# First SIMO Harmonic Radar Based on the SFCW Concept and the HR Transfer Function
## 2 The HR Equation and HR Transfer Function
### Realization of the HR Tag Matrix
In practice, this figure can be used as the criterion for the 1 dB harmonic compression point if the nonlinear element, as the matching network, the PIN diode switch, and the transmission lines will introduce at least 1...1.5 dB of insertion loss. The design of the matching network in combination with the harmonic balance simulation model of the diode was checked for this limit and optimized for maximum conversion gain and bandwidth at lower input powers, including a DC bias voltage sweep of the Schottky diode. A typical harmonic balance simulation result of the complete circuit including higher harmonics is shown in Figure 8 for a DC bias voltage of 0.5 V.  
Due to the narrowband nature of the distributed element matching network, and higher order harmonics from 7 GHz upwards are substantially attenuated, no unwanted interference of systems operating in these higher frequency bands is to be expected, especially when the tuned bandpass response of the tag's harmonic TX patch antenna is also taken into account. Figure 8: Illustration of the simulated spectrum at the doubler output for an input power of \(-20\;\mathrm{dBm}\) at 2.45 GHz and a DC bias voltage of \(+0.5\;\mathrm{V}\), obtained second harmonic conversion gain \(-15\;\mathrm{dB}\). Figure 7: Circuit diagram of the tag RF circuit for frequency doubling with on-off-switching. The aforementioned HR tag cells can then be tessellated in one more dimension to form the mixed frequency switched reflection matrix. For our first experimental setup, the tags were placed in a 3-by-5 pattern to match the maximum space available in the standard RF prototype PCB manufacturing process of the contract manufacturer. The full switched harmonic radar tag matrix is shown in Figure 9.  
In the configuration shown, it is possible to measure 15 different complex transmission paths with this matrix without moving the MUT or any other mechanical movement of the system. For these measurements, it is guaranteed that the positions of the antennas are optimally maintained, which is very helpful for many evaluation procedures. In order to control the individual HR tag cells of the matrix, a digital control unit was developed (Figure 10), which consists of a STM32F4 microcontroller, four quad channel SPI DACs (MCP4728), 16 operational amplifiers (TLV274) for output voltage scaling and associated support circuitry. With this control unit, it is possible to set individual bias voltages for each cell element in the range of \(-3\) V to \(+5\) V in 12 bits of resolution by the control software of the system from a PC via USB serial interface. Additionally, a CAN bus interface is also supported for controlling the operation of the matrix at longer distances from the controlling PC. Figure 7.0 Sketch of the realized mixed frequency switched reflection matrix, RHCP-polarized 2.45 GHz and LHCP-polarized 4.9 GHz, 3 by 5 HR-cell configuration. Dimensions: \(265\times 260\times 4\) mm\({}^{3}\). Since the bias settings of each tag cell element can be individually controlled, a calibration routine for maximum conversion gain during the on-state and the minimal amount of harmonic return signal in the off-state can be run for each element, its values stored and later re-applied during actual measurements. This procedure helps to account for non-avoidable part to part variations in the assembly process of the PCB and for manufacturing variances present between each of the diodes used in the cells and is performed in situ to account for environmental effects. The complete measurement setup is controlled by a custom application written in Python, which controls both the configuration and measurement taken by the VNA system as well as the operation of the mixed frequency switched reflection matrix.