# Design of a Double-Matched Cross-Polar Single Antenna Harmonic Tag
## 4 Electromagnetic Analysis of Assembled Doubler Network and Antenna  
We proceed to analyze the electromagnetic performance of the harmonic tag as a whole by assembling the doubler network and the antenna. This involves simulating the combined effect of the doubler circuit integrated within the annular antenna layout  
Figure 11: Radiation patterns of the gain expressed in dB: (**a**) results obtained at 1.7 GHz for \(\phi=0\); (**b**) results obtained at 1.7 GHz for \(\phi=90\); (**c**) results obtained at 3.4 GHz for \(\phi=0\); (**d**) results obtained at 3.4 GHz for \(\phi=90\). In the figures, the green curves represent the gain plot of \(\theta\) component, and the red ones are the \(\phi\) component.  
Figure 12: Surface currents flowing on the surface of the annular patch: (**a**) currents at 1.7 GHz; (**b**) currents at 3.4 GHz.  
using Ansys HFSS. The primary objective of this analysis is to examine the impact of this integration on the behavior of the tag at the two resonant frequencies, 1.7 GHz and 3.4 GHz.  
For this purpose, we calculate the monostatic Radar Cross-Section (RCS) of the tag at the two considered frequencies. To analyze the effect of the coupling between the doubler circuit and the antenna, we compare the RCS obtained when the doubler circuit is integrated inside the antenna with the RCS computed by terminating the antenna port on a load that incorporates the frequency-dependent scattering parameters of the doubler circuit alone. This approach allows us to isolate the impact of the circuit integration on the antenna's scattering properties. The simulation is performed in Ansys HFSS, modeling a pair of plane waves impinging on the tag from the boresight direction with linearly polarized electric fields, one vertically and one horizontally polarized.  
The results, shown in Figure 13, compare the RCS of the assembled tag with that of the antenna alone. A strong agreement between the two cases indicates that integrating the doubler circuit inside the antenna does not significantly alter its electromagnetic behavior. In the vertical polarization case (dotted lines), the RCS exhibits a deep notch at 1.7 GHz, corresponding to the resonance of the antenna operating in the \(TM_{11}\) mode. A smaller notch at 3.4 GHz is mainly due to the matching condition between the antenna and the doubler circuit at that frequency. Conversely, in the horizontal polarization case (solid lines), the deep notch occurs at 3.4 GHz, corresponding to the resonance of the \(TM_{21}\) mode, while the smaller notch at 1.7 GHz is again influenced by the matching conditions between the antenna and the doubler circuit.  
The presence of these deep notches confirms that the antenna efficiently absorbs incident radiation at the corresponding frequencies. This result demonstrates that the tag effectively receives a vertically polarized plane wave at 1.7 GHz and backscatters a horizontally polarized wave at 3.4 GHz, ensuring the intended harmonic response.  
Figure 13: RCS for vertical polarization (dotted lines): comparison between the antenna alone (violet dotted line) and the complete tag (i.e., antenna including the doubler circuit) (black dotted line). The deep notch at 1.7 GHz corresponds to the resonance of the antenna operating with \(TM_{11}\) mode; the small notch at 3.4 GHz mainly depends on the matching condition between the antenna and the doubler circuit at that frequency. RCS for horizontal polarization (solid lines): comparison between the antenna alone (blue line) and the complete tag (i.e., antenna including the doubler circuit) (red line). The deep notch at 3.4 GHz corresponds to the resonance of \(TM_{21}\) mode, while the small notch at 1.7 GHz depends on the matching conditions between the antenna and the doubler circuit.