# First SIMO Harmonic Radar Based on the SFCW Concept and the HR Transfer Function
## 6 Verification of the HR Transfer Function
One sequence contains the following measurement: the initial reference measurement without a DUT that is stored for normalization of the data acquired during the run, a measurement of the reference configuration with normalization applied to check for drift and data validity, the measurement of the 3 dB, 6 dB, 10 dB, and 20 dB attenuators inserted into the reference plane and finally another re-measurement of the reference configuration, which is then used for the normalization of the following run. The results were calculated from the complex average of \(n=10\) measurements. This complex measurement sequence was carried out to minimize the influence of system drift upon the results. Additionally, the measurement of the reference configuration with normalization applied to check for drift and data validity is performed in the same way as in the previous section. Figure 18: Representation of the accurate measurement results of the transmission scattering parameters for a 3 dB (**A**), 6 dB (**B**), 10 dB (**C**), and 20 dB (**D**) SMA attenuator for both frequency bands used by the HR system. Fundamental frequency forward transmission data (\(S^{I}_{21}\)) and the axis shown in blue, harmonic frequency reverse transmission data (\(S^{II}_{12}\)) and the axis shown in red. Measurements obtained by a Rohde & Schwarz ZVA67 VNA, step-size 1 MHz, IF BW 100 Hz, UOSM 2-port calibration using a Rosenberger 3.5 mm calibration kit, port 1 connector reference plane male, port 2 connector reference plane female. the mean received scalar harmonic return power \(\overline{P_{\text{Meas}}^{II}}\) in the harmonic return frequency band is also acquired for each measurement. The results for \(S_{11,\text{Norm}}^{II,I}\) obtained by these measurements are shown in Figure 19 (solid colored lines) in addition to calculated model values (dashed black line). It is important to note that the frequency axis only shows the harmonic return frequency for reasons of clarity, instead of the formally correct 2-tuple (\(f_{i}^{I}\), \(f_{i}^{II}\)) associated with the mixed frequency S-parameter. The measurement results obtained for the three lower value attenuators (3 dB, 6 dB, and 10 dB) show a very good signal-to-noise ratio and a good agreement with the data obtained by the simple square-law transfer function model of Equation (15) applied to the one-port nonlinear element, especially considering that no systematic error correction was applied to the data obtained by the HR system and the limited repeatability of normal SMA connectors. In these measurements, the observed error of the HR data compared to the model is less than 1 dB in magnitude and less than 4\({}^{\circ}\) in phase. We believe these minor  
Figure 19: Illustration of the \(S_{11,\text{M}}^{II,I}\) results obtained by evaluating the theoretical HR transfer function model using the S-parameters for the 3 dB (**A**), 6 dB (**B**), 10 dB (**C**), and 20 dB (**D**) SMA attenuators shown in Figure 18 (dashed black line), and the measurement results of the HR system of four different measurement runs (colored solid lines) for each of the attenuators. Only the harmonic frequency axis is shown for clarity. residual errors are due to a combination of different factors, mainly the idealization of the doubler but also due to the nonexistent systematic error correction (when compared to a VNA) and the limited connector repeatability in this setup. Based on this assumption, we consider the proof of the HR transfer function to be satisfied. While the results of the the 20 dB attenuator measurement shown in Figure 19 show a larger amount of error compared to the other results, the mean received scalar harmonic return power \(\overline{P_{\text{Meas}}^{II}}\) values shown in Table 1 serve to put these results into perspective and show the performance of this HR setup, since the harmonic return power values were only around \(-147\) dBm for this DUT, which shows that the limited signal-to-noise ratio is the limiting factor here.