**4. Conclusions**

The current paper proposes a novel theoretical approach to estimating the power conversion efficiency (PCE) of RF–DC converters for WPT applications. The approach relies on using the two-frequency harmonic balance (2F-HB) method in conjunction with full-wave simulations of the circuit PCB. A comparative numerical study showed that when applied to multi-tone signals, the 2F-HB appreciably outperforms the multi-dimensional harmonic balance method (MHB), conventional harmonic balance method (HB), and transient analysis (TA) in terms of required CPU time. The results of the HB and the MHB have been obtained using the commercially available Keysight ADS circuit simulator, whereas those of TA were computed by means of the LTSpice in conjunction with the shooting method (SM) implemented as a MATLAB script. To evaluate the accuracy of the theoretical model, the authors performed experimental measurements for the RF–DC converter prototype based on the voltage doubler rectifier topology. The PCE of the voltage doubler circuit was calculated and measured for different RF–DC converter matching network elements and different average input signal power levels and waveforms in the sub-GHz band.

The numerical results obtained using the proposed theoretical model have been found to be in good agreemen<sup>t</sup> with the results measured experimentally, which firmly attests the consistency between the simulations and experiments. The calculation accuracy reaches 0.37%. Furthermore, the results obtained for different values of the matching network elements exhibit the existence of optimal combinations for achieving the highest PCE, thus demonstrating the potential of the proposed estimation method in the design of highly efficient RF–DC converters.

Although only a voltage doubler was considered in this work, the applicability range of this approach is not limited to such a simple circuit, as it is capable of handling a wide range of RF–DC converter topologies involving an arbitrary number of diodes. The new method allows for editing and fine-tuning the design of an RF–DC converter much quicker than previous methods due to accelerated PCE estimation, which is 96 times faster than the broadly used harmonic balance method.

**Author Contributions:** Conceptualization, J.S. and A.L.; funding acquisition, A.L.; investigation, J.E., R.K. and D.C.; methodology, J.E., J.S. and A.L.; project administration, A.L.; software, J.E., R.K., R.B. and D.C.; supervision, J.S.; validation, R.B.; visualization, J.E. and D.C.; writing—original draft, J.E., R.B. and D.C.; writing—review and editing, R.K., R.B., J.S. and A.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Latvian Council of Science, gran<sup>t</sup> No. lzp-2020/2-0344, "Radio Frequency Wireless Power Transfer for Wireless Sensor Network Applications".

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
