Características y regulación del complejo SNF1 de S cerevisiae

WSN are commonly used in environments where the communication path between the nodes is not lossy (i.e air). However, WUSN nodes are buried under the surface and therefore their communication path is partially or in some cases completely through the ground. Soil is a lossy medium for electromagnetic waves (Trinchero et al., 2009) and therefore EM waves are attenuated in soil significantly more compared to air. Soil is also a complex material and many of its properties such as composition, mineralogy, density and water content directly affect its dielectric properties, which in turn affect the EM propagation and attenuation. Additionally soil is a very dynamic medium. Soil conditions such as water content can significantly change (i.e. after a rainfall). Soil composition also can vary significantly within a short space. Another complexity is that dielectric properties of soil vary based on the EM wave frequency. This complex and dynamic nature of soil makes predicting the attenuation of EM signals very complicated. Creating an efficient and reliable underground wireless communication link is one of the main challenges faced by WUSNs. Therefore, understanding the EM wave propagation in soil is essential for the development of a successful wirelesses underground sensor network for pipeline monitoring.

Different empirical models exist in the literature which predict the dielectric properties of the soil based on its composition and water content (Peplinski et al., 1995a; Mironov and Dobson, 2004; Mironov, 2004). The dielectric properties of a soil can also be measured via Time Domain Reflectometry (TDR) or Vector Network Analyser (VNA) based techniques (Logsdon, 2005; Van-Dam et al., 2005; Topp et al., 2000). Empirical and semi-empirical models exist in the literature (Akyildiz et al., 2009; Ghazanfari et al., 2011; Chaamwe et al., 2010; Bogena et al., 2009; Li et al., 2007) that aim to predict the attenuation of EM waves

attenuation in soil based on soil dielectric properties are the CRIM-Fresnel model proposed by Bogena et al. (2009) and the modified Friis model proposed by Li et al. (2007). In order to understand the propagation of EM waves in different media it is important to first understand how electromagnetic waves are propagated through free space.

EM wave propagation in free space

Friis, (1946) introduced a formula (Equation (2.1)) for calculation of the received power, !_!(!) as a function of internode distance in free space for a transmitter receiver setup.

!_!(!) =!!!!!!!! 4! !_!!

(2.1)

Where !_! is the transmitter power, !_! and !_! are the transmitter and receiver antenna gains, and ! is the distance between the transmitter and receiver and ! is the wavelength of the EM wave in open space.

EM wave propagation in soil based on modified-Friis model

Akyildiz and Stuntebeck (2006) proposed a “link budget” formula based on the Friis transmission equation to act as a framework for EM wave propagation models in soil. This is given by Equation (2.2). In this model a correction factor is added to equation (2.1) in order to reflect the losses in soil medium.

!_! = !_!+ !_!+ !_!− !_!− !_! (2.2) Where !_! is the path loss in soil (medium) due to material absorption and !_! is the path loss in free space and is given by Equation (2.3).

!!= 20!"#

4!" !

(2.3)

Li et al. (2007) propose a model for the calculation of path losses in soil based on the “link budget” formula presented in Equation (2.2). In this model the path loss in the medium !

calculated considering three main differences between propagation of EM waves in soil compared to open space. Firstly, the EM wave propagation speed is different in soil compared to open space, which results in a different wavelength for the signal. Secondly, the attenuation of the amplitude of the signal is dependent on the frequency. Thirdly, correlation between phase velocity and signal frequency in soil causes colour scattering and delay distortion (Li et al., 2007). Based on this model the total path loss caused by the medium !! can be divided

into the attenuation losses caused by the change in wavelength !_!! and the attenuation losses caused by material absorption !_∝ and is given by Equation (2.4):

!! = !!!+ !∝ (2.4)

Attenuation losses caused by a change in wavelength !!! is given by Equation (2.5)

!_!!= 20!"#! !! !

(2.5)

Where the wavelength in free space is !! =_!! , (! = 3×10!!/! and ! is the signal frequency

in Hz) and the wavelength of the signal in soil is ! = !!_! where ! is the phase shifting constant. Therefore !!! is given by Equation (2.6):

!_!! = 154 − 20 log ! + 20log!(!) (2.6) Losses due to attenuation !! is given by Equation (2.7):

!!= 8.68!! (2.7)

Where !!is the attenuation constant. The combined total losses in soil !! is therefore given by

Equation (2.8):

Substitution of the above mentioned parameters with their equations results in Equation (2.9), which calculates the overall path loss based on Modified-Friis model for EM wave propagation in soil.

!! = 6.4 + 20 log ! + 20log!(!) + 8.68!" (2.9)

Where ! and ! are given by equations (2.10) and (2.11).

(2.10)

(2.11)

Where ! is the angular frequency (! = 2!"), ! is the magnetic permeability and is assumed to be 1. Li et al. (2007) used Peplinski’s dielectric mixing formula published by Peplinski et al. (1995b) in their research to calculate the real and imaginary parts of the complex permittivity value of soil in their paper and subsequent papers (Akyildiz et al., 2009; Vuran and Akyildiz, 2010). However, the mixing formula presented in these papers is incorrect and is based on a wrong formula initially published by Peplinski et al. (1995b) and shortly after corrected in (Peplinski et al., 1995a). For this reason comparison of the results from Akyildiz et al. (2009) and Vuran and Akyildiz (2010) are not presented in this thesis.

EM wave propagation in soil based on CRIM-Fresnel model

Bogena et al. (2009) propose a semi-empirical model based on a Complex Refractive Index Model (CRIM) to quantify signal attenuation in WUSN. Similar to the Modified-Friis model CRIM-Fresnel model is also based on the link budget formula presented in Equation (2.2). In

α = ω µ !ε 2 1+ !! ε ! ε " # $ % & ' 2 −1 ) * + + , - . . β = ω µ !ε 2 1+ !! ε ! ε " # $ % & ' 2 +1 ( ) * * + , - -

this model losses due to signal reflection are included in the total attenuation of signals Atot

(Yoon, 2013; Chaamwe et al., 2010; Bogena et al., 2009). However, the dielectric permittivity of soil is calculated based on the CRIM model, which takes into account the permittivity of soil !_!, water !_! and air !_! at a specific EM wave frequency. Based on Bogena et al. (2009) the total attenuation losses Atot is given by Equation (2.12).

!!"!= !!! + !! (2.12)

Where !_! is the attenuation due to material absorption from Dane and Topp (2002) and !_! is the attenuation due to reflection. !_! can be calculated using Equation (2.13).

!! = 10!"#

2! 1 + !

(2.13)

The reflection coefficient R, with an assumption that magnetic permeability can be neglected, is calculated by Equation (2.14).

! = 1 − ! 1 + !

! _(2.14)

The authors of Bogena et al. (2009) claim that their proposed CRIM-Fresnel model is better suited for an initial approximation of EM waves propagation in soil compared to the Modified-Friis model proposed by Li et al. (2007) due to the fact that the dielectric mixing model used by that model (Peplinski et al., 1995a) is not supported by a large data base. However, the CRIM-Fresnel model presented in Bogena et al. (2009) is not validated by field trials and its authors acknowledge that field trials are required for furthur evaluation of the model.

Comparison of existing RF propagation models in soil

signal attenuation in soil. Figure 2.21 illustrates the total attenuation calculated by these two models.

Figure 2.21 Comparison of the Modified-Friis and CRIM-Fresnel RF propagation models As can be seen from Figure 2.21, the signal attenuation increases with an increase in frequency in both models. Therefore higher operational frequencies will have a shorter range compared to lower operational frequencies given the same input power and receiver sensitivity. This is consistent with findings from Chaamwe et al. (2010). Additionally it can be shown from Figure 2.21 that there is a significant difference between the predicted values by these models, which increase at higher frequencies.