# Low-Profile Harmonic Transponder for IoT Applications
## 4 Experimental Results
### Link Budget Power and Interference Analysis  
Several wireless communication devices operate around the \(2.45\,\mathrm{GHz}\) frequency, including Wi-Fi, Zigbee, Bluetooth, and RFID. Therefore, these devices often interfere with each other. The effects of the coexistence of different standards in the same band are complicated and significant since the interference is spatially and temporally variant. Therefore, modeling the noise, with interference as a Gaussian component that is flat in space and time, is inaccurate when one considers interference from co-located technologies. However, this problem is addressed heavily in the literature from the protocol and communication layer perspectives [21]. On the other hand, this paper addresses the noise and interference problem from the radar perspective. Therefore, the radar cross section (RCS) of the harmonic transponder is considered to describe its performance in a similar way to the conventional radar equation. the RCS of the harmonic transponder including the diode can be described by (1) [22]. \[\sigma_{h}=\mathrm{A_{df}}\cdot\mathrm{CL}\cdot\mathrm{G_{dh}}=\frac{\lambda^ {2}}{4\pi}\mathrm{G_{df}}\cdot\mathrm{CL}\cdot\mathrm{G_{dh}} \tag{1}\]  
where \(\sigma_{h}\) is the harmonic transponder RCS, \(\mathrm{A_{df}}\) is the effective area at the fundamental frequency, \(\mathrm{CL}\) is the previously explained conversion efficiency or loss, and \(\mathrm{G_{df}}\), \(\mathrm{G_{dh}}\) are the realized gains of the harmonic transponder at fundamental and harmonic frequencies, respectively. According to the well-known radar equation, the received signal is explained by (2). \[P_{\mathrm{r}}=\frac{\mathrm{P_{t}}\mathrm{G_{t}}\mathrm{G_{r}}\lambda_{h}^{2} }{(4\pi)^{3}(R)^{4}}\sigma_{h} \tag{2}\]  
where \(G_{\mathrm{t}},G_{\mathrm{r}}\) are the gain of transmitting and receiving antennas, respectively, \(\lambda_{h}\) is the wavelength at harmonic frequency, and \(R\) is the transponder distance from the reader. Furthermore, to mitigate interference noise, we perform coherent averaging processing  
Figure 10: Transponder simulated and measured RCS. by sending \(M\) times interrogation signals. This solution comes from the radar detection theory, and the SNR is improved by \(M\) times, compared to noise and interference. Link Budget Measurement  
The measurement setup is explained in Figure 11, where the transmission path consists of a signal generator with 20 dBm transmitted power. The employed signal generator, which is from Keysight (N5182B MXG X-Series), is not ideal and generates harmonics with a level of \(-35\) dB. The Low Pass Filter (LPF) is employed to suppress the transmitter generated harmonics to increase the receiver dynamic range. The same is at the receiver side--the spectrum analyzer is with the direct conversion topology--and thus, the mixer of the receiver end also produces harmonics from the received low-level fundamental signals. Thus, the High Pass Filter (HPF) is utilized to suppress the fundamental frequency at the receiver input and further increases the dynamic range. The spectrum analyzer is set to 10 MHz receiving bandwidth and to 1 MHz intermediate frequency (IF) bandwidth with an averaging factor of 10 samples per measurement snapshot; thus, the final result represents an averaged value of 100 measurements. Therefore, a signal of up to \(-100\) dBm can be detected. The generator is connected to LPF and a Log Periodic Antenna (LPDA). The insertion loss of the cables together with the LPF is \(\approx\)3.5 dB at 2.45 GHz, and the LPDA gain is \(\approx\)2 dBi at the same frequency. The LPDA is horizontally aligned with the transponder, as shown in Figure 11. The realized gain values of transponder antennas are \(\approx\)1.3 dBi and \(\approx\)3.5 dBi for the fundamental and harmonic frequencies, respectively. The reader receiving antenna is with \(\approx\)3.5 dBi gain at harmonic frequency.