# Design of a Double-Matched Cross-Polar Single Antenna Harmonic Tag
## 5 Prototype Realization and Measurements
### Measurements of the Complete Tag  
The functionality of the complete tag, shown in Figure 18, has been assessed by performing backscattering measurement using the setup shown in Figure 19. It comprises two identical Vivaldi antennas, the Anritsu 2830A, and the two band-reject filters used previously. The Vivaldi antennas are positioned 60 cm away from the tag (deployed on the floor) and are oriented orthogonally to each other to check the cross-polarized behavior of the tag. The Vivaldi antennas exhibit impedance matching with a reflection coefficient below \(-10\) dB over a frequency range from 1.4 GHz to 12 GHz, and a maximum simulated gain of 6 dBi at 1.7 GHz and 6.5 dBi at 3.4 GHz. Continuous wave (CW) signals are transmitted to the tag with a power level of 9 dBm, covering frequencies from 1.62 GHz to 1.72 GHz with a 5 MHz step. The spectral lines in the second harmonic received on the spectrum analyzer are displayed in Figure 20. As evident, a maximum received power level of \(-67\) dBm is achieved at 3.4 GHz, consistent with the reflection coefficients of the matching circuit and the annular ring antenna. In Figure 20, it can be observed that the tag's response is highest when optimally matched in the first harmonic and degrades as the frequency moves away from this point.  
The measured values are consistent with those predicted by the harmonic radar theory described by Equation (2), where symbols \(P_{Rx}^{2/6}\) and \(P_{Tx}^{f_{0}}\) stand for power received at second harmonic (i.e., \(2f_{0}\)) and transmitted at fundamental frequency \(f_{0}\), respectively. \(G_{Rx}^{2/6}\) and \(G_{Tx}^{f_{0}}\) are gains of receiving (@\(2f_{0}\)) and transmitting (@\(f_{0}\)) Vivaldi antennas, \(\lambda_{0}\) is the wavelength at fundamental frequency, \(R\) is the distance of the tag, which has gain \(G_{Rig}^{2/6}\) at second harmonic, and \(C_{Tag}^{2/6}\) is the scale factor of the doubler circuit that has been retrieved from measurements shown in Figure 16. Evidently, Equation (2) does not account for the losses  
Figure 18: Prototype of the final harmonic tag.  
in the cables and filters of the measurement setup (Figure 19); therefore, the transmitted and received power is intended at the antenna terminals.  
\[P_{Rx}^{2/_{0}}=\frac{1}{4}(P_{Tx}^{f_{0}}G_{Tx}^{f_{0}}G_{Tag}^{f_{0}})^{2}C_{Tag }^{2/_{0}}G_{Tag}^{2/_{0}}G_{Rx}^{2/_{0}}\left(\frac{\lambda_{0}}{4\pi R}\right)^{6} \tag{2}\]  
Figure 19: Measurement scenario of the harmonic tag: the tag rests on the floor while two Vivaldi antennas arranged orthogonally and suspended by means of wooden slats are used to transmit and receive.  
Figure 20: Spectrum measured in second harmonic when the distance between the tag and Vivaldi antennas is about 0.6 m.  
Denoting with \(L\) the losses of cables and filters used for measurements, the actual received power is \(P_{Rx}=P_{Rx}^{2f_{0}}-L\). Graphs of \(P_{Rx}\) are shown in Figure 21 as function of tag distance for different values of the transmitted power. The received power decreases rapidly with the distance from the tag but, for a sufficient transmitted power (for example 20 dBm), the tag can be read from a distance greater than 3 m. The asterisks shown in the picture report the value of the measured received power for a transmitted power of 9 dBm (at the output port of generator) when the tag is at 60 cm and 100 cm of distance. It is evident that the measurements agree well with the theoretical curve.