EMF Exposure

Above, we have also delimited the local exposure limits as set by ICNIRP assuming 1 W of RF charging power at the device and uninterrupted transmissions such that the results coming from 6-mins averaging match the instantaneous results. Notably, in very near-field conditions such that d′ ≥ 15 m, the incident EMF exposure is below the safety limits for r ≤ 1.8 cm and f ≤ 30 GHz, which might be enough for safely charging a phone in human hands if the receive antenna and phone are properly placed and hold.

These results are for local incident power density, while getting quantitative insights on the whole body EMF exposure, as for a person holding the device, may be much more intricate, as it depends on the body’s build. A child holding the ER would have much more EMF exposure than an adult, as the entire body is closer to the device. How to estimate the incident power density for the whole body in near-field conditions is open for research, and conservative methodologies are in general preferred. It might be easier to compute volumetric, rather than area, power/energy densities, but this either requires some research on corresponding EMF exposure limit values or proper procedures for quantities conversions. 

Regarding local incident energy density, one must note that this EMF exposure constraint is set to avoid high peaks of power densities for up to several minutes that would still meet the incident power density constraint. If, on the contrary, the instantaneous incident power density remains below or equal to the 6-min average value, the incident energy density constraint will always be met. In any case, the 6-min averaging of power and energy densities gives some flexibility to potential charging protocols and thus must certainly be explored with dedicated research. Anyway, cautious strategies for the deployment and operation of RF-WPT systems are needed. They must provide transparent EMF radiation exposure guarantees for the end users.

We study a cost-effective single RF chain PB architecture embedding a reflecting intelligent surface and a single antenna feeder. 

We model the PB’s average power consumption and obtain a closed-form approximation for the point-to-point charging scenario where the device position varies randomly. Moreover, we estimate the local EMF exposure in the device’s vicinity by leveraging a Monte Carlo integration method. 

Above, the left-hand figure shows the PB's average power consumption as a function of the operating frequency and the boresight gain. Notably, the increasing trend of the average power consumption curve results from the joint effect of increasing the number of RIS's passive elements and driving the PA at a higher power level to compensate for the increasing frequency-dependent channel losses. Moreover, increasing the boresight gain results in lower average power consumption as the RIS becomes more directive. Moreover, notice that the gap between our derived closed-form frequency-dependent power consumption expression and the simulation results reduces when increasing the gain. 

Meanwhile, the right-hand figure shows the average RF power density as a function of the operating frequency and measured at different distances from the device using 1000 probes uniformly distributed on the d-radius sphere. The reader can notice that the average RF power density decreases as the radius of the d-radius sphere around the device increases, indicating that the energy is mostly focused in the device's nearby vicinity. This trend becomes more prominent as the operating frequency increases. Finally, we can verify the compliance of this WPT system according to the ICNIRP regulations on the incident power density, which recommend a maximum of 40W/m^2 and 55/f_c(GHz)^ 0.177 in the frequency ranges 2-6~GHz and 6-300~GHz, respectively, for local exposure. 

Above, we illustrate the power consumption of RIS/DMA-based ETs as a function of frequency for a single-ER setup together with the power density at 15 cm from the ER. The ER is 3m away from the ET and receives 1 W of RF power. 

RIS and DMA-based architectures exhibit similar performance. Still, a RIS-based ET seems preferable at lower frequencies, although it may be more costly than DMA’s. All this depends on the scenario geometry and the number of ERs.  Interestingly, the performance of RIS-based ETs with only two control bits per element is near optimal (obtained with infinite-resolution RIS). Meanwhile, increasing the operation frequency is appealing for satisfying the EMF radiation exposure constraints given a fixed form factor and charging distance. Indeed, ICNIRP regulations are met for frequencies above 6.2 GHz in both RIS and DMA-based setups.

A critical LIS optimization challenge arises with increasing frequency since the number of variables, i.e., antenna elements’ phase shifts configuration, becomes massive, overwhelming conventional optimization solvers. Two aggravating factors are that: i) for RIS, the phase shifts are discrete; ii) for DMA, more antenna elements can fit a certain form factor and they have a Lorentzian-form response. 

Based on the illustrated results and after dealing with the previous challenges, one can speculate that end-to-end PTEs in the order of 10% may be realized when using greater form-factor LIS-based ETs.