# Design of a Double-Matched Cross-Polar Single Antenna Harmonic Tag
## 2 Doubled-Matched Doubler Circuit  
In wireless sensing systems, the efficient transfer of RF energy between the antenna and the tag's circuitry is crucial for optimal performance. To achieve this, a well-designed matching circuit is required. In this section, we focus on the design considerations and implementation of a single-port doubler that is matched at two frequencies: the fundamental and its second harmonic. Figure 1: Schema of the proposed harmonic tag: a single-port dual-band harmonic circuit (i.e., a doubled-matched doubler) connected to a dual-band antenna. The circuit includes the used Schottky diode, inductors, and capacitors with lumped element models. Specifically, to obtain even more realistic results, the S-parameter models of the individual components (provided by the manufacturers, in our case, Murata [32]) are included in the simulator. The presence of these components significantly reduced the circuit's size compared to a fully microstrip version [33]. This design strategy has been carried out with the aim of making the doubler circuit integrable with a small antenna to compose the tag. The Schottky diode is a key component in the tag's matching circuit that is responsible for the generation and extraction of harmonic frequencies. The design of a single-port doubler plays a vital role in achieving impedance matching between the antenna and the diode, ensuring maximum power transfer and effective harmonic generation. The dual-band network of the doubler circuit was first designed using AWR Microwave Office [34]. The design process considers a Teflon substrate (\(e_{r}=2.1\), \(\tan\delta=0.0027\)) with a thickness of \(h=1.5\) mm. The selected operating frequencies is 1.7 GHz (fundamental) and its double value, 3.4 GHz (second harmonic). The layout of the final circuit, shown in Figure 2, has been obtained through a two-step optimization process. The first step is performed by means of a Harmonic Balance analysis (under AWR), taking into account the nonlinearity of the used diode. The corresponding optimization has been subjected to the following constraints: (i) the incident power level at the port of the network is set to \(-30\) dBm since this is a reasonable level in practical applications; (ii) the reflection coefficient at the considered frequencies is set to be less than \(-20\) dB; (iii) the conversion loss (i.e., the power difference between the input power to the circuit and the backscattered power at the second harmonic) is less than 30 dB. In our design, we chose an HSMS-2850 zero-bias Schottky diode, well-suited to operate in a small-signal regime (Pin \(<-20\) dBm). Each lumped component has an effect on the behavior of the doubler circuit, and a possible variation of their value has been analyzed individually. Variations of about 10% of the inductor \(L_{1}\) cause a shift in the matching bands of the reflection coefficient (greater at first harmonic, smaller at second harmonic). A similar variation of the capacitor \(C_{1}\) gives a shift in the first harmonic matching band but does not affect the second harmonic. On the contrary, a change of 10% in inductor \(L_{2}\) shifts the second harmonic but does not affect the fist harmonic matching band. Capacitor \(C_{2}\), instead, can shift both first and  
Figure 2: Layout of the single-port double-matched doubler circuit for the Schottky HSMS-2850 (Avago Technologies [35]) diode obtained after a two-step optimization (i.e., AWR and HFSS). Dimensions are in millimeters. The table shows the names and the nominal values of the components used. \(L_{1}\) and \(C_{1}\), and \(L_{2}\) and \(C_{2}\) are in parallel with each other, respectively. second harmonic matching bands for a change in its value. On the contrary, variations in the value of the capacitor \(C_{3}\) do not introduce significant shifts in matching bands in the reflection coefficient but affect the length of the microstrip line connected to the cathode of the Schottky diode at the second harmonic (around 3.4 GHz).