## 4 Components and System
### Antennas
#### 4.2.2 Simulation and Measurement  
In this section, a Vivaldi antenna is modeled in CST Microwave Studio and investigated for its matching and radiation pattern. Again, Rogers RO4350B with \(\varepsilon_{\mathrm{r}}=3.66\) and a thickness of \(0.254\,\mathrm{mm}\) is used as substrate. Figure 8 shows the basic antenna structure. On the bottom side is the ground plane with the tapered slotline. The antenna is fed via the SMA end launch connector on the left side. This feeds into a microstrip line with an initial impedance of \(50\,\mathrm{\SIUnitSymbolOhm}\). The microstrip line is routed across the gap and terminated with a \(\lambda/4\) open stub, creating a current maximum in the gap area and efficiently coupling the energy into the slot. The slotline is similarly terminated on the left side with a \(\lambda/4\) shorted stub. This causes the energy to propagate in the direction of the taper. The circular implementation of the stub allows for a wider bandwidth match. To minimize the impedance change at the transition to the slotline, the linewidth and thus the impedance of the feed line is reduced evenly until both impedances are equal. Due to the symmetrical design, a horizontally and vertically symmetrical antenna pattern results. Figure 9 shows the simulated matching of the presented antenna with the reference plane on the microstrip line. Also shown is the measurement of the realized antenna with the reference plane at the SMA connector. The antenna is well matched between \(8.5\) and \(12\) GHz with \(S_{11}<-17\) dB. At \(8\) GHz the matching is reduced to \(-13\) dB. Simulation and measurement  
Figure 8: Simulation model (**a**) and manufactured Vivaldi Antenna (**b**) with end launch SMA connectors. agree within the expected range. The additional minima indicate reflections, as they can be caused by the SMA-to-microstrip transition, which was not included in the simulation. From the distribution of the E-field in Figure 10, the expansion of the field components along the tapered slot can be observed. In addition, field components are visible, which propagate around the ground plane and radiate sideways and backward. This is part of the reason for the limited suppression of the side lobes. These field components can be further attenuated with corrugated structures [29] or absorber material at the side edges. The fabricated antenna was fully characterized by an antenna measurement system. Figure 11 shows the absolute gain determined in the process, including losses and mismatch. There is a notable variation with frequency, but this is in rough agreement with the simulation. The gain increases with rising frequency, as the antenna size-to-wavelength ratio increases accordingly. Figure 12 compares the antenna pattern in the E-plane. Measurements were taken at the center frequency of \(10\,\mathrm{GHz}\) in the main direction, so \(\theta=\phi=0\). The shape of the main lobe agrees very well with the simulation. The half-width is about \(68^{\circ}\). The position of the side lobes varies, but the average magnitude is in the range of the simulated values. Small deviations due to the measurement setup are possible as well. Due to the very broadband radar measurements, the frequency dependence of the antenna parameters must be taken into account. In general, the width of the main lobe of a Vivaldi antenna decreases with rising frequency and the gain increases accordingly, as can already be seen in Figure 11. The size and position of the side lobes also vary. Due to the linear frequency sweep of the FMCW method and the subsequent signal processing, all received signals are integrated. This represents an averaging of the antenna parameters over frequency. Figure 13 shows the influence of such an averaging on the gain. Side lobes and zeros balance each other out, resulting in a very flat response outside the main lobe  
Figure 10: Simulated E-field on the antenna surface. Figure 9: Simulated and measured S-parameters of the proposed Vivaldi antenna. and a side lobe suppression of about 10 dB.