# Design of a Double-Matched Cross-Polar Single Antenna Harmonic Tag
## 3 Antenna Design
### Antenna Design Procedure  
The antenna structure is designed using Ansys HFSS. The substrate material is the same as previously indicated for the doubler network. The initial configuration of the antenna is shown in Figure 6, where the two feeding lines are connected together and only one port feeds the antenna (for semplicity, the adding of protusion is considered later on). Figure 5: Schema of a modified annular ring microstrip antenna fed by a microstrip line and connected to an open-circuit stub. Red arrows represent currents, crosses position of nulls (minima) of currents, circles maxima of current. Currents of \(TM_{21}\) mode are affected by currents over the stub (protrusion). On the right side is shown the corresponding radiation pattern. The antenna design procedure encompassed several steps. The initial one involves the dimensioning and simulation of the annular ring's geometry [38], but it did not yield the impedance matching condition on both desired frequency bands. To achieve impedance matching at the second harmonic, a rectangular indent is added at the end of the horizontal microstrip feeding line. The application of this geometric modification, as shown in Figure 6b, facilitates the relocation of the feeding point, effectively ensuring impedance matching at 3.4 GHz. The reflection coefficient for the layouts depicted in Figure 6 is reported in Figure 7.  
The use of the dual-microstrip feed permits the control of the desired relationship between the two bands. If one branch is removed or disconnected, the dual-band matching characteristic is lost. Figure 6: (**a**) Initial layout of the annular ring antenna with relevant symbolic dimensions; (**b**) Application of the rectangular indent near the feed point located on the horizontal microstrip line. Figure 7: Reflection coefficient obtained in simulation for the layouts shown in Figure 6.  
Regarding the radiation pattern, the results obtained from the electromagnetic simulator demonstrate that, at 1.7 GHz, the typical radiation pattern of a patch antenna is observed. Nevertheless, at 3.4 GHz (second harmonic), a null of the gain is present where it would have been beneficial to have a peak (\(\theta=0\), \(\phi=0\)) (see Figure 8). To achieve a maximum radiation pattern at \(\theta=0\), \(\phi=0\), even at the second resonant frequency, a rectangular protrusion (like a stub) has been added to the annular ring antenna and positioned on the opposite side of the rectangular indent. This modification is illustrated in Figure 9, which also includes a circular slot whose function is explained below. Figure 8: Radiation pattern of the gain expressed in dBi: (**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 \(\theta\) component, and the light blue ones are the \(\phi\) component. Figure 9: Layout of the annular ring antenna provided with the holed protrusion (stub) placed in the opposite direction from the rectangular indent. The rationale of this geometric alteration is based on altering the path of currents at 3.4 GHz in such a way to increase the radiation in the boresight direction. Also, a circular slot has been added at the crossing of the protrusion with the ring of the antenna; it is used to to make the route of the currents less intertwined at the insertion point (since the protrusion is large). Furthermore, it is beneficial to the gain that remains unchanged at 1.7 GHz while it increases by 0.5 dB at 3.4 GHz; instead, the polarizations at the two resonances are linear and orthogonal to each other. The final dimensions of the antenna with the protrusion and slot are obtained through an optimization process using HFSS electromagnetic simulator, with the primary objective of maintaining dual-band matching at 1.7 GHz and 3.4 GHz (see Table 1). The results obtained from the simulator are presented in Figures 10-12.