# The Impact of an Electric Machine Body on EM Wave Propagation in RTMS
## 3 Modeling Electromagnetic Propagation in a Rotating Machine
### Monopole Antennae Design  
The primary objective was to determine the feasibility of signal detection in a rotor-embedded machine (REM). To achieve this, we integrated an appropriate electric circuit and a suitable antenna with the sensor. The chosen monopole satisfied these criteria: efficient and suitable antenna gain, compact size, and stability of antenna parameters across a broad range of rotors and stators.  
In theory, multiple antenna types met these criteria, categorically falling within three primary groups: electrical antennas, magnetic antennas, and combinations of both. An  
Figure 2: HFSS implementation of the SM for the squirrel cage induction motor.  
tennas like patch antennas, IFAs (inverted-F antennas), and monopole antennas were considered within the scope of applicability [32; 33].  
Our initial focus was on the monopole antenna, consisting of a strand positioned above a large metal plane, taking into account wavelengths of two to three lambdas at least.  
For our investigation, a design was created featuring a metal piece spanning the surface of a PCB (printed circuit board). A monopole antenna has a height of 3.16 cm and a radius of 0.1 cm. Utilizing HFSS, we simulated this structure, requiring approximately 15 min for the simulation process. Figure 3 visually depicts the HFSS design of the monopole antenna.  
Our simulations were conducted with two different setups. The first was in an open space above a ground plane situated between two antennas. In the other case, we included all the machine components: rotor, stator, shaft, and carcass.  
In both instances, both antennas shared the same position and orientation. To reduce reflection waste, the matching network was fine-tuned separately for each case, setting the corresponding parameters at the zero position.  
The propagation factor is [34; 35]:  
\[F_{p}=\left(\frac{|S_{21}|^{2}}{\Big{(}\Big{(}1-|S_{11}|^{2}\Big{)}\Big{(}1-|S_ {22}|^{2}\Big{)}e_{t}e_{r}\Big{)}}\right) \tag{1}\]  
where \(S_{11}\) is the coefficient at the input of the adaptation network and the antenna of the transmitter, \(S_{21}\) is the transmission coefficient from Port 1 to Port 2, \(S_{22}\) is the reflection coefficient at the receiver, \(e_{t}\) is the efficiency of the transmitting antenna, and \(e_{r}\) is the radiation efficiency of the receiving antenna.  
Following the calculation of parameter \(S\), the actual \(F_{p}\) was derived using Equation (1). The outcomes of the simulation are presented in Table 1.  
As shown in the table, the calculated propagation factor (\(F_{p}\)) for electromagnetic transmission and reception decreases with the addition of each component of the rotating machine. This means that as more parts are added to the machine, the efficiency of signal transmission and reception declines. Each new component introduces more obstacles and potential sources of interference, which disrupt the electromagnetic waves and reduce the overall effectiveness of the communication system.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Parameter Name** & **Open Space** & **Carcass, Stator, Rotor and Shaft** \\ \hline \(|S_{11}|\) & 0.053328 & 0.991953 \\ \(|S_{21}|\) & 0.019153 & 0.000354 \\ \(|S_{22}|\) & 0.107855 & 0.096884 \\ \(|F_{p}\) (\(10^{-5}\))\(|\) & 36.49 & 0.83 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The calculated \(F_{p}\).  
Figure 3: The design of the monopole antenna.