# SDR-Enabled Multichannel Real-Time Measurement System for In Situ EMF Exposure Evaluation
## 2 Materials and Methods  
### The Proposed Sensor  
In this section a compact three-axial probe able to measure the three components of the E field will be discussed in detail. Since the complete analysis of the E/H field requires a 6-channel measurement system, not available during the measurement sessions, in this work, we will focus our attention on the E-field probe solution. However, it should be noted that the geometry lends itself to the realization of a sensor for measuring both the E and H field, as will be briefly discussed in this section. The E-field sensor is composed of three identical orthogonally positioned probes, offering an isotropic response in 1-6 GHz frequency band with low perturbation of the incident field. It was built using 3 identical miniature commercial field probes (PBS-1 set from Aaronia A.G.) [30]. The position of the probes was chosen to maintain orthogonal positions between the 3 cartesian axes by fixing the probes on a custom-made plexiglass tripod. Since their tips could not be superimposed practically, a very small air volume gap was delimited by the dimensions of the tips during the measurements. Based on the probe tip dimensions and the distance between the probes, the measurement volume was defined as a sphere with a radius of 1 cm. Figure 1a presents a schematic description of the designed E-field sensor and its intended connections. As noted above, the geometry of the sensor also represents a good starting point for a three-axial E- and H-field probe, that is currently under development. This can be obtained by adding three orthogonal coil antennas, as shown in Figure 1b. The close positioning of the probe dipoles can cause mutual coupling, which could limit the effectiveness of the probe [31]. Mutual coupling is usually analyzed in transmission mode, while analysis in reception mode is less commonly discussed. An accurate evaluation can be obtained using full-wave simulations. Numerical simulations are a powerful tool that, however, suffer from some drawbacks. The solution depends on the specific incident field that changes with the impinging direction in case of simple single plane wave, and in more complex way in case of there not being plane-wave incident field. Furthermore, the numerical solution makes it difficult to clarify the mechanisms at the basis of the mutual coupling, whose understanding can be useful in the design of the probe. In the following, we will follow a different approach, that is, new at the best knowledge of the authors, based on a simplified analysis of the problem. Even if the solution suffers from some approximations, this approach has the advantage to give some insights of the physics of the problem and to give a simple estimation of the impact of the mutual coupling on the measured quantity. With reference to a harmonic regime, let us consider an antenna in reception mode, (Figure 2) closed on a load having impedance \(Z_{\mathrm{L}}\) that models the receiver. The antenna can be modeled as a Thevenin circuit [31], wherein \(V_{0}\) is voltage at the gap of the antenna closed on an open circuit, and \(Z_{\mathrm{IN}}\) is the input impedance of the antenna in reception mode. The energy dissipated on the load \(Z_{\mathrm{L}}\) is the 'useful' energy, i.e., the energy available for applications. However, \(Z_{\mathrm{IN}}\) also has a real part, and consequently, some energy dissipates on the impedance \(Z_{\mathrm{IN}}\). This energy is re-irradiated by the antenna. In general, the re-irradiated energy depends on the mismatch between the two impedances \(Z_{\mathrm{L}}\) and \(Z_{\mathrm{IN}}\). In case of perfectly matched load (\(Z_{\mathrm{L}}=Z_{\mathrm{IN}}\)*), the re-irradiated energy is equal to the energy absorbed by the load. With reference to Figure 3, let us consider a simple model consisting of two receiving elements placed at very close distance, and an incident plane wave \(E_{i}\) (blue arrow).