

Office (hard walls) | 3 |

Office (soft walls) | 2.6 |

Open space | 2.5 |

During the passage of the electromagnetic wave by a barrier a damping occurs depending on the barriers material. As shown in the table below, this attenuation may be crucial. These losses are measured for the most used building materials. The values for the gradient coefficient and for the wave attenuation are obtained from (3) and are valid in the frequency range from 300 to 1000 MHz.

Tab. 2 Attenuation of the wave caused by the barriers

Material |
Attenuation (dB) |

Concrete | 13 - 20 |

Window | 1.8 |

Floor | 13 |

0.25 "Glass | 0.8 |

0.5 "Glass | 2 |

32 " Timber | 2.8 |

3.5 " Brick | 3.5 |

10.5 " Brick | 7 |

4 " Concrete | 12 |

8 " Concrete | 23 |

12 " Concrete | 35 |

8 " Masonry | 12 |

24 " Masonry | 28 |

Figure 2: Distribution of the signal strength in the space with barrier

## List of references

- SANGHERA, Paul a K.V.S. RAO. How to cheat at deploying and securing RFID: impedance-matching and size-reduction techniques [online]. Burlington, MA: Syngress Pub., c2007, xviii, 343 p. [cit. 2014-10-24]. ISBN 15-974-9230-2.
- LOTT, M. a I. FORKEL. A multi-wall-and-floor model for indoor radio propagation: impedance-matching and size-reduction techniques [online]. Burlington, MA: Syngress Pub., c2007, xviii, 343 p. [cit. 2014-10-24]. ISBN 10.1109/vetecs.2001.944886.
- ATMEL. Range Calculation for 300 MHz to 1000 MHz Communication Systems: Range Calculation. 05/2010. 20 s. Dostupné z: http://www.atmel.com/Images/doc9144.pdf