# First SIMO Harmonic Radar Based on the SFCW Concept and the HR Transfer Function
## 2 The HR Equation and HR Transfer Function
The nonlinear change of the transmission behavior of a frequency doubler \(\Delta S^{II,I}_{43}\) only influences the magnitude according to the following formulas:  
\[\Delta S^{II,I}_{43}=\frac{S^{II,I}_{43}|_{P_{MUT}_{2}}}{S^{II,I}_{43}|_{P_{ Ref}}}\quad,\quad\Delta S^{II,I}_{43}=S^{I}_{21,\text{MUT}_{2}}\quad, \tag{9}\]  
Figure 2: Illustration of the HR transfer function with the two-port S parameters of the material-under-test (MUT, ports 1 and 2) and the nonlinear part of the doubler (ports 3 and 4). The signal chain of the HR frontend starts with the generation of the stimulus illumination signal by the TX module of the VNA system. This signal is stabilized in its output power by a calibrated automatic level control loop and is repeatable in its phase relative to the reference clock of the system, even in fractional-N synthesis frequency hopping operation, which mitigates the need for an output signal measurement in the system as generally employed in VNAs (see [18] for background and derivation). In this setup, the TX module either generates a discrete set of consecutive sinusoidal signals of differing frequencies centered around 2.45 GHz (SFCW) or a configurable CW tone. This signal is subsequently low-pass filtered by a diplexer forming an absorptive low-pass filter to remove any residual harmonic content produced by the signal synthesis process and avoid the subsequent amplification of these residual interference products. The filtered signal is then amplified by a linear driver gain block and a subsequent power amplifier to an output power of up to 33 dBm. Considerable output power back off (at least 7 dB) is employed to operate the PA in a linear region. Since even the most linear power amplifiers generally show a weak nonlinear behavior, the amplified output signal is then filtered again by an absorptive low-pass filter, which also helps to avoid inadvertent load-pulling on the PA by presenting a resistive termination for the second harmonic. Finally, the stimulus signal is then filtered again using a reflective 4.9 GHz band-stop filter with 60 dB suppression which ensures that any residual harmonics that occur are reduced to the absolute minimum before the illumination signal is radiated by the fundamental frequency antenna into the scene. In the receiving path of the experimental setup, a reflective band-pass filter centered around the harmonic frequency of 4.9 GHz is used to suppress fundamental frequency break-through, which could lead to unwanted localized harmonic generation in the rest of the signal receiving chain, which especially includes the following MMIC gain block used to amplify the harmonic return signal for the mixed-frequency VNA receiver module. A picture of the assembled harmonic radar front-end electronics hardware setup is shown in \[\sigma_{2}=d_{2}\cdot G_{TXT}\cdot\left[\frac{G_{RXT}\lambda_{1}^{2}}{4\pi} \right]^{2} \tag{2}\]0  
\[\sigma_{2}=d_{2}\cdot G_{TXT}\cdot\left[\frac{G_{RXT}\lambda_{1}^{2}}{4\pi} \right]^{2} \tag{2}\]1 Picture of the HR front-end microwave electronics without the dual-band TX/RX antenna. \[\sigma_{2}=d_{2}\cdot G_{TXT}\cdot\left[\frac{G_{RXT}\lambda_{1}^{2}}{4\pi} \right]^{2} \tag{2}\]2 Schematic block diagram of the HR front-end electronic and the dual-band antenna. The HR interrogator uses a custom planar dual-band patch antenna array for the TX (centered at 2.45 GHz, 4 elements) and the RX signal (centered at 4.9 GHz, 5 elements). Opposing circular polarizations (2.45 GHz RHCP, 4.9 GHz LHCP) were chosen to improve the isolation between RX/TX array elements and allow for a compact antenna layout, where the 4.9 GHz patch elements are nested between the larger 2.45 GHz patches. Besides the obvious reduction in overall size, this arrangement of the patch elements also reduces the signal loss introduced by diffraction and refraction of the waves by the MUT for a non or weakly dispersive MUT in a non-perpendicular surface orientation.